Experimental Fluid Mechanics
R.J. Adrian · M. Gharib · W. Merzkirch
D. Rockwell · J.H. Whitelaw
T. Liu
J.P. Sullivan
Pressure and
Temperature Sensitive
Paints
Tianshu Liu
NASA Langley Research Center
MS 493, Hampton, VA 23681-0001
USA
Prof. John P. Sullivan
Purdue University
School of Aeronautics and Astronautics
315 N. Grant St. Grissom Hall
West Lafayette, IN 47907-2023
USA
ISBN 3-540-22241-3
Springer Berlin Heidelberg New York
Library of Congress Control Number: 2004109333
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Series Editors
Prof. R.J. Adrian
University of Illinois at Urbana-Champaign
Dept. of Theoretical and Applied Mechanics
216 Talbot Laboratory
104 South Wright Street
Urbana, IL 61801
USA
Prof. M. Gharib
California Institute of Technology
Graduate Aeronautical Laboratories
1200 E. California Blvd.
MC 205-45
Pasadena, CA 91125
USA
Prof. Dr. W. Merzkirch
Universität Essen
Lehrstuhl für Strömungslehre
Schützenbahn 70
45141 Essen
Germany
Prof. Dr. D. Rockwell
Lehigh University
Dept. of Mechanical Engineering and Mechanics
Packard Lab.
19 Memorial Drive West
Bethlehem, PA 18015-3085
USA
Prof. J.H. Whitelaw
Imperial College
Dept. of Mechanical Engineering
Exhibition Road
London SW7 2BX
UK
Preface
The aim of this book is to provide a systematic description of pressure and
temperature sensitive paints (PSP and TSP) developed since the 1980s for
aerodynamics/fluid mechanics and heat transfer experiments. PSP is the first
global optical technique that is able to give non-contact, quantitative surface
pressure visualization for complex aerodynamic flows and provide tremendous
information on flow structures that cannot be easily obtained using conventional
pressure sensors. TSP is a valuable addition to other global temperature
measurement techniques such as thermographic phosphors, thermochromic liquid
crystals and infrared thermography. This book mainly covers research made in
the United States, Japan, Germany, France, Great Britain and Canada. Excellent
work on PSP in Russia has been described in the book “Luminescent Pressure
Sensors in Aerodynamic Experiments” by V. E. Mosharov, V. N. Radchenko and
S. D. Fonov of the Central Aerohydrodynamic Institute (TsAGI).
We are truly grateful to our colleagues in the field of PSP and TSP for kindly
providing their paper drafts, offering comments, and allowing us to use their
published results. Without their helps, this book cannot be completed. Especially,
we would like to thank the following individuals and organizations:
T. Amer, K. Asai, J. H. Bell, T. J. Bencic, O. C. Brown, G. Buck, A. W. Burner,
S. Burns, B. Campbell, B. F. Carroll, L. N. Cattafesta, J. Crafton, R. C. Crites, G.
Dale, R. H. Engler, R. G. Erausquin, W. Goad, L. G. Goss, J. W. Gregory, M.
Gounterman, M. Guille, M. Hamner, J. M. Holmes, C. Y. Huang, J. P. Hubner, J.
Ingram, H. Ji, R. Johnston, J. D. Jordan, M. Kameda, M. Kammeyer, J. T.
Kegelman, N. Lachendro, J. Lepicovsky, Y. Le Sant, X. Lu, Y. Mebarki, R. D.
Mehta, K. Nakakita, C. Obara, D. M. Oglesby, T. G. Popernack, W. M. Ruyten,
H. Sakaue, E. T. Schairer, K. S. Schanze, M. E. Sellers, Y. Shimbo, K. Teduka, S.
D. Torgerson, B. T. Upchurch, A. N. Watkins.
NASA, ONR, AFOSR, Boeing, Raytheon, Japanese NAL.
Table of Contents
1.
2.
3.
4.
5.
Introduction .................................................................................................... 1
1.1. Pressure Sensitive Paint ....................................................................... 2
1.2. Temperature Sensitive Paint ................................................................ 8
1.3. Historical Remarks ............................................................................ 11
Basic Photophysics....................................................................................... 15
2.1. Kinetics of Luminescence.................................................................. 15
2.2. Models for Conventional Pressure Sensitive Paint ............................ 18
2.3. Models for Porous Pressure Sensitive Paint ...................................... 24
2.3.1. Collision-Controlled Model .................................................... 26
2.3.2. Adsorption-Controlled Model................................................. 27
2.4. Thermal Quenching ........................................................................... 31
Physical Properties of Paints ........................................................................ 33
3.1. Calibration ......................................................................................... 33
3.2. Typical Pressure Sensitive Paints ...................................................... 34
3.3. Typical Temperature Sensitive Paints................................................ 45
3.4. Cryogenic Paints................................................................................ 50
3.5. Multi-Luminophore Paints................................................................. 54
3.6. ‘Ideal’ Pressure Sensitive Paint ......................................................... 56
3.7. Desirable Properties of Paints............................................................ 58
Radiative Energy Transport and Intensity-Based Methods .......................... 61
4.1. Radiometric Notation......................................................................... 61
4.2. Excitation Light ................................................................................. 62
4.3. Luminescent Emission and Photodetector Response......................... 65
4.4. Intensity-Based Measurement Systems ............................................. 69
4.4.1. CCD Camera System .............................................................. 70
4.4.2. Laser Scanning System ........................................................... 74
4.5. Basic Data Processing........................................................................ 75
Image and Data Analysis Techniques........................................................... 81
5.1. Geometric Calibration of Camera...................................................... 82
5.1.1. Collinearity Equations............................................................. 82
5.1.2. Direct Linear Transformation ................................................. 85
5.1.3. Optimization Method .............................................................. 87
5.2. Radiometric Calibration of Camera ................................................... 92
5.3. Correction for Self-Illumination ........................................................ 95
5.4. Image Registration........................................................................... 102
5.5. Conversion to Pressure .................................................................... 105
5.6. Pressure Correction for Extrapolation to Low-Speed Data.............. 107
5.7. Generation of Deformed Surface Grid............................................. 112
X
6.
7.
8.
Table of Contents
Lifetime-Based Methods ............................................................................ 115
6.1. Response of Luminescence to Time-Varying Excitation Light ....... 116
6.1.1. First-Order Model ................................................................. 116
6.1.2. Higher-Order Model ............................................................. 118
6.2. Lifetime Measurement Techniques.................................................. 118
6.2.1. Pulse Method ........................................................................ 118
6.2.2. Phase Method........................................................................ 119
6.2.3. Amplitude Demodulation Method ........................................ 121
6.2.4. Gated Intensity Ratio Method ............................................... 123
6.3. Fluorescence Lifetime Imaging ....................................................... 128
6.3.1. Intensified CCD Camera ....................................................... 128
6.3.2. Internally Gated CCD Camera .............................................. 130
6.4. Lifetime Experiments ...................................................................... 131
Uncertainty ................................................................................................. 137
7.1. Pressure Uncertainty of Intensity-Based Methods........................... 137
7.1.1. System Modeling .................................................................. 137
7.1.2. Error Propagation, Sensitivity and Total Uncertainty ........... 138
7.1.3. Photodetector Noise and Limiting Pressure Resolution........ 141
7.1.4. Errors Induced by Model Deformation ................................. 144
7.1.5. Temperature Effect ............................................................... 145
7.1.6. Calibration Errors.................................................................. 145
7.1.7. Temporal Variations in Luminescence and Illumination ...... 146
7.1.8. Spectral Variability and Filter Leakage ................................ 146
7.1.9. Pressure Mapping Errors....................................................... 146
7.1.10. Paint Intrusiveness ................................................................ 147
7.1.11. Other Error Sources and Limitations .................................... 148
7.1.12. Allowable Upper Bounds of Elemental Errors...................... 149
7.1.13. Uncertainties of Integrated Forces and Moments.................. 150
7.2. Pressure Uncertainty Analysis for Subsonic Airfoil Flows ............. 151
7.3. In-Situ Calibration Uncertainty ....................................................... 156
7.3.1. Experiments .......................................................................... 156
7.3.2. Simulation ............................................................................. 159
7.4. Pressure Uncertainty of Lifetime-Based Methods ........................... 163
7.4.1. Phase Method........................................................................ 163
7.4.2. Amplitude Demodulation Method ........................................ 164
7.4.3. Gated Intensity Ratio Method ............................................... 166
7.5. Uncertainty of Temperature Sensitive Paint .................................... 169
7.5.1. Error Propagation and Limiting Temperature Resolution..... 169
7.5.2. Elemental Error Sources ....................................................... 170
Time Response ........................................................................................... 175
8.1. Time Response of Conventional Pressure Sensitive Paint............... 175
8.1.1. Solutions of Diffusion Equation............................................ 175
8.1.2. Pressure Response and Optimum Thickness......................... 178
8.2. Time Response of Porous Pressure Sensitive Paint ......................... 182
8.2.1. Deviation from the Square-Law............................................ 182
8.2.2. Effective Diffusivity ............................................................. 183
8.2.3. Diffusion Timescale.............................................................. 186
Table of Contents
XI
8.3.
8.4.
Measurements of Pressure Time Response...................................... 187
Time Response of Temperature Sensitive Paint .............................. 194
8.4.1. Pulse Laser Heating on Thin Metal Film .............................. 195
8.4.2. Step-Like Jet Impingement Cooling ..................................... 198
9. Applications of Pressure Sensitive Paint .................................................... 201
9.1. Low-Speed Flows ............................................................................ 201
9.1.1. Airfoil Flows ......................................................................... 201
9.1.2. Delta Wings, Swept Wings and Car Models......................... 207
9.1.3. Impingement Jet.................................................................... 214
9.2. Subsonic, Transonic and Supersonic Wind Tunnels........................ 215
9.2.1. Aircraft Model in Transonic Flow ........................................ 215
9.2.2. Supercritical Wing at Cruising Speed ................................... 221
9.2.3. Transonic Wing-Body Model ............................................... 223
9.2.4. Laser Scanning Pressure Measurement on Transonic Wing . 225
9.2.5. Boundary Layer Control in Supersonic Inlets....................... 226
9.3. Hypersonic and Shock Wind Tunnels.............................................. 230
9.3.1. Expansion and Compression Corners ................................... 230
9.3.2. Moving Shock Impinging to Cylinder Normal to Wall......... 236
9.4. Cryogenic Wind Tunnels ................................................................. 237
9.5. Rotating Machinery ......................................................................... 242
9.5.1. Laser Scanning Measurements.............................................. 242
9.5.2. CCD Camera Measurements................................................. 247
9.6. Impinging Jets.................................................................................. 249
9.7. Flight Tests ...................................................................................... 256
9.8. Micronozzle ..................................................................................... 260
10. Applications of Temperature Sensitive Paint ............................................. 263
10.1. Hypersonic Flows .......................................................................... 263
10.2. Boundary-Layer Transition Detection ........................................... 270
10.3. Impinging Jet Heat Transfer .......................................................... 275
10.4. Shock/Boundary-Layer Interaction ................................................ 280
10.5. Laser Spot Heating and Heat Transfer Measurements ................... 282
10.6. Hot-Film Surface Temperature in Shear Flow ............................... 289
References .................................................................................................. 293
Appendix A. Calibration Apparatus ........................................................... 313
Appendix B. Recipes of Typical Pressure and
Temperature Sensitive Paints................................................. 317
Appendix C. Vendors ................................................................................. 319
Color Plates ................................................................................................ 321
Index........................................................................................................... 327
1. Introduction
Quantitative measurements of surface pressure and temperature in wind tunnel
and flight testing are essential to understanding of the aerodynamic performance
and heat transfer characteristics of flight vehicles. Pressure data are required to
determine the distribution of aerodynamic loads for the design of a flight vehicle,
while temperature data are used to estimate heat transfer on the surface of the
vehicle. Pressure and temperature measurements provide critical information on
important flow phenomena such as shock, flow separation and boundary-layer
transition. In addition, accurate pressure and temperature data play a key role in
validation and verification of computational fluid dynamics (CFD) codes.
Traditionally, surface pressure is measured by utilizing a pressure tap or orifice at
a location of interest connected through a small tube to a pressure transducer
(Barlow et al. 1999). Hundreds of pressure taps are needed to obtain an
acceptable pressure field on a complex aircraft model. Manufacturing, tubing and
preparing such a model for wind tunnel testing is very labor-intensive and costly.
For thin models such as supersonic transports, military aircraft and small fan
blades, installation of a large number of pressure taps is impossible. Furthermore,
pressure measurements at discrete taps ultimately limit the spatial resolution of
measurements such that some details of a complex flow field cannot be revealed.
Similarly, a surface temperature field is traditionally measured using temperature
sensors such as thermocouples and resistance thermometers distributed at discrete
locations (Moffat 1990).
Since the 1980s, new optical sensors for measuring surface pressure and
temperature have been developed based on the quenching mechanisms of
luminescence. These luminescent molecule sensors are called pressure sensitive
paint (PSP) and temperature sensitive paint (TSP). Compared with conventional
techniques, they offer a unique capability for non-contact, full-field measurements
of surface pressure and temperature on a complex aerodynamic model with a
much higher spatial resolution and a lower cost. Therefore, they provide a
powerful tool for experimental aerodynamicists to gain a deeper understanding of
rich physical phenomena in complex flows around flight vehicles.
Both PSP and TSP use luminescent molecules as probes that are incorporated
into a suitable polymer coating on an aerodynamic model surface. In general, the
luminophore and polymer binder in PSP and TSP can be dissolved in a solvent;
the resulting paint can be applied to a surface using a sprayer or brush. After the
solvent evaporates, a solid polymer coating in which the luminescent molecules
are immobilized remains on the surface. When a light of a proper wavelength
illuminates the paint, the luminescent molecules are excited and the luminescent
2
1. Introduction
light of a longer wavelength is emitted from the excited molecules. Figure 1.1
shows a schematic of a generic luminescent paint layer emitting radiation under
excitation by an incident light.
Detector
(CCD, PMT, PD)
Excitation light
(UV, laser, LED)
Optical Filter
Calibrated output
for pressure &
temperature
Emission
Luminescent molecule
Binder (polymer, porous solid)
Fig. 1.1. Schematic of a luminescent paint (PSP or TSP) on a surface
The luminescent emission from a paint layer can be affected by certain physical
processes. The main photophysical process in PSP is oxygen quenching that
causes a decrease of the luminescent intensity as the partial pressure of oxygen or
air pressure increases. The polymer binder for PSP is oxygen permeable, which
allows oxygen molecules to interact with the luminescent molecules in the binder.
For certain fast-responding PSP, a mixture of the luminophore and solvent is
directly applied to a porous solid surface. In fact, PSP is an oxygen-sensitive
sensor. By contrast, the major mechanism in TSP is thermal quenching that
reduces the luminescent intensity as temperature increases. TSP is not sensitive to
air pressure since the polymer binder used for TSP is oxygen impermeable, while
due to the thermal quenching PSP is intrinsically temperature-sensitive. After
PSP and TSP are appropriately calibrated, pressure and temperature can be
remotely measured by detecting the luminescent emission. PSP and TSP are
companion techniques because they not only utilize luminescent molecules as
probes, but also use the same measurement systems and similar data processing
methods.
1.1. Pressure Sensitive Paint
The basic concepts of pressure sensitive paint (PSP) are simple. After a photon of
radiation with a certain frequency is absorbed to excite the luminophore from the
ground electronic state to the excited electronic state, the excited electron returns
1.1. Pressure Sensitive Paint
3
to the unexcited ground state through radiative and radiationless processes. The
radiative emission is called luminescence (a general term for both fluorescence
and phosphorescence). The excited state can be deactivated by interaction of the
excited luminophore molecules with oxygen molecules in a radiationless process;
that is, oxygen molecules quench the luminescent emission. According to
Henry’s law, the concentration of oxygen in a PSP polymer is proportional to the
partial pressure of oxygen in gas above the polymer. For air, pressure is
proportional to the oxygen partial pressure. So, for higher air pressure, more
oxygen molecules exist in the PSP layer and as a result more luminescent
molecules are quenched. Hence, the luminescent intensity is a decreasing
function of air pressure.
The relationship between the luminescent intensity and oxygen concentration
can be described by the Stern-Volmer relation. For experimental aerodynamicists,
a convenient form of the Stern-Volmer relation between the luminescent intensity
I and air pressure p is
I ref
I
= A+ B
p
p ref
,
(1.1)
where I ref and p ref are the luminescent intensity and air pressure at a reference
condition, respectively. The Stern-Volmer coefficients A and B, which are
temperature-dependent due to the thermal quenching, are experimentally
determined by calibration. Theoretically speaking, the intensity ratio I ref / I can
eliminate the effects of non-uniform illumination, uneven coating and nonhomogenous luminophore concentration in PSP. In typical tests in a wind tunnel,
I ref is taken when the tunnel is turned off and hence it is often called the wind-off
intensity (or image); likewise, I is called the wind-on intensity (or image). Figures
1.2 and 1.3 show, respectively, the luminescent intensity as a function of pressure
at the ambient temperature and the corresponding Stern-Volmer plots for three
PSPs: Ru(ph2-phen) in GE RTV 118, Pyrene in GE RTV 118 and PtOEP in GP
197.
A measurement system for PSP or TSP is generally composed of paint,
illumination light, photodetector, and data acquisition/processing unit. Figure 1.4
shows a generic CCD camera system for both PSP and TSP. Many light sources
are available for illuminating PSP/TSP, including lasers, ultraviolet (UV) lamps,
xenon lamps, and light-emitting-diode (LED) arrays. Scientific-grade chargecoupled device (CCD) cameras are often used as detectors because of their good
linear response, high dynamic range and low noise. Other commonly-used
photodetectors are photomultiplier tubes (PMT) and photodiodes (PD). A generic
laser-scanning system, as shown in Fig. 1.5, typically uses a laser with a
computer-controlled scanning mirror as an illumination source and a PMT as a
detector along with a lock-in amplifier for both intensity and phase measurements.
Optical filters are used in both systems to separate the luminescent emission from
the excitation light.
4
1. Introduction
7
Ru(ph2-phen) in GE RTV 118
Pyrene in GE RTV 118
PtOEP in GP 197
6
5
I/Iref
4
3
2
1
0
0.0
0.2
0.4
0.6
0.8
1.0
p/pref
Fig. 1.2. The luminescent intensity as a function of pressure for three PSPs at the ambient
temperature, where pref is the ambient pressure and Iref is the luminescence intensity at the
ambient conditions.
1.0
0.8
Iref/I
0.6
0.4
Ru(ph2-phen) in GE RTV 118
0.2
Pyrene in GE RTV 118
PtOEP in GP 197
0.0
0.0
0.2
0.4
0.6
0.8
1.0
p/pref
Fig. 1.3. The Stern-Volmer plots for three PSPs at the ambient temperature, where pref is the
ambient pressure and Iref is the luminescence intensity at the ambient conditions.
1.1. Pressure Sensitive Paint
5
Fig. 1.4. Generic CCD camera system for PSP and TSP
Once PSP is calibrated, in principle, pressure can be directly calculated from
the luminescent intensity using the Stern-Volmer relation. Nevertheless, practical
data processing is more elaborate in order to suppress the error sources and
improve the measurement accuracy of PSP. For an intensity-based CCD camera
system, the wind-on image often does not align with the wind-off reference image
due to aeroelastic deformation of a model in wind tunnel testing. Therefore, the
image registration technique must be used to re-align the wind-on image to the
wind-off image before taking a ratio between those images. Also, since the SternVolmer coefficients A and B are temperature-dependent, temperature correction is
certainly required since the temperature effect of PSP is the most dominant error
source in PSP measurements. In wind tunnel testing, the temperature effect of
PSP is to a great extent compensated by the in-situ calibration procedure that
directly correlates the luminescent intensity to pressure tap data obtained at welldistributed locations on a model during tests. To further reduce the measurement
uncertainty, additional data processing procedures are applied, including image
6
1. Introduction
summation, dark-current correction, flat-field correction, illumination
compensation, and self-illumination correction. After a pressure image is
obtained, to make pressure data more useful to aircraft design engineers, data in
the image plane should be mapped onto a model surface grid in the 3D object
space. Therefore, geometric camera calibration and image resection are necessary
to establish the relationship between the image plane and the 3D object space.
Besides the intensity-ratio method for a single-luminophore PSP, lifetime
measurement systems and multi-luminophore PSP systems have also been
developed. Theoretically speaking, the luminescent lifetime is independent of the
luminophore concentration, illumination level and coating thickness. Hence, the
lifetime method does not require the reference intensity (or image) and it is ideally
immune from the troublesome ratioing process in the intensity-ratio method for a
deformed model. Similarly, one of the purposes of developing the multipleluminophore PSP system is to eliminate the need of the wind-off reference image
and reduce the error associated with model deformation. Another goal of using
the multiple-luminophore PSP system is to compensate the temperature effect of
PSP.
Computer
Laser
Modulator
Lock-in Amplifier
PMT
2D Scanner
Laser Beam
Luminescence
Painted Model
Fig. 1.5. Generic laser scanning lifetime system for PSP and TSP
1.1. Pressure Sensitive Paint
7
Most PSP measurements have been conducted in high subsonic, transonic and
supersonic flows on various aerodynamic models in both large production wind
tunnels and small research wind tunnels. PSP is particularly effective in a range
of Mach numbers from 0.3 to 3.0. Figure 1.6 shows a typical PSP-derived
pressure field on the F-16C model at Mach 0.9 and the angle-of-attack of 4
degrees, which was obtained by Sellers and his colleagues (Sellers 1998a, 1998b,
2000; Sellers and Brill 1994) at the Arnold Engineering Development Center
(AEDC). For PSP measurements in large wind tunnels, the accuracy of PSP is
typically 0.02-0.03 in the pressure coefficient, while in well-controlled
experiments the absolute pressure accuracy of 1 mbar (0.0145 psi) can be
achieved. In short-duration hypersonic tunnels (Mach 6-10), measurements
require very fast time response of PSP and minimization of the temperature effect
of PSP. Binder-free, porous anodized aluminum (AA) PSP has been used in
hypersonic flows and rotating machinery since it has a very short response time of
30–100 µs in comparison with a timescale of about 0.5 s for a conventional
polymer-based PSP. Furthermore, because AA-PSP is a part of an aluminum
model, an increase of the surface temperature in a short duration is relatively small
due to the high thermal conductivity of aluminum. Since a porous PSP usually
exhibits the pressure sensitivity at cryogenic temperatures, AA-PSP and polymerbased porous PSP have been used for pressure measurements in cryogenic wind
tunnels where the oxygen concentration is extremely low and the total temperature
is as low as 90 K.
Fig. 1.6. PSP image for the F-16C model at Mach 0.9 and the angle-of-attack of 4 degrees.
From Sellers (2000)
8
1. Introduction
PSP measurements in low-speed flows are difficult since a very small change
in pressure must be resolved and the major error sources must be minimized to
obtain acceptable quantitative pressure results.
Some low-speed PSP
measurements were conducted on delta wings where upper surface pressure
exhibited a relatively large change induced by the leading-edge vortices. In
addition, experiments were conducted on airfoils, car models and impinging jets at
speeds as low as 20 m/s. The pressure resolution of PSP in low-speed flows is
ultimately limited by the photon shot noise of a CCD camera. Instead of pushing
PSP instrumentation to the limit in low-speed flows, the pressure-correction
method was proposed to recover the incompressible pressure coefficient from PSP
results obtained in subsonic flows at suitably higher Mach numbers by removing
the compressibility effect.
Since PSP is a non-contact technique, it is particularly suitable to pressure
measurements on high-speed rotating blades in rotating machinery where
conventional techniques are difficult to use. Both CCD camera and laser scanning
systems have been used for PSP measurements on rotating blades in turbine
engines and helicopters. Impinging jets were used in some studies as a canonical
flow for testing the performance of PSP systems. Flight test is a challenging area
where PSP has showed its advantages as a non-contact, optical pressure
measurement technique. The pressure distributions on wings and parts of aircrafts
have been measured using film-based camera systems in early in-flight
experiments and a laser scanning system in recent flight tests.
1.2. Temperature Sensitive Paint
Temperature sensitive paint (TSP) is a polymer-based paint in which the
temperature-sensitive luminescent molecules are immobilized. The quantum
efficiency of luminescence decreases with increasing temperature; this effect
associated with temperature is thermal quenching that serves as the major working
mechanism for TSP. Over a certain temperature range, a relation between the
luminescent intensity I and absolute temperature T can be written in the Arrhenius
form
ln
E §1
I( T )
1
= nr ¨ −
¨
I ( Tref )
R © T Tref
·
¸,
¸
¹
(1.2)
where Enr is the activation energy for the non-radiative process, R is the universal
gas constant, and Tref is a reference temperature in Kelvin. Figures 1.7 and 1.8
show, respectively, the temperature dependencies of the luminescent intensity and
the Arrhenius plots for three TSPs: Ru(bpy) in Shellac, Rodamine-B in dope and
EuTTA in dope. The procedure for applying TSP to a surface is basically the
same as that for PSP. Not only does TSP use the same measurement systems
shown in Figs. 1.4 and 1.5, but also most data processing methods for TSP are
similar to those for PSP. Ideally, TSP can be used in tandem with PSP to correct
1.2. Temperature Sensitive Paint
9
the temperature effect of PSP and simultaneously obtain the temperature and
pressure distributions. Compared to conventional temperature sensors, TSP is a
global measurement technique that is able to obtain the surface temperature
distribution with reasonable accuracy at a much higher spatial resolution.
o
A family of TSPs has been developed, covering a temperature range of –196 C
o
o
to 200 C. The accuracy of TSP is typically 0.2-0.8 C. TSP has been used in
various aerodynamic experiments to measure the temperature and heat transfer
distributions. In hypersonic wind tunnel tests, TSP not only visualized flow
transition patterns, but also provided quantitative heat transfer data calculated
based on quasi-steady and transient heat transfer models. Figure 1.9 shows a
windward-side heat transfer image of the lower half of the waverider model at
Mach 10 at 0.57 s after the wind tunnel started to run (Liu et al. 1995b), where the
2
gray intensity bar denotes heat flux in kW/m . TSP is an effective technique for
visualizing boundary-layer transition from laminar to turbulent flow. Due to a
significant difference in convection heat transfer between the laminar and
turbulent flow regimes, TSP can visualize a surface temperature change across the
transition line. In low-speed wind tunnel tests, a model is typically heated or
cooled to increase the temperature difference. However, in high-speed flows,
friction heating often produces a sufficient temperature difference for TSP
transition visualization. Cryogenic TSPs have been used to detect boundary-layer
transition on airfoils in cryogenic wind tunnels over a range of the total
temperatures from 90 K to 150 K. Complemented with other techniques, TSP has
been used to study the relationship between heat transfer and flow structures in an
acoustically excited impinging jet. The mapping capability of TSP allows
quantitative visualization of the impingement heat transfer fields controlled
(enhanced or suppressed) by acoustical excitation. The heat transfer fields in
complex separated flows induced by shock/boundary-layer interactions have also
been studied using TSP. A novel heat transfer measurement technique has been
developed, which combines a laser scanning TSP and a laser spot heating units
into a single non-intrusive system. An infrared laser was used to generate local
heat flux and convection heat transfer was determined based on a transient heat
transfer model from the surface temperature response measured using TSP. This
system was applied to quantitative heat transfer measurements in complex flows
on a 75-degree swept delta wing and around an intersection of a strut and a wall.
Through an optical magnification system, TSP can achieve a very high spatial
resolution over the surface of a small object like MEMS devices. TSP has been
used to measure the surface temperature field of a miniature flush-mounted hotfilm sensor in a flat-plate turbulent boundary layer.
1. Introduction
1.5
EuTTA-dope
I(T)/I(Tr)
Ru(bpy)-Shellac
1.0
0.5
Rhodamine-B-dope
0.0
0
20
40
60
80
T (deg. C)
Fig. 1.7. Temperature dependencies of the luminescent intensity for three TSPs
0.5
0.0
ln[I(T)/I(Tr)]
10
Ru(bpy)-Shellac
-0.5
-1.0
Rodamine-B-dope
-1.5
EuTTA-dope
-2.0
-2.5
-0.6
-0.4
-0.2
3
0.0
-1
(1/T - 1/Tr )10 ( K )
Fig. 1.8. The Arrhenius plots for three TSPs
0.2
1.3. Historical Remarks
11
Fig. 1.9. Heat transfer image obtained using TSP on the windward side of the waverider at
Mach 10. From Liu et al. (1995b)
1.3. Historical Remarks
The working principles of PSP are based on the oxygen quenching of
luminescence that was first discovered by H. Kautsky and H. Hirsch (1935). The
quenching effect of luminescence by oxygen was used to detect small quantities of
oxygen in medical applications (Gewehr and Delpy 1993) and analytical
chemistry (Lakowicz 1991, 1999) before experimental aerodynamicists realized
its utility as an optical sensor for measuring air pressure on a surface. J. Peterson
and V. Fitzgerald (1980) demonstrated a surface flow visualization technique
based on the oxygen quenching of dye fluorescence and revealed the possibility of
using oxygen sensors for surface pressure measurements. Pioneering studies of
applying oxygen sensors to aerodynamic experiments were initiated independently
by scientists at the Central Aero-Hydrodynamic Institute (TsAGI) in Russia and
the University of Washington in collaboration with the Boeing Company and the
NASA Ames Research Center in the United States.
The conceptual
transformation from oxygen concentration measurement to surface pressure
measurement was really a critical step for aerodynamic applications of PSP,
signifying a paradigm shift from conventional point-based pressure measurement
to global pressure mapping.
G. Pervushin and L. Nevsky (1981) of TsAGI, inspired by the work of I.
Zakharov et al. (1964, 1974) on oxygen measurement, suggested the use of the
oxygen quenching phenomenon for pressure measurements in aerodynamic
experiments. The first PSP measurements at TsAGI were conducted at Mach 3 on
a sphere, a half-cone and a flat plate with an upright block that were coated with a
long-lifetime luminescent paint excited by a flash lamp. Their PSP was
acriflavine or beta-aminoanthraquinone in a matrix consisting of silichrome,
starch, sugar and polyvinylpyrrolidone. A photographic film camera was used for
imaging the luminescent intensity field. The results obtained in these tests were in
reasonable agreement with the known theoretical solution and pressure tap data
(Ardasheva et al. 1982, 1985). Another TsAGI group consisting of A. Orlov, V.
12
1. Introduction
Mosharov, S. Fonov and V. Radchenko started their research in 1983 to improve
the accuracy of PSP by measuring the lifetime (the decay time). In their first tests
on a cone-cylinder model at Mach 2.5 and 3.0, they used a photomultiplier tube as
a detector and a pulsed Argon laser mechanically scanned over a surface to excite
a newly developed PSP (Radchenko 1985). Unfortunately, they found that the
lifetime measurements suffered from very strong temperature sensitivity (about
o
7%/ C) and a very long lifetime (about several minuets) of their first PSP. As a
result, their effort has been exclusively focused on the development of intensitybased techniques since 1985. At TsAGI, a number of proprietary PSP
formulations have been developed and applied to various subsonic, transonic,
supersonic, shock, dynamic tunnels, and rotating machinery (Bukov et al. 1992,
1993; Troyanovsky et al. 1993; Mosharov et al. 1997). The imaging devices used
at TsAGI covered a range of photographic film cameras, TV cameras, scientific
grade CCD cameras and photomultiplier tubes with laser scanning systems. In the
later 1980s, TsAGI marketed its PSP technology through the Italian firm INTECO
and issued a one-page advertisement in the magazine ‘Aviation Week & Space
Technology’ in February 12, 1990. Interestingly, scientists in the Western World
were not aware of Russia’s work on PSP until reading the advertisement. Then,
TsAGI’s PSP system was demonstrated in several wind tunnel tests at the Boeing
Company in 1990 and Deutsche Forschungsanstalt fur Luft- und Raumfahrt
(DLR) in Germany in 1991, which attracted widespread attention of researchers in
the aerospace community (Volan and Alati 1991).
PSP was independently developed by a group of chemists led by M. Gouterman
and J. Callis at the University of Washington (UW) in the late 1980s (Gouterman
et al. 1990; Kavandi et al. 1990). The chemists at UW were initially interested in
use of porphyrin compounds as an oxygen sensor for biomedical applications.
After stimulating discussions with experimental aerodynamicists J. Crowder of the
Boeing Company and B. McLachlan of NASA Ames, Gouterman and Callis
understood the important implication of oxygen sensors in aerodynamic testing
and started to develop a luminescent coating applied to surface for pressure
measurements. Their classical PSP used platinum-octaethylporphorin (PtOEP) as
a luminescent probe molecule in a proprietary commercial polymer mixture called
GP-197 made by the Genesee Company. In 1989, using PtOEP in GP-197, M.
Gouterman and J. Kavandi conducted PSP measurements on a NACA 0012 airfoil
model (3-in chord and 9-in span) in the 25×25 cm wind tunnel at NASA Ames
Fluid Dynamics Laboratory. The model was spray coated with a commercial
white epoxy Krylon base-coat and then sprayed with PtOEP in GP-197. An UV
lamp was used for excitation, and an analog camera interfaced to an IBM-AT
computer with an 8-bit frame grabber for image acquisition. The model was set at
o
the angle-of-attack of 5 and the Mach numbers ranged from 0.3 to 0.66. Their
data showed very favorable agreement with pressure tap data, clearly indicating
the formation of a shock on the upper surface of the model as the Mach number
increases (Kavandi et al. 1990; McLachlan et al. 1993a). More importantly, this
work established the basic procedures for intensity-based PSP measurements such
as image ratioing and in-situ calibration. Following the tests at NASA Ames,
Kavandi demonstrated the same PSP system in the Boeing Transonic Wind
1.3. Historical Remarks
13
Tunnel on various commercial airplane models, which was briefly discussed by
Crowder (1990). Several proprietary paint formulations have been developed at
UW, and successfully applied to wind tunnel testing at the Boeing Company and
NASA Ames (McLachlan et al. 1993a, 1993b, 1995; McLachlan and Bell 1995;
Bell and McLachlan 1993, 1996; Gouterman 1997).
Excellent work on PSP was also made at the former McDonnell Douglas (MD,
now the Boeing Company at St. Louis) (Morris et al. 1993a, 1993b; Morris 1995;
Morris and Donovan 1994; Donovan et al. 1993; Dowgwillo et al. 1994, 1996;
Crites 1993; Crites and Benne 1995). MD PSPs were mainly based on Ruthenium
compounds that were successfully used in subsonic, transonic and supersonic
flows for a generic wing-body model, a full-span ramp, F-15 model, and a
converging-diverging nozzle. Other major PSP research groups in the United
States include NASA Langley, NASA Glenn, Arnold Engineering Development
Center (AEDC), United States Air Force Wright-Patterson Laboratory, Purdue
University, and University of Florida. European researchers in DLR (Germany),
British Aerospace (BAe, UK), British Defense Evaluation and Research Agency
(DERA, UK), and Office National d’Etudes et de Recherches Aerospatiales
(ONERA, France) have been active in the field of PSP (Engler et al. 1991, 1992;
Engler and Klein 1997a, 1997b; Engler 1995; Davies et al. 1995; Lyonnet et al.
1997). In Japan, the National Aerospace Laboratory (NAL), in collaboration with
Purdue and a number of Japanese universities, developed cryogenic and fastresponding PSPs (Asai 1999; Asai et al. 2001, 2003). More and more research
institutions all over the world are becoming interested in developing PSP
technology because of its obvious advantages over conventional techniques.
Brown (2000) gave a historical review with personal notes and recollections from
some pioneers on early PSP development.
Before the advent of polymer-based luminescent TSPs, thermographic
phosphors and thermochromic liquid crystals have been used for measuring the
surface temperature distributions in heat transfer and aerothermodynamic
experiments. Thermographic phosphors are usually applied to a surface in the
form of insoluble powder or crystal in contrast to polymer-based luminescent
TSPs although both techniques utilize the temperature dependence of
luminescence. A family of thermographic phosphors can cover a temperature
range from room temperature (293 K) to 1600 K, which overlaps with the
temperature range of polymer-based TSPs from cryogenic temperature (about 100
K) to 423 K. In this sense, thermographic phosphors and polymer-based
luminescent TSPs are complementary to cover a broader range from cryogenic to
high temperatures. L. Bradley (1953) explored aerodynamic application of
thermographic phosphors mixed with binders and ceramic materials to measure
surface temperature. Then, thermographic phosphors were used for temperature
measurements in high-speed wind tunnels (Czysz and Dixon 1969; Buck 1988,
1989, 1991; Merski 1998, 1999), gas turbine engines (Noel et al. 1985, 1986,
1987; Tobin et al. 1990; Alaruri et al. 1995), and fiber-optic thermometry systems
(Wickersheim and Sun 1985). Allison and Gillies (1997) gave a comprehensive
review on thermographic phosphors. Thermochromic liquid crystals applied to a
black surface selectively reflect light and hue varies depending on the temperature
14
1. Introduction
of the surface, which allows measurement of the surface temperature in a
o
relatively narrow range from 25 to 45 C. After E. Klein (1968) used liquid
crystals in aerodynamic testing, this technique for global temperature
measurement has been used in turbine machinery (Jones and Hippensteele 1988;
Hippensteele and Russell 1988; Ireland and Jones 1986), hypersonic tunnels
(Babinsky and Edwards 1996), and turbulent flows (Smith et al. 2000).
Polymer-based TSPs are relatively new compared to thermographic phosphors
and thermochromic liquid crystals. P. Kolodner and A. Tyson (1982, 1983a,
1983b) of the Bell Laboratory used a Europium-based TSP in a polymer binder to
measure the surface temperature distribution of an operating integrated circuit. A
family of TSPs have been developed at Purdue University and used in low-speed,
supersonic and hypersonic aerodynamic experiments (Campbell et al. 1992, 1994;
Campbell 1994; Liu et al. 1992b, 1994a, 1994b, 1995a, 1995b, 1996, 1997a,
o
1997b). Two typical TSPs are EuTTA in model airplane dope (-20 to 100 C) and
o
o
Ru(bpy) in Shellac (0 to 90 C). Several cryogenic TSPs (-175 to 0 C) were first
discovered at Purdue University (Campbell et al. 1994) and used for transition
detection in cryogenic flows (Asai et al. 1997c; Popernack et al. 1997). Further
development of cryogenic TSPs was made at Purdue (Eransquin 1998a, 1998b),
NAL in Japan (Asai et al. 1997c; Asai and Sullivan 1998) and NASA Langley.
TSP formulations were also studied at the University of Washington (Gallery
1993) and one of the paints was used for boundary-layer transition detection at
NASA Ames (McLachlan et al. 1993b).
PSP and TSP have become an active and growing interdisciplinary research
area, offering the promise of quantitative pressure and temperature mapping on
the one hand and giving new technical challenges on the other hand. Useful
reviews were given by Crites (1993), McLachlan and Bell (1995a), Crites and
Benne (1995), Liu et al. (1997b), Mosharov et al. (1997), Bell et al. (2001), and
Sullivan (2001). This book provides a systematic and detailed description of all
the technical aspects of PSP and TSP, including basic photophysics, paint
formulations and their physical properties, radiative energy transport,
measurement methods and systems, uncertainty, time response, image and data
analysis techniques, and various applications in aerodynamics and fluid
mechanics.
2. Basic Photophysics
2.1. Kinetics of Luminescence
Pressure sensitive paint (PSP) and temperature sensitive paint (TSP) are,
respectively, based on the oxygen and thermal quenching processes of
luminescence which are reversible processes in molecular photoluminescence.
The general principles of luminescence are described in detail by Rebek (1987),
Becker (1969) and Parker (1968). The different energy levels and photophysical
processes of luminescence for a simple luminophore can be clearly described by
the Jablonski energy-level diagram shown in Fig. 2.1. The lowest horizontal line
represents the ground-state energy of the molecule, which is normally a singlet
state denoted by S0. The upper lines are energy levels for the vibrational states of
excited electronic states. The successive excited singlet and triplet states are
denoted by S1 and S2, and T1, respectively. As is normally the case, the energy of
the first excited triplet state T1 is lower than the energy of the corresponding
singlet state S1.
A photon of radiation is absorbed to excite the luminophore from the ground
electronic state to excited electronic states ( S 0 → S 1 and S 0 → S 2 ). The
excitation process is symbolically expressed as S 0 + !ν → S 1 , where ! is the
Plank constant and ν is the frequency of the excitation light. Each electronic
state has different vibrational states, and each vibrational state has different
rotational states. The excited electron returns to the unexcited ground state by a
combination of radiative and radiationless processes. Emission occurs through the
radiative processes called luminescence. The radiation transition from the lowest
excited singlet state to the ground state is called fluorescence, which is expressed
as S 1 → S 0 + !ν f . Fluorescence is a spin-allowed radiative transition between
two states of the same multiplicity. The radiative transition from the triplet state
to the ground state is called phosphorescence ( T1 → S 0 + !ν p ), which is a spinforbidden radiative transition between two states of different multiplicity. The
lowest excited triplet state, T1, is formed through a radiationless transition from S1
by intersystem crossing ( S 1 → T1 ). Since phosphorescence is a forbidden
transition, the phosphorescent lifetime is typically longer than the fluorescent
lifetime.
Luminescence is a general term for both fluorescence and
phosphorescence.
16
2. Basic Photophysics
Singlet Excited States
Internal
Conversion
Triplet Excited
State
Vibrational
Relaxation
S2
Interstystem
Crossing
S1
Energy
T1
Adsorption
Fluorescence
Internal
and
External
Conversion
Phosphorescence
So
Ground
State
Vibrational
Relaxation
Fig. 2.1. Jablonsky energy-level diagram
Radiationless deactivation processes mainly include internal conversion (IC),
intersystem crossing (ISC) and external conversion (EC). The internal conversion
(IC) is a spin-allowed radiationless transition between two states of the same
multiplicity ( S 2 → S 1 , S 1 → S 0 ). Typically, this process is expressed as
S 1 → S 0 + ∆ , where ∆ denotes heat released. IC appears to be particularly
efficient when two electronic energy levels are sufficiently close. The intersystem
crossing (ISC) is a spin-forbidden radiationless transition between two states of
the different multiplicity, which are expressed as S 1 → T1 + ∆ and T1 → S 0 + ∆ .
Phosphorescence depends to a large extent on the population of the triplet state
( T1 ) from the excited singlet state ( S 1 ) by the intersystem crossing. In addition,
deactivation of an excited electronic state may involve interaction and energy
transfer between the excited molecules and the environment like solutes, which
are called external conversion (EC).
The excited singlet and triplet states can be deactivated by interaction of the
excited molecules with the components of a system. These bimolecular processes
are quenching processes, including collisional quenching (diffusion or nondiffusion controlled), concentration quenching, oxygen quenching, and energy
transfer quenching. The oxygen quenching of luminescence is the major
photophysical mechanism for PSP. Due to the oxygen quenching, air pressure on
2.1. Kinetics of Luminescence
17
an aerodynamic model surface is related to the luminescent intensity by the SternVolmer equation that will be further discussed. The quantum efficiency of
luminescence in most molecules decreases with increasing temperature because
the increased frequency of collisions at elevated temperatures improves the
possibility for deactivation by the external conversion. This effect associated with
temperature is the thermal quenching, which is the major photophysical
mechanism for TSP.
The population of the excited singlet states ( S 1 ) and triplet states ( T1 ) at any
given time depends on the competition among different photophysical processes
listed in Table 2.1. The singlet state population [ S 1 ] and triplet state population
[ T1 ] are described by the following first-order kinetic model
d [ S1 ]
= I a − ( k f + k ic + k isc( s1 −t1 ) + k q( s ) [ Q ])[ S 1 ]
dt
d [ T1 ]
= k isc ( s1 −t1 ) [ S 1 ] − ( k p + k isc( t1 − s0 ) + k q( t ) [ Q ])[ T1 ]
dt
,
(2.1)
where I a is the light absorption rate of generating the excited singlet states, [ Q ]
is the population of the quencher Q, k f and k p are, respectively, the rate
constants for fluorescence and phosphorescence, k isc( s1 −t1 ) and k isc( t1 − s0 ) are,
respectively, the rate constants for the intersystem crossings S 1 → T1 and
T1 → S 0 , k ic is the rate constant for the internal conversion, and k q( s ) and k q( t )
are the rate constants for the quenching in the singlet states and triplet states,
respectively. The light absorption rate I a = k s 1 [ S 0 ] is proportional to the
population [ S 0 ] in the ground state and the rate constant of excitation k s 1 . After
a pulse excitation, the times required for the populations in the excited singlet
state and triplet state to decay to 1/e of the initial value are, respectively,
τ f = 1 / ( k f + k ic + k isc( s1 −t1 ) + k q ( s ) [ Q ])
τ p = 1 / ( k p + k isc( t1 − s0 ) + k q( t ) [ Q ]) .
(2.2)
The time constants τ f and τ p are defined as the fluorescent and phosphorescent
lifetimes, respectively. Usually, the lifetime of a specific photophysical process is
defined as the reciprocal of the corresponding rate constant. Typical values of the
lifetimes for different photophysical processes are listed in Table 2.1. When the
intersystem crossing from T1 back to S 1 ( T1 → S 1 + ∆ ) is included in the kinetic
model, extra terms k isc ( t1 − s1 ) [ T1 ]
and − k isc( t1 − s1 ) [ T1 ]
should be added,
respectively, to the right-hand sides of Eq. (2.1) for [ S 1 ] and [ T1 ] , where
k isc( t1 − s1 ) is the rate constant for the intersystem crossing T1 → S 1 . In this case,
18
2. Basic Photophysics
the kinetic model becomes a coupled system of equations (Mosharov et al. 1997;
Bell et al. 2001). Since S 1 is a higher energy state than T1 , this intersystem
crossing is thermally activated and therefore the rate constant for the process
T1 → S 1 is temperature-dependent.
Table 2.1. Photophysical processes involving electronically excited states
Step
Process
Rate
Lifetime (s)
Excitation
S 0 + !ν → S 1
k s1 [ S0 ]
10 −15
Fluorescence (F)
S 1 → S 0 + !ν f
k f [ S1 ]
10 −11 − 10 −6
Internal Conversion (IC)
S1 → S 0 + ∆
k ic [ S 1 ]
10 −14 − 10 −11
Intersystem Crossing (ISC)
S 1 → T1 + ∆
k isc( s1 −t1 ) [ S 1 ]
10 −11 − 10 −8
Phosphorescence (P)
T1 → S 0 + !ν p
k p [ T1 ]
10 −3 − 10 2
Intersystem Crossing (ISC)
T1 → S 0 + ∆
k isc( t1 − s0 ) [ T1 ]
2.2. Models for Conventional Pressure Sensitive Paint
From a standpoint of engineering application, it is unnecessary to analyze all the
intermediate photophysical processes and their interactions. Therefore, a lumped
model for luminescence (fluorescence and phosphorescence) is given here by
considering the main processes: excitation, luminescent radiation, non-radiative
deactivation, and quenching. The luminophore is excited by a photon from a
ground state L0 to an excited state L* , i.e., L0 + !ν → L* . The excited state L*
returns to the ground state L0 by either a radiative process (emission) or a
radiationless process (deactivation). In the radiative process, the luminescent
kr
emission releases energy of !ν l , that is L* ⎯⎯→
L0 + !ν l , where k r is the rate
constant for the radiation process and ν l is the frequency of the luminescent
emission. In the deactivation process, L* returns to L0 by releasing heat, which
k nr
is expressed as L* ⎯⎯
⎯→ L0 + ∆ , where k nr is the rate constant for the combined
effect of all the non-radiative processes. If temperature around a luminophore
molecule increases, the deactivation rate increases, reducing the radiative process
from L* . Thus, the rate constant k nr for the non-radiative processes is
temperature-dependent. The quenching process by a quencher Q is expressed as
kq
L* + Q ⎯⎯→ L0 + Q* , where k q is the rate constant of the quenching process
2.2. Models for Conventional Pressure Sensitive Paint
19
and Q* denotes the excited quencher. The molecular oxygen O2 in the ground
state is an efficient quencher for both the excited singlet and triplet states. The
molecular oxygen is excited to O2* once it quenches luminescence, i.e.,
L* + O2 → L0 + O2* . By combining the rates of emission, deactivation and
quenching processes, the rate of change of the population of the excited state
[ L* ] is given by the first-order equation
d [ L* ]
= I a − ( k r + k nr + k q [ Q ])[ L* ] .
dt
(2.3)
The rate of excitation is I a = k s 1 [ L0 ] , where [ L0 ] is the population in the
ground state and k s 1 is the rate constant for excitation.
At a steady state
d [ L* ] / dt = 0 , without quenching ( [ Q ] = 0 ), we have
*
I a = ( k r + k nr )[ L ] .
(2.4)
The amount of luminophore molecules in a given excited state is described by
the quantum yield of luminescence defined by
Φ=
rate of luminescence
.
rate of excitation
(2.5)
The quantum yield Φ for the luminescent emission from L* with the quencher Q
is expressed by
[ *]
I
kr
,
(2.6)
Φ = kr L =
=
k r + k nr + k q [ Q ] I a
Ia
where I is the luminescent intensity. The quantum yield without quenching is
[ *]
Φ0 = k r L =
Ia
I
kr
= 0
k r + k nr I a
,
(2.7)
where I 0 is the luminescent intensity without quenching. Dividing Φ 0 by Φ , we
obtain the well-known Stern-Volmer relation
Φ0 I 0
kq
=
= 1+
[ Q ] = 1 + k qτ 0 [ Q ] ,
I
Φ
k r + k nr
where τ 0 = 1 /( k r + k nr ) is the luminescent lifetime without quenching.
luminescent lifetime with the quencher is
τ =
1
+
+
k r k nr k q [ Q ]
.
(2.8)
The
(2.9)
20
2. Basic Photophysics
Thus, Eq. (2.8) can be written as
Φ0 / Φ = τ 0 / τ .
(2.10)
When the quencher is oxygen, the Stern-Volmer equation is
I0 τ 0
=
= 1 + k qτ 0 [ O2 ] .
τ
I
(2.11)
In general, the rate constants k nr and k q for the non-radiative and quenching
processes are temperature-dependent. The temperature dependency of k nr can be
decomposed into a temperature-independent term and a temperature-dependent
term modeled by the Arrhenius relation (Bennett and McCartin 1966; Song and
Fayer 1991), i.e.,
E nr
),
(2.12)
k nr = k nr 0 + k nr 1 exp( −
RT
where k nr 0 = k nr ( T = 0 ) and k nr 1 are the rate constants for the temperatureindependent and temperature-dependent processes, respectively, Enr is the
activation energy for the non-radiative process, R is the universal gas constant,
and T is the absolute temperature in Kelvin. The temperature dependency of the
rate constant k q for the quenching process is related to oxygen diffusion in a
homogenous polymer layer used for a conventional PSP. According to the
Smoluchowski relation, the rate constant k q for the oxygen quenching can be
described by
k q = 4π R AB N 0 D
(2.13)
where R AB is an interaction distance between the luminophore and oxygen
molecules, and N 0 is the Avogadro's number. The diffusivity D has the
temperature dependency modeled by the Arrhenius relation
D = D0 exp( −
ED
),
RT
(2.14)
where E D is the activation energy for the oxygen diffusion process. Therefore,
from Eq. (2.9), the reciprocal of the luminescent lifetime is
1
τ
= k r + k nr 0 + k nr 1 exp( −
E nr
E
) + 4πR AB N 0 D0 exp( − D ) [ O2 ] polymer
RT
RT
(2.15)
According to Henry's law, the oxygen population [ O2 ] polymer in a polymer binder
is proportional to the partial pressure of oxygen pO2 or air pressure p , i.e.,
[ O2 ] polymer = S pO2 = S φ O2 p
(2.16)
2.2. Models for Conventional Pressure Sensitive Paint
21
where S is the oxygen solubility in a polymer binder layer and φ O2 is the mole
fraction of oxygen in the testing gas. The mole fraction of oxygen φ O2 is 21% in
the atmosphere, but it varies depending on testing facilities. For example, φ O2 is
-4
only a few ppm (1ppm = 10 %) in a cryogenic wind tunnel where the working gas
is nitrogen. Defining the permeability P0 = SD0 , from Eq. (2.15), we have
1
τ
= ka + K p ,
(2.17)
where the coefficients k a and K are defined as
k a = k r + k nr 0 + k nr 1 exp( −
E
E nr
) and K = 4πR AB N 0 P0 exp( − D )φ O2 . (2.18)
RT
RT
In aerodynamic applications, it is difficult to obtain the zero-oxygen condition
since the working gas in most wind tunnels is air containing 21% oxygen. Thus,
instead of using the zero-oxygen condition, we usually utilize the zero-speed
(wind-off) condition as a reference. Taking a luminescent intensity ratio between
the wind-off and wind-on conditions, we obtain the Stern-Volmer equation
suitable to aerodynamic applications
I ref
I
=
τ ref
p
.
= A polymer ( T ) + B polymer ( T )
τ
p ref
(2.19)
The Stern-Volmer coefficients in Eq. (2.19) are
A polymer = A polymer ,ref
K
ka
, and B polymer = B polymer , ref
,
k aref
K ref
(2.20)
where the reference coefficients are defined as
A polymer , ref =
1 + K ref
p ref
1
and B polymer , ref =
.
p ref / k aref
k aref / K ref + p ref
(2.21)
The subscript ‘polymer’ specifically denotes a conventional polymer-based PSP;
it will be seen that porous PSPs have somewhat different forms of the SternVolmer coefficients. Eq. (2.19) indicates that a ratio between the luminescent
intensities in the wind-on and wind-off conditions is required to determine air
pressure. This intensity-ratio method is commonly employed in PSP and TSP
measurements.
Using the expressions for k a and K , we can write A polymer and B polymer as a
function of temperature
ª 1 + ξ exp( − E nr RT ) º
»
A polymer = A polymer , ref «
«¬ 1 + ξ exp( − E nr R T ref ) »¼
22
2. Basic Photophysics
ª E
D
B polymer = B polymer , ref exp «−
«¬ R T ref
·º
§ Tref
¨
− 1¸ » ,
¸»
¨ T
¹¼
©
(2.22)
where the factor ξ is defined as ξ = k nr 1 /( k r + k nr 0 ) . For ( T − Tref ) / Tref << 1 ,
the linearized expressions for A polymer and B polymer are
ª
E nr
A polymer = A polymer , ref «1 + η
R
T ref
«¬
ª
ED
B polymer = B polymer , ref «1 +
R
T ref
«¬
§ T − Tref
¨
¨ T ref
©
§ T − Tref
¨
¨ T ref
©
·º
¸»
¸»
¹¼
·º
¸» ,
¸»
¹¼
(2.23)
where the factor η is
η=
ξ exp( − E nr RTref )
.
1 + ξ exp( − E nr R T ref )
(2.24)
Clearly, the Stern-Volmer coefficients A polymer and B polymer satisfy the following
constraint
A polymer ( Tref ) + B polymer ( Tref ) = 1 .
(2.25)
Eq. (2.23) indicates that the Stern-Volmer coefficient B polymer depends on the
activity energy E D for the oxygen diffusion process; this implies that the
temperature sensitivity of PSP is mainly related to the oxygen diffusion. Indeed,
experiments conducted by Gewehr and Delpy (1993) and Schanze et al. (1997) for
two different oxygen sensors showed that the temperature dependency of the
oxygen diffusivity in a polymer dominated the temperature effect of PSP. This
finding has an important implication in the design of low-temperature-sensitive
PSP formulations; the low-temperature-sensitive PSP should have a polymer
binder with the low activation energy for oxygen diffusion. In another special
case where E D ≈ E nr and η ≈ 1 over a certain range of temperature, the
coefficients A polymer ( T ) and B polymer ( T ) have the same temperature dependency;
thus a ratio between A polymer ( T ) and B polymer ( T ) becomes temperature
independent. PSP satisfying the above conditions is so-called ‘ideal’ PSP (see
Section 3.6). This paint is advantageous for correcting the temperature effect
since the Stern-Volmer relation becomes temperature independent when the
intensity ratio scaled by a single temperature-dependent factor is used as a
similarity variable.
In many PSP measurements, the linear Stern-Volmer relation Eq. (2.19) is
sufficiently accurate in a certain range of pressure. However, over an extended
range of the partial pressure of oxygen or air pressure, the non-linear Stern-
2.2. Models for Conventional Pressure Sensitive Paint
23
Volmer behavior becomes appreciable for microheterogeneous PSPs (Carraway et
al. 1991a; Xu et al. 1994; Hartmann et al. 1995). The main physical mechanisms
behind the non-linear Stern-Volmer characteristics are associated with
microheterogeneity of the environment of a probe molecule and deviation from
Henry’s law. Solid-state matrices like polymers may provide numerous different
kinds of environments for a probe molecule, resulting in the non-exponential
decay or multiple-exponential decay of luminescence. In some cases, a double
exponential model is sufficient for the decay; thus the oxygen quenching of
luminescence in microheterogeneous systems is described by a two-component
model
−1
º
I0 ª
f 01
f 02
=«
+
» ,
I
¬ 1 + K SV 1 [ O 2 ] 1 + K SV 2 [ O 2 ] ¼
where
f 01 and
(2.26)
f 02 are the fractional intensity contributions of the two
components in the absence of oxygen ( f 01 + f 02 = 1 ), K SV 1 and K SV 2 are the
Stern-Volmer constants of the two components. Furthermore, for the probe
molecule incorporated into a polymer, dual sorption mechanisms are considered
and thus the oxygen concentration is related to the applied partial pressure by
adsorption isotherm. These mechanisms are responsible for a slight deviation of
the actual concentration from that given by Henry’s law. The analytical form of
dual sorption in a polymer is obtained by adding the Langmuir isotherm to
Henry’s law, i.e.,
b pO2
,
(2.27)
[ O2 ] polymer = S pO2 + C’
1 + b pO2
where C’ is the Langmuir gas capacity due to adsorption and b is the Langumir
affinity coefficient. Based on the dual sorption model Eq. (2.27), Hubner and
Carroll (1997) suggested an extended form of the Stern-Volmer relation
I ref
I
= A+ B
D ( p / p ref )
p
+C
.
p ref
1 + D ( p / p ref )
(2.28)
Eq. (2.28) was able to give a good fit to experimental data for some PSPs. From a
standpoint of aerodynamic applications, an empirical form of the non-linear SternVolmer relation is usually given by a polynomial
2
§ p ·
p
¸ +.
= A( T ) + B( T )
+ C( T ) ¨
¨ p ref ¸
I
p ref
©
¹
I ref
(2.29)
24
2. Basic Photophysics
2.3. Models for Porous Pressure Sensitive Paint
In the preceding section, the photophysical models for a conventional polymer
PSP are discussed. Nevertheless, according to the work of Sakaue (1999), the
photophysical models for a porous PSP or open PSP system are different. In
general, pores in a porous PSP are macroscopic, which are much larger than the
size of an oxygen molecule. Figure 2.2 shows schematically a comparison of a
conventional polymer PSP with a porous PSP. In a conventional polymer PSP, as
shown in Fig. 2.2(a), the oxygen molecules in the working gas permeate into a
polymer binder layer and quench the luminescence. In contrast, as illustrated in
Fig. 2.2(b), a porous PSP has a much larger open surface to which the
luminophore molecules are directly applied; the oxygen molecules can directly
quench the luminescence without having to permeate into a binder layer.
Therefore, the use of a porous material as a binder for PSP offers two advantages.
First, a porous PSP can achieve a very fast time response (in the order of
microseconds) for unsteady PSP measurements; secondly, it makes PSP
measurements possible at cryogenic temperatures at which oxygen diffusion is
prevented through a conventional homogeneous polymer.
Oxygen Molecules
Oxygen Permeation
Incident Light
Luminescence
Polymer Layer
(a)
Luminophore
Model
Incident Light
Luminescence
Oxygen Molecules
Porous Material
Surface
(b)
Luminophore
Model Surface
Oxygen Quenching
Fig. 2.2. Schematic of (a) conventional polymer PSP and (b) porous PSP. From Sakaue
(1999)
2.3. Models for Porous Pressure Sensitive Paint
25
The oxygen quenching process in a porous PSP is different from that in a
conventional polymer PSP. Figures 2.3(a) and (b) illustrate two scenarios of the
oxygen quenching in a porous PSP; in both cases, a luminophore molecule is
adsorbed on a porous surface opened to the working gas. In Fig. 2.3(a), a gaseous
oxygen molecule collides to a luminophore molecule, resulting in the oxygen
quenching; in this case, the oxygen quenching process is controlled by a collision
between the gaseous oxygen molecule and luminophore molecule adsorbed on the
surface. In other case, as illustrated in Fig. 2.3(b), an adsorbed oxygen molecule
can cause quenching by diffusing to a luminophore molecule and hence the
oxygen quenching process is related to adsorption and diffusion of the oxygen
molecule into the luminophore molecule. Wolfgang and Gafney (1983) studied
the oxygen quenching of tris(2,2'-bipyridyl)ruthenium (Ru(bpy)) on a porous
Vycor glass and reported that Ru(bpy) was quenched by either a gaseous oxygen
molecule colliding to the adsorbed Ru(bpy) or an adsorbed oxygen molecule.
gaseous oxygen
adsorbed oxygen
collision
porous surface
porous surface
surface diffusion
oxygen quenching
(b): Adsorption Controlled Model
quencher: adsorbed oxygen
process: adsorption/surface diffusion
luminophore
(a): Collision Controlled Model
quencher: gaseous oxygen
process: collision
Fig. 2.3. Oxygen quenching mechanisms for porous PSP: (a) Collision controlled model;
(b) Adsorption controlled model. From Sakaue (1999)
Two photophysical models were developed by Sakaue (1999) to describe the
oxygen quenching on a porous surface by considering the Eley-Rideal (ER)
mechanism and Langmuir-Hinshelwood (LH) mechanism. The ER mechanism is
a target annihilation reaction between a gaseous oxygen molecule and an adsorbed
luminophore molecule; it is a collision-controlled reaction (Samuel et al. 1992).
The LH mechanism, which is adsorption/surface-diffusion-controlled, is a reaction
between an adsorbed oxygen molecule and an adsorbed luminophore molecule
(Hinshelwood 1940). Samuel et al. (1992) studied the oxygen quenching of
Ru(bpy) on a porous silica surface over a temperature range of 88-353 K and
reported that at low temperatures the oxygen quenching was diffusion-controlled
(the LH type). As temperature increased, the reaction remained the LH type in
nature, but it was increasingly influenced by the target annihilation reaction (the
26
2. Basic Photophysics
ER type). At higher temperatures, the reaction was no longer the LH type, which
was dominated by the ER type reaction. In these cases, the rate constant kq for the
oxygen quenching and the oxygen concentration [O2] were described in a different
manner from that for a conventional polymer binder.
2.3.1. Collision-Controlled Model
When the rate constant kq for the oxygen quenching and the oxygen concentration
[O2] are considered in a collision-controlled reaction, the Stern-Volmer relation is
called the collision-controlled model to distinguish from the diffusion-controlled
relation (or adsorption-controlled model). The rate of collision of the oxygen
*
molecules on a porous surface is [ O2 ] c* / 4 , where c is the average speed of the
molecules. According to the theory of ideal gas, one knows
[ O2 ] =
N 0 pO2
RT
and c* =
8RT
(2.30)
π Mm
where pO2 is the partial pressure of oxygen, T is the absolute temperature in
Kelvin, Mm is the molar mass, R is the universal gas constant, and N0 is the
Avogadro's number.
The rate of the oxygen quenching is modeled by a product of an effective
contact area σeff and the collision rate
k q [ O2 ] =
σ eff [ O2 ] c *
4
=
σ eff N 0 p O2
2π M m RT
=
σ eff N 0 φ O2 p
2π M m RT
.
(2.31)
Hence, the rate of the oxygen quenching is proportional to the partial pressure of
oxygen or air pressure, but is inversely proportional to the square root of
temperature. The Stern-Volmer relation for the luminescent lifetime then
becomes
σ eff N 0 φ O2
1
= ka +
p
(2.32)
τ
2π M m RT
For aerodynamic applications, the Stern-Volmer relation for the collisioncontrolled quenching process can be written as
p
I ref
= Acollision ( T ) + B collision ( T )
.
I
p ref
(2.33)
In Eq. (2.33), the Stern-Volmer coefficients are
Acollision = Acollision, ref
T ref
k a and B
,
collision = B collision ,ref
T
k aref
(2.34)
2.3. Models for Porous Pressure Sensitive Paint
27
where the coefficients at the reference conditions are defined as
Acollision , ref = 1 /( 1 + ζ ) , B collision , ref = ζ /( 1 + ζ ) ,
ζ =
σ eff N 0φ O2 p ref
k aref
2π M m R Tref
.
(2.35)
Although Eq. (2.33) has the same form as that for a conventional polymer binder,
the Stern-Volmer coefficients Acollision and Bcollision have different physical meanings.
The coefficient Bcollision has weaker temperature dependency that is inversely
proportional to the square root of temperature. In contrast, the temperature
dependency of Acollision has the same form as that for a conventional polymer binder;
linearization of Eq. (2.34) at T = Tref leads to
ª
E nr
Acollision = Acollision , ref «1 +
R T ref
«¬
§ T − Tref
¨
¨ T ref
©
·º
¸» .
¸»
¹¼
(2.36)
2.3.2. Adsorption-Controlled Model
Besides the collision-controlled quenching, an adsorbed oxygen molecule on a
porous surface can also quench the luminescence; if this is the dominant
mechanism, the oxygen quenching is controlled by adsorption and surface
diffusion of the adsorbed oxygen on the porous surface.
The oxygen
concentration on a porous surface, [O2]ads, can be described by the fractional
coverage of oxygen on the porous surface
θ=
[ O2 ] ads
[ O2 ] adsM
,
(2.37)
where [O2]adsM is the maximum oxygen concentration on the porous surface. The
Stern-Volmer equation is then written as
I0 = 1 + τ
k q 0 [ O2 ] adsM θ ,
I
(2.38)
and accordingly the convenient form of the Stern-Volmer relation for
aerodynamic applications is
θ
I ref
= A( T ) + B( T )
,
(2.39)
I
θ ref
where
A=
k q [ O2 ] adsM θ ref
ka
and B =
.
k a + k qref [ O2 ] adsM θ ref
k a + k qref [ O2 ] adsM θ ref
(2.40)
28
2. Basic Photophysics
The rate constant kq for the oxygen quenching, which is surface-diffusioncontrolled, can be described by (Freeman and Doll 1983)
0
k q = 2πR AB λ B D = k q exp( − E sdiff / RT ) ,
(2.41)
where RAB is the relative distance between an adsorbed oxygen and an adsorbed
luminophore, and D is the diffusivity and the parameter λΒ is a ratio of the
modified first-order and second-order Bessel functions of the second kind.
Basically, kq is temperature-dependent due to the Arrhenius relation
D = D0 exp( − E sdiff / RT ) .
To describe θ, either the Langmuir isotherm or the Freundlich isotherm can be
used (Carraway et al. 1991b). The Langmuir isotherm relates θ to the partial
pressure of oxygen pO2 in the working gas by
θ=
b p O2
1 + b p O2
.
(2.42)
The factor b in Eq. (2.42) is a function of temperature (Butt 1980)
σ eff
b=
kd
2π M m RT
exp( − E ads / RT ) = b0
exp( − E ads / RT )
T
,
(2.43)
where kd is the desorption rate constant per unit surface area and Eads is the heat of
adsorption. Since the oxygen concentration is [ O2 ] = b pO2 , Eq. (2.38) becomes
b pO2 1 + bref pO2 ref
I ref
= ALangmuir + B Langmuir
1 + b p O2
I
bref pO2 ref
.
(2.44)
Eq. (2.44) is the adsorption-controlled model derived from the Langmuir
isotherm; for [ O2 ] = b pO2 << [ O2 ] adsM , it can be approximated by
pO2
I ref
= ALangmuir ( T ) + B Langmuir ( T )
pO2 ref
I
,
(2.45)
.
(2.46)
where the Stern-Volmer coefficients are
ALangmuir =
B Langmuir =
ka
+
[
O
k a k qref
2 ] adsM b ref p O2 ref
k q [ O2 ] adsM b pO2 ref
k a + k qref [ O2 ] adsM bref pO2 ref
The coefficient ALangmuir has the same temperature dependency as that for a
conventional polymer PSP and that in the collision-controlled model, i.e.,
2.3. Models for Porous Pressure Sensitive Paint
ALangmuir = ALangmuir , ref
ka
k aref
,
29
(2.47)
and the linearized form for ALangmuir is
ª
E nr
ALangmuir = ALangmuir , ref «1 +
R
T ref
«¬
§ T − T ref
¨
¨ T ref
©
·º
¸» .
¸»
¹¼
(2.48)
Hence, Eq. (2.48) indicates that ALangmuir is related to the temperature dependency of
the non-radiative processes of the luminophore. On the other hand, BLangmuir has the
following temperature dependency
ª − E l § T ref
·º
kq b
T ref
¨
¸» , (2.49)
exp «
= B Langmuir , ref
−
1
B Langmuir = B Langmuir , ref
¨
¸
T
k qref b ref
«¬ R T ref © T
¹»¼
where E l = E sdiff + E ads . Rewriting Eq. (2.49) in an exponential form yields
ª
El
B Langmuir = B Langmuir , ref exp «−
«¬ R T ref
· 1 § T ref
§ T ref
¨¨
− 1¸¸ + ln¨¨
¹ 2 © T
© T
·º
¸¸» ,
¹»¼
(2.50)
and furthermore, linearization of Eq. (2.50) at T = Tref gives
ª
EL
B Langmuir = B Langmuir , ref «1 +
R T ref
«¬
§ T − T ref
¨
¨ T ref
©
·º
¸» ,
¸»
¹¼
(2.51)
where E L = El − R Tref / 2 = E sdiff + E ads − R Tref / 2 . Clearly, the temperature
dependency of the coefficient BLangmuir, Eq. (2.51), is associated with both surface
diffusion and adsorption; but it has the similar form to Eq. (2.23) for a
conventional polymer layer. The reference Stern-Volmer coefficients ALangmuir , ref
and B Langmuir , ref
(their lengthy expressions are not given here) satisfy the
constraint ALangmuir , ref + B Langmuir , ref = 1 .
The Freundlich isotherm can serve as another model for surface adsorption
θ = bF ( p O2 )γ
(2.52)
where the coefficient and exponent are
bF =
b0
T
γ
exp( − E ads / RT ) and γ =
RT
E adsM
.
(2.53)
The exponent γ is an empirical parameter that is temperature-dependent. For a
known γref at a known reference temperature Tref, EadsM is given by
30
2. Basic Photophysics
E adsM =
R T ref
.
γ ref
(2.54)
Substituting Eqs. (2.52), (2.53) and (2.54) into Eq. (2.39), we obtain the non-linear
Stern-Volmer equation
§ pO
I ref
2
= AFreundlich ( T ) + B Freundlich ( T ) ¨
¨ p O ref
I
© 2
·
¸
¸
¹
γ
(2.55)
where
AFreundlich =
B Freundlich =
ka
γ ref
k a + k qref [ O2 ] absM b Fref ( pO2 ref )
k q [ O2 ] absM b F ( pO2 ref )
γ ref
γ ref
k a + k qref [ O2 ] absM b Fref ( pO2 ref )
.
(2.56)
The coefficient AFreundlich has the same temperature dependency as that in other
models
ka
,
(2.57)
AFreundlich = AFreundlich , ref
k aref
and the linearized form for AFreundlich is
ª
E nr
AFreundlich = AFreundlich , ref «1 +
R T ref
«¬
§ T − T ref
¨
¨ T ref
©
·º
¸» .
¸»
¹¼
(2.58)
.
(2.59)
The coefficient BFreundlich has the temperature dependency
B Freundlich = B Freundlich , ref
γ
k q b F ( pO2 ref )
γ ref
k qref b Fref ( pO2 ref )
Substituting Eqs. (2.41) and (2.53) into (2.59) yields
B Freundlich = B Freundlich , ref
( T ref )
Tγ
( p O2 ref )γ
γ ref
( pO2 ref )
γ ref
ª −Ef
exp «
«¬ R T ref
§ T ref
·º
¨
¸» ,
−
1
¨ T
¸
©
¹ »¼
(2.60)
where E f = E sdiff + E ads . When an approximation γref ≈ γ is used for a small
temperature change, the expression for B Freundlich becomes
B Freundlich
§ T ref
= B Freundlich , ref ¨¨
© T
·
¸
¸
¹
γ ref
ª −Ef
exp «
¬« R T ref
§ T ref
·º
¨
¸
¨ T − 1¸ » ,
©
¹»¼
(2.61)
2.4. Thermal Quenching
31
which is similar to BLangmuir. After rewriting all the terms in Eq. (2.61) in an
exponential form, linearization at T = Tref yields
ª
EF
B Freundlich = B Freundlich , ref «1 +
R T ref
«¬
§ T − Tref
¨
¨ T ref
©
·º
¸» ,
¸»
¹¼
(2.62)
where
E F = − E sdiff − E ads + γ ref R T ref
ª §p
«ln¨ O2 ref
« ¨¨ T ref
«¬ ©
·
¸−
¸¸
¹
º
1»
.
2»
»¼
(2.63)
Similar to the Langmuir-type model, the coefficient BFreundlich has the temperature
dependency associated with surface diffusion and adsorption. However, the
photophysical model Eq. (2.55) describes the non-linear behavior of the SternVolmer plot for a porous PSP.
2.4. Thermal Quenching
For TSP where the paint layer is not oxygen-permeable such that no oxygen
quenching occurs, from Eq. (2.8), the quantum yield of luminescence is simply
given by
kr
I
Φ =
.
(2.64)
=
Ia
k r + k rn
The temperature dependency of the non-radiative processes k nr can be
decomposed into a temperature-independent term and a temperature-dependent
term modeled by the Arrhenius relation (Bennett and McCartin 1966; Song and
Fayer 1991; Schanze et al. 1997)
E nr
),
(2.65)
k nr = k nr 0 + k nr 1 exp( −
RT
where k nr 0 = k nr ( T = 0 ) and k nr 1 are the rate constants for the temperatureindependent and temperature-dependent processes, respectively, Enr is the
activation energy for the non-radiative process, R is the universal gas constant,
and T is the absolute temperature in Kelvin. From Eqs. (2.64) and (2.65), we have
ln
I ( T )[ I ( 0 ) − I ( Tref )]
I ( Tref )[ I ( 0 ) − I ( T )]
=
E nr
R
§1
¨ − 1
¨ T Tref
©
·
¸,
¸
¹
(2.66)
where I ( 0 ) = I ( T = 0 ) is the luminescent intensity at the absolute zero
temperature.
For | I ( T ) − I ( Tref ) | / I ( 0 ) << 1 and I ( T )I ( Tref ) /[ I ( 0 )] 2 << 1
32
2. Basic Photophysics
over a certain temperature range, a relation between the luminescent intensity and
temperature can be approximately written in the Arrhenius form
ln
E §1
I( T )
1
= nr ¨ −
I ( Tref )
R ¨© T Tref
·
¸.
¸
¹
(2.67)
Theoretically speaking, the Arrhenius plot of ln[ I ( T ) / I ( Tref )] versus 1/T gives
a straight line of the slope Enr/R. Experimental results indeed indicate that the
simple Arrhenius relation Eq. (2.67) is able to fit data over a certain temperature
range. However, for some TSPs, experimental data may not fully obey the simple
Arrhenius relation over a wider range of temperature. Thus, as an alternative, an
empirical functional relation between the luminescent intensity and temperature is
I( T )
= f ( T / Tref ) ,
(2.68)
I ( Tref )
where f ( T / Tref ) could be a polynomial, exponential or other function to fit
experimental data over a working temperature range. Either Eq. (2.67) or Eq.
(2.68) can serve as an operational form of the calibration relation for TSP in
practical applications.
3. Physical Properties of Paints
3.1. Calibration
In order to quantitatively measure air pressure with PSP, the relationship
between the luminescence signal (intensity, lifetime or phase) and air pressure
should be experimentally determined by calibration. Apparatus for calibration
of PSP over a temperature range of 90-423 K are described in Appendix A. A
generic calibration set-up consists of a pressure chamber, excitation light source
and photodetector. A PSP sample is placed in the pressure chamber where
pressure can be adjusted from vacuum to high pressures. The surface
temperature of the PSP sample is controlled using a heating/cooling device and
measured using a temperature sensor. The PSP sample is excited by an
illumination source (e.g. UV lamp, LED array or laser) through a window of the
pressure chamber. The luminescent emission from the paint sample, after
filtered by a band-pass optical filter, is measured using a photodetector (e.g.
photodiode, PMT or CCD camera), and the photodetector output is acquired
with a PC over a range of pressures and temperatures. Therefore, the
correspondence between the luminescence signal and pressure, which is usually
described by the Stern-Volmer equation, is established over a range of
temperatures. Typical calibration results for a number of PSP formulations
based on Platinum Porphrins, Ruthenium complexes and Perlene/Pyrene are
given in the following sections. The calibration set-up for PSP can be used for
TSP calibration when the surface temperature of a paint sample varies while
pressure in the chamber is kept constant. Calibration data for TSP are typically
presented as an Arrhenius plot over a certain temperature range; typical
calibration results for TSP formulations are given in Sections 3.3 and 3.4.
The most common calibrations for PSP and TSP are based on measurements of
the luminescent intensity as a function of pressure and/or temperature. As
discussed before, however, the luminescent lifetime (or phase) is also a function
of pressure and/or temperature. In a lifetime calibration apparatus, a pulsed (or
modulated) excitation light source is used, and after an exciting pulse light ceases
the exponential decay of the luminescent intensity is measured using a fastresponding photodetector and recorded with a PC or an oscilloscope. The
luminescent lifetime can be determined by fitting data with a single exponential
function or multiple-exponential function for certain paints over a range of
pressures and temperatures. Early instrument for measuring the luminescent
34
3. Physical Properties of Paints
lifetime was described by Brody (1957) and Bennett (1960), and the current state
of luminescent lifetime measurement systems in photochemistry and medical
applications was comprehensively reviewed by Lakowicz (1991, 1999). The
Stern-Volmer relations between the lifetime and oxygen partial pressure (or
concentration) for oxygen sensitive luminescent materials were determined by
Gewehr and Delpy (1993), Gord et al. (1995), Sacksteder et al. (1993), Xu et al.
(1994), and Papkovsky (1995). Lifetime calibration results for TSPs and
thermographic phosphors were also reported by Sholes and Small (1980), Grattan
et al. (1987), Bugos (1989), Noel et al. (1985), and Lakowicz (1999). A more
detailed discussion on the lifetime and phase methods is given in Chapter 6.
3.2. Typical Pressure Sensitive Paints
A typical PSP is prepared by dissolving a luminescent dye and a polymer binder
in a solvent; the order of mixing the components and the relative concentration of
the components may change the characteristics of the paint. Chlorinated organic
solvents such as dichloromethane and trichloroethane have been used for making
PSP. The selection of a polymer binder for PSP is important, which should be
based on a balanced consideration of its oxygen permeability, temperature effect,
humidity effect, adhesion, mechanical stability, photodegradation, and other
required properties. Silicone rubbers, GP-197, silica gel and sol-gel-derived
coatings have been used as binders for PSPs and oxygen sensors (Wan 1993;
Gallery 1993; Xu et al. 1994; MacCraith et al. 1995; Jordan et al. 1999a, 1999b).
Other polymers and porous materials that are potentially useful for PSP can be
found in the literature of polymers (Krevelen 1976; Mulder 1991; Fried 1995;
Robinson and Perlmutter 1994). The permeability, solubility and diffusion
coefficients of a polymer binder are related to the pressure sensitivity and time
response of PSP. Furthermore, the behavior of PSP depends on interaction
between a probe molecule and its surrounding polymer. The microenvironment of
the probe molecule in the polymer binder can significantly affect the
luminescence and quenching behavior (Hartmann et al. 1995; Meier et al. 1995;
Xu et al. 1994; Lu and Winnik 2001; Lu et al. 2001). Also, it was observed that a
basecoat might affect the behavior of PSP (Coyle et al. 1995). A useful review on
quenching of luminescence by oxygen in polymer films was given by Lu and
Winnik (2000), stressing on luminescent materials and polymers.
Table 3.1 lists some PSP formulations along with their spectroscopic properties
and the Stern-Volmer coefficients. In Table 3.1, the Stern-Volmer coefficients
A( T )
and
B( T )
are the coefficients in the linear relation
I ref / I = A( T ) + B( T ) p / pref at the room temperature of about 20 C, where the
o
reference pressure p ref is the ambient pressure of 1 atm. For certain PSPs that do
not completely obey the linear Stern-Volmer relation, the coefficients A( T ) and
B( T ) are estimated by fitting data over a finite linear range. The results are
collected from the theses and papers by Wan (1993), Burns (1995), Baron et al.
3.2. Typical Pressure Sensitive Paints
35
(1993), Kavandi et al. (1990), and McLachlan et al. (1993a, 1995), which
documented the absorption spectra, emission spectra, and Stern-Volmer plots of
oxygen-sensing luminophores and supporting polymer matrices. Table 3.1 also
include a number of proprietary PSPs developed by TsAGI (Troyanovsky et al.
1993; Bukov et al. 1993), the former McDonnell Douglas (now Boeing at St.
Louis) (Morris et al. 1993a, 1993b; Morris 1995), the University of
Washington/NASA Ames (McLachlan and Bell 1995) and NASA Langley
(Oglesby and Jordan 2000). Some PSP formulations of the former McDonnell
Douglas have been patented (Schwab and Levy 1994). Generally speaking, a
good PSP has the Stern-Volmer coefficient B( T ) larger than 0.5, indicating
acceptable pressure sensitivity for quantitative measurements (Oglesby et al.
1995a).
Table 3.1. Pressure sensitive paints
Luminophore
Binder
Excitation Emission Stern-Volmer
wavelength wavelength coefficients
(nm)
(nm)
A
B
H2TSPP
H2(Me2N)TFPP
H2TCPP
H2TNMPP
H2TTMAPP
Perylene dibutyrate
Perylene dye
PtTFPP
silica gel
silica gel
silica gel
silica gel
silica gel
silica gel
silica gel
silica gel
DuPont Chrom.
Polystyrene
FEM
400
400
410
420
410
457
480, 530
390
PtTFPP
PtTFPP
PtOEP
Pyrene
Ru(bpy)
Ru(ph2-phen)
[Ru(ph2-phen)3] 2+
FIB
GP-197
silica gel
GE RTV 118
silica gel
silica gel
GE RTV118
GP-134/silica
650, 709
650
709
661, 714
653, 710
520
550, 570
650
390
650
390
366, 543
650
650
360-390
337, 457
337, 457
470
600
600
337
620
NASA-Ames PSP
McDonnell Douglas
PSP
TsAGI LPSL2
blue
320-350
425-550
0.58
0.43
0.40
0.43
0.40
0.33
0.47
0.27
0.50
0.29
0.17
0.42
0.56
0.61
0.60
0.60
0.67
0.53
0.72
0.52
0.69
0.83
0.13
0.32
0.12
0.12
0.33
0.17
0.27
0.22
0.87
0.70
0.88
0.88
0.68
0.84
0.75
0.78
0.38
0.62
0.18
0.82
0.25
0.75
Lifetime Temp.
at room coeff.
temp.
(%/0C)
(micro s)
~0
~0
0.013
50
4.5
0.35
-2.1
-1.8
-4.3
-1.4
50
-1.0
-1.7
-~0
3
4.7
0.3
-1.3
-0.78
-1.5
-0.3
Reference
Purchase
source
Wan (1993)
Wan (1993)
Wan (1993)
Wan (1993)
Wan (1993)
Burns (1995)
Wan (1993)
Wan (1993),
Burns (1995)
Porphyrin
Porphyrin
Porphyrin
Aldrich
Aldrich
Pylam
Aldrich
Porphyrin
Burns (1995)
NASA
Langley
ISSI
Porphyrin
Burns (1995)
Burns (1995)
Aldrich
GFS Chem.
Xu et al.
(1994)
McLachlan
and Bell
(1995)
Dowgwillo et
al. (1994)
Bukov et al.
(1993)
NASA Ames
McDonnell
Douglas
TsAGI
Three families of luminescent dyes, Platinum Porphyrins, Ruthenium
Polypyridyls and Pyrene derivatives, have been commonly used for making PSP.
Recipes of three PSP formulations are given in Appendix B. The Platinum
Porphyrin compounds, which can be excited by either an UV light or a green light,
emit red luminescence. They are very sensitive to oxygen, but they often have a
long lifetime and low luminescent intensity at the atmospheric pressure. The
Ruthenium compounds also emit red luminescence when excited by either an UV
light or a blue light. They are very photo-stable, but are difficult to incorporate
into polymer systems. The Pyrene derivatives, which are UV excited, emit blue
36
3. Physical Properties of Paints
luminescence. The Pyrene derivatives have weak temperature sensitivity;
however, they suffer from photodegradation and sublimation.
Figure 3.1 shows the chemical structure, and absorption and emission spectra
for platinum meso-tetra(pentafluorophenyl)porphine (PtTFPP). Figures 3.2 and
3.3 show the Stern-Volmer plots and temperature dependencies for two PtTFPP
PSP formulations: PtTFPP in the FIB polymer (poly-heptafluoro-n-butyl
methacrylate-co-hexafluorisopropyl methacrylate) developed by the University of
Washington (Gouterman and Carlson 1999) and PtTFPP in the FEM polymer
(poly-tifluoro-ethylmethacrylate-co-isobutylmethacrylate) developed by NASA
Langley (Oglesby and Jordan 2000). In these figures, the lower temperature
sensitivity of PSP at vacuum represents the intrinsic temperature dependency of
the luminophore, while the higher temperature sensitivity of PSP at the
atmospheric pressure indicates an additional temperature effect on the oxygen
diffusion in the polymer.
F
F
F
F
F
F
F
F
N
F
N
F
Pt
F
N
F
N
F
F
F
F
(a)
F
F
F
F
(b)
Fig. 3.1. (a) Chemical structure of PtTFPP, (b) absorption and emission spectra of PtTFPP.
From Puklin et al. (2000)
3.2. Typical Pressure Sensitive Paints
37
1 .4
1 .3
2 4 .4 o
3 4 .7 o
4 5 .7 o
5 5 .3 o
1 .2
1 .1
1 .0
C
C
C
C
I
ref
/I
0 .9
0 .8
0 .7
0 .6
0 .5
0 .4
I ref = I a t 1 4 . 7 0 p si a a i r a t 2 4 . 4 o C
0 .3
0 .2
0 .1
0 .0
0 .0
0 .1
0 .2
0 .3
0 .4
0 .5
0 .6
0 .7
0.8
0 .9
1.0
1 .1
P /P r e f
(a)
Relative Emission Intensity
1 .0
-0.46%/ o C
vacuum
0 .9
-1.00%/ o C
0 .8
1 atm
0 .7
20
30
40
T e m p e ra tu re ( o C )
50
60
(b)
Fig. 3.2. (a) The Stern-Volmer plots, and (b) temperature dependency for PtTFPP in the
FIB Polymer. From Oglesby and Jordan (2000)
38
3. Physical Properties of Paints
1 .5
1 .4
25.1o
35.6o
45.5o
55.6o
1 .3
1 .2
1 .1
C
C
C
C
1 .0
Iref /I
0 .9
0 .8
0 .7
0 .6
0 .5
0 .4
I r e f = I a t 1 4 . 7 0 p si a a i r a t 2 5 . 1 o C
0 .3
0 .2
0 .1
0 .0
0.0
0 .1
0.2
0 .3
0 .4
0 .5
0 .6
0 .7
0 .8
0.9
1 .0
1 .1
P /P r e f
(a)
1.0
Relative Emission Intensity
vacuum
-0.64%/o C
0.9
1 atm
0.8
-1.4%/o C
0.7
20
30
40
50
Temperature (o C )
(b)
Fig. 3.3. (a) The Stern-Volmer plots, and (b) temperature dependency for PtTFPP in the
FEM polymer (NASA Langley). From Oglesby and Jordan (2000)
3.2. Typical Pressure Sensitive Paints
39
2.2
85
FIB
FEM
SOLGEL
UNICOAT
PAR
2.0
80
1.8
75
ST (%/deg)
SP (%/bar)
1.6
70
65
1.4
1.2
1.0
60
FIB
FEM
SOLGEL
UNICOAT
PAR
55
0.8
0.6
0.4
50
10
15
20
25
T (deg. C)
30
35
40
0.0
0.5
1.0
1.5
2.0
2.5
p/pref
Fig. 3.4. Pressure sensitivity (SP) and temperature sensitivity (ST) for PtTFPP in five
different polymer binders, where Pref = 1 bar and Tref = 10°C. From Mebarki and Le Sant
(2001)
In order to examine the effect of a polymer binder on the properties of PSP,
Mebarki and Le Sant (2001) calibrated five PSP formulations that used the same
porphyrin molecule, PtTFPP, with different polymer binders. Two formulations,
the PAR PSP from the Institute for Aerospace Research (IAR) of NRC in Canada
(Mebarki 2000) and the FEM PSP from NASA Langley (Oglesby and Upchurch
1999), are not commercially available. Other paints, the FIB PSP originally
developed by the University of Washington (Gouterman and Carlson 1999), solgel PSP (Jordan et al. 1999a, 1999b) and the Uni-Coat PSP (Mebarki 2000), were
commercially produced by Innovative Scientific Solutions Inc. (ISSI). Except for
the Uni-Coat PSP that did not require a primer layer, the commercial FIB and solgel PSP formulations were supplied with their respective primers. To simplify the
application procedures and solve adhesion problems, the FIB active layer was
applied on the top of the Tristar (DHMS C4.01TY3) white epoxy primer that was
also used as a screen layer for both the FEM PSP and PAR PSP. It was found that
the primer had no effect on the pressure or temperature sensitivity of the active
layer. However, the polymer binder (or permeable matrix) in which the porphyrin
molecule was immobilized affected both the pressure and temperature sensitivities
of the paint. To evaluate the performance of PSP, the pressure sensitivity and
temperature sensitivity are defined as SP = ∆( I ref / I ) / ∆P (in % per bar) and
ST = −∆( I / I ref ) / ∆T (in % per degree), respectively. The pressure sensitivity
was calculated in a pressure range of 0.15-2 bars and the temperature sensitivity
was determined in a temperature range of 10-35°C. Figure 3.4 shows the pressure
sensitivity SP as a function of temperature and the temperature sensitivity ST as
a function of pressure. The pressure sensitivity SP varied from 55% to nearly
40
3. Physical Properties of Paints
80% per bar, depending on the polymer binder used and temperature as well. The
FIB PSP formulation had nearly constant pressure sensitivity over a temperature
range of 10-40°C. The Uni-Coat and sol-gel PSP formulations had a similar linear
dependency of the pressure sensitivity SP on temperature; the temperature
sensitivity ST ranges from 0.6% to 1.6% per degree. The temperature sensitivity
was somewhat affected by pressure for all the PSP formulations except the FIB
PSP. The FIB PSP also has the lowest temperature sensitivity among them.
Figure 3.5 shows the chemical structure, and absorption and emission spectra
of Bathophen Ruthenium Chloride (Ru(ph2-phen) or Ru(dpp)). Ruthenium-based
oxygen sensors have been studied extensively by analytical chemists (Bacon and
Demas 1987; Carraway et al. 1991a, 1991b; Sacksteder et al. 1993; Xu et al. 1994;
Klimant and Wolfbeis 1995). The Ruthenium-based PSP formulations have been
developed and used for wind tunnel testing by the former McDonnell Douglas
(now Boeing at St. Louis) (Schwab and Levy 1994). Figure 3.6 shows the SternVolmer plots for Ru(dpp) in GE RTV 118 added with silica gel particles at
different temperatures; Figure 3.7 shows the luminescent lifetime as a function of
o
pressure for Ru(dpp) in GE RTV 118 at 22 C.
N
N
Ru2+ N
N
N
N
Intensity (arbitrary units)
(a)
Absorption
200
300
400
Luminescence
500
600
700
800
900
Wavelength (nm)
(b)
Fig. 3.5. (a) Chemical structure, and (b) Absorption and emission spectra of Ru(ph2-phen)
or Ru(dpp)
3.2. Typical Pressure Sensitive Paints
41
1.0
243K
253K
258K
263K
268K
273K
283K
293K
linear fit
0.9
0.8
Iref/I
0.7
0.6
0.5
0.4
0.3
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
P/Pref
Fig. 3.6. The Stern-Volmer plots for Ru(ph2-phen) or Ru(dpp) in GE RTV 110 added with
silica gel particles, where the reference pressure pref is 14.5 psi and reference temperature is
293 K. From Lachendro (2000)
1.4
5
Ru(ph2-phen)
in GE RTV 118
4
1.2
3
0.8
0.6
2
τref/τ
Lifetime τ (µs)
1.0
0.4
τ
τref/τ
1
0.2
0
0.0
0
200
400
600
800
P (mmHg)
Fig. 3.7. Lifetime-pressure relation for Ru(ph2-phen) in GE RTV 118 at 22 C, where τref is
the lifetime at the ambient pressure (1 atm). From Liu et al. (1997b)
o
Figure 3.8 shows the chemical structure and absorption and emission spectra of
Pyrene. The Pyrene-based PSP formulations were developed by TsAGI/OPTROD
in Russia (Fonov et al. 1998). One of them was the binary paint (B1 PSP) in
which a pressure-insensitive reference component was added to correct the
excitation light variations on a surface in performing a ratio between the wind-on
and wind-off images. Figure 3.9 shows the Stern-Volmer plots at different
temperatures for Pyrene complex in GE RTV 118. Obviously, this Pyrene-based
42
3. Physical Properties of Paints
o
PSP exhibits weak temperature dependency over a temperature range of 17-40 C.
Note that Perylene and its derivatives like Green Gold (perylene dibutylate) were
also used as a luminescent dye for PSP. Besides TsAGI, ONERA in France and
DLR in Germany developed Pyrene-based PSP formulations as well (Engler et al.
2001a). The PyGd PSP formulation developed by ONERA contained Pyrene as a
pressure-sensitive dye and a gadolinium oxysulfide as a reference component.
Figure 3.10 shows the emission spectrum of the PyGd PSP excited at 325 nm.
The two components in the paint absorbed an ultraviolet excitation light and
emitted at sufficiently different wavelengths such that the emissions from the two
components can be separated using optical filters. Figure 3.11 shows the SternVolmer plots at the ambient temperature for three Pyrene-based PSP formulations:
PyGd, B1 and PdGd. Because the temperature sensitivity of the reference
component was similar to that of the Pyrene dye in the PyGd PSP, the temperature
effect can be compensated by taking a ratio between the luminescent intensities
from the pressure-sensitive component (Pyrene) and reference component. As a
result, the PyGd PSP displayed very low temperature sensitivity of 0.05%/K. A
number of ‘Göttingen Dyes’ (GD) were developed by DLR and the University of
Göttingen, and three stable Pyrene-based paints, GD145, GD146 and GD147,
were tested in wind tunnels (Engler and Klein 1997b). Figure 3.12 shows the
pressure sensitivities of the Göttingen PSP formulations. A shortcoming of
Pyrene-based paints is that sublimation may occur when temperature is greater
o
than 40 C.
(a)
Emission
(b)
Wavelength (nm)
Fig. 3.8. (a) Chemical structure of Pyrene, and (b) absorption and emission spectra of
Pyrene. From Mebarki (2001)
3.2. Typical Pressure Sensitive Paints
43
intensity (A.U)
Fig. 3.9. The Stern-Volmer plots for Pyrene in GE RTV 118, where the excitation source is
filtered at 334±5 nm and the luminescent emission is filtered at >450 nm. The reference
conditions are Tref = 17°C and Pref = 1bar. Sublimation of Pyrene occurs initially at 40°C,
o
resulting in an intensity decrease and thus a different curve at 50 C. From Mebarki (2001)
vacuum
Pref=1bar
300
400
500
600 λ (nm)
Fig. 3.10. Emission spectra of a binary Pyrene-based PSP (PyGd) at 1 bar and vacuum.
From Engler et al. (2001a)
44
3. Physical Properties of Paints
1.02
1
0.98
Iref/I
0.96
0.94
0.92
0.9
PyGd
0.88
PdGd
0.86
0.84
0.82
B1
0.84
0.86
0.88
0.9
0.92
0.94
0.96
0.98
1
1.02
P/Pref
Fig. 3.11. The Stern-Volmer plots for three Pyrene-based PSP formulations (PyGd, PdGd,
and B1) used at ONERA. From Engler et al. (2001a)
Fig. 3.12. The Stern-Volmer plots for the Göttingen Pyrene-based PSP formulations (GD
145, GD 146, and GD 147). From Engler et al. (2001a)
3.3. Typical Temperature Sensitive Paints
45
3.3. Typical Temperature Sensitive Paints
Like PSP, TSP is prepared by dissolving a luminescent dye and a binder in a
solvent. Many commercially available resins and epoxies can serve as polymer
binders for TSP if they are not oxygen permeable and do not degrade the activity
of the probe luminophore molecule. Table 3.2 lists some TSP formulations as
well as the spectroscopic properties, temperature sensitivities and useful
temperature measurement ranges. Data are collected from Campbell (1993) and
Gallery (1993) and other sources. For a comparison between different TSP
formulations, the maximum logarithmic slope max{ d [ln( I / I ref )] / dT } is used
as an indicator of the temperature sensitivity for TSP over a certain temperature
range, where I ref is the reference luminescence intensity. Here, the logarithmic
slope is used since it is independent of the reference intensity that is different in
various sources. Two proprietary TSP formulations and two high-temperature
thermographic phosphors are also included in Table 3.2 for comparison. Figure
3.13 shows typical temperature dependencies of the luminescent intensity for a
number of TSP formulations. Some of them have been used to measure the
temperature and heat transfer fields in various applications (Kolodner and Tyson
1982, 1983a, 1983b; Romano et al. 1989; Campbell et al. 1993, 1994; Liu et al.
1995a, 1995b, 1996; Hamner et al. 1994; Asai et al. 1996, 1997c).
Table 3.2. Temperature sensitive paints
Luminophore
Binder
Coumanin
CuOEP
PMMA
GP-197
EuTTA
Perylene
Perylenedicarboximide
Pyronin B
Pyronin Y
Rhodamine B
Ru(bpy)
Ru(bpy)/Zeolite
Dope
Dope
PMMA
PMMA
Dope
Dope
Shellac
Poly
Vinyl
Alcohol
GP-197
Poly
Vinyl
Alcohol
Ru(trpy)
Ru(trpy)/Zeolite
La2O2S:Eu
Y 2O3:Eu
NASA-Ames (Univ. of
Washington) TSP
McDonnell Douglas
TSP
Excitation Emission Useful
wavelength wavelength temperature
(nm)
(nm)
range
(degree C)
UV
20 to 100
480-515
-180 to 20
Max.
log
slope
(%/0C)
-0.4
-2.9
Lifetime
at room
temp.
(micro s)
350
330-450
480-515
460-580
460-580
460-590
320, 452
320, 452
-3.9
-1.9
-0.7
-4.6
-5.5
-1.8
-0.93
-4.1
500
0.005
550-590
588
588
-20 to 80
0 to 100
50 to 100
50 to 100
0 to 100
0 to 80
0 to 90
-20 to 80
310, 475
310, 475
620
620
-170 to -50 -1.34
-180 to 80 -1.8
337
266
537
611
100 to 200 -3.5
510 to 1000 -1.88
612
430-580
UV
340-500
>500
0 to 50
-3.9
-5 to 90
-2.7
0.004
5
Reference
Purchase
source
Campbell (1993)
Campbell et al.
(1994)
Liu (1996)
Campbell (1994)
Campbell (1993)
Campbell (1993)
Campbell (1993)
Sullivan (1991)
Liu (1996)
Campbell et al.
(1994)
Purdue
Purdue
Campbell (1993)
Campbell et al.
(1994)
100
1400
Noel et al. (1985)
Alaruri et al.
(1995)
McLachlan et al
(1993b)
Cattafesta and
Moore (1995)
Kodak
Aldrich
Aldrich
Aldrich
Aldrich
Aldrich
GFS Chem.
GFS Chem.
Purdue
Purdue
Allison Eng.
Univ. of
Washington
McDonnell
Douglas
46
3. Physical Properties of Paints
1.2
1.0
I/Iref
0.8
8
5
0.6
7
6
0.4
4
0.2
1
2
3
0.0
-150
-100
-50
0
50
100
150
T (deg. C)
Fig. 3.13. Temperature dependencies of the luminescence intensity for TSP formulations:
(1) Ru(trpy) in Ethanol/Methanol, (2) Ru(trpy)(phtrpy) in GP-197, (3) Ru(VH127) in GP197, (4) Ru(trpy) in DuPont ChromaClear, (5) Ru(trpy)/Zeolite in GP-197, (6) EuTTA in
dope, (7) Ru(bpy) in DuPont ChromaClear, (8) Perylenedicarboximide in Sucrose
o
Octaacetate. (Tref = -150 C). From Liu et al. (1997b)
Two typical TSP formulations are Ru(bpy) in an automobile clear coat (DuPont
ChromaClear) binder and EuTTA in model airplane dope (see Appendix B); both
are easy to prepare and use. Figure 3.14(a) shows the chemical structure of
tris(2,2’-bipyridyl) ruthenium or Ru(bpy) and Figure 3.14(b) shows the absorption
and emission spectra of Ru(bpy) that are similar to those of Ru(dpp) for PSP.
Ru(bpy) can be excited by a UV lamp, nitrogen laser, argon laser, doubled YAG
laser or blue LED array. Since the Stokes shift is large (the emission peak at
about 620 nm), the excitation light can be easily separated from the luminescent
emission using an optical filter. An automobile urethane clear coat, which is
usually used as a top coat on most automobiles, is used as a polymer binder for
Ru(bpy); particularly, DuPont ChromaClear 7500S is used, but other brands
should work as well. The advantage of this binder is that it is oxygen
impermeable, readily available, and easy to spray although some pressure
sensitivity was observed at very high pressures and temperatures. Figure 3.13
shows the temperature dependency of the luminescent intensity for Ru(bpy) in
DuPont ChromaClear along with other TSP formulations. Ru(bpy) can also
mixed with a Shellac binder; the Ru(bpy)-Shellac TSP is similar to Ru(bpy) in
DuPont ChromaClear in terms of the temperature sensitivity. It is also easy to
apply. Figures 3.15 and 3.16 show, respectively, the Arrhenius plot and lifetime
for the Ru(bpy)-Shellac TSP compared with the EuTTA-dope TSP.
3.3. Typical Temperature Sensitive Paints
N
N
N
2+
N
Ru
N
47
N
Intensity (arb. units)
(a)
Absorption
200
300
(b)
400
Emission
500
600
700
800
900
Wavelength (nm)
Fig. 3.14. (a) Chemical structure of Ru(bpy), and (b) absorption and emission spectra of
Ru(bpy)
1
ln[I(T)/I(Tref)]
0
-1
-2
EuTTA-dope
Ru(bpy)-Shellac
-3
-0.8
-0.6
-0.4
-0.2
0.0
3
0.2
0.4
-1
(1/T - 1/Tref)10 (K )
Fig. 3.15. The Arrhenius plots for two TSP formulations: EuTTA-dope TSP and Ru(bpy)Shellac TSP, where Tref = 293 K. From Liu et al. (1997b)
3. Physical Properties of Paints
Lifetime of Ru(bpy)-Shellac (µs)
7
2.5
Ru(bpy)-Shellac
EuTTA-dope
6
2.0
5
1.5
4
1.0
3
0.5
2
1
Lifetime of EuTTA-dope (ms)
48
0.0
0
20
40
60
80
Temperature (degree C)
Fig. 3.16. Lifetime-temperature relations for two Ru(bpy)-Shellac TSP and EuTTA-dope
TSP. From Liu et al. (1997b)
S
O
F
F
O
F
F
F
F
Eu
O
O
O
S
F
Intensity (arb. units)
(a)
O
Absorption
300
(b)
F
F
350
400
450
S
Emission
500
550
600
650
700
Wavelength (nm)
Fig. 3.17. (a) Chemical structure of EuTTA, (b) absorption and emission spectra of EuTTA
3.3. Typical Temperature Sensitive Paints
49
Another good TSP is based on Europium (III) Thenoyltrifluoroacetonate or
EuTTA whose structure and the absorption and emission spectra are shown in Fig.
3.17. Obviously, a UV lamp or a nitrogen laser can be used for excitation.
EuTTA has a high quantum yield and a large Stokes shift (the emission peak at
about 620 nm). The binder used with this luminphore is a clear model airplane
dope that, like DuPont ChromaClear and Shellac, is readily available, easy to
spray, and oxygen impermeable. Figures 3.15 and 3.16 show, respectively, the
Arrhenius plot and lifetime for the EuTTA-dope TSP along with those for the
Ru(bpy)-Shellac TSP.
Thermographic phosphors and thermochromic liquid crystals are also
temperature sensitive coatings for measuring the surface temperature distributions.
Similar to polymer-based TSPs, thermographic phosphors utilize the thermal
quenching of the luminescent emission from ceramic materials that are doped or
activated with rare-earth elements (Allison and Gillies 1997). However, they are
usually in the form of insoluble powders or crystals in contrast to a polymer-based
TSP where luminescent molecules are immobilized in a polymer matrix. The
luminescent intensity (or lifetime) of thermographic phosphor and polymer-based
TSP follows the same functional relation I ∝ [ 1 + a0 exp( − a1 / T )] −1 . Figure
3.18 shows the measurement envelops of thermographic phosphors and polymerbased luminescent TSPs. A family of thermographic phosphors can cover a
temperature range of 273-1600 K, which overlaps with the temperature range of
the polymer-based TSP family from 90 to 423 K. Hence, a combination of
thermographic phosphors and polymer-based luminescent TSPs can cover a very
broad range from cryogenic to high temperatures. The measurement systems
(intensity- and lifetime-based systems) for thermographic phosphors are
essentially the same as those for polymer-based luminescent TSPs. The emission
spectrum of certain phosphor has multiple distinct lines that have very different
temperature sensitivities.
Thus, an emission-intensity ratio between the
temperature-sensitive and -insensitive lines can eliminate the effect of nonuniform illumination on a surface. Note that certain emission lines of certain
phosphors are also temperature sensitive in cryogenic conditions. Thermochromic
liquid crystals selectively reflect light depending on the surface temperature, and
hence the dominant wavelength or hue of the reflected light varies monotonically
o
with temperature over a relatively narrow temperature range of about 32-42 C
(Smith et al. 2000). For comparison, Figure 3.18 plots the normalized hue of a
typical thermochromic liquid crystal as a function of temperature; the temperature
sensitivity of the thermochromic liquid crystal is high over a narrow temperature
range.
50
3. Physical Properties of Paints
Normalized Luminescent Intensity or Hue
1.4
Measurement Envelop of TSPs
Measurement Envelop of Phosphors
Typical Calibration Curve for Liquid Crystal
1.2
1
0.8
0.6
0.4
0.2
0
0
200
400
600
800
1000 1200
Temperature (Kelvin)
1400
1600
1800
Fig. 3.18. Measurement envelops for polymer-based TSPs and thermographic phosphors
along with a typical normalized calibration curve of thermochromic liquid crystal
3.4. Cryogenic Paints
A challenging problem is application of PSP in cryogenic wind tunnels like the
NASA Langley National Transonic Facility (NTF) and European Transonic Wind
Tunnel Facility (ETW). Porous materials were usually used as binders for PSP at
cryogenic temperatures. Porous material has a large exposure surface area where
the probe luminophore can be directly applied and luminescence can be directly
quenched by oxygen. The use of porous materials as binders allows PSP
measurements at cryogenic temperatures and achieves fast time response as well
(in the order of microseconds). Various porous materials were investigated as
binders for PSP, including a thin layer chromatography (TLC) plate (Baron et al.
1993), hydrothermal coating (Bacsa and Gratzel 1996), sol-gel (MacCraith et al.
1995; Jordan et al. 1999a, 1999b), tape-casting (Scroggin 1999), anodized
aluminum (Asai 1997a), anodized titanium and porous paper filter (Erausquin
1998; Erauquin et al. 1998).
Aluminum can be anodized to create a thin aluminum oxide layer on the
surface through an electrochemical process. Anodized aluminum (AA) is highly
porous with 10-100 nm micropores uniformly distributed on the surface. AA-PSP
is made by adsorbing the luminophore into the pores on the AA surface (Asai
1997a). Figure 3.19 shows the Stern-Volmer plot for an AA-PSP, Ru(dpp) on
anodized aluminum, compared with a conventional polymer-based PSP (Ru(dpp)
in RTV) at cryogenic temperatures. This AA-PSP still exhibits good sensitivity to
oxygen even at 100 K, whereas the conventional PSP loses its sensitivity to
oxygen at 150 K. Upchurch et al. (1998) and Asai et al. (2000, 2002) developed a
polymer-based cryogenic PSP that used highly porous Poly(TMSP) as a binder.
3.4. Cryogenic Paints
51
To compare the two cryogenic PSP formulations, Figure 3.20 shows the SternVolmer plots for the Poly(TMSP)-based PSP and AA-PSP that use Ru(dpp) as a
luminescent dye; both PSPs exhibit the non-linear behavior in the Stern-Volmer
plot.
2.0
AA-PSP (pO ref=14Pa, T=100K)
2
Iref/I
1.5
1.0
0.5
conventional PSP (pO ref=14Pa, T=150K)
2
0.0
0.0
0.5
1.0
1.5
p /p
O2
2.0
2.5
3.0
3.5
O2ref
Fig. 3.19. The Stern-Volmer plots for a porous AA-PSP and a conventional PSP with
silicone rubber as a binder at cryogenic temperatures. Both PSP formulations uses Ru(ph2phen) as a probe luminophore. From Sakaue (1999)
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
É ÑÉÑÉ ÑÉ
É
É
Ñ
T=100K
ÉÉ Ñ
É
ÉÉ
Ñ
ÉÉ
Ñ
É
ÉÉ
ÑÑ
ÉÉ
Ñ
Ñ
ÉÉ ÑÑÑ
É ÑÑÑ
É ÑÑ
Ñ poly(TMSP)
Ñ
ÉÑÑ
É anodized
É
ÑÑ
0
200 400 600 800 1000
oxygen concentration, ppm
Fig. 3.20. Comparison of Poly(TMSP) PSP with anodized aluminum (AA) PSP at 100 K,
where excitation is at 400±50 nm and emission is at 650±50 nm. From Asai et al. (2000)
A family of the luminescent molecules Ru(trpy) (see Fig. 3.21 for the chemical
structure) has been studied for making cryogenic TSP formulations since it is
found that these compounds are temperature sensitive at cryogenic temperatures
(Campbell 1994; Erausquin 1998; Iijima et al. 2003). They have very intense
emission at low temperatures, but they are nearly fully quenched at the room
temperature. The absorption and emission spectra of the family of Ru(trpy) are
52
3. Physical Properties of Paints
very similar to those of Ru(dpp) and Ru(bpy). The Ru(trpy) compounds, which
can be excited by either a UV light or blue light, emit red luminescence. Various
[Ru(trpy)2] molecules with different ligands were synthesized (Erausquin 1998).
The dynamics of the metal-to-ligand bond, as well as the electron donating or
accepting characteristics of the ligand, has a significant effect on the temperature
sensitivity of a luminescent molecule. Thus, this would enable synthesis of a
molecule specifically designed to respond with high sensitivity over a certain
range of cryogenic temperatures.
DuPont ChromaClear (CC) is selected as a binder for cryogenic TSP due to its
low oxygen diffusivity and good surface adhesion at cryogenic temperatures
(Erausquin 1998). Figure 3.22 shows a comparison of several synthesized
[Ru(trpy)2] compounds in the polymers CC and GP-197. In general, interaction
between a polymer binder and a luminescent molecule can affect the mobility of
the metal-to-ligand bonds, changing the temperature dependency of the paint.
Figure 3.23 shows the temperature dependencies for [Ru(trpy)(phtrpy)](PF6)2 in
two different polymer binders CC and GP-197. Other Ruthenium compounds
have a good response at cryogenic temperatures as well, as shown in Table 3.3
that summarizes the temperature sensitivities and useful temperature ranges for
cryogenic TSP formulations calibrated by Erausquin (1998).
N
N
N
Ru
N
Fig. 3.21. Chemical structure of Ru(trpy)
I(T) / Iref(T)
1.6
1.4
[Ru(trpy)2] in CC
[Ru(trpy)(phtrpy)](PF6)2
1.2
[Ru(ppd-trpy)2](TFPB)2 in CC
1.0
[Ru(trpy)(VH-127)](PF6)2 in GP-197
0.8
0.6
0.4
0.2
0.0
-200
-150
-100
-50
0
50
Temperature (oC)
Fig. 3.22. Comparison of Ru(trpy)-based cryogenic TSP formulations, where CC denotes
DuPont ChromaClear. From Erausquin (1998)
3.4. Cryogenic Paints
53
1.6
GP-197
Chromaclear
1.4
I(T) / Iref(T)
1.2
1.0
0.8
0.6
0.4
0.2
0.0
-200
-150
-100
-50
0
50
Temperature (oC)
Fig. 3.23. Temperature calibration for cryogenic TSPs: [Ru(trpy)(phtrpy)](PF6)2 in GP-197
and DuPont ChromaClear. From Erausquin (1998)
Table 3.3. Cryogenic temperature sensitive paints
Paint
[Rh(bzq)2Cl]2 in CC
Useful temp.
Temp. sensi. coeff.
range ( C)
∆(I/Iref)/∆T
-175 to -130
-0.0191
o
[Rh(bzq)2(phen)](PF6) in CC
-100 to –50
-0.0107
[Ru(trpy)] in CC
-175 to –85
-0.0112
[Ru(trpy)(4'-C6F5-trpy)](NO3)2 in CC
-175 to –50
-0.0081
[Ru(trpy)(4'-Cl-trpy)](Cl2) in CC
-175 to –50
-0.0106
[Ru(trpy)(4'-NC-trpy)](NO3)2 in CC
-150 to –50
-0.0078
[Ru(phtrpy)(Cltrpy)](NO3)2 in CC
-175 to –50
-0.0093
[Ru(trpy)(4'-TfO-trpy)](NO3)2 in CC
-175 to –50
-0.0101
[Ru(trpy)(MeStrpy)](NO3)2 in CC
-175 to –75
-0.0105
[Ru(trpy)(phtrpy)](PF6)2 in GP-197
-175 to –50
-0.0114
[Ru(trpy)(phtrpy)](PF6)2 in CC
-150 to –100
-0.0142
[Ru(trpy)(ppd-trpy)](TFPB)2 in CC
-175 to –50
-0.0097
[Ru(trpy)(phyphen)](TFPB)2 in CC
-175 to –50
-0.0090
[Ru(trpy)(SO2Me-trpy)](PF6)2 in CC
-175 to –75
-0.0104
[Ru(trpy2)](TFPB)2 in CC
-170 to –75
-0.0114
[Ru(ppd-trpy)2](TFPB)2 in CC
-175 to –75
-0.0149
[Ru(trpy)(Vh127)](PF6)2 in GP-197
-175 to –75
-0.0154
54
3. Physical Properties of Paints
3.5. Multiple-Luminophore Paints
The intensity-based method for PSP and TSP requires a ratio between the wind-on
and wind-off images of a painted model. When a model moves in a nonhomogenous illumination filed during a test, the image-ratio method inevitably
causes inaccuracy in determining pressure and temperature. A multipleluminophore paint is designed to eliminate the need for a wind-off reference
image. Generally, a two-luminophore PSP consists of a pressure-sensitive
luminophore and a pressure-insensitive reference luminophore; similarly, a twoluminophore TSP combines a temperature-sensitive luminophore with a
temperature-insensitive reference luminophore.
The probe and reference
luminophores can be excited by the same illumination light. Ideally, there is no
overlap between the emission spectra of the probe and reference luminophores
such that the luminescent emissions from the two components can be completely
separated using optical filters. Theoretically, a ratio I λ1 / I λ2 between the probe
and reference images could able to eliminate the effects of spatial non-uniform
illumination, paint thickness and luminophore concentration, where I λ1 and I λ2
are the luminescent intensities at the emission wavelengths λ1 and λ 2 ,
respectively. However, McLean (1998) pointed out that since two luminophores
cannot be perfectly mixed, the simple two-color intensity ratio I λ1 / I λ2 cannot
completely compensate the effect of non-homogenous dye concentration. In this
case, a ratio of ratios ( I λ1 / I λ2 ) /( I λ1 / I λ2 )0 should be used to correct the effects
of non-homogenous dye concentration and paint thickness variation, where the
subscript 0 denotes the wind-off condition.
Besides the above combinations of luminophores, a temperature-sensitive
luminophore, which cannot be quenched by oxygen, can be combined with an
oxygen-sensitive luminophore. This two-luminophore temperature/pressure paint
can be used for correcting the temperature effect of PSP. In particular, when the
temperature dependencies of the two luminophores are close, a two-color intensity
ratio between the two luminophores exhibits a very weak temperature dependency
(Engler et al. 2001a). Figure 3.24 shows a ratio of ratios of a two-luminophore
PSP (PtTFPP in FIB with a proprietary reference luminophore) as a function of
pressure at different temperatures (Crafton et al. 2002). Clearly, the data at
different temperatures overlap, and a ratio of ratios of this PSP is almost
o
Furthermore, a multipletemperature insensitive in a range of 5-45 C.
luminophore PSP can be developed to correct the temperature effect as well as the
effect of non-uniform illumination simultaneously.
3.5. Multiple-Luminophore Paints
55
1.5
Ro/R
1.2
0.9
5C
15 C
25 C
35 C
45 C
0.6
0.3
0
0
0.3
0.6
0.9
1.2
1.5
P/Po
Fig. 3.24. Ratio of ratios of a two-luminophore PSP (PtTFPP in FIB with a reference
luminophore) as a function of pressure at different temperatures, where R = I λ1 / I λ2 and
R0 = ( I λ1 / I λ2 )0 are the two-color intensity ratios between the probe and reference
luminophores at the run and reference conditions, respectively. From Crafton et al. (2002)
Oglesby et al. (1995b) used PtOEP or PtTFPP as a pressure probe luminophore
and Fluorol Green Gold 084 (3,9-perylenedicarboxylic acid, bis(2methylpropyl)ester) as a reference luminophore in the GP-197 polymer. Harris
and Gouterman (1995, 1998) used PtTFPP as a pressure-sensitive luminophore
2+
and incorporated a solid-state phosphor BaMg2Al16O27:Eu (BaMgAl) as a
reference luminophore in an Acrylic copolymer. Since BaMgAl is insoluble, the
reference luminophore was not uniformly distributed and therefore the paint
suffers from the effect of the uneven layer thickness. TsAGI/OPTROD developed
the proprietary two-luminophore PSP formulations, LPS B1 and LPS B12 (Bukov,
et al. 1997; Lyonnet, et al. 1997). Three pressure sensitive paints with an internal
temperature sensitive luminophore were also tested by Oglesby et al. (1996),
where EuTTA, MgOEP and Ru(bpy) were used as temperature-sensitive reference
luminophores. Hradil et al. (2002) used Ru(dpp) as a pressure probe molecule and
manganese-activated magnesium fluorogermanate (MFG) as a thermographic
phosphor. The preliminary results showed that two-luminophore PSPs indeed
enabled point-by-point correction for the temperature effect of PSP.
Buck (1988, 1989, 1991) used a blue-green Radelin thermographic phosphor
for aerothermodynamic testing that intrinsically exhibited two narrow-band
emission peaks at 450 nm and 520 nm. It was found that a ratio of the blue to
green emission intensity was a function of temperature, but independent of the UV
illumination intensity. Another two-color phosphor system used a green-red
mixture of rare-earth and Radelin phosphors for a broader range of temperatures.
Buck (1988, 1989) gives a detailed description of the multiple-color phosphor
thermography system developed at NASA Langley.
56
3. Physical Properties of Paints
3.6. ‘Ideal’ Pressure Sensitive Paint
A perfect PSP should be completely temperature independent. According to Eq.
(2.23), a temperature insensitive PSP should have such small activity energy E D
for the oxygen diffusion process that the Stern-Volmer coefficient B polymer is a
weak function of temperature over a certain range of temperature. However, since
the excited-state decay rates of a luminophore are intrinsically temperature
dependent, it is unlikely to develop an absolutely temperature-insensitive PSP
whose the Stern-Volmer coefficients A polymer and B polymer are constants. Instead,
researchers seek a so-called ‘ideal’ PSP exhibiting invariant temperature
dependency at different pressures over a certain range of temperatures (Puklin et
al. 1998; Coyle et al. 1999; Bencic 1999; Ji et al. 2000). Note that the term ‘ideal
PSP’ does not accurately describe the invariant property of this special paint.
Nevertheless, since this term has been used in the PSP community, we adopt it
here and discuss its true meaning below.
Consider the Stern-Volmer relation in the following form
I0(T )
= 1 + K SV ( T ) p ,
I ( p ,T )
(3.1)
where I 0 ( T ) = I ( p = 0 ,T ) is the luminescent intensity at zero pressure (vacuum)
and K SV ( T ) is related to the coefficients A polymer ( T ) and B polymer ( T ) by
K SV ( T ) = [ B polymer ( T ) / A polymer ( T )] / p ref .
(3.2)
If the coefficients A polymer ( T ) and B polymer ( T ) have the same temperature
dependency, the Stern-Volmer coefficient K SV ( T ) becomes temperature
independent. According to Eq. (2.23), this situation may occur under the
conditions E D ≈ E nr and η ≈ 1 over a certain range of temperatures. Therefore,
for an ‘ideal’ PSP, the Stern-Volmer coefficient K SV ( T ) in Eq. (3.1), rather than
the coefficients A polymer ( T ) and B polymer ( T ) , is temperature independent.
Consequently, the Stern-Volmer relation in the form for aerodynamic application
can be written as
I ref
p
,
(3.3)
= A polymer , ref + B polymer , ref
g( T )
p ref
I
where the function g ( T ) is defined as
ª
ED
g ( T ) = «1 +
R T ref
«¬
§ T − Tref
¨
¨ T ref
©
·º
¸»
¸»
¹¼
−1
ª
E nr
= «1 +
R T ref
«¬
§ T − Tref
¨
¨ T ref
©
·º
¸»
¸»
¹¼
−1
(3.4)
3.6. ‘Ideal’ Pressure Sensitive Paint
57
and the coefficients A polymer , ref and B polymer , ref are temperature independent given
the reference conditions. For an ‘ideal’ PSP, the Stern-Volmer relation Eq. (3.3)
enjoys such similarity that it is invariant at different temperatures for the variable
g( T )I ref / I . The temperature effect of PSP is concentrated in a single scaling
factor g ( T ) ; this similarity simplifies the temperature correction procedure for
PSP.
Ji et al. (2000) developed a bichromophic molecule Ru-Pyrene for an ‘ideal’
PSP, which, as shown in Fig. 3.25, consisted of a covalently linked assembly of a
Ruthenium (II) polypyridyl complex and Pyrene. They also synthesized the MPP
acrylate polymer binder for Ru-Pyrene. Figure 3.26(a) shows the Stern-Volmer
plots for the Ru-pyrene/MPP PSP at pressures ranging from 0.005 to 1 atm and
o
temperatures from 25 to 55 C. The Stern-Volmer plots at different temperatures
are collapsed onto a single curve. Figure 3.26(b) illustrates the temperature
dependency of the Ru-Pyrene/MPP PSP at 0.005, 0.14, 0.55 and 1 atm, indicating
that the temperature dependency of this PSP is independent of pressure.
Fig. 3.25. Chemical structure of Ru-pyrene. From Ji et al. (2000)
Fig. 3.26. (a) The Stern-Volmer plots for Ru-pyrene/MPP PSP at eight pressures ranging
o
from 0.005 to 1 atm and four temperatures from 25 to 55 C; (b) the temperature
dependency of Ru-pyrene/MPP PSP at pressures of 0.005, 0.14, 0.55 and 1 atm. From Ji et
al. (2000)
58
3. Physical Properties of Paints
3.7. Desirable Properties of Paints
As pointed out before, PSP or TSP is prepared by dissolving a luminescent dye
and a polymer binder in a solvent solution; the resulting mixture is then applied on
a surface by spraying, brushing or dipping. After the solvent evaporates, a thin
coating of the paint remains on the surface, in which the luminescent molecules
are immobilized in the polymer matrix. The polymer binder is an important
ingredient of the paint adhering to the surface of interest. In some cases, the
polymer matrix is only a passive anchor; in other cases, the polymer may
significantly affect the photophysical behavior of the paint through complicated
interaction between the luminescent molecule and the macromolecule of the
polymer. Since how the polymer affects the photophysical processes in the paint
is not well understood, it is basically a trial and error process to find an optimal
combination of a luminophore and a polymer. A good paint (PSP or TSP) for
aerodynamic applications should have certain required physical and chemical
properties. The following discussion is focused on the required properties of PSP
while some requirements are generally applicable to TSP. A general strategy for
the development of improved PSP formulations was proposed by Benne et al.
(2002).
Pressure Response
The Stern-Volmer coefficients of PSP should be chosen to match the pressure
range on a tested article and the performance requirements of a photodetector (e.g.
CCD camera) used in particular measurements. A large Stern-Volmer coefficient
B( T ) generally indicates a good pressure response. However, for aerodynamic
experiments at high pressures, a large Stern-Volmer coefficient B( T ) of PSP
may cause unwanted severe oxygen quenching in the ambient reference
conditions, considerably reducing the luminescent emission from the paint and
therefore the signal-to-noise ratio (SNR) of a photodetector.
Luminescent Output
The luminescent emission of a luminophore is characterized by the quantum yield
(or efficiency); it is generally desirable to have as high a luminescent output as
possible to maximize the SNR of a photodetector. The luminescent intensity is
proportional to the concentration of the probe molecules over a certain range.
However, it cannot be increased indefinitely by increasing the dye concentration;
if the concentration is too high, self-quenching of luminescence occurs. Similarly,
the luminescent intensity is no longer linearly proportional to the excitation light
intensity at a very high excitation level, and eventually it saturates when the
excitation light intensity increases further.
Paint Stability
Ideally, the luminescent intensity of PSP should not change with time under
excitation. Usually, the luminescent intensity decreases with time due to
photodegradation of a luminophore (Egami and Asai 2002). A decrease in the
luminescent intensity could also be due to the presence of certain chemicals other
than oxygen that can quench the luminescence. The polymer binder undergoes
3.7. Desirable Properties of Paints
59
aging, which can change its characteristics with respect to the oxygen solubility
and diffusivity. As a result, the Stern-Volmer coefficients of PSP may be altered.
Response Time
The response time of PSP is mainly determined by oxygen diffusion through a
paint layer when the luminescent lifetime is much shorter than the diffusion
timescale. The high porosity of the paint will increase the time response. The
need for fast time response depends on a particular application; a short response
time of PSP is required for unsteady aerodynamic measurements. For steady-state
measurements, however, the use of a fast-responding PSP does not necessarily
offer an advantage. For a highly oxygen-permeable PSP with a short response
time, the Stern-Volmer coefficient B( T ) is usually large, and thus weak
luminescence of PSP in the ambient conditions may lead to a low SNR.
Temperature Sensitivity
A good PSP should have a weak temperature effect. The temperature sensitivity
arises from two sources: the intrinsic temperature dependency of a luminophore
and the temperature dependency of the solubility and diffusivity of oxygen in a
polymer matrix. The latter is a major contributor to the temperature sensitivity of
PSP.
Physical Characteristics
The physical properties of a polymer binder, such as adhesion, hardness, coating
smoothness and thickness, should be considered prior to a test. Adhesion should
be strong enough to sustain skin friction on a surface particularly in high-speed
flows, which is related to surface tension, solvent softening and chemical bonding.
Hardness primarily depends on the type of polymers, the molecular weight and the
degree of cross-linking. For example, silicone rubbers (or RTVs) are generally
soft, whereas Acrylates and methacrylates are generally hard. Smoothness
depends primarily on paint itself and application techniques; for most paints
uniform leveling of the paint is essential to a smooth finish. The coating thickness
is very dependent on application techniques for both the basecoat and PSP
topcoat. It is generally desirable to minimize the coating roughness and thickness
to avoid any effect on the aerodynamic characteristics of a model. Typically, the
maximum rms roughness of a coating should be less than 0.25 µm, and the
coating thickness ranges from 20 to 40 µm.
Chemical Characteristics
Toxicity of paint is a major concern of safety; toxic solvents such as chlorinated
solvents should be avoided. Painter must be protected against contact with paint
spray through the use of fresh air breathing equipment and adequate ventilation.
The paint must be easily sprayed, leveled, and cured to give the specified physical
characteristics of coating under different environmental conditions in wind
tunnels. The solvent evaporation rate must be controlled under different
conditions of temperature and humidity. Since the wind tunnel time is expensive,
application of the paint should be as fast as possible. The curing temperature must
o
be reasonable (less than 100 C); if the curing temperature is too high, it is difficult
to achieve uniform curing over different metal materials. In addition, paint
removal and reapplication on a model is a practical issue in wind tunnel testing.
60
3. Physical Properties of Paints
Some paints, particularly those designed for good and robust adhesion, are
difficult to remove and generally require an aggressive paint stripper like
methylene chloride. This introduces problems with toxicity and insuring adequate
ventilation.
4. Radiative Energy Transport
and Intensity-Based Methods
4.1. Radiometric Notation
Luminescent radiation from a luminescent paint (PSP or TSP) on a surface
involves two major transport processes of radiative energy. The first process is
absorption of an excitation light through a paint layer and the second process is
luminescent radiation that is an absorbing-emitting process in the paint layer.
These processes can be described by the transport equations of radiative energy
(Modest 1993; Pomraning 1973). The luminescent intensity emitted from a paint
layer in plane geometry can be analytically determined by solving the transport
equations. Thus, the corresponding photodetector output can be derived for an
analysis of measurement system performance and uncertainty. Before doing a
detailed analysis, it is necessary to discuss the radiometric notation. In the
literature of PSP and TSP, the term ‘luminescent intensity’ or ‘fluorescent
intensity’, which is usually denoted by the capital English letter ‘I’, has been
widely used. In a strict radiometric sense, the luminescent intensity I is the
luminescent radiance defined as the radiant energy flux (power) per unit solid
angle and per unit projected area of an elemental surface of PSP or TSP (units:
-2
-1
-1
-2
-1
watt-m -sr or J-s -m -sr ).
Z
Incident light
θ
Emission
Y
φ
X
Fig. 4.1. Incident excitation light and luminescent emission in a local polar coordinate
system
62
4. Radiative Energy Transport and Intensity-Based Methods
The radiance is a function of both position and direction, which is graphically
represented by a cone of a solid angle element in radiometry as shown in Fig. 4.1.
The direction of the radiance (incident or emitting radiance) is given by the polar
angle ș (measured from the surface normal) and the azimuthal angle φ
(measured between an arbitrary axis on the surface and the elemental solid angle
on the surface) in a local coordinate system. In radiometry, the radiance is
conventionally denoted by the captical English letter ‘L’. The term ‘intensity’ is
sometimes confusing because its definition is different in a number of different
-1
disciplines. In radiometry, the radiant intensity (units: watt-sr ), denoted by the
letter ‘I’, is the radiant flux per unit solid angle, which is different from the
radiance (McCluney 1994; Wolfe 1998). However, in the literature of radiative
heat transfer, the radiative intensity, denoted by the same letter ‘I’, is essentially
equivalent to the radiance in radiometry (Modest 1993). In order to avoid
confusion in notation, we specifically define the luminescent intensity ‘I’ as the
luminescent radiance from PSP or TSP, which is consistent with the notation and
terminology commonly used in the literature of PSP and TSP. In a general case,
we still use the traditional radiometric notation ‘L’ to denote the radiance in other
radiometric measurements and modeling. The spectral radiance such as I Ȝ and
L Ȝ at a wavelength λ (units: watt-m -sr -nm ) is usually denoted by a subscript
-2
-1
-1
λ ; the radiance I (or L) is the integration of the spectral radiance I Ȝ (or L Ȝ ) over
a certain range of the radiation wavelengths. Since the radiation from a
luminescent molecule is isotropic, a plausible assumption is that the luminescent
radiance from PSP or TSP is independent of the azimuthal angle φ . Under this
assumption, an analysis of transport of the luminescent radiative energy in PSP or
TSP is considerably simplified. The following analysis is given for PSP, but it is
also valid for TSP that is treated as a special case of PSP when the oxygen
quenching vanishes.
4.2. Excitation Light
We consider a PSP layer with a thickness h on a wall, as shown in Fig. 4.2.
Suppose that PSP is not a scattering medium and scattering exists only at the wall
surface. When an incident excitation light beam with a wavelength λ1 enters the
layer, without scattering and other sources for the excitation energy, the incident
light is attenuated due to absorption through the PSP medium. In plane geometry
where the luminescent intensity (radiance) is independent of the azimuthal angle,
the intensity of the incident excitation light with λ1 can be described by
µ
d I Ȝ−1
dz
+ ȕ Ȝ1 I Ȝ−1 = 0 ,
(4.1)
4.2. Excitation Light
63
where I Ȝ−1 is the incident excitation light intensity, µ = cos ș is the cosine of the
polar angle ș , and ȕ Ȝ 1 is the extinction coefficient of the PSP medium for the
incident excitation light with λ1.
The extinction coefficient ȕ Ȝ1 = İ Ȝ1 c is a
product of the molar absorptivity İ Ȝ1 and luminescent molecule concentration c .
Again, note that the spectral intensity is defined as radiative energy transferred per
-2
unit time, solid angle, spectral variable and area normal to the ray (units: watt-m -1
-1
sr -nm ). The superscript ‘-‘ in I Ȝ−1 indicates the negative direction in which the
light enters the layer. The incident angle ș ranges from ʌ / 2 to 3 ʌ /2
( −1 ≤ µ ≤ 0 ) (see Fig. 4.2).
Incident excitation
light
q
0
Luminescence
Z
θ
Air
PSP
h
+
Ιλ2
+
Ιλ 2
θ
θ
−
Ιλ 2
−
Ιλ1
+
Ιλ1
θ
O
Wall
Reflected/scattered
luminescent light
Reflected/scattered
excitation light
Fig. 4.2. Radiative energy transports in a luminescent paint layer
For the collimated excitation light, the boundary value for Eq. (4.1) is the
component penetrating into the PSP layer,
I Ȝ−1 (z = h) = ( 1 − ȡ Ȝap1 ) q0 E Ȝ 1 (Ȝ 1 ) į(µ − µ ex ) ,
(4.2)
where q0 and E Ȝ 1 (Ȝ 1 ) are the radiative flux and spectrum of the incident
excitation light, respectively, ȡ Ȝap1 is the reflectivity of the air-PSP interface, µex is
the cosine of the incident angle of the excitation light, and į(µ ) is the Dirac-delta
function. The solution to Eq. (4.1) is
I Ȝ−1 = ( 1 − ȡ Ȝap1 ) q0 E Ȝ 1 (Ȝ 1 ) į(µ − µex ) exp [( ȕ Ȝ 1 / µ)(h − z)] . ( −1 ≤ µ ≤ 0 )
(4.3)
This relation describes a decay of the incident excitation light intensity through
the layer. The incident excitation light flux at the wall integrated over the ranges
of ș from either ʌ to ʌ / 2 or ʌ to 3 ʌ /2 is
64
4. Radiative Energy Transport and Intensity-Based Methods
q Ȝ−1 ( z = 0 ) = −
³
0
−1
I Ȝ−1 (z = 0) µ dµ ≅ C d ( 1 − ȡ Ȝap1 ) q 0 E Ȝ 1 (Ȝ 1 ),
(4.4)
where C d is the coefficient representing the directional effect of the excitation
light, that is,
C d = − µ ex exp( ȕ Ȝ 1 h / µ ex ) . ( −1 ≤ µ ex ≤ 0 )
(4.5)
When the incident excitation light impinges on the wall, the light reflects and
re-enters into the layer. Without a scattering source inside PSP, the intensity of
the reflected and scattered light from the wall is described by
µ
d I Ȝ+1
dz
+ ȕ Ȝ1 I Ȝ+1 = 0 ,
(4.6)
where I Ȝ+1 is the excitation light intensity in the positive direction emanating from
the wall. As shown in Fig. 4.2, the range of µ is 0 ≤ µ ≤ 1 ( 0 ≤ ș ≤ ʌ /2 and
−ʌ / 2 ≤ ș ≤ 0 ) for the outgoing reflected and scattered excitation light. The
superscript ‘+’ indicates the outgoing direction from the wall. For the wall that
reflects diffusely, the boundary condition for Eq. (4.6) is
I Ȝ+1 (z = 0) = ȡ Ȝwp1 q Ȝ−1 ( z = 0 ) = C d ȡ Ȝwp1 ( 1 − ȡ Ȝap1 ) q0 E Ȝ 1 (Ȝ 1 ),
(4.7)
where ȡ Ȝwp1 is the reflectivity of the wall-PSP interface for the excitation light.
The solution to Eq. (4.6) is
(0 ≤ µ ≤ 1 )
I Ȝ+1 = C d ȡ Ȝwp1 ( 1 − ȡ Ȝap1 ) q0 E Ȝ 1 (Ȝ 1 ) exp ( − ȕ Ȝ 1 z / µ).
(4.8)
At a point inside the PSP layer, the net excitation light flux is contributed by
the incident and scattering light rays from all the possible directions. The net flux
is calculated by adding the incident flux (integrated over ș = ʌ to ʌ /2 and
ș = ʌ to 3ʌ /2 ) and scattering flux (integrated over
ș = 0 to − ʌ /2 ). Hence, the net excitation light flux is
( q Ȝ 1 )net = − 2
³
0
−1
I Ȝ−1 µ dµ − 2
³
0
1
ș = 0 to ʌ /2
I Ȝ+1 µ dµ
and
(4.9)
≅ C d ( 1 − ȡ ) q0 E Ȝ 1 (Ȝ 1 )[ exp ( − ȕ Ȝ 1 z /µex ) + ȡ exp ( −3 ȕ Ȝ 1 z / 2)] .
ap
Ȝ1
wp
Ȝ1
Note that the derivation of Eq. (4.9) uses an approximation of the exponential
integral of third order, E 3 (x) ≅ (1/2) exp ( −3 x / 2) .
4.3. Luminescent Emission and Photodetector Response
65
4.3. Luminescent Emission and Photodetector Response
After the luminescent molecules in PSP absorb the energy from the excitation
light with a wavelength λ1, they emit luminescence with a longer wavelength λ2
due to the Stokes shift. Luminescent radiative transfer in PSP is an absorbingemitting process; the luminescent light rays from the luminescent molecules
radiate in both the inward and outward directions.
For the luminescent emission toward the wall, the luminescent intensity I Ȝ−2
can be described by
µ
d I Ȝ−2
dz
+ ȕ Ȝ2 I Ȝ−2 = S Ȝ2 (z) ,
( −1 ≤ µ ≤ 0 )
(4.10)
where S Ȝ2 (z) is the luminescent source term and the extinction coefficient
ȕ Ȝ2 = İ Ȝ2 c is a product of the molar absorptivity İ Ȝ2 and luminescent molecule
concentration c .
S Ȝ2 (z) is assumed to be
The luminescent source term
proportional to the extinction coefficient for the excitation light, the quantum
yield, and the net excitation light flux filtered over a spectral range of absorption.
Therefore, a model for the luminescent source term is expressed as
S Ȝ 2 (z) = Φ ( p, T ) E Ȝ 2 ( Ȝ 2 )
³
∞
0
(q Ȝ 1 )net ȕ Ȝ 1 Ft 1 ( Ȝ 1 ) dȜ 1 ,
(4.11)
where Φ ( p, T ) is the luminescent quantum yield that depends on air pressure (p)
and temperature (T), E Ȝ 2 (Ȝ 2 ) is the luminescent emission spectrum, and
Ft 1 ( Ȝ1 ) is a filter function describing the optical filter used to insure the
excitation light within the absorption spectrum of the luminescent molecules.
With the boundary condition I Ȝ−2 (z = h) = 0 , the solution to Eq. (4.10) is
§ ȕȜ2 z · 1 ª
¸ «
I Ȝ−2 = exp ¨ −
¨
µ ¸µ«
©
¹ ¬
³
z
0
§ ȕȜ2 z ·
¸ dz −
S Ȝ2 ( z ) exp ¨
¨ µ ¸
©
¹
³
h
0
§ ȕȜ2 z ·
¸ dz
S Ȝ2 ( z ) exp ¨
¨ µ ¸
©
¹
( −1 ≤ µ ≤ 0 )
º
».
»
¼
(4.12)
The incoming luminescent flux toward the wall at the surface (integrated over
ș = ʌ to ʌ /2 and ș = ʌ to 3ʌ /2 ) is
q Ȝ−2 ( z = 0 ) = − 2
where
³
0
−1
I Ȝ−2 (z = 0) µ dµ ,
(4.13)
66
4. Radiative Energy Transport and Intensity-Based Methods
I Ȝ−2 ( z = 0 ) = −
1
µ
³
h
0
S Ȝ2 ( z ) exp (
ȕȜ2 z
µ
)dz .
We consider the luminescent emission in the outward direction and assume that
the scattering occurs only at the wall. The outgoing luminescent intensity I Ȝ+2 can
be described by
µ
d I Ȝ+2
dz
+ ȕ Ȝ2 I Ȝ+2 = S Ȝ2 (z) .
(0 ≤ µ ≤ 1)
(4.14)
Similar to the boundary condition for the scattering excitation light, a fraction of
the incoming luminescent flux q Ȝ− 2 ( z = 0 ) is reflected diffusely from the wall.
Thus, the boundary condition for Eq. (4.14) is
I Ȝ+2 (z = 0) = ȡ Ȝwp2 q Ȝ−2 ( z = 0 ) = − 2 ȡ Ȝwp2
³
0
−1
I Ȝ−2 (z = 0) µ dµ ,
(4.15)
where ȡ Ȝwp2 is the reflectivity of the wall-PSP interface for the luminescent light.
The solution to Eq. (4.14) with the boundary condition Eq. (4.15) is
§ ȕȜ2 z · ª 1
¸«
I Ȝ+2 = exp ¨ −
¨
µ ¸«µ
¹¬
©
³
º
§ ȕȜ2 z ·
¸ dz + I + ( z = 0 )» .
S Ȝ2 ( z ) exp¨
Ȝ2
¨ µ ¸
0
»
¹
©
¼
z
( −1 ≤ µ ≤ 0 )
(4.16)
At this stage, the outgoing luminescent intensity I Ȝ+2 can be readily calculated by
substituting the source term Eq. (4.11) into Eq. (4.16). In general, I Ȝ+2 has a nonlinear distribution across the PSP layer, which is composed of the exponentials of
ȕ Ȝ 1 z and ȕ Ȝ2 z . For simplicity of algebra, we consider an asymptotic but
important case ʊ an optically thin PSP layer.
When the PSP layer is optically thin ( ȕ Ȝ 1 h , ȕ Ȝ 2 h , ȕ Ȝ 1 z and ȕ Ȝ2 z <<1), the
asymptotic expression for I Ȝ+2 is simply
I Ȝ+2 ( z ) = Φ ( p, T ) q0 E Ȝ 2 (Ȝ 2 )K 1 (ȕ Ȝ 1 / µ)( z + 2 ȡ Ȝwp2 h µ) , ( −1 ≤ µ ≤ 0 )
where
K 1 = ȕ Ȝ−11
³
∞
0
ȕ Ȝ 1 E Ȝ 1 (Ȝ 1 ) C d ( 1 − ȡ Ȝap1 )( 1 + ȡ Ȝwp1 )Ft 1 ( Ȝ1 ) dȜ1 .
(4.17)
4.3. Luminescent Emission and Photodetector Response
67
Eq. (4.17) indicates that for an optically thin PSP layer the outgoing luminescent
intensity is proportional to the extinction coefficient (a product of the molar
absorptivity and luminescent molecule concentration), paint layer thickness,
quantum yield of the luminescent molecules, and incident excitation light flux.
The term K 1 represents the combined effect of the optical filter, excitation light
scattering and direction of the incident excitation light. The outgoing luminescent
intensity averaged over the layer is
< I Ȝ+2 > = h −1
³
h
0
I Ȝ+2 (z) dz = h Φ ( p, T ) q0 E Ȝ 2 (Ȝ 2 )K 1 (ȕ Ȝ 1 / µ) M(µ ),
(4.18)
where M ( µ ) = 0.5 + 2 ȡ Ȝwp2 µ. The outgoing luminescent energy flow rate Q Ȝ+2
(radiant flux) on an area element A s of the PSP paint surface collected by a
detector is
Q Ȝ+2 = A s
³
ȍ
< I Ȝ+2 > cos ș dȍ = ȕ Ȝ 1 h Φ ( p, T ) q0 E Ȝ 2 (Ȝ 2 ) K 1 < M > A s ȍ
,
(4.19)
where Q Ȝ+2 is equivalent to the spectral radiant flux in radiometry (watt-nm ), ȍ
-1
is a collecting solid angle of the detector, and the extinction coefficient
ȕ Ȝ1 = İ Ȝ1 c is a product of the molar absorptivity İ Ȝ1 and luminescent molecule
concentration c . The coefficient < M > represents the effect of reflection and
scattering of the luminescent light at the wall, which is defined as
< M > = ȍ −1
³
ȍ
M(µ ) dȍ = 0.5 + ȡ Ȝwp2 ( µ1 + µ 2 ) ,
where µ1 = cos ș1 and µ 2 = cos ș 2 are the cosines of two polar angles in the solid
angle ȍ .
Imaging system
aperture area,
A0 = ʌ D2 /4
Source area
Image of source area
AI
As
R1
R2
Fig. 4.3. Schematic of an imaging system
68
4. Radiative Energy Transport and Intensity-Based Methods
The response of a photodetector to the luminescent emission can be derived
based on a model of an optical system (Holst 1998). Consider an optical system
located at a distance R1 from a luminescent source area, as shown in Fig. 4.3. The
collecting solid angle with which the lens is seen from the source can be
approximated by ȍ ≈ A 0 / R12 , where A0 = ʌ D 2 /4 is the imaging system entrance
aperture area, and D is the effective diameter of the aperture. Using Eq. (4.19)
and additional relations A s / R12 = A I / R22 and 1 / R1 + 1 / R2 = 1 / fl , we obtain
the radiative energy flux onto the detector
(QȜ 2 )det =
ʌ AI Top Tatm
ȕ Ȝ h Φ ( p, T ) q0 E Ȝ 2 (Ȝ 2 ) K 1 < M > ,
4 F 2 (1 + M op )2 1
(4.20)
where F = fl / D is the f-number, M op = R2 / R1 is the optical magnification, fl
is the system’s effective focal length, AI is the image area, and Top and Tatm are
the system’s optical transmittance and atmospheric transmittance, respectively.
The output of the detector is
V =G
³
∞
0
Rq (Ȝ 2 ) (Q Ȝ 2 )det Ft 2 ( Ȝ2 )dȜ2 ,
(4.21)
where Rq (Ȝ 2 ) is the detector’s quantum efficiency, G is the system’s gain, and
Ft 2 ( Ȝ2 ) is a filter function describing the optical filter for the luminescent
emission. The dimension of V/G is [V/G] = J/s. Substitution of Eq. (4.20) into
Eq. (4.21) yields
V =G
AI
ʌ
ȕ Ȝ h Φ ( p, T ) q0 K 1 K 2 ,
4 F 2 (1 + M op ) 2 1
(4.22)
where
K2 =
³
∞
0
Top Tatm E Ȝ 2 (Ȝ 2 )< M > Rq (Ȝ 2 ) Ft 2 ( Ȝ2 )dȜ2 .
The term K 2 represents the combined effect of the optical filter, luminescent light
scattering, and system response to the luminescent light. The above analysis is
made based on an assumption that the radiation source is on the optical axis. In
general, the off-axis effect is taken into account by multiplying a factor cos 4 θ p in
the right-hand side of Eq. (4.22), where θ p is the angle between the optical axis
and light ray through the optical center (McCluney 1994).
Eq. (4.19) gives the directional dependency of the luminescent radiant flux
Q Ȝ+2 ∝ 1 + 2 ρ λwp2 [cos( θ − ∆θ / 2 ) + cos( θ + ∆θ / 2 )] ,
(4.23)
4.4. Intensity-Based Measurement Systems
69
where ∆θ = θ 2 − θ 1 is the difference between two polar angles in the solid angle
ȍ . Clearly, the luminescent radiant flux contains a constant irradiance term and
a Lambertian term that is proportional to the cosine of the polar angle θ . Le Sant
(2001b) measured the directional dependency of the luminescent emission of the
OPTROD’s B1 PSP composed of a derived Pyrene dye and a reference
component. Figure 4.4 shows the normalized luminescent intensity as a function
of the viewing polar angle for the B1 paint and the B1 paint with talc compared
with the theoretical distribution Eq. (4.23) with ρ λwp2 = 0.5 and ∆θ = 4 degrees.
The experimental directional dependency remains nearly constant for both paints
o
until the viewing polar angle is larger than 60 . The theoretical distribution for a
non-scattering paint fails to predict the flatness of the experimental directional
distributions of the luminescent emission. This is because the simplified theoretical analysis does not consider scattering particles (e.g. talc and solid reference
component particles) re-directing and re-distributing both the excitation light and
luminescent light inside the paints. A more complete analysis of the radiative
energy transport in a luminescent paint with scattering particles requires a
numerical solution of an integro-differential equation (Modest 1993).
Normalized Luminescent Intensity
1.2
1.0
0.8
0.6
Theory
B1 PSP without talc
B1 PSP with talc
0.4
0.2
-100
-80
-60
-40
-20
0
20
40
60
80
100
Polar Angle (degree)
Fig. 4.4. Directional dependency of the luminescent emission from the B1 paint and B1
paint with talc, compared with the theoretical directional distribution for a non-scattering
paint. Experimental data for the B1 paints are from Le Sant (2001b)
4.4. Intensity-Based Measurement Systems
The photodetector output V responding to the luminescent emission, Eq. (4.22),
is re-written as
V = Ȇ c Ȇ f ȕ Ȝ1 h q0 Φ ( p, T ) .
(4.24)
70
4. Radiative Energy Transport and Intensity-Based Methods
The parameters Ȇ c and Ȇ f
are Ȇ c = ( ʌ / 4) G AI [ F 2 (1 + M op ) 2 ] −1 and
Ȇ f = K 1 K 2 , which are related to the imaging system (camera) performance and
filter parameters, respectively. The quantum yield Φ ( p, T ) is described by
Φ ( p,T) = k r /( k r + k nr + k q S φO2 p ) , where kr is the radiative rate constant, knr is
the radiationless deactivation rate constant, kq is the quenching rate constant, p is
air pressure, S is the solubility of oxygen, and φ O2 is the volume fraction of
oxygen in air. In PSP applications, the intensity-ratio method is commonly used
to eliminate the effects of spatial variations in illumination, paint thickness, and
molecule concentration. Without any model deformation, air pressure p is related
to a ratio between the wind-off and wind-on outputs by the Stern-Volmer relation
Vref
V
= A( T ) + B( T )
p
.
p ref
(4.25)
The essential elements of a measurement system for PSP and TSP include
illumination sources, optical filters, photodetectors and data acquisition/processing
units. In terms of the detectors and illumination sources used, measurement
systems can be generally categorized into CCD camera system and laser scanning
system with a single-sensor detector. Since each system has advantages over the
other, researchers can choose one most suitable to meet the requirements for their
specific experiments.
4.4.1. CCD Camera System
A CCD camera system is most commonly used for PSP and TSP measurements in
wind tunnel tests. Figure 1.4 shows a schematic of a CCD camera system. The
luminescent paint (PSP or TSP) is applied to a model surface, which is excited to
luminesce by an illumination source such as UV lamp, LED array or laser. The
luminescent emission is filtered optically to eliminate the illuminating light before
projecting onto a CCD sensor. Images (wind-on and wind-off images) are
digitized and transferred to a computer for data processing. In order to correct the
dark current in a CCD camera, a dark current image is acquired when no light is
incident on the camera. A ratio between the wind-on and wind-off images is taken
after the dark current image is subtracted from both images, resulting in a
luminescent intensity ratio image. Then, using the calibration relation for the
paint, the distribution of the surface pressure or temperature is computed from the
intensity ratio image.
Scientific grade cooled CCD digital cameras are ideal imaging sensors for PSP
and TSP, which can provide a high intensity resolution (12 to 16 bits) and high
spatial resolution (typically 512×512, 1024×1024, up to 2048×2048 pixels).
Because a scientific grade CCD camera exhibits a good linear response and a high
signal-to-noise ratio (SNR) up to 60 dB, it is particularly suitable to quantitative
measurement of the luminescent emission (LaBelle and Garvey 1995). The major
4.4. Intensity-Based Measurement Systems
71
disadvantages of a scientific grade CCD camera are its high cost and a very slow
frame rate. Less expensive consumer grade CCD video cameras were used in
early PSP and TSP measurements (Kavandi et al. 1990; Engler et al. 1991;
McLachlan et al. 1992); the intensity resolution of a CCD video camera is
typically 8 bits with a conventional frame grabber. When there is a large pressure
variation over a model surface, a consumer grade video CCD camera can be used
as an alternative to give acceptable quantitative results after the camera is
carefully calibrated to correct the non-linearity of the radiometric response
function of the camera (see Chapter 5). The low SNR of a video camera can be
improved by averaging a sequence of images to reduce the random noise. In
addition, film-based camera systems were occasionally used in special PSP
measurements like flight tests (Abbitt et al. 1996).
The performance of a CCD array is characterized by the responsivity, charge
well capacity and noise. From these quantities, the minimum signal, maximum
signal, signal-to-noise ratio and dynamic range can be estimated (Holst 1998;
Janesick 1995). These performance parameters are critical for quantitative
radiometric measurements of the luminescent emission, which can be estimated
based on the camera model and noise models (Holst 1998). Here, the most
relevant concepts are briefly discussed. The responsivity, the efficiency of
generating electrons by a photon, is determined by the spectral quantum efficiency
Rq ( λ ) of a detector.
The full-well capacity specifies the number of
photoelectrons that a pixel can hold before charge begins to spill out, thus
reducing the response linearity. The maximum signal is proportional to the fullwell capacity. Normally, the well size is approximately proportional to the pixel
size. Therefore, in a fixed CCD area, increasing the effective pixel size to
enhance the SNR may reduce the spatial resolution. The dynamic range, defined
as the maximum signal (or the full-well capacity) divided by the rms readout noise
(or noise floor), loosely describes the camera’s ability to measure both low and
high light levels.
The minimum signal is limited by the camera noises, including the photon shot
noise, dark current, reset noise, amplifier noise, quantization noise, and fixed
pattern noise. The photon shot noise is associated with the discrete nature of
photoelectrons obeying the Poisson statistics in which the variance is equal to the
mean. The dark current is due to thermally generated electrons, which can be
reduced to a very low level by cooling a CCD device. The reset noise is
associated with resetting the sense node capacitor that is temperature-dependent.
The amplifier noise contains two components: 1/f noise and white noise; the array
manufacturer usually provides this value and calls it the readout noise, noise
equivalent electrons, or noise floor. By careful optimization of the camera
electronics, the readout noise or noise floor can be reduced to as low as 4-6
electrons. The quantization noise results from the analog-to-digital conversion.
The fixed pattern noise (the pixel-to-pixel variation) is due to differences in pixel
responsivity, which is called the scene noise, pixel noise, or pixel nonuniformity
as well.
72
4. Radiative Energy Transport and Intensity-Based Methods
Noise Electrons (rms)
10000
Total Noise
1000
100
Noise Floor
10
Fixed Pattern Noise
Photon Shot Noise
1
10
100
1000
10000
100000
Photoelectrons
Fig. 4.5. Noise curves of CCD for the noise floor = 50e and non-uniformity U = 0.25%
Although various noise sources exist, for many applications, it is sufficient to
consider the photon shot noise, noise floor, and fixed pattern noise due to pixel
nonuniformity. Thus, according to the Poisson statistics, the total system noise
< nsys > is given by
2
< nsys > = < nshot
> + < n 2floor > + < n 2pattern > = n pe + < n 2floor > + ( Un pe )2
,
(4.26)
2
> , < n 2floor > and < n 2pattern > are the variances of the photon shot
where < nshot
noise, noise floor and pattern noise, respectively, n pe is the number of collected
photoelectrons, and U is the pixel nonuniformity. Accordingly, the signal-to-noise
ratio (SNR) is
SNR = n pe / n pe + < n 2floor > + ( Un pe ) 2
.
(4.27)
Figure 4.5 shows the total noise, photon shot noise, noise floor (readout noise),
and fixed pattern noise of a CCD as a function of the number of photoelectrons for
< n 2floor > 1 / 2 = 50e and U = 0.25%. For a very low photon flux, the noise floor
dominates. As the incident light flux increases, the photon shot noise dominates.
At a very high level of the incident light flux, the noise may be dominated by the
fixed pattern noise.
When the photon shot noise dominates, the SNR
asymptotically approaches to
SNR = n pe , and the dynamic range is
( n pe )max / < n floor > , where ( n pe )max is the full-well capacity. The dark current
only affects those applications where the SNR is low. In most applications of PSP
4.4. Intensity-Based Measurement Systems
73
and TSP, the pressure and temperature resolutions are limited by the photon shot
noise. Table 4.1, which is adapted from Crites (1993), lists the performance
parameters of some CCD sensors.
Table 4.1. Characteristics of CCD Sensors
CCD
TH7883PM
TH7895B
TH896A
TK512CB
TK1024F
Pixel array
384×586
512×512
1024×1024
512×512
1024×1024
1024×1024
Full well (e)
180000
290000
350000
700000
450000
256000
o
TK1024B
Temperature ( C)
-45
-45
-40
-40
-40
-40
Dark current (e)
8
8
25
4
3
6
Readout Noise (e)
12
6
6
10
9
9
Quantum efficiency
40%
40%
40%
80%
35%
80%
Peak wavelength (nm)
700
670
670
650
670
650
The selection of an appropriate illumination source depends on the absorption
spectrum of a luminescent paint and optical access of a specific facility. An
illumination source must provide a sufficiently large number of photons in the
wavelength band of absorption without saturating the luminescence and causing
serious photodegradation. It is desirable for a source to generate a reasonably
uniform illumination field over a surface such that the measurement uncertainty
associated with model deformation can be reduced. A continuous illumination
source should be stable and a flash source should be repeatable. A variety of
illumination sources are commercially available. Pulsed and continuous-wave
lasers with fiber-optic delivery systems were used in wind tunnel tests (Morris et
al. 1993a, 1993b; Crites 1993; Bukov et al. 1992; Volan and Alati. 1991; Engler et
al. 1991, 1992; Lyonnet et al. 1997). Lasers have obvious advantages in terms of
providing narrow band intense illumination. Very stable blue LED arrays were
developed for illuminating paints (Dale et al. 1999). LED arrays are attractive as
an illumination source since they are light in weight and they produce little heat;
they can be suitably distributed to form a fairly uniform illumination field. In
addition, they can be easily controlled to generate either continuous or modulated
illumination. Other light sources reported in the literature of PSP and TSP include
xenon arc lamps with blue filters (McLachlan et al. 1993a), incandescent
tungsten/halogen lamps with blue filters (Morris et al. 1993a; Dowgwillo et al.
1994) and fluorescent UV lamps (Liu et al. 1995a, 1995b). The spectral
characteristics of illumination sources can be found in The Photonics Design and
Applications Handbook (1999). Crites (1993) discussed some available light
sources from a viewpoint of PSP application.
Optical filters are used to separate the luminescent emission from the excitation
light, or separate the luminescent emissions from different luminophores. There
are two kinds of filters: interference filters and color glass filters. Interference
filters select a band of light through a process of constructive and destructive
interference. They consist of a substrate onto which chemical layers are vacuum
deposited in such a fashion that the transmission of certain wavelengths is
74
4. Radiative Energy Transport and Intensity-Based Methods
enhanced, while other wavelengths are either reflected or absorbed. Band-pass
interference filters only transmit light in a spectral band; the peak wavelength and
spectral width can be tightly controlled. Edge interference filters only transmit
light above (long pass) or below (short pass) a certain wavelength. Color glass
filters are used for applications that do not need precise control over wavelengths
and transmission intensities. The ratio of transmission to blocking is a key filter
characteristic. All filters are sensitive to the angle of incidence of the incoming
light. For interference filters, the peak transmission wavelength decreases as the
angle of incidence deviates from the normal, while the bandwidth and
transmission characteristics generally remain unchanged. For color glass filters,
an increase of the incident angle increases the transmission path, reducing the
transmission efficiency.
4.4.2. Laser Scanning System
A generic laser scanning system for PSP and TSP is shown in Fig. 1.5. A lowpower laser beam is focused to a small point and scanned over a model surface
using a computer-controlled mirror to excite the paint on a model. The
luminescent emission is detected using a low-noise photodetector (e.g. PMT); the
photodetector signal is digitized with a high-resolution A/D converter in a PC and
processed to calculate pressure or temperature based on the calibration relation for
the paint. When the laser beam is modulated, a lock-in amplifier can be used to
reduce the noise. Furthermore, the phase angle between the modulated excitation
light and responding luminescence can be obtained using a lock-in amplifier for
phase-based PSP and TSP measurements. The laser can be scanned continuously
or in steps; it is synchronized to data acquisition such that the position of the laser
spot on the model is known. In order to compensate for a laser power drift, the
laser power variation is monitored using a photodiode. The laser scanning
systems for PSP and TSP measurements were discussed by Hamner et al. (1994),
Burns (1995), Torgerson et al (1996), and Torgerson (1997).
Compared to a CCD camera system, a laser scanning system offers certain
advantages. Since a low-noise PMT is used to measure the luminescent emission,
before an analog output from the PMT is digitized, standard SNR enhancement
techniques are available to improve the measurement accuracy. Amplification and
band-limited filtering can be used to improve the SNR. The signal is then
digitized with a high-resolution A/D converter (12 to 24 bits). Additional noise
reduction can be accomplished using a lock-in amplifier when the laser beam is
modulated. The laser scanning system is able to provide uniform illumination
over a surface by scanning a single laser spot. The laser power is easily monitored
and correction for the laser power drift can be made for each measurement point.
The laser scanning system can be used for PSP and TSP measurements in a
facility where optical access is so limited that a CCD camera system is difficult to
use.
4.5. Basic Data Processing
75
4.5. Basic Data Processing
The most basic processing procedure in the intensity-based method for PSP and
TSP is taking a ratio between the wind-on image and the wind-off reference image
to correct the effects of non-homogenous illumination, uneven paint thickness and
non-uniform luminophore concentration. However, this ratioing procedure is
complicated by model deformation induced by aerodynamic loads, which results
in misalignment between the wind-on and wind-off images. Therefore, additional
correction procedures are required to eliminate (or reduce) the error sources
associated with model deformation, the temperature effect of PSP, selfillumination, and camera noises (dark current and fixed pattern noise).
Figure 4.6 shows a generic data processing flowchart for intensity-based
measurements of PSP and TSP with a CCD camera. A laser scanning system has
similar data processing procedures for intensity-based measurements. The windon and wind-off images are acquired using a CCD camera. Usually, a sequence of
acquired images is averaged to reduce the random noise like the photon shot
noise. The dark current image and ambient lighting image are subtracted from
data images to eliminate the dark current noise of the CCD camera and the
contribution from the ambient light. The dark current image is usually acquired
when the camera shutter is closed. In a wind tunnel environment, there is always
weak ambient light that may cause a bias error in data images. The ambient
lighting image is acquired when the shutter is open while all controllable light
sources are turned off. The integration time for the dark current image and
ambient lighting image should be the same as that for data images. The data
images are then divided by the flat-field image to correct the fixed pattern noise.
At a very high signal level, this correction is necessary since the fixed pattern
noise may surpass the photon shot noise. Ideally, the flat-field image is acquired
from a uniformly illuminated scene. A simple but less accurate approach is use of
several diffuse scattering glasses mounted in the front of the lens of the camera to
generate an approximately uniform illumination field.
When a uniform
illumination field cannot be achieved, a more complex noise-model-based
approach can be used to obtain the fixed pattern noise field for a CCD camera
(Healey and Kondepudy 1994). Normally, a scientific grade CCD camera has a
good linear response of the camera output to the incident irradiance of light.
However, conventional CCD video cameras often exhibit a non-linear response to
the incident light intensity; in this case, a video camera should be radiometrically
calibrated to correct the non-linearity. A simple but useful radiometric camera
calibration technique is described in Chapter 5.
76
4. Radiative Energy Transport and Intensity-Based Methods
Wind-On Image
Wind-Off Image
Correction for Dark Current, Ambient
Light & Fixed Pattern Noise
Correction for Non-Linearity
of Response of Detector
Registered & Corrected
Wind-On Image
Corrected Wind-Off
Image
Image Registration
Ratio Image
Self-Illumination
Correction
PSP/TSP Image
PSP/TSP Calibration
PSP/TSP Data
on 3D Grid
Image Resection
Forces & Moments/Heat Transfer
Fig. 4.6. Generic data processing flowchart for intensity-based PSP and TSP measurements
In this stage, even though the noise-corrected wind-on and wind-off images are
obtained, we cannot yet calculate a ratio of the wind-off image over the wind-on
image, Vref / V , for conversion to a pressure or temperature image. This is
because the wind-on image may not align with the wind-off image due to model
deformation produced by aerodynamic loads. A ratio between those non-aligned
images can lead to a considerable error in calculation of pressure or temperature
using a calibration relation. Also, some distinct flow features such as shock,
boundary layer transition and flow separation could be smeared. In order to
correct the non-alignment problem, the image registration technique should be
used to match the wind-on image to the wind-off image (Bell and McLachlan
1993, 1996; Donovan et al. 1993). The image registration technique is based on a
mathematical transformation ( x' , y' ) ( x , y ) , which empirically maps the
deformed wind-on image coordinate ( x' , y' ) onto the reference wind-off image
coordinate ( x , y ) . For a small deformation, an image registration transformation
is well described by polynomials
m
m
( x, y ) = (
¦
i , j =0
aij x' i y' j ,
¦ b x'
ij
i
y' j ) .
(4.28)
i , j =0
Geometrically, the constant terms, linear terms, non-linear terms in Eq. (4.28)
represent translation, rotation and scaling, and higher-order deformation of a
4.5. Basic Data Processing
77
model in the image plane, respectively. In measurements of PSP and TSP, black
fiducial targets are placed in the locations on a model where deformation is
appreciable. The displacement of these marks in the image plane represents
perspective projection of real model deformation in the 3D object space. From
the corresponding centroids of the targets in the wind-on and wind-off images,
the polynomial coefficients aij and bij in Eq. (4.28) can be determined using
least-squares method. More targets will increase the statistical redundancy and
improve the precision of least-squares estimation. For most wind tunnel tests, a
second-order polynomial transformation (m = 2) is found to be sufficient. As a
pure geometric correction method, however, the image registration technique
fails to take into account a variation in illumination level on a model due to
model movement in a non-homogenous illumination field. An estimate of this
error requires the knowledge of the illumination field and the movement of the
model relative to the light sources. Bell and McLachlan (1993, 1996) gave an
analysis on this error in a simplified circumstance and found that this error was
small if the illumination light field was nearly homogenous and model
movement was small. Experiments showed that the image registration
technique considerably improved the quality of PSP and TSP images
(McLachlan and Bell 1995). Weaver et al. (1999) utilized spatial anomalies
(dots formed from aerosol mists in spraying) in a basecoat and calculated a pixel
shift vector field of a model using a spatial correlation technique similar to that
used in particle image velocimetry (PIV). Based on the shift vector field, the
wind-on image was registered. Le Sant et al. (1997) described an automatic
scheme for target recognition and image alignment. A detailed discussion on
the image registration technique is given in Chapter 5.
After a ratio of the wind-off image over the registered wind-on image is taken,
a pressure or temperature image can be obtained using the calibration relation (the
Stern-Volmer relation for PSP or the Arrhenius relation for TSP). Compared to
relatively straightforward conversion of an intensity ratio image to a temperature
image, conversion to a pressure image is more difficult since the intensity ratio
image of PSP is a function of not only pressure, but also temperature. The
temperature effect of PSP often has a dominant contribution to the total
uncertainty of PSP measurements if it is not corrected. When the Stern-Volmer
coefficients A( T ) and B( T ) are determined in a priori laboratory PSP
calibration and the temperature field on the surface are known, the pressure field
can be, in principle, calculated from a ratio image. The need of temperature
correction provoked the development of multiple-luminophore PSP and tandem
use of PSP with TSP. The surface temperature distribution can be measured using
TSP and infrared (IR) cameras. Also, the temperature field can be given by
theoretical and numerical solutions to the motion and energy equations of flows.
Unfortunately, experiments have shown that the use of a priori laboratory PSP
calibration with a correction for the temperature effect still leads to a systematic
error in the derived pressure distribution due to certain uncontrollable factors in
wind tunnel environment. To correct this systematic error, pressure tap data at a
number of locations are used to correlate the intensity ratio values to the pressure
tap data; this procedure is referred to as in-situ calibration of PSP. In the worst
78
4. Radiative Energy Transport and Intensity-Based Methods
case where A( T ) and B( T ) are not known and the surface temperature field is
not given, in-situ calibration is still able to give a pressure field. However, the
accuracy of interpretation of PSP data between the pressure taps is not guaranteed
especially when the gradients of the pressure and temperature fields between the
taps are large. Obviously, the selection of the locations of the pressure taps is
critical to assure the accuracy of in-situ calibration. The pressure tap data at the
discrete locations for in-situ calibration should reasonably cover the pressure
distribution on the surface. The in-situ calibration uncertainty of PSP is discussed
in Chapter 7.
PSP and TSP data in images have to be mapped onto a surface grid of a model
in the 3D object space since the pressure and temperature fields on the surface
grid are more useful for engineers and researchers. Further, this mapping is
necessary for extraction of aerodynamic loads and heat transfer and for
comparison with CFD results. In the literature of PSP and TSP, this mapping
procedure is often called image resection. Note that the meaning of resection in
the PSP and TSP literature is somewhat broader and looser than the strict one in
photogrammetry. From the standpoint of photogrammetry, a key of this procedure
is geometric camera calibration by solving the perspective collinearity equations
to determine the camera interior and exterior orientation parameters, and lens
distortion parameters. Once these parameters in the collinearity equations relating
the 3D object space to the image plane are known, PSP and TSP data in images
can be mapped onto a given surface grid in the 3D object space. A detailed
discussion on analytical photogrammetric techniques is given in Chapter 5. In
most PSP and TSP measurements conducted so far, data in images are mapped
onto a rigid CFD or CAD surface grid of a model. However, when a model
experiences a significant aeroelastic deformation in wind tunnel tests, mapping
onto a rigid grid misrepresents the true pressure and temperature fields.
Therefore, a deformed surface grid of a model should be generated for PSP and
TSP mapping. Liu et al. (1999) discussed generation of a deformed surface grid
based on videogrammetric model deformation measurements conducted along
with PSP/TSP measurements (see Chapter 5). Finally, the integrated aerodynamic
forces and moments can be calculated from the pressure distribution on the
surface. For example, the lift is given by FL = ¦ p i ( n • l L ∆S )i , where n is the
unit normal vector of a panel on the surface, ∆S is the area of the panel, and l L is
the unit vector of the lift. Similarly, the integrated quantities of heat transfer can
be obtained from the surface temperature fields based on appropriate heat transfer
models.
The self-illumination correction is implemented after the luminescent
intensity data are mapped on a surface grid in the 3D object space. The socalled self-illumination is a phenomenon that the luminescent emission from one
part of a model surface illuminates another surface, thus increasing the observed
luminescent intensity of the receiving surface and producing an additional error
in calculation of pressure and temperature. This distorting effect often occurs
on the surfaces of neighboring components such as wind/body junctures and
concave surfaces. The self-illumination depends on the surface geometry, the
luminescent field, and the reflecting properties of a paint layer. Assuming that a
4.5. Basic Data Processing
79
paint surface is Lambertian, Ruyten (1997a, 1997b, 2001a) developed an
analytical model and a numerical scheme for correcting the self-illumination
effect. The self-illumination correction scheme is discussed in Chapter 5.
One of the original purposes of developing two-luminophore PSPs is to
simplify the data processing for PSP. The dependency of a two-color intensity
ratio I λ1 / I λ2 on pressure p and temperature T is generally expressed as
I λ1 / I λ2 = f ( p , T ) , where I λ1 and I λ2 are the luminescent intensities at the
emission wavelengths λ1 and λ 2 , respectively. Ideally, a two-color intensity
ratio can eliminate the effect of spatially non-uniform illumination on a surface.
However, since two luminophores cannot be perfectly mixed, the simple twocolor intensity ratio I λ1 / I λ2 cannot completely compensate the effect of nonhomogenous dye concentration.
In this case, a ratio of ratios
( I λ1 / I λ2 ) /( I λ1 / I λ2 )0 should be used to correct the effects of non-homogenous
dye concentration and paint thickness variation, where the subscript 0 denotes the
wind-off condition (McLean 1998). Since the wind-off images are required, the
ratio-of-ratios method still needs image registration. The ratio-of-ratios approach
was also applied to non-pressure-sensitive reference targets to compensate the
effect of non-homogenous illumination on a moving model (Subramanian et al.
2002).
5. Image and Data Analysis Techniques
This Chapter describes image and data analysis techniques used in various
processing steps for PSP and TSP.
For quantitative PSP and TSP
measurements, cameras should be geometrically calibrated to establish the
accurate relationship between the image plane and the 3D object space and map
data in images onto a surface grid in the object space. Analytical camera
calibration techniques, especially the Direct Linear Transformation (DLT) and
the optimization calibration method, are discussed. Since PSP and TSP are
based on radiometric measurements, an ideal camera should have a linear
response to the luminescent radiance. For a camera having a non-linear
response, radiometric camera calibration is required to determine the
radiometric response function of the camera for correcting the image intensity
before taking a ratio between the wind-on and wind-off images. A simple but
effective technique is described here for radiometric camera calibration. The
self-illumination of PSP and TSP may cause a significant error near a
conjuncture of surfaces when a strong exchange of the radiative energy occurs
between neighboring surfaces. The numerical methods for correcting the selfillumination are generally described and the errors associated with the selfillumination are estimated for a typical case. The self-illumination correction is
usually made on a surface grid in the object space since it highly depends on the
surface geometry.
A standard procedure in the intensity-based method for PSP and TSP is to
take a ratio between the wind-on and wind-off images to eliminate the effects of
non-homogenous illumination intensity, dye concentration, and paint thickness.
However, since a model deforms due to aerodynamic loads, the wind-on image
does not align with the wind-off image. The image registration technique based
on a mathematical transformation between the wind-on and wind-off images is
described to re-align these images. A crucial step for PSP is to accurately
convert the luminescent intensity to pressure; cautious use of the calibration
relations with a correction of the temperature effect of PSP is discussed. PSP
measurements in low-speed flows are particularly difficult since a very small
pressure change has to be sufficiently resolved by PSP. The pressure-correction
method is described as an alternative to extrapolate the incompressible pressure
coefficient from PSP measurements at suitably higher Mach numbers by
removing the compressibility effect. The final processing step for PSP and TSP
is to map results in images onto a model surface grid in the object space. When
a model has a large deformation produced by aerodynamic loads, a deformed
surface grid should be generated for more accurate PSP and TSP mapping. A
methodology for generating a deformed wing grid is proposed based on
82
5. Image and Data Analysis Techniques
videogrammetric
aeroelastic
deformation
simultaneously with PSP and TSP measurements.
measurements
conducted
5.1. Geometric Calibration of Camera
5.1.1. Collinearity Equations
After the results of pressure and temperature are extracted from images of PSP
and TSP, it is necessary to map the data onto a surface grid in the 3D object space
(or physical space) to make the results more useful for design engineers and
researchers.
The collinearity equations in photogrammetry provide the
perspective relationship between the 3D coordinates in the object space and
corresponding 2D coordinates in the image plane (Wong 1980; McGlone 1989;
Mikhail et al. 2001; Cooper and Robson 2001; Liu 2002). A key problem in
quantitative image-based measurements is camera calibration to determine the
camera interior and exterior orientation parameters, and lens distortion parameters
in the collinearity equations. Simpler resection methods have often been used in
PSP and TSP systems to determine the camera exterior orientation parameters
under an assumption that the interior orientation and lens distortion parameters are
known (Donovan et al. 1993; Le Sant and Merienne 1995). The standard Direct
Linear Transformation (DLT) was also used to obtain the interior orientation
parameters in addition to the exterior orientation parameters (Bell and McLachlan
1993, 1996). An optimization method for comprehensive camera calibration was
developed by Liu et al. (2000), which can determine the exterior orientation,
interior orientation and lens distortion parameters (as well as the pixel aspect ratio
of a CCD array) from a single image of a 3D target field. The optimization
method, combined with the DLT, allows automatic camera calibration without an
initial guess of the orientation parameters; this feature particularly facilitates PSP
and TSP measurements in wind tunnels. Besides the DLT, a closed-form
resection solution given by Zeng and Wang (1992) is also useful for initial
estimation of the exterior orientation parameters of a camera based on three
known targets.
Figure 5.1 illustrates the perspective relationship between the 3D coordinates
( X, Y, Z ) in the object space and the corresponding 2D coordinates (x, y) in the
image plane. The lens of a camera is modeled by a single point known as the
perspective center, the location of which in the object space is ( X c ,Yc ,Z c ) .
Likewise, the orientation of the camera is characterized by three Euler orientation
angles. The orientation angles and location of the perspective center are referred
to in photogrammetry as the exterior orientation parameters. On the other hand,
the relationship between the perspective center and the image coordinate system is
defined by the camera interior orientation parameters, namely, the camera
principal distance c and the photogrammetric principal-point location ( x p ,y p ) .
5.1. Geometric Calibration of Camera
83
The principal distance, which equals the camera focal length for a camera focused
at infinity, is the perpendicular distance from the perspective center to the image
plane, whereas the photogrammetric principal-point is where a perpendicular line
from the perspective center intersects the image plane. Due to lens distortion,
however, perturbation to the imaging process leads to departure from collinearity
that can be represented by the shifts dx and dy of the image point from its ‘ideal’
position on the image plane. The shifts dx and dy are modeled and characterized
by the lens distortion parameters.
Z
Y
Object point
X
O
Object space
y
Perturbed
image point
Model
Perspective center
c
dy
Principal point
dx
yp
x
xp
Ideal
image point
Image plane
Fig. 5.1. Camera imaging process and the interior orientation parameters
The perspective relationship is described by the collinearity equations
x − x p + d x =− c
m11 ( X − X c ) + m12 ( Y − Yc ) + m13 ( Z − Z c )
U
= −c
W
m31 ( X − X c ) + m32 ( Y − Yc ) + m33 ( Z − Z c )
,
y − y p + d y =− c
(5.1)
m21 ( X − X c ) + m22 ( Y − Yc ) + m23 ( Z − Z c )
V
= −c
W
m31 ( X − X c ) + m32 ( Y − Yc ) + m33 ( Z − Z c )
where mij (i, j = 1, 2, 3) are the elements of the rotation matrix that are functions
of the Euler orientation angles ( ω ,φ ,κ ) ,
84
5. Image and Data Analysis Techniques
m11 = cos φ cos κ
m12 = sin ω sin φ cos κ + cos ω sin κ
m13 = − cos ω sin φ cos κ + sin ω sin κ
m21 = − cos φ sin κ
m22 = − sin ω sin φ sin κ + cos ω cos κ
(5.2)
m23 = cos ω sin φ sin κ + sin ω cos κ
m31 = sin φ
m32 = − sin ω cos φ
m33 = cos ω cos φ .
The orientation angles ( ω ,φ ,κ ) are essentially the pitch, yaw, and roll angles of a
camera in an established coordinate system. The terms dx and dy are the image
coordinate shifts induced by lens distortion, which can be modeled by a sum of
the radial distortion and decentering distortion (Fraser 1992; Fryer1989)
d x=d xr + d xd and d y =d y r + d y d ,
(5.3)
where
d x r = K 1 ( x' − x p ) r 2 + K 2 ( x' − x p ) r 4 ,
d y r = K 1 ( y' − y p ) r 2 + K 2 ( y' − y p ) r 4 ,
d x d = P1 [ r 2 + 2( x' − x p ) 2 ] + 2 P2 ( x' − x p )( y' − y p ) ,
(5.4)
d y d = P2 [ r 2 + 2( y' − y p ) 2 ] + 2 P1 ( x' − x p )( y' − y p ) ,
r 2 = ( x' − x p ) 2 + ( y' − y p )2 .
Here, K1 and K2 are the radial distortion parameters, P1 and P2 are the decentering
distortion parameters, and x’ and y’ are the undistorted coordinates in the image
plane. When lens distortion is small, the unknown undistorted coordinates can be
approximated by the known distorted coordinates, i.e., x' ≈ x and y' ≈ y . For
large lens distortion, an iterative procedure can be employed to determine the
appropriate undistorted coordinates to improve the accuracy of estimation. The
following iterative relations can be used: ( x' )0 = x and ( y' )0 = y ,
( x' )k +1 = x + d x [( x' ) k ,( y' )k ] and ( y' )k +1 = y + d y [( x' ) k ,( y' ) k ] , where the
superscripted iteration index is k = 0 , 1, 2 .
The collinearity equations Eq. (5.1) contain a set of the camera parameters to
be determined by camera calibration; the parameter sets ( ω ,φ ,κ , X c ,Yc , Z c ) ,
(c, x p , y p ) , and (K 1 , K 2 , P1 , P2 ) in Eq. (5.1) are the exterior orientation, interior
orientation, and lens distortion parameters of a camera, respectively. Analytical
camera calibration techniques have been used to solve the collinearity equations
5.1. Geometric Calibration of Camera
85
with the lens distortion model for the camera exterior and interior parameters
(Rüther 1989; Tsai 1987). Since Eq. (5.1) is non-linear, iterative methods of leastsquares estimation have been used as a standard technique for the solution of the
collinearity equations in photogrammetry (Wong 1980; McGlone 1989).
However, direct recovery of the interior orientation parameters is often impeded
by inversion of a nearly singular normal-equation-matrix in least-squares
estimation. The singularity of the normal-equation-matrix mainly results from
strong correlation between the exterior and interior orientation parameters. In
order to reduce the correlation between these parameters and enhance the
determinability of (c, x p , y p ) , Fraser (1992) suggested the use of multiple camera
stations, varying image scales, different camera roll angles and a well-distributed
target field in three dimensions. These schemes for selecting suitable calibration
geometry improve the properties of the normal equation matrix. In general,
iterative least-squares methods require a good initial guess to obtain a convergent
solution. Mathematically, the singularity problem can be treated using the
singular value decomposition that produces the best solution in a least-squares
sense. Also, the Levenberg-Marquardt method can stay away to some extent from
zero pivots (Marquardt 1963).
Nevertheless, multiple-station, multiple-image methods for camera calibration
are not easy to use in a wind tunnel environment where only a limited number of
windows are available for cameras and the positions of cameras are fixed. Thus, it
is highly desirable for PSP and TSP to have a single-image, easy-to-use
calibration method devoid of the singularity problem and an initial guess. In the
computer vision community, Tsai’s two-step method is particularly popular.
Instead of directly solving the standard collinearity equations Eq. (5.1), Tsai
(1987) used a radial alignment constraint to obtain a linear least-squares solution
for a subset of the calibration parameters, whereas the rest of the parameters
including the radial distortion parameter are estimated by an iterative scheme.
Tsai’s method is fast, but less accurate than the standard photogrammetric
methods. In addition, the radial alignment constraint prevents this method from
incorporating a more general model of lens distortion. Here, we first discuss the
DLT that can automatically provide initial values of the camera parameters and
then describe an optimization method for more comprehensive calibration of a
camera.
5.1.2. Direct Linear Transformation
The Direct Linear Transformation (DLT), originally proposed by Abdel-Aziz and
Karara (1971), can be very useful to determine approximate values of the camera
parameters. Rearranging the terms in the collinearity equations leads to the DLT
equations
L1 X + L2 Y + L3 Z + L4 − ( x+ d x )( L9 X + L10 Y + L11 Z + 1 ) = 0
.
(5.5)
L5 X + L6 Y + L7 Z + L8 − ( y + d y )( L9 X + L10 Y + L11 Z + 1 ) = 0
86
5. Image and Data Analysis Techniques
The DLT parameters L1 , L11 are related to the camera exterior and interior
orientation parameters ( ω ,φ ,κ , X c ,Yc , Z c ) and (c, x p , y p ) (McGlone 1989).
Unlike the standard collinearity equations Eq. (5.1), Eq. (5.5) is linear for the DLT
parameters when the lens distortion terms dx and dy are neglected. In fact, the
DLT is a linear treatment of what is essentially a non-linear problem at the cost of
introducing two additional parameters. The matrix form of the linear DLT
L = ( L1 , L11 )T ,
equations for M targets is
B L = C , where
C = ( x1 , y1 , x M , y M )T , and B is the 2M×11 configuration matrix that can be
directly obtained from Eq. (5.5). A least-squares solution for L is formally given
by L = (B T B) −1 B T C without using an initial guess. The camera parameters can
be extracted from the DLT parameters from the following expressions
x p = ( L1 L9 + L2 L10 + L3 L11 )L2 ,
y p = ( L5 L9 + L6 L10 + L7 L11 )L2 ,
c = ( L21 + L22 + L23 )L2 − x 2p
,
φ = sin −1 ( L9 L ) ,
ω = tan −1 ( − L10 / L11 ) ,
κ = cos −1 ( m11 / cos( φ )) ,
m11 = L( x p L9 − L1 ) / c ,
L = − ( L29 + L210 + L211 )−1 / 2 ,
§ Xc ·
§ L1
¨ ¸
¨
¨ Yc ¸ = − ¨ L5
¨ ¸
¨
© Zc ¹
© L9
L2
L6
L10
L3 · § L4 ·
¸¨ ¸
L7 ¸ ¨ L8 ¸ .
¸¨ ¸
L11 ¹ © 1 ¹
Because of its simplicity, the DLT is widely used in both non-topographic
photogrammetry and computer vision. When dx and dy cannot be ignored,
however, iterative solution methods are still needed and the DLT loses its
simplicity. In general, the DLT can be used to obtain fairly good values of the
exterior orientation parameter and the principal distance, although it gives a poor
estimate for the principal-point location (x p ,y p ) (Cattafesta and Moore 1996).
Therefore, the DLT is valuable since it can provide initial approximations for
more accurate methods like the optimization method discussed below for
comprehensive camera calibration.
5.1. Geometric Calibration of Camera
87
5.1.3. Optimization Method
In order to develop a simple and robust method for comprehensive camera
calibration, the singularity problem must be dealt with to solve the collinearity
equations. Liu et al. (2000) proposed an optimization method based on the
following insight. Strong correlation between the interior and exterior orientation
parameters leads to the singularity of the normal-equation-matrix in least-squares
estimation for a complete set of the camera parameters. Therefore, to eliminate
the singularity, least-squares estimation is used for the exterior orientation
parameters only, while the interior orientation and lens distortion parameters are
calculated separately using an optimization scheme. This optimization method
contains two separate, but interacting procedures: resection for the exterior
orientation parameters and optimization for the interior orientation and lens
distortion parameters.
When the image coordinates (x, y) are given in pixels, we express the
collinearity equations Eq. (5.1) as
f 1 = S h x n − x p + d x + cU / W = 0
f 2 = S v y n − y p + d y + cV / W = 0
,
(5.6)
where Sh and Sv are the horizontal and vertical pixel spacings (mm/pixel) of a CCD
array, respectively. In general, the vertical pixel spacing is fixed and known for a
CCD camera, but the effective horizontal spacing may be variable. Thus, an
additional parameter, the pixel-spacing-aspect-ratio S h / S v , is introduced. We
define Ȇ ex = ( Ȧ, ij, ț, X c , Yc , Z c )T for the exterior orientation parameters and
Ȇ in = (c, x p , y p , K 1 , K 2 , P1 , P2 , S h / S v )T for the interior orientation and lens
distortion parameters in addition to the pixel-spacing-aspect-ratio. For given
values of Ȇ in , and a set of known points (targets) pn =(x n ,y n )T and
Pn =(X n ,Yn ,Z n )T , a solution for Ȇ ex in Eq. (5.6) can be found using an iterative
least-squares method, referred to as resection in photogrammetry. The linearized
collinearity equations for targets (n = 1, 2, , M) are written as
V = ǹ ( ǻȆ ex ) − l , where ǻȆ ex is the correction term for the exterior
orientation parameters, V is the 2M×1 residual vector, A is the 2M×6
configuration matrix, and l is the 2M×1 observation vector. The configuration
matrix A and observation vector l in the linearized collinearity equations are
§ (∂ f 1 / ∂ Ȇ ex )1 ·
§ ( f 1 )1 ·
¸
¨
¸
¨
¨ (∂ f 2 / ∂ Ȇ ex )1 ¸
¨ ( f 2 )1 ¸
¸
¨
¸
¨
(5.7)
A=¨
¸ and l = − ¨ ¸ ,
¨ (∂ f 1 / ∂ Ȇ ex ) ¸
¨ ( f 1 )M ¸
M
¸
¨
¸
¨
¨( f2 ) ¸
¨ (∂ f 2 / ∂ Ȇ ex ) ¸
M ¹
M ¹
©
©
88
5. Image and Data Analysis Techniques
where
the
operator
∂ /∂ Ȇ ex
is
defined
as
( ∂ /∂ Ȧ,∂ /∂ ij,∂ /∂ ț, ∂ /∂ X c , ∂ /∂Yc , ∂ /∂ Z c ) and the subscript denotes a target. The
components of the vectors ∂ f 1 / ∂ Ȇ ex and ∂ f 2 / ∂ Ȇ ex are
∂ f1
c
U
= { m12 ( Z − Z c ) − m13 ( Y − Yc ) − [ m32 ( Z − Z c ) − m33 ( Y − Yc )]} ,
∂Ȧ W
W
∂ f1
c
U
=
[ −cos ț W − (cos ț U − sin ț V)] ,
∂ij W
W
∂ f 1 cV
=
W
∂ț
,
∂ f1
U
c
= ( −m11 + m31 ) ,
∂Xc W
W
∂ f1
c
U
= ( −m12 + m32 ) ,
∂Yc W
W
∂ f1
c
U
= ( −m13 + m33 ) ,
∂Zc W
W
∂ f2
c
V
= { m22 ( Z − Z c ) − m23 ( Y − Yc ) − [ m32 ( Z − Z c ) − m33 ( Y − Yc )]} ,
∂Ȧ W
W
∂ f2
c
V
=
[sin ț W − (cos ț U − sin ț V)] ,
∂ij W
W
∂ f2
cU
=−
W
∂ț
,
∂ f2
c
V
= ( −m 21 + m31 ) ,
∂Xc W
W
∂ f2
c
V
= ( −m22 + m32 ) ,
∂Yc W
W
∂ f2
c
V
= ( −m23 + m33 ) .
∂Zc W
W
A least-squares solution to minimize the residuals V for the correction term is
ǻȆ ex =(AT A) −1 AT l . In general, the 6 × 6 normal-equation-matrix ( AT A ) can
be inverted without any singularity problem since the interior orientation and lens
5.1. Geometric Calibration of Camera
89
distortion parameters are not included in least-squares estimation. To obtain such
Ȇ ex that the correction term ǻȆ ex becomes zero, the Newton-Raphson iterative
method is used for solving the non-linear equation (AT A) −1 AT l = 0 for Ȇ ex .
This approach converges over a considerable range of the initial values of Ȇ ex .
Therefore, for given Ȇ in , the corresponding exterior orientation parameter Ȇ ex
can be obtained, which are symbolically expressed as Ȇ ex = RESECTION( Ȇ in ) .
At this stage, the exterior orientation parameters Ȇ ex are not necessarily correct
unless the given interior orientation and lens distortion parameters Ȇ in are
accurate. Obviously, an extra condition is needed to obtain correct Ȇ in and the
determination of Ȇ in is coupled with the resection for Ȇ ex . An optimization
scheme to obtain the correct Ȇ in is described as follows.
We notice that the correct values of Ȇ in are intrinsic constants for a
camera/lens system, and they are independent of the target locations
p n = (x n ,y n )T in the image plane and Pn = (X n ,Yn ,Z n )T in the object space.
Mathematically, Ȇ in is an invariant under a transformation ( p n ,Pn ) ( p m ,Pm )
( m≠n ). Therefore, for the correct values of Ȇ in , the parameters (c, x p , y p ) are
invariant under the transformation ( p n ,Pn ) ( p m ,Pm ) ( m≠n ). In other words,
for the correct values of Ȇ in , the standard deviation of (c, x p , y p ) calculated over
all the targets from the collinearity equations should be zero, i.e.,
M
std(x p ) = [ ¦ ( x p − < x p > ) 2 /( M − 1 ) ] 1/2 = 0 , where std denotes the standard
n =1
deviation and < > denotes the mean value. Furthermore, since std ( x p ) ≥ 0 is
always valid, the correct Ȇ in must correspond to the global minimum point of the
function std ( x p ) . Hence, the determination of the correct Ȇ in becomes an
optimization problem to seek such values of Ȇ in that the objective function
std ( x p ) is minimized, i.e., std ( x p ) → min . To solve this multiple-dimensional
optimization problem, the sequential golden section search technique is used
because of its robustness and simplicity. Since (c, x p , y p ) are estimated from Eq.
(5.1) for given Ȇ ex , the optimization scheme for Ȇ in is coupled with the
resection scheme for Ȇ ex . Other appropriate objective functions can also be
used; an obvious choice is the root-mean-square (rms) deviation of the calculated
object space coordinates of all the targets from the measured ones. In fact, it is
found that std ( x p ) or std ( y p ) is equivalent to this rms deviation in the
optimization problem.
The quantities std ( x p ) and std ( y p ) for optimization have a simple
topological structure near the global minimum point, exhibiting a single ‘valley’
structure in the parametric space (Liu et al. 2000). Generally, the topological
90
5. Image and Data Analysis Techniques
structure of std ( x p ) or std ( y p ) depends on three-dimensionality of a target
field; stronger three-dimensionality of the target field produces a steeper ‘valley’
in topology, leading to faster convergence. The topological structure of std ( x p )
or std ( y p ) can also be affected by random disturbances on the targets. Larger
noise in images leads to a slower convergence rate and produces a larger error in
optimization computations. Although the simple ‘valley’ topological structure
allows convergence of optimization computation over a considerable range of the
initial values, appropriate initial values are still required to obtain a converged
solution. The DLT can provide such initial values for the exterior orientation
parameters ( Ȧ, ij, ț , X c , Yc , Z c ) and the principal distance c . Combined with the
DLT, the optimization method allows rapid and comprehensive automatic camera
calibration to obtain a total of 14 camera parameters from a single image without
requiring a guess of the initial values.
Fig. 5.2. Step target plate for camera calibration
The optimization method was used for calibrating a Hitachi CCD camera with
a Sony zoom lens (12.5 to 75 mm focal length) and an 8 mm Cosmicar television.
As shown in Fig. 5.2, a three-step target plate with a 2-in step height provided a
3D target field for camera calibration, on which 54 circular retro-reflective targets
of a 0.5-in diameter spaced out 2 inches apart are placed. Figure 5.3 shows the
principal distance given by the optimization method versus zoom setting for the
Sony zoom lens. Figures 5.4 and 5.5 show, respectively, the principal-point
location and radial distortion coefficient K1 as a function of the principal distance
for the Sony zoom lens. The results given by the optimization method are in
reasonable agreement with measurements for the same lens using optical
equipment in laboratory (Burner 1995). The optimization method was also used
to calibrate the same Hitachi CCD camera with an 8 mm Cosmicar television lens.
Table 5.1 lists the calibration results given by the optimization method compared
well with those obtained using optical equipment.
In order to determine accurately the interior orientation parameters, a target
field should fill up an image for camera calibration. In large wind tunnels,
however, a camera is often located far from a model such that the target field
looks small in the image plane. In this case, a two-step approach is suggested that
determines the interior and exterior orientation parameters separately. First,
placing a target plate near a camera to produce a sufficiently large target field in
the image plane, we can determine accurately the interior orientation parameters
5.1. Geometric Calibration of Camera
91
using the optimization method. Next, assuming that the determined interior
orientation parameters are fixed for locked camera setting, we obtain the exterior
orientation parameters using a resection scheme from the target field in a given
wind-tunnel coordinate system.
90
Principal distance c (mm)
80
Optimization algorithm
Linear fit
70
60
50
40
30
20
10
10
20
30
40
50
60
70
80
Zoom setting (mm)
Fig. 5.3. Principal distance vs. zoom setting for a Sony zoom lens. From Liu et al. (2000)
2
Optimization algorithm
xp or yp (mm)
Laser illumination technique
1
yp
0
xp
-1
10
20
30
40
50
60
70
80
90
c (mm)
Fig. 5.4. Principal-point location as a function of the principal distance for a Sony zoom
lens connected to a Hitachi camera. From Liu et al. (2000)
92
5. Image and Data Analysis Techniques
0.0010
Optimization algorithm
Burner (1995)
0.0005
K1 (mm-2)
0.0000
-0.0005
-0.0010
-0.0015
-0.0020
10
20
30
40
50
60
70
80
90
c (mm)
Fig. 5.5. The radial distortion coefficient as a function of the principal distance for a Sony
zoom lens connected to a Hitachi camera. From Liu et al. (2000)
Table 5.1. Calibration for Hitachi CCD camera with 8 mm Cosmicar TV lens
Interior orientation
c (mm) xp (mm)
yp (mm)
Sh /Sv
K1 (mm-2)
K2 (mm-4)
Optimization
8.133
0.2014
0.99238
0.0026
3.3×10
Optical techniques
8.137
-0.156
-0.168
0.2010
0.99244
0.0027
-5
-5
4.5×10
P1 (mm-1)
P2 (mm-1)
1.8×10
-4
3×10
1.7×10
-4
-5
7×10-5
5.2. Radiometric Calibration of Camera
Since PSP and TSP are based on radiometric measurements, a CCD camera used
for measurements should have a good linear response of the electrical output to
the scene radiance. However, there are many stages of image acquisition that may
introduce non-linearity; for example, video cameras often include some form of
‘gamma’ mapping. When the radiometric response function of a camera is
known, the non-linearity can be corrected. Here, a simple algorithm is described
to determine the radiometric response function of a camera from a scene image
taken in different exposures. First, we define I ( x ) as a linear radiometric
response to the scene radiance and m [ I ( x )] as the measurement of I ( x ) by
camera electronic circuitry that may produce a non-linear electrical output.
Actually, the measurement m [ I ( x )] is the brightness or gray level of an image,
where x is the image coordinates. The non-dimensional response function
relating I ( x ) to m [ I ( x )] is defined by
5.2. Radiometric Calibration of Camera
I ( x ) / I max = f [ ξ ( x )] ,
93
(5.8)
where ξ ( x ) = m[ I ( x )] / m( I max ) is the non-dimensional measurement of I ( x )
normalized by the maximum value and I max corresponds to the maximum
radiance in the scene. Recovery of f (ξ ) is the task of the radiometric calibration
of a camera.
Two images of a scene are taken in two different exposures. According to the
camera formula (Holst 1998), I ( x ) is proportional to the integration time t INT
and inversely proportional to the square of the f-number F. Thus, we have the
following functional equation for f (ξ ) ,
f (ξ 1 ) / f ( ξ 2 ) = R12 ,
(5.9)
where the subscripts 1 and 2 denote the image 1 and image 2, and the factor R12 is
defined as
I
( t / F 2 )1
.
(5.10)
R12 = max 2 INT
I max 1 ( t INT / F 2 )2
Since m( I max ) corresponds to I max , the boundary condition for
f (ξ = 1) = 1 . We assume that f (ξ ) can be expanded as
f (ξ ) =
f (ξ ) is
N
¦ c φ (ξ ) ,
n
(5.11)
n
n =0
where the base functions φ n ( ξ ) are the Chebyshev functions although other
orthogonal functions and non-orthogonal functions like polynomials can also be
used. Substitution of Eq. (5.11) to Eq. (5.9) leads to the following equations for
the coefficients c n
N
¦ c [φ ( ξ
n
n
1
) − R12 φ n ( ξ 2 )] = 0 ,
n =0
N
¦ c φ (1) = 1 .
(5.12)
n n
n =0
For selected M pixels in a scene image, Eq. (5.12) constitutes a system of M+1
equations for the N+1 unknowns c n ( M ≥ N ). For a given R12 , a least-squares
solution for c n can be found. In practice, since the factor R12 is not exactly
known a priori, we use an approximate value of R12
R12 ≈
m( I max 2 ) ( t INT / F 2 )1
m( I max 1 ) ( t INT / F 2 )2
.
An iteration scheme can be used to give an improved value of R12 . Figure 5.6
shows two images taken by a Cannon digital still camera (EOS D30) at two
94
5. Image and Data Analysis Techniques
different f-numbers of F = 4.0 and F = 5.6, where Ansel Adams’ photograph of
Mirror Lake of Yosemite was used as a test scene providing a broad range of the
gray levels for radiometric calibration. Figure 5.7 shows the radiometric response
function of the camera retrieved from the two images, where six terms of the
Chebyshev functions in Eq. (5.11) were used. The response function of the
Cannon digital still camera exhibits a non-linear behavior; it is also different for
the red, green and blue (RGB) color channels.
(a)
(b)
Fig. 5.6. Two images of Mirror Lake of Yosemite (Ansel Adams 1935) taken by a Cannon
digital still camera (EOS D30) at different F-numbers (a) F = 4.0 and (b) F = 5.6 for
radiometric calibration of the camera
Camera Response Function, I/Imax
1.0
R
G
B
0.8
0.6
0.4
0.2
0.0
0.0
0.2
0.4
0.6
0.8
1.0
m(I)/m(Imax)
Fig. 5.7. Response functions of a Cannon digital still camera (EOS D30) for the R, G, and
B color channels obtained from radiometric calibration
5.3. Correction for Self-Illumination
95
5.3. Correction for Self-Illumination
The self-illumination of PSP and TSP results from the luminescent contribution to
a point on a surface from all visible neighboring points; it becomes appreciable
near a conjuncture of two surfaces and on a concave surface (Ruyten 1997a,
1997b, 2001a; Ruyten and Fisher 2001; Le Sant 2001b). Although the selfillumination can be to certain extent suppressed by taking a ratio between a windon image and a wind-off image, it cannot be eliminated without considering an
exchange of the radiative energy between neighboring surfaces, which may
produce an error in data reduction of PSP and TSP. Therefore, we need to know
how much the radiative energy leaves from an area element and travels toward
another element. The geometric relations for this inter-surface process are known
as view factors, configuration factors, shape factors, or angle factors (Modest
1993). We consider diffuse surfaces that absorb and emit diffusely, and also
reflect the radiative energy diffusely. The view factor dFdA i − dA j between two
infinitesimal surface elements dAi and dA j , as shown in Fig. 5.8, is defined as a
ratio between the diffuse energy leaving dAi directly toward and intercepted by
dA j and the total diffuse energy leaving dAi , which is expressed as
dFdA i − dA j =
cos θ i cos θ j
π | X ij |
2
dA j =
( ni • X ij )( n j • X ij )
π | X ij |4
dA j ,
(5.13)
where n i (or n j ) is the unit normal vector of dAi (or dA j ), X ij is the position
vector directing from dAi toward dA j , and θ i (or θ j ) is the angle between the
position vector X ij and the normal n i (or n j ). The view factors leaving dAi
directly toward the total surface A j or leaving A j toward dAi , or leaving A j
toward Ai can be similarly defined by integrating dFdA i − dA j (Modest 1993). The
law of reciprocity dAi dFdA i −dA j = dA j dFdA j −dA i is valid for these view factors. The
view factor is a function of the geometric parameters. Methods for evaluating the
view factors were discussed by Modest (1993) and a large collection of the view
factors for simple geometric configurations was complied by Howell (1982). For
partially specular surfaces, the determination of the view factors is more
complicated since the bidirectional reflectance distribution function (BRDF) of the
paint must be known (Nicodemus et al. 1977; Asmail 1991).
96
5. Image and Data Analysis Techniques
Xj
nj
θj
dAj
Xij
ni
θi
Xi
dAi
Fig. 5.8. Radiative exchange between two surface elements
The self-illumination correction is applied to an image intensity (or brightness
intensity) field denoted by I in this sub-section after it is mapped onto a model
surface grid in the object space. Because the image intensity is proportional to the
luminescent energy flow rate, the image intensity I i at an area element dAi is a
sum of the local intrinsic intensity I i( 0 ) and an integration of the contributions
from all the neighboring elements, i.e.,
N
I i = I i( 0 ) + ρ λwp2
¦I
j =1
j
dFdA j − dAi dA j
,
(5.14)
where ρ λwp2 is the reflectivity of the wall-paint interface at the luminescent
wavelength. In simulations, given a set of the intrinsic intensities I i( 0 ) , the image
intensity I i affected by the self-illumination can be obtained using a simple
iteration scheme
N
I i( n+1 ) = I i( 0 ) + ρ λwp2
¦I
j =1
(n)
j
dFdA j −dA i dA j
.
(5.15)
The more efficient Gauss-Seidel iteration scheme was used by Ruyten and Fisher
(2001). In measurements, since the image intensity I i is known in PSP and TSP
images, an explicit relation is used to correct the self-illumination and recover the
intrinsic intensity I i( 0 ) , i.e.,
N
I i( 0 ) = I i − ρ λwp2
¦I
j =1
j
dFdA j −dA i dA j
.
(5.16)
5.3. Correction for Self-Illumination
97
The steps for correcting the self-illumination are: (1) measuring the reflectivity
ρ λwp2 ; (2) defining a surface grid consisting of N surface elements dAi ; (3)
evaluating the view factors dFdA j −dA i ; (4) mapping the image intensity I i onto the
surface grid; (5) calculating the intrinsic (corrected) intensity I i( 0 ) using Eq.
(5.16); and (6) calculating a ratio of the intrinsic (self-illumination-corrected)
intensities and converting it to pressure or temperature. Ruyten and Fisher (2001)
conducted a numerical simulation of correcting the self-illumination for a PSP test
of the Alpha jet and found that the error associated with the self-illumination in
PSP measurements could reach several percents of actual pressure.
plate 2
plate 1
dA1
α
Fig. 5.9. Wedge-shaped conjunction of two plates
Here, we consider a simple but representative geometric configuration, a
wedge-shaped conjunction of two infinitely large plates, as shown in Fig. 5.9; this
case allows an analytical estimate of the error induced by the self-illumination.
The image intensity at a location on the plate 1 is
I 1 = I 1( 0 ) + ρ λwp2
³I
2
dFdA2 −dA1 dA2 .
(5.17)
plate 2
Assuming that the image intensity at the plate 2 is homogenous, by integrating the
view factor for this configuration (Modest 1993), we obtain the image intensity at
the plate1 affected by the plate 2
I 1 ≈ I 1( 0 ) + ε 1 I 2 ,
(5.18)
where the parameter ε 1 = ρ λwp2 ( 1 + cos α ) / 2 represents the combined effect of the
angle α between the plates and reflectivity. Clearly, the self-illumination
decreases from the maximum value at α = 0 o to zero at α = 180 o . A reciprocal
relation gives the image intensity at the plate 2
98
5. Image and Data Analysis Techniques
I 2 ≈ I 2( 0 ) + ε 1 I 1 .
(5.19)
When the parameter ε 1 is small, the image intensity ratio at the plate 1 is
0)
I 1 ref / I 1 ≈ ( I 1( ref
/ I 1( 0 ) ) ( 1 + ε 1 ε 2 ) .
(5.20)
0)
− I 2( 0 ) / I 1( 0 ) reflects the difference of the relative
The parameter ε 2 = I 2( 0ref) / I 1( ref
influence of the plate 2 on the pate 1 between the wind-off reference and wind-on
conditions. Using the Stern-Volmer relation for PSP, we obtain an estimate for
the pressure error associated with the self-illumination for the wedge
configuration
§ A p( 0 )
| p − p( 0 ) |
≈ ε1 | ε 2 | ¨ + (0 )
(0 )
¨ B p ref
p ref
©
·
¸,
¸
¹
(5.21)
(0 )
where A and B are the Stern-Volmer coefficients, and p ( 0 ) and p ref
are,
respectively, the intrinsic PSP-derived pressures in the wind-on and wind-off
reference conditions that are not affected by the self-illumination. Similarly, using
the Arrhenius relation for TSP, we have an estimate for the temperature error
associated with the self-illumination for the wedge configuration
|T − T (0 ) |
R
≈ ε1 | ε2 |
E nr
T (0 )
,
(5.22)
where R is the universal gas constant, E nr is the activity energy of TSP, and
T ( 0 ) is the intrinsic TSP-derived temperature that is not affected by the selfillumination.
The above discussion is based on an assumption that the luminescent paint
surface is a diffuse surface or Lambertian surface. Nevertheless, a real paint
surface is neither Lambertian nor specular. To characterize reflection on a general
surface, the bidirectional reflectance distribution function (BRDF) was introduced
by Nicodemus et al. (1977). As shown in Fig. 5.10, the incident radiance is
generally a function of the incident direction defined by the incident polar angle
and azimuthal angle ( θ i ,φ i ) , i.e.,
Li = Li ( θ i ,φ i ) .
(5.23)
The reflection radiance Lr ( θ i ,φ i ;θ r ,φ r ) is quantitatively characterized by the
BRDF
f r ( θ i ,φ i ;θ r ,φ r ) = dLr ( θ i ,φ i ;θ r ,φ r ) / dEi ( θ i ,φ i ) .
(5.24)
where ( θ r ,φ r ) defines the direction of reflection and the infinitesimal incident
irradiance dE i ( θ i ,φ i ) over a solid angle element dω i is
5.3. Correction for Self-Illumination
dEi ( θ i ,φ i ) = Li ( θ i ,φ i ) cosθ i dω i .
99
(5.25)
-1
The BRDF has a unit of steradian . Here, the conventional radiometric notations
L and E are used for radiance and irradiance, which are also applicable to the
luminescent emission.
The BRDF depends on a surface roughness distribution. For a perfectly diffuse
surface where the reflection radiance is isotropic, i.e., Lr = const . , the BRDF is
f r = 1 / π (Horn and Sjoberg 1979). For a general surface, the BRDF can be
derived based on either the wave equation for electromagnetic waves or
geometrical optics models (Beckmann and Spizzichino 1963; Torrance and
Sparrow 1967; Nayar et al. 1991). Asmail (1991) gave a bibliographical review
on the BRDF. From a viewpoint of application, empirical expressions for the
scattered radiance from a rough surface are very useful due to their simplicity
(Cook and Torrance 1981; Haussecker 1999). An empirical model for a single
light source is
Lr ( X ) = ρ a E a ( X ) + ρ d Els ( X )( N T Ls ) + ρ s Els ( X ) p( R T V ) ,
(5.26)
where the first, second and third terms are, respectively, the contributions from the
ambient reflection, diffuse reflection, and specular reflection. In Eq. (5.26), ρ a ,
ρ d , and ρ s , are the empirical reflection coefficients for the ambient reflection,
diffuse reflection, and specular reflection. As shown in Fig. 5.10, the vectors N ,
Ls , R , and V are, respectively, the unit normal vector of a surface, the unit
vector directing the light source from the surface, the unit main directional vector
of the specular reflection, and the unit viewing vector. E a ( X ) and Els ( X ) are
the irradiances for the ambient environment and light sources, respectively. The
function p( R T V ) is the directional distribution of the specular reflection,
describing the spreading of scattered light. Phong (1975) gave a power function
p( R T V ) = ( R T V )n . In general, the main directional vector of the specular
reflection, R , is a function of the incident direction of light − Ls . Although there
are certain theories for predicting the specular direction R (Torrance and Sparrow
1967), R is not known for a general surface. The unknowns in Eq. (5.26), such as
R , the reflection coefficients, and the parameters in p( R T V ) , have to be
determined experimentally by calibration.
Le Sant (2001b) measured the BRDF for the B1 PSP paint with talc using a
BRDF calibration rig. As illustrated in Fig. 5.11, the BRDF calibration rig
included a lamp for illumination and a spectrometer to measure the reflected light
from a sample. The lamp emitted white light, enabling the calibration of the
o
o
BRDF in the visible range; the lamp moved from 0 at the vertical position to 60 .
o
o
The zenith (or polar) angle of the spectrometer moved from 0 to 60 and the
o
o
o
azimuth angle moved from 0 to 180 , where 180 was in the opposite direction of
the emission. Figure 5.12 shows the measured BRDF for the B1 paint, which was
nearly Lambertian when the zenith (or polar) angle of illumination was 10°, while
specular reflection occurred when the zenith angle increased further. The
100
5. Image and Data Analysis Techniques
maximum value was always achieved in the specular direction. The low value
obtained at the azimuth angle of 0° was incorrect since the spectrometer was in the
front of the lamp and thus the PSP sample was no longer illuminated. The
measured BRDF showed a superposition of diffuse reflection and specular
reflection. A specular peak was observed at the zenith angle of 60° as well as a
secondary peak at the azimuth angle of 90°. The value of the diffuse reflection
factor depended on the zenith angle of illumination. Le Sant (2001b) was able
achieve a good fit to the measured BRDF using the modified Phong model (Phong
1975), as shown in Fig. 5.13, and the modeled BRDF captured the main features
of the measured BRDF except the secondary specular peaks.
LI
θE
V
N
R
θH
φH
Fig. 5.10. Vectors of incident, reflecting, and viewing directions
zenith
(spectrometer)
zenith
(illumination)
0°
180°
90°
90°
azimuth
0°
Fig. 5.11. The zenith (or polar) and azimuth angles in the BRDF calibration rig. From Le
Sant (2001b)
5.3. Correction for Self-Illumination
BRDF
BRDF
0.4
0.4
0.2
0.2
0.2
0.1
0.1
0.1
60
0
60
0
180
zenith
20
zenith
20
azimuth
zenith
80
20
0
0
40
0.6
50
0.4
60
0.4
0.2
0.2
60
0
0.1
60
0
180
10
180
40
160
140
zenith
zenith
azimuth
10
40
160
azimuth
80
10
40
20
20
0
0
0
azimuth
60
40
20
120
100
20
80
60
140
30
120
100
20
180
40
160
140
30
120
100
80
0
50
50
60
0.4
0.3
0.1
50
20
0.5
0.3
0.1
60
BRDF
0.5
0.3
30
0
0.6
BRDF
0.5
40
azimuth
40
20
0
0.6
0
80
60
10
40
20
0
BRDF
zenith
120
100
azimuth
60
10
40
160
140
30
120
100
20
0
180
40
160
140
30
80
60
10
180
40
160
140
120
100
0
50
50
50
30
0.4
0.3
0.3
0.3
40
0.5
30
0.5
20
0.5
60
0.6
0.6
0.6
BRDF
10
101
0
0
Fig. 5.12. The measured BRDF of the B1 paint at the illumination zenith angles of 10, 20,
30, 40, 50 and 60 degrees. From Le Sant (2001b)
BRDF
BRDF
10
20
0.5
0.4
30
0.5
0.4
0.2
0.1
0.1
60
0
60
0
180
zenith
80
20
zenith
80
0.4
0
180
160
140
30
120
100
20
80
60
10
azimuth
0.2
0.1
60
0
50
180
40
160
0.1
60
0
50
180
40
160
140
30
zenith
120
100
20
80
60
10
40
40
20
0.4
0.3
0.2
0.2
40
60
0.4
0.5
0.3
0.1
50
0.6
BRDF
0.5
0.3
60
0
0.6
50
0.5
azimuth
40
20
0
BRDF
40
0
80
60
10
0
0.6
0
20
40
20
0
0
BRDF
zenith
120
100
azimuth
60
10
40
20
0
160
140
30
120
100
azimuth
60
10
180
40
160
140
30
120
100
20
180
40
160
140
30
0
50
50
50
40
0.4
0.3
0.2
0.2
0.1
zenith
0.5
0.3
0.3
60
0.6
0.6
0.6
BRDF
140
30
zenith
120
100
20
80
azimuth
60
10
0
azimuth
40
20
0
20
0
0
Fig. 5.13. The modeled BRDF of the B1 paint at the illumination zenith angles of 10, 20,
30, 40, 50 and 60 degrees using the modified Phong model. From Le Sant (2001b)
Le Sant (2001b) also studied the self-illumination in a corner to validate a
correction algorithm. The corner was painted with a Pyrene-based paint providing
an image significantly affected by the self-illumination near the junction of the
two plates, as shown in Fig. 5.14. Then, the left plate was covered with a black
sheet, removing the effect of the self-illumination on the right plate, as shown in
102
5. Image and Data Analysis Techniques
the right image in Fig. 5.14. Figure 5.15 shows results before and after correcting
the self-illumination based on the diffuse surface model and the Phong model.
The self-illumination correction was effective; the self-illumination effect was
reduced to 15% from about 40% near the junction. This paint behaved mostly like
a diffuse paint such that the Phong model did not exhibit a significant
improvement. Although the Phong model might improve the accuracy of
correction for a surface with strong specular reflection, the computation time for
the Phong model was much longer than that for the diffuse surface model.
Fig. 5.14. Self-illumination in a corner coated with PSP. From Le Sant (2001b)
0.16
with SI effect
0.15
0.14
0.13
diffuse model
0.12
0.11
Phong model
0.10
0
10
20
30
without SI
40 X (mm) 50
Fig. 5.15. Self-illumination correction using the diffuse and Phong models. From Le Sant
(2001b)
5.4. Image Registration
The intensity-based method for PSP and TSP requires a ratio between the wind-on
and wind-off images of a painted model. Since a model deforms due to
aerodynamic loads, the wind-on image does not align with the wind-off image;
therefore these images have to be re-aligned before taking a ratio between the
images. The image registration technique, developed by Bell and McLachlan
(1993, 1996) and Donovan et al. (1993), is based on an ad-hoc transformation that
5.4. Image Registration
103
maps the deformed wind-on image coordinates ( xon , yon ) onto the reference
wind-off image coordinates ( xoff , yoff ) . In order to register the images, some
black fiducial targets are placed on a model. When the correspondence between
the targets in the wind-off and wind-on images is established, a transformation
between the wind-off and wind-on image coordinates of the targets can be
expressed as
x off =
aij φ i ( x on )φ j ( y on )
.
(5.27)
y off =
bij φ i ( xon )φ j ( y on )
¦
¦
The base functions φ i ( ξ ) are either the orthogonal functions like the Chebyshev
functions or the non-orthogonal power functions φ i ( x ) = x i used by Bell and
McLachlan (1993, 1996) and Donovan et al. (1993). Given the image coordinates
of the targets placed on a model, the unknown coefficients aij and bij can be
determined using least-squares method to match the targets between the wind-on
and wind-off images. For image warping, one can also use a 2D perspective
transform (Jähne 1999)
x off =
a 11 x on + a 12 y on + a 13
a 31 x on + a 32 y on + 1
.
(5.28)
a 21 x on + a 22 y on + a 23
y off =
a 31 x on + a 32 y on + 1
Although the perspective transform is non-linear, it can be reduced to a linear
transform using the homogeneous coordinates. The perspective transform is
collinear that maps a line into another line and a rectangle into a quadrilateral.
Therefore, Eq. (5.28) is more restricted than Eq. (5.27) for PSP and TSP
applications.
Before the image registration technique is applied, the targets must be
identified and their centroid locations in images must be determined. The target
centroid ( xc , y c ) is defined as
¦¦ x I ( x , y ) / ¦¦ I ( x , y ) ,
= ¦¦ y I ( x , y ) / ¦¦ I ( x , y )
xc =
i
i
i
i
i
yc
i
i
i
i
i
(5.29)
where I ( xi , y i ) is the gray level on an image. When a target contains only a few
pixels and the target contrast is not high, the centroid calculation using the
definition Eq. (5.29) may not be accurate. Another method for determining the
target location is to maximize the correlation between a template f ( x , y ) and the
target scene I ( x , y ) (Rosenfeld and Kak 1982). The correlation coefficient C fI
is defined as
104
5. Image and Data Analysis Techniques
C fI =
³³ f ( x + x , y + y )I ( x , y )dxdy
³³ f ( x , y )dxdy ³³ I ( x , y )dxdy
0
2
0
.
(5.30)
2
For the continuous functions f ( x , y ) and I ( x , y ) , one can determine the location
( x0 , y0 ) of the target by maximizing C fI . However, it is found that for small
targets in images, sub-pixel misalignment between the template and the scene can
significantly reduce the value of C fI even when the scene contains a perfect
replica of the template. To enhance the robustness of a localization scheme,
Ruyten
(2001b)
proposed
an
augmented
template
f ( x , y ) = f 0 ( x , y ) + f x ∆ x + f y ∆ y , where f 0 ( x , y ) represented a conventional
template and f x and f y are the partial derivatives of f ( x , y ) . The additional
shift parameters ( ∆ x , ∆ y ) allowed more robust and accurate determination of the
target locations.
In PSP and TSP measurements, operators can manually select the targets and
determine the correspondence between the wind-off and wind-on images.
However, PSP and TSP measurements with multiple cameras in production wind
tunnels may produce hundreds or thousands of images in a given test; thus, image
registration becomes very labor-intensive and time-consuming. It is non-trivial to
automatically establish the point-correspondence between images taken by
cameras at different viewing angles and positions. This problem is generally
related to the epipolar geometry in which a point on an image corresponds to a
line on another image (Faugeras 1993).
Ruyten (1999) discussed the
methodologies for automatic image registration including searching targets,
labeling targets and rejecting false targets. Unlike ad-hoc techniques, the
searching technique based on photogrammetric mapping is more rigorous. Once
cameras are calibrated and the position and attitude of a tested model are
approximately given by other techniques (such as accelerators and
videogrammetric techniques), the targets in the images can be found using
photogrammetric mapping from the 3D object space to the image plane (see
Section 5.1).
The aforementioned methods of using a single transformation for the whole
image is a global approach for image registration. A local approach proposed by
Shanmugasundaram and Samareh-Abolhassani (1995) divides an image domain
into triangles connecting a set of targets based on the Delaunay triangulation (de
Berg et al. 1998). For a triangle defined by the vertex vectors R1 , R2 and R2 , a
point in the plane of the triangle can be described by a vector
u1 R1 + u 2 R2 + u 3 R3 , where (u 1 , u 2 , u 3 ) are referred to as the parametric
(barocentric) coordinates and a constraint u1 + u 2 + u 3 = 1 is imposed. When a
wind-on pixel is identified inside a triangle and its parametric coordinates is given,
the corresponding wind-off pixel can be determined by using the same parametric
coordinates in the vertex vectors of the corresponding triangle in the wind-off
image. Finally, the image intensity at that pixel is mapped from the wind-on
5.5. Conversion to Pressure
105
image to the wind-off image. This approach is basically a linear interpolation
assuming that the relative position of a point inside a triangle to the vertices is
invariant under a transformation from the wind-on image to the wind-off image.
Weaver et al. (1999) proposed a so-called Quantum Pixel Energy Distribution
(QPED) algorithm that utilizes local surface features to calculate a pixel shift
vector using a spatial correlation method. The local surface features could be
targets, pressure taps, and dots formed from aerosol mists in spraying on a
basecoat. Similar to particle image velocimetry (PIV), the QPED algorithm can
give a field of the displacement vectors when the registration marks or features are
dense enough. Based on the shift vector field, the wind-on image can be
registered. Although the QPED algorithm is computationally intensive, it can
provide the local displacement vectors at certain locations to complement the
global image registration techniques. A comparative study of different image
registration techniques was made by Venkatakrishnan (2003).
5.5. Conversion to Pressure
In PSP measurements, conversion of the luminescent intensity to pressure is
complicated by the temperature effect of PSP especially when the surface
temperature distribution is not known. Empirically, a priori calibration relation
between air pressure and the relative luminescent intensity is expressed by a
polynomial
2
I ref
§ I ref ·
p
¸ .
= C1 ( T ) + C2 ( T )
+ C3 ( T ) ¨¨
¸
I
pref
© I ¹
(5.31)
The experimentally determined coefficients C1 , C2 and C3 in Eq. (5.31) can be
expressed as a polynomial function of temperature. If a distribution of the surface
temperature is not given and the thermal conditions in a priori laboratory
calibrations are different from those in wind tunnel tests, a priori relation Eq.
(5.31) cannot be directly applied to conversion to pressure. To deal with this
problem, a short-cut approach is in-situ PSP calibration that directly correlates the
luminescent intensity to pressure data from taps distributed on a model surface. In
this case, the constant coefficients C1 , C2 and C3 in Eq. (5.31) are determined
using least-squares method to achieve the best fit to the pressure tap data over a
certain range of pressures. Through in-situ calibration, the effect of a non-uniform
surface temperature distribution is actually absorbed into a precision error of leastsquares estimation. When the temperature effect of PSP overwhelms a change of
the luminescent intensity produced by pressure, in-situ calibration has a large
precision error. In addition, when the pressure tap data do not cover the full range
of pressure on a surface, in-situ PSP conversion may lead to a large bias error in
data extrapolation outside the calibration range of pressures.
106
5. Image and Data Analysis Techniques
A hybrid method between in-situ and a priori methods is the so-called K-fit
method originally suggested by M. Morris and recapitulated by Woodmansee and
Dutton (1998). Eq. (5.31) is re-written as
2
ª
§ I off ·
§
I off · º
p
¸ + C3 ( T ) ¨ K I
¸ »,
= K P «C1 ( T ) + C2 ( T )¨¨ K I
¨
«
poff
I ¸¹
I ¸¹ »
©
©
¬
¼
(5.32)
where I off = I ( poff ,Toff ) is the luminescent intensity in the wind-off conditions,
and K I = I ref / I off and K P = pref / poff are called the K-factors. The reference
conditions under which a priori calibration is made in a laboratory are generally
different from the wind-off conditions in a wind tunnel. While the factor
K P = pref / poff is known, the factor K I = I ref / I off is generally not known and
has to be determined since illumination conditions and photodetectors used in
laboratory may be different from those in wind tunnel. Given the coefficients C1 ,
C2 and C3 at a known temperature on an isothermal surface, K I can be
determined using a single data point from pressure taps. When the surface
temperature data near a number of pressure taps are provided by other techniques
like TSP and IR camera, a more accurate value of K I can be obtained using leastsquares method with larger statistical redundancy. In the worst case where the
surface temperature distribution is totally unknown, assuming an average
temperature over the surface, we still able to estimate K I by fitting the pressure
tap data. Similar to in-situ calibration, the effect of a non-uniform temperature
distribution is absorbed into a precision error of least-squares estimation for K I .
Bencic (1999) used a similarity variable of the luminescent intensity to scale
the temperature effect of certain PSP
I ref
I
= g( T )
corr
I ref
I
,
(5.33)
where g( T ) was a function of temperature to be determined by a priori
calibration. Under this similarity transformation, the calibration curves for the
paint at different temperatures collapsed onto a single curve with the temperatureindependent coefficients, i.e.,
I ref
p
= C1 + C2
I
pref
corr
§ I ref
+ C3 ¨
¨ I
©
2
·
¸ .
¸
corr ¹
(5.34)
In this case, instead of using a 2D calibration surface in the parametric space, only
a single one-parameter relation Eq. (5.34) was used to convert the luminescent
intensity ratio to pressure. Bencic (1999) found that this similarity was valid for a
5.6. Pressure Correction for Extrapolation to Low-Speed Data
107
Ruthenium-based PSP used at NASA Glenn. In fact, as pointed out in Section
3.6, this similarity is a property of the so-called ‘ideal’ PSP that obeys the
following relations (Puklin et al. 1998; Coyle et al. 1999)
I ( p,T ) / I ( p,Tref ) = g( T ) ,
I ref ( pref ,Tref )
I ( p,Tref )
= g( T )
I ref ( pref ,Tref )
I ( p,T )
.
(5.35)
Puklin et al. (1998) found that PtTFPP in FIB polymer was an ‘ideal’ PSP over a
certain range of temperatures. Note that this similarity (or invariance) is not the
universal property of a general PSP.
5.6. Pressure Correction
for Extrapolation to Low-Speed Data
PSP is particularly effective in high subsonic, transonic and supersonic flow
regimes. However, in low-speed flows where the Mach number is typically less
than 0.3, PSP measurement is a challenging problem since a very small pressure
change may not be sufficiently resolved by PSP. The major error sources, notably
the temperature effect, image misalignment and CCD camera noise, must be
minimized to obtain acceptable quantitative pressure results at low speeds. The
resolution of PSP measurements is eventually limited by the photon shot noise of
a CCD camera. Liu (2003) proposed a pressure-correction method as an alterative
to extrapolate low-speed pressure data without directly attacking the intrinsic
difficulty of PSP instrumentation for low-speed flows. This method is able to
obtain the incompressible pressure coefficient from PSP measurements at suitably
higher Mach numbers (typically Mach 0.3-0.6) by removing the compressibility
effect.
It is noticed that there is a significant difference between the responses of the
absolute pressure p and the pressure coefficient C p to the freestream Mach
number M ∞ .
The sensitivity of C p to the Mach number for M ∞2 << 1 is
estimated by
M ∞ dC p
(5.36)
≈ M ∞2 .
C p dM ∞
In contrast, the sensitivity of pressure to the Mach number is approximately
M∞
d( p − p∞ )
S p − p∞ =
≈ 2.
(5.37)
( p − p ∞ ) dM ∞
SC p =
For
M ∞2 << 1 ,
SC p
is much smaller than
S p − p∞ ; for
M ∞ = 0.3
and
dM ∞ / M ∞ = 10% , the relative change of the absolute pressure difference is
d ( p − p∞ ) /( p − p∞ ) ≈ 20% , while the relative change of C p is only
108
5. Image and Data Analysis Techniques
dC p / C p ≈ 0.9% .
Clearly, PSP can take the advantage of the relative
insensitivity of C p to the Mach number to obtain the approximate incompressible
pressure coefficient distribution at suitably higher Mach numbers. Furthermore,
the compressibility effect can be corrected using the pressure-correction methods.
Historically, the pressure-correction formulas were derived in order to
extrapolate the pressure coefficient in subsonic compressible flows from the
incompressible flow theory and low-speed pressure measurements. In contrast,
for PSP applications, the pressure-correction formulas are used to transform the
compressible C p to the corresponding incompressible C pinc . The theoretical
foundation for pressure correction in 2D potential flows is well established. The
linearized theory for subsonic compressible flows gives the Prandtl-Glauert rule
(Anderson 1990)
C p = C pinc / 1 − M ∞2 .
(5.38)
The use of a hodograph solution of the non-linear potential equation gives the
Karman-Tsien rule (Anderson 1990)
C pinc
Cp =
.
(5.39)
§
·C
2
M
pinc
¨
¸
∞
1 − M ∞2 + ¨
¨ 1 + 1 − M ∞2 ¸¸ 2
©
¹
For PSP measurements on 2D airfoils at suitably high Mach numbers, both the
Prandtl-Glauert rule and Karman-Tsien rule can be used to recover the
incompressible pressure coefficient. Bell and Hand (1998) used the PrandtlGlauert rule for the purpose of improving the image ratioing procedure of PSP to
obtain a pseudo wind-off pressure coefficient at a suitably low velocity. For
complex 3D viscous flows such as separated flows, however, a general pressurecorrection method is required.
Liu (2003) developed an iterative pressure-correction method for 3D flows.
For M ∞2 << 1 , a pressure field can be generally expressed as a power series of
M ∞2 . The pressure-correction formula for a general surface Z = S ( X ,Y ) has a
functional form composed of an incompressible term and a compressible
correction term
C p ≈ C pinc + M ∞2 F [ X ,Y , S ( X ,Y )] .
(5.40)
Eq. (5.40) is valid for not only potential flows, but also complex viscous flows
over a 3D body. Because C pinc = C pinc [ X ,Y , S ( X ,Y )] is a function of X and Y,
we can, in principle, eliminate X in the correction function F [ X ,Y , S ( X ,Y )] by
using C pinc and Y. Therefore, since the correction function F [ X ,Y , S ( X ,Y )] is
not specified yet, the equivalent form to Eq. (5.40) is
C p ≈ C pinc + M ∞2 F ( C pinc ,Y ) .
(5.41)
Eq. (5.41) indicates that the pressure correction in 3D flows depends on not only
C pinc , but also one space coordinate Y. Note that the functional form of Eq. (5.41)
remains valid after the coordinate Y is switched to another coordinate X. When
5.6. Pressure Correction for Extrapolation to Low-Speed Data
109
C p does not change along the coordinate Y, Eq. (5.41) is naturally reduced to the
method for 2D and axisymmetrical flows.
polynomial function, Eq. (5.41) becomes
By writing F ( C pinc ,Y ) as a
N
¦ a (Y )C
C p ≈ C pinc + M ∞2
n
n
pinc
.
(5.42)
n =0
When the distributions of C p and C pinc are known along an intersection between
the plane Y = const . and the surface Z = S ( X ,Y ) , the coefficients a n ( Y ) can be
determined using least-squares method. In wind tunnel measurements, pressure
tap data in subsonic flow and the corresponding low-speed flow can be used to
establish the relationship between C p and C pinc . However, this approach is not
convenient for PSP measurements in wind tunnels since extra pressure tap data are
required. Here, an iterative method is proposed to recover C pinc from C p data at
two different subsonic Mach numbers M ∞1 and M ∞ 2 . The biggest advantage of
this method is that C pinc can be directly obtained from two PSP images taken at
M ∞1 and M ∞ 2 without use of additional pressure tap data.
Denote C p 1 and C p 2 as the pressure coefficients at M ∞1 and M ∞ 2 ,
respectively, and assume M ∞1 < M ∞ 2 . Given the distributions of C p 1 and C p 2
along an intersection between the plane Y = const . and surface Z = S ( X ,Y ) , we
need to solve the following equations to recover C pinc and a n ( Y )
N
C p1 ≈ C pinc + M ∞2 1
¦ a ( Y )C
n
n
pinc
n =0
N
C p 2 ≈ C pinc + M ∞2 2
¦ a ( Y )C
n
n
pinc
.
(5.43)
n =0
An iteration scheme for solving Eq. (5.43) is described below.
(1) Give the initial distribution C pinc( k ) = C p1 (k = 0) as a function of X along an
intersection between Y = const . and Z = S ( X ,Y ) in the object space (a row or
column in the image plane). Here, k is the iteration index number; (2) Determine
the coefficients a n( k ) ( Y ) ( n = 0 ,1 N ) in the polynomial from a system of
equations
( C p 2 − C pinc( k ) ) / M ∞2 2 =
N
n
¦ a n( k ) ( Y ) C pinc
(k )
using
least-squares
n =0
method; (3) Substitute a n ( Y ) into C pinc( k +1 ) ≈ C p1 − M ∞2 1
N
n
¦ a n( k ) ( Y ) C pinc
(k )
to
n =0
obtain the corrected value C pinc( k +1 ) ; (4) Go back to Step (2), replace C pinc( k ) by
the corrected value
C pinc( k +1 )
and iterate until the converged results
110
5. Image and Data Analysis Techniques
C pinc = Lim C pinc( k ) and a n ( Y ) = Lim a n( k ) ( Y ) ( n = 0 ,1 N ) are obtained; (5)
k →∞
k →∞
Output the final C pinc = C pinc [ X ,Y , S ( X ,Y )] and a n ( Y ) .
After processing for a large set of intersections, we can recover the distribution
of C pinc on the whole surface. Unlike the classical pressure-correction formulas
for 2D flows, this iterative method is a non-local approach that has to be done
along an intersection. The selection of the order N of the polynomial in Eq. (5.43)
depends on the complexity of the Mach number effect on the pressure distribution
along the intersection. For 2D flows and near-2D flows, N = 2 is sufficient; for
more complex flows, the order of the polynomial could be higher. The number of
available data points on an intersection eventually limits the order of the
polynomial.
For PSP, data processing is typically done in the image plane rather than in the
object space. Therefore, for convenience, the pressure-correction method should
be used in the image plane. The aforementioned analysis is made in an arbitrary
object-space coordinate system ( X ,Y , Z ) or a general non-orthogonal curvilinear
coordinate system on a surface. Since there is a one-to-one projection mapping
between the image plane ( x , y ) and the surface Z = S ( X ,Y ) , the iterative
pressure correction method can be directly applied to rows or columns in PSP
images.
There are limitation conditions for application of the iterative pressurecorrection method (actually for any pressure-correction method). First, the two
Mach numbers M ∞1 and M ∞ 2 should be lower than the critical Mach number at
which flow becomes sonic at certain point on a surface. Secondly, the pressurecorrection method relies on an assumption that the pressure distribution does not
have a drastic change due to the Reynolds number effect as the Mach number
increases from M ∞ = 0 to M ∞1 and M ∞ 2 . When the Reynolds number effect on
pressure overwhelms the effect of the Mach number, the pressure-correction
method cannot produce correct results because the flow pattern has been
qualitatively changed. This situation may happen on a high-lift model under
certain testing conditions in certain flow separation regions that are particularly
sensitive to the Reynolds number effect. Fortunately, there is a large class of
flows in which the Reynolds number does not significantly affect the surface
pressure distribution, such as attached flows and certain separated flows whose
separation and re-attachment lines are fixed. For these flows, the pressurecorrection method is applicable.
The iterative pressure-correction method was validated for flows over a circular
cylinder, sphere, prolate spheroid, transonic body and delta wing (Liu 2003).
Figure 5.16 shows the incompressible C pinc distribution on a circular cylinder
recovered by the iterative pressure-correction method along with the results
obtained using the Prandtl-Glauert rule and Karman-Tsien rule. The iterative
method produced excellent recovery of C pinc given by the incompressible solution
of potential flow over a cylinder (Lighthill 1954). The Karman-Tsien rule also
gave a good correction while the Prandtl-Glauert rule was not accurate in the low-
5.6. Pressure Correction for Extrapolation to Low-Speed Data
111
pressure region C p = [ −3,−2 ] . The iterative method used the C p distributions at
M ∞1 = 0.4 and M ∞ 2 = 0.6 . The order of polynomial was N = 2 and the solution
for C pinc converged after 10 iterations. Both the Karman-Tsien rule and PrandtlGlauert rule used C p at M ∞ = 0.4 to recover C pinc . Figure 5.17 shows the
pressure correction for a prolate spheroid of a fineness ratio of 6 at the angle of
o
attack of 5.6 and zero ellipsoidal coordinate (Matthews 1953). The iterative
method used C p data at M ∞1 = 0.6 and M ∞ 2 = 0.8 . Even though these Mach
numbers are quite high, the iterative method still produced good results since the
Mach numbers were less than the critical Mach number of 0.904 in this case. To
examine the capability of the iterative pressure-correction method for complex
vortical separated flows, it was also used to recover C pinc on the upper surface of
o
a 65 delta wing; the recovered C pinc distributions showed a correct trend as the
Mach number increases.
2
Cpinc, Iterative method
Cpinc, Karman-Tsien
Cpinc, Prandtl-Glauert
Incompressible solution
1
0
Cp
-1
-2
-3
Mach 0.4
-4
Mach 0.6
Cylinder
-5
0
1
2
3
theta (radian)
Fig. 5.16. Pressure correction for a circular cylinder to recover the incompressible pressure
coefficient. From Liu (2003)
112
5. Image and Data Analysis Techniques
0.4
Prolate spheroid
of fineness ratio 6
0.3
Cpinc, Iterative method
Mach 0.0
Mach 0.6
Mach 0.8
Cp
0.2
0.1
AoA = 5.6 deg
omega = 0 deg
0.0
-0.1
-0.2
0
10
20
30
40
50
Percent distance from nose
Fig. 5.17. Pressure correction for a prolate spheroid to recover the incompressible pressure
coefficient. From Liu (2003)
5.7. Generation of Deformed Surface Grid
For a more accurate representation of data, PSP and TSP results in images should
be mapped onto a deformed surface grid of a model rather than a rigid surface grid
when the model undergoes a large deformation in wind tunnel tests. Aeroelastic
deformation data for a model can be obtained using videogrammetric model
deformation (VMD) measurement technique (Burner and Liu 2001). Hence, PSP
and TSP systems should be integrated with a VMD system for fusion of pressure
and temperature data with deformation data (Bell and Burner 1998; Liu et al.
1999). There are two approaches for integration of PSP/TSP with VMD. The
first approach uses PSP/TSP simultaneously with VMD as a separate and
independent system, while VMD, that is operated under the PSP/TSP lighting and
surface conditions, provides deformation data for generating a deformed surface
grid. The advantage of this approach is that the structure of a PSP/TSP system is
not changed and PSP/TSP operation suffers no interference from VMD operation
in large production wind tunnels. In contrast, the second approach uses the same
camera for both PSP/TSP and VMD measurements at the same time; VMD
software is integrated as an additional part of the PSP/TSP software package.
Instead of a nearly normal view of a camera for pure PSP/TSP application, the
combined system requires an oblique viewing angle of a camera to achieve good
position sensitivity for VMD measurements.
Usually, VMD gives wing deformation characterized by the twist and bending
of a wing. When the local translation and twist are measured by VMD at different
spanwise locations of a wing, a transformation of translation and rotation can be
used to generate a deformed surface grid of the wing. At a spanwise location Y,
5.7. Generation of Deformed Surface Grid
113
the deformed coordinate ( X ' ,Y ' , Z' ) on a wing surface grid is locally related to
the non-deformed grid coordinate ( X ,Y , Z ) by
§ X' ·
§ X · § T ( Y )·
¸
¨ ¸ = R( Y )¨ ¸ + ¨ x
¨ Z' ¸
¨ Z ¸ ¨ T ( Y )¸ .
© ¹
© ¹ © z
¹
(5.44)
The translation vector at a spanwise location Y of the wing is (Tx , Tz ) and the
rotational matrix is
sin ștwist ·
§ cos ștwist
¸,
(5.45)
R(Y) = ¨¨
¸
© − sin ș twist cos ș twist ¹
where the twist ș twist is a function of the spanwise location Y. When the bending
relative to the wingspan is small, the spanwise location does not change much,
i.e., Y ' ≈ Y , and the wing airfoil section remains the same. For illustration, we
consider a fictional wing with a NACA0012 airfoil section and assume that the
spanwise distributions of twist and bending are given by ștwist = − 5(Y/b)3 ,
Tz = 0.08 b (Y/b)3 and Tx = 0 , where b is the semi-span of the wing. Figure 5.18
shows a deformed surface grid generated using a transformation of translation and
rotation.
Fig. 5.18. Generation of a deformed surface grid of a wing based on videogrammetric
deformation measurements. From Liu et al. (1999)
6. Lifetime-Based Methods
Compared with the widely used intensity-based method, the greatest advantage of
the lifetime-based method is that a relation between the luminescent lifetime and
pressure is not dependent on the illumination intensity. Therefore, the problem
associated with non-uniform illumination in the intensity-based method becomes
essentially irrelevant to the lifetime method. Theoretically speaking, lifetime
measurement is also insensitive to luminophore concentration, paint thickness,
photodegradation and paint contamination; thus a wind-off reference intensity
image (or signal) is not required and the troubles associated with model
deformation do not exist. The lifetime method for PSP and TSP can be applied to
both a laser scanning system and an imaging system. Davies et al. (1995)
developed a pulsed laser scanning system to directly determine the luminescent
lifetime and used it to measure the pressure distributions on a cylinder in subsonic
flows and on a wedge at Mach 2. Torgerson et al. (1996) developed a portable,
modulated, two-dimensional laser scanning system that can simultaneously
measure both the luminescent intensity and phase angle; this system was used to
measure the surface pressure distributions in a low-speed impinging jet and on an
airfoil in transonic flow. The system was further refined by Lachendro et al.
(1998) and used to measure the pressure distributions on a wing of a Beechjet in
flight tests. A fluorescent lifetime imaging (FLIM) system for PSP and TSP has
become promising as solid-state imaging technology makes a rapid advance. The
FLIM system, originally proposed by biochemists for oxygen detection in a small
area (Szmacinski and Lakowicz 1995; Hartmann and Ziegler 1996), was used for
PSP measurements in wind tunnels at DERA (Holmes 1998). DERA’s FLIM
system comprised a phase-sensitive camera, modulated blue LED array,
associated control hardware and computer. This Chapter discusses the response of
the luminescent emission to a time-varying excitation light and describes the
luminescent lifetime measurement techniques, including the pulse method, phase
method, amplitude demodulation method and gated intensity ratio method.
Although the discussion is focused on PSP, these techniques are generally
applicable to TSP as well. Measurement uncertainty of the lifetime methods is
discussed in Chapter 7. Similar analyses of the lifetime-based techniques were
given by Goss et al. (2000) and Bell (2001).
116
6. Lifetime-Based Methods
6.1. Response of Luminescence
to Time-Varying Excitation Light
6.1.1. First-Order Model
The lifetime method for PSP and TSP is based on the response of luminescence to
a time-varying excitation light. The response of the luminescent emission I from a
paint to an excitation light E(t) can be described as a first-order system
dI / d t = − I / IJ + E( t) ,
where IJ is the luminescent lifetime.
solution to Eq. (6.1) is
I (t) =
³
t
0
(6.1)
With the initial condition I(0) = 0 , a
exp[ − ( t − u ) / IJ ] E( u ) du .
(6.2)
For a pulse light E(t) = Am į(t) , the luminescent response is simply an
exponential decay
I (t) = Am exp( − t / IJ ) .
(6.3)
We consider a general periodic excitation light that is expressed as a Fourier series
§a
E(t) = Am ¨ 0 +
¨ 2
©
∞
¦[a
n =1
n
·
cos(n Ȧt ) + bn sin(n Ȧ t ) ] ¸ ,
¸
¹
(6.4)
where Ȧ = 2ʌ f is the circular frequency of the excitation light. Substitution of
Eq. (6.4) into Eq. (6.2) yields the luminescent response after a short transient
process
∞
§ a
a n cos(n Ȧt − ijn ) + bn sin(n Ȧ t − ijn ) ·¸
I (t) = Am IJ ¨¨ 0 +
(6.5)
¸¸ .
2 2 2
¨ 2
+
n =1
1
n
Ȧ
IJ
©
¹
¦
Here, the phase angles ijn are related to the luminescent lifetime by
tan ijn = n Ȧ IJ .
(6.6)
In the simplest case where the sinusoidally modulated excitation light is
E(t) = Am [ 1 + H sin( Ȧ t )] , the luminescent response Eq. (6.5) is reduced to
I (t) = Am IJ [ 1 + H M eff sin(Ȧt − ij) ] ,
(6.7)
6.1. Response of Luminescence to Time-Varying Excitation Light
117
where M eff = (1 + IJ 2 Ȧ 2 ) −1 / 2 is the effective amplitude modulation index, Am is
the amplitude, and H is the modulation depth. The phase angle ij is related to
the luminescent lifetime simply by
tan ij = Ȧ IJ .
(6.8)
Other waveforms of the excitation light include square and triangle. Figure 6.1
shows the luminescent response to typical periodic excitations with the square,
sine and triangle waveforms for the non-dimensional lifetime of Ȧ IJ = ʌ /10 .
2 .5
E x c ita tio n L ig h t
Intensity
2 .0
L u m in e s c e n c e
1 .5
1 .0
0 .5
0 .0
0
2
4
6
8
10
12
10
12
10
12
ω t (ra d ia n )
(a) Square waveform
4 .0
E x c ita tio n L ig h t
3 .5
L u m in e s c e n c e
Intensity
3 .0
2 .5
2 .0
1 .5
1 .0
0 .5
0
2
4
6
8
ω t ( r a d ia n )
(b) Sine waveform
5
E x c ita tio n L ig h t
Intensity
4
L u m in e s c e n c e
3
2
1
0
0
2
4
6
8
ω t (ra d ia n )
(c) Triangle waveform
Fig. 6.1. Response of luminescence to time-varying excitations of the square, sine and
triangle waveforms for Ȧ IJ = ʌ /10
118
6. Lifetime-Based Methods
6.1.2. Higher-Order Model
In a micro-heterogeneous polymer matrix, the multiple-exponential luminescent
emission decay can be observed in contrast to the single-exponential decay in a
homogeneous medium (Carraway et al. 1991a; Sacksteder et al. 1993; Xu et al.
1994). This is associated with the fact that the host matrix has domains that vary
with respect to their interaction with the luminescent probe molecules; as a result,
the excited molecules decay at different rates, depending on their environments.
Consider a paint system consisting of a number of independently emitting species
with different single-exponential lifetimes IJ i ( i = 1, 2, 3, ) and relative
contributions. The multiple-exponential luminescent decay is described as
I (t) =
Į i exp( − t / IJ i ) ,
(6.9)
¦
where Į i is the weighting constant for the ith component. The luminescent
lifetime of each component obeys the Stern-Volmer relation
IJ 0 i / IJ i = 1 + K SV i p ,
(6.10)
where K SV i is the Stern-Volmer coefficient for the ith component. Hence, a
higher-order model is needed to describe the luminescent response of an
inhomogeneous PSP to a time-varying excitation light. We consider a third-order
model
a 0 d 3 I / dt 3 + a 1 d 2 I / dt 2 + a 2 dI / dt + a 3 I = E( t ) .
(6.11)
With the initial conditions I ( 0 ) = I' ( 0 ) = I' ' ( 0 ) = 0 , a solution for (6.11) is
I (t) =
³
3
t
E( u )
0
¦ Į exp[ − ( t − u ) / IJ
i
i
] du .
(6.12)
i =1
The lifetimes IJ i are related to the weighting constants Į i through the roots of the
characteristic equation a 0 s 3 + a 1 s 2 + a 2 s + a 3 = 0 . The weighted mean lifetime
is usually expressed as < IJ > = ¦ Į i IJ i / ¦ Į i . A general model for the nonexponential decay of luminescence was discussed by Ruyten (2004) and Ruyten
and Sellers (2004) considering the continuous decay rate spectrum and excitation
response function.
6.2. Lifetime Measurement Techniques
6.2.1. Pulse Method
Our goal is to measure the luminescent lifetime and to determine air pressure
through the Stern-Volmer relation. A variety of methods can be used to extract
the lifetime from the luminescent response to a time-varying excitation light. The
pulse method is the most direct method widely used in photochemistry (Lakowicz
6.2. Lifetime Measurement Techniques
119
1991, 1999). After PSP is excited by a pulsed illumination light, the luminescent
decay is measured using a fast-responding photodetector and acquired using a PC
or an oscilloscope. The lifetime is calculated by fitting the time-resolved data
with a single exponential function or a multiple-exponential function. This direct
time-domain approach was used by Davies et al. (1995) for lifetime measurements
of PSP. For certain PSP with multiple distinct lifetimes, the pulse method allows
simultaneous determination of pressure and temperature if the lifetimes have
sufficiently different Stern-Volmer coefficients as a function of temperature. In
this case, given the lifetimes ( IJ i ), a system of equations for pressure and
temperature are
IJ i ref
p
= Ai ( T ) + Bi ( T )
, ( i = 1, 2, N , N ≥ 2 )
(6.13)
IJi
p ref
In principle, unknown pressure and temperature can be simultaneously determined
by solving Eq. (6.13).
6.2.2. Phase Method
The phase method is a frequency-domain technique that detects a phase shift of
the luminescent signal with respect to the modulated excitation light (Torgerson et
al. 1996; Torgerson 1997). Figure 6.2 shows the working principle of the phase
method with a lock-in amplifier.
For the sinusoidal excitation light
E(t) = Am [ 1 + H sin( Ȧ t )] , the corresponding modulated luminescent signal
from a photodetector is mixed with the in-phase and quadrature reference signals,
i.e., sin( Ȧ t ) and cos( Ȧ t ) . Next, the use of a low-pass filter generates the DC
components Vc = − Am IJ H M eff sin (ij ) and Vs = Am IJ H M eff cos (ij ) , which are related
to the phase angle ij between the luminescent emission and excitation light. A
ratio between these filtered signals yields a quantity tan ij = Ȧ IJ = − Vc / Vs that is
uniquely related to the lifetime for a fixed modulation frequency. Therefore,
pressure is given by
§
·
−1 ¨ Ȧ IJ 0
¸
p = K SV
(6.14)
¨ tan ij − 1¸ .
©
¹
The sensitivity of the phase angle ij to pressure is defined as
dϕ
∂τ
ω
Sp =
.
(6.15)
=
2
dp 1 + ( ωτ ) ∂p
The optimal modulation frequency to achieve the maximum sensitivity S p is
(6.16)
ȦIJ = 1 .
It must be noted that the maximum sensitivity to pressure does not tell the whole
story if the noise is not taken into account. Besides good sensitivity to pressure,
the signal-to-noise ratio (SNR) should be also considered in order to select the
optimal modulation frequency. At a higher frequency, the modulation amplitude
120
6. Lifetime-Based Methods
and DC components from PSP decrease, resulting in a lower SNR. Figure 6.3 is a
Bode plot showing the response of a typical PSP, PtTFPP in polymer/ceramic
composite, to the modulation frequency; the behavior of this PSP is very close to
the first-order system.
E(t) = A m [ 1 + H sin( Ȧ t )]
PSP
I (t) = A m IJ [ 1 + H M
cos( Ȧt)
Mixer
eff
sin( Ȧ t − ij) ]
Low-Pass
Filter
V c = − Am IJ H M
sin( Ȧt)
Mixer
Low-Pass
Filter
eff
sin( ij )
V s = Am IJ H M
eff
cos( ij )
Divider
tan( ij ) = Ȧ IJ = − V c / V s
Fig. 6.2. Block diagram of the phase method
3
0
-3
-6
-9
0.07psi
2.32psi
5.37psi
8.49psi
11.42psi
14.68psi
dB
-12
-15
-18
-21
3rd Order Fit
-24
-27
-30
-33
102
103
104
105
Freqeuncy(Hz)
Fig. 6.3. The Bode plot of PSP (PtTFPP in polymer/ceramic composite) at –30°C. From
Lachendro (2000)
6.2. Lifetime Measurement Techniques
121
6.2.3. Amplitude Demodulation Method
The amplitude demodulation method was used for fluorescent lifetime
measurements of tagged biological specimens in a flow cytometer (Deka et al.
1994). For the sinusoidally modulated excitation light, the luminescent response
is given by Eq. (6.7) and the effective amplitude modulation index is
M eff = (1 + IJ 2 Ȧ 2 ) −1 / 2 . Clearly, for a fixed modulation frequency, the lifetime
can be obtained from measurement of the effective modulation index.
Combination of the Stern-Volmer relation Eq. (6.10) with M eff = (1 + IJ 2 Ȧ 2 ) −1 / 2
yields an expression for pressure as a function of the effective amplitude
modulation index M eff
§
·
¸
1 ¨ Ȧ IJ 0 M eff
p=
−1¸ .
(6.17)
¨
2
K SV ¨ 1 − M
¸
eff
©
¹
To measure the effective amplitude modulation index M eff , Deka et al. (1994)
used the following expression
I ( t ) − I min ( t min )
,
(5.18)
M eff = H −1 max max
I max ( t max ) + I min ( t min )
where t max and t min were the times at which the modulated oscillating luminescent
signal went through the maximum intensity I max ( t max ) and minimum intensity
I min ( t min ) , respectively.
Here, as illustrated in Fig. 6.4, a simpler scheme is proposed to determine
M eff by calculating the time-averaged quantities of the modulated luminescent
signal. Define the time-averaged oscillating luminescent signal
1 T
< I > = Lim
I ( t ) dt .
(6.19)
T →∞ 2T
−T
The mean and standard deviation of the luminescent intensity I(t) are
³
< I > = Am IJ and std ( I ) = < ( I − < I > )2 > 1 / 2 = Am IJ H M eff / 2 . Therefore,
taking a ratio between these quantities, we obtain a simple formula for the
effective amplitude modulation index M eff = (1 + IJ 2 Ȧ 2 ) −1 / 2
std ( I )
< E > std ( I )
.
(6.20)
=
<I>
std ( E ) < I >
It is emphasized that Eq. (6.20) is valid only for the sinusoidally modulated
excitation light E(t) = Am [ 1 + H sin( Ȧ t )] . Instrumentation for utilizing this
methodology is particularly simple since only the mean and standard deviation of
the sinusoidal luminescent intensity and excitation light intensity are required.
The optimal modulation frequency can be obtained by maximizing the
sensitivity of M eff to pressure
M eff = 2 H −1
122
6. Lifetime-Based Methods
2 Ȧ2 IJ
∂τ
.
2 2 3/2
dp
(1 + Ȧ IJ ) ∂p
The optimal modulation frequency for the maximum sensitivity is
Sp =
d ( M eff )
=
(6.21)
(Ȧ IJ)op = ( 1 + 7 ) / 3 ≈ 1.215 .
(6.22)
For a typical PSP, Ru(dpp) in GE RTV 118, having the lifetime IJ = 4.7 µs at the
ambient conditions, the optimal modulation frequency is 41 kHz. Figure 6.5
shows the effective amplitude modulation index M eff as a function of the relative
pressure p/p ref at different sinusoidal modulation frequencies for this PSP having
Clearly, the selection of the
the lifetime IJ = IJ ref / ( 0.17 + 0.84 p/p ref ) .
modulation frequency affects the performance of the system.
E(t) = A m [ 1 + H sin( Ȧ t )]
PSP
I (t) = A m IJ [ 1 + H M eff sin( Ȧ t − ij) ]
std ( I ) = 2 A m IJ H M eff
< I > = Am IJ
Divider
M eff = ( 1 + IJ 2 Ȧ 2 )−1 / 2 =
2 H −1 std ( I ) / < I >
Fig. 6.4. Block diagram of the amplitude demodulation method
6.2. Lifetime Measurement Techniques
123
1.2
Modulation frequency = 5 kHz
1.0
24 kHz
Meff
0.8
0.6
50 kHz
0.4
100 kHz
0.2
0.0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
P/Pref
Fig. 6.5. The effective amplitude modulation index M eff as a function of relative pressure
o
at different sinusoidal modulation frequencies for Ru(dpp) in GE RTV 118 for T = 20 C
and pref = 1 atm
6.2.4. Gated Intensity Ratio Method
The gated intensity ratio method, as illustrated in Fig. 6.6, gates the modulated
luminescent signal by applying two gain functions over two different intervals,
i.e.,
I1 =
³
I ( t ) G1 ( t ) dt and I 2 =
∆ T1
³
I ( t ) G 2 ( t ) dt ,
∆ T2
(6.23)
where the gain functions G1 ( t ) and G2 ( t ) are certain time-varying functions. A
ratio between the gated intensity integrals, I 2 / I 1 , is a function of the luminescent
lifetime for given modulation parameters. In the simplest case, the gain function
is a top-hat function or a square function where G1 ( t ) = G2 ( t ) = 1 in the time
intervals ǻ T1 and ǻ T2 and G1 ( t ) = G2 ( t ) = 0 elsewhere.
In this case, the
square waveform of G1 ( t ) and G2 ( t ) serves as an ‘on-off’ gating function. The
functional form for the excitation light and gain function can be selected to meet
the requirements for a specific test. Common combinations are a pulse excitation
with a square gain function (pulse-square), a sine-waveform excitation with a
square gain function (sine-square), a square-waveform excitation with a square
gain function (square-square), and a sine-waveform excitation with a sinewaveform gain function (sine-sine) (Goss et al. 2000).
124
6. Lifetime-Based Methods
E(t, r )
PSP
I (t, r )
I2 =
³
∆ T2
I1 =
I ( t , r ) G 2 ( t ) dt
³
∆ T1
I ( t , r ) G 1 ( t ) dt
Divider
I 2 /I 1 = F ( IJ )
Fig. 6.6. Block diagram of the gated intensity method
The modulated luminescent intensity is integrated over a gate time interval
from 0 to 1/2f (0 to π in Ȧ t ) and over a gate time interval from 1/2f to 1/f (π to
2π in Ȧ t ) relative to a modulated excitation light. For the Fourier-series-form of
the modulated excitation light Eq. (6.4), a ratio between the two integrals is
I 2 /I 1 =
³
1/f
³
I dt
1/2f
1/2f
0
Idt =
ʌ − D( ωτ )
,
ʌ + D( ωτ )
(6.24)
where
D(Ȧ IJ) =
2
a0
∞
[1 + ( −1) n +1 ] (a n n Ȧ IJ + bn )
n( 1 + n 2Ȧ2 IJ 2 )
¦
n =1
.
Obviously, the ratio I 2 / I 1 is only a function of the non-dimensional lifetime Ȧ IJ
and therefore is related to pressure when the modulation frequency is fixed. In
particular, the gated intensity ratio for the sinusoidally modulated excitation light
E(t) = Am [ 1 + H sin( Ȧ t )] has a simple form
I 2 /I 1 =
³
1/f
I dt
1/2f
³
1/2f
0
Idt =
ʌ (1 + Ȧ 2 IJ 2 ) − 2 H
ʌ (1 + Ȧ 2 IJ 2 ) + 2 H
.
(6.25)
6.2. Lifetime Measurement Techniques
125
Figure 6.7 shows the gated intensity ratio I 2 / I 1 as a function of the nondimensional lifetime Ȧ IJ for the excitation light with the square, triangle, sine and
cosine waveforms. Although the lifetime is always positive, Figure 6.7 plots the
ratio I 2 / I 1 over a range of −6 ≤ Ȧ IJ ≤ 6 to exhibit the global behavior of I 2 / I 1
as a function of Ȧ IJ . The behavior of I 2 / I 1 depends on the waveform of the
modulated excitation light. Figure 6.8 shows the gated intensity ratio I 2 / I 1 as a
function of the relative pressure p/p ref at different modulation frequencies for a
typical PSP, Ru(dpp) in GE RTV 118, when the sinusoidal excitation light has the
modulation depth of H = 1.
2.4
triangle wave
2.0
cosine wave
sine wave
I2/I1
1.6
1.2
0.8
0.4
square wave
0.0
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
ωτ (radian)
Fig. 6.7. The gated intensity ratio as a function of the non-dimensional luminescent lifetime
1.2
Modulation frequency
= 200 kHz
1.0
100 kHz
I2/I1
0.8
0.6
50 kHz
0.4
25 kHz
0.2
5 kHz
0.0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
P/Pref
Fig. 6.8. The gated intensity ratio as a function of pressure at different modulation
o
frequencies for Ru(dpp) in GE RTV 118 (T = 20 C and Pref = 1 atm) when the modulated
excitation is sinusoidal
126
6. Lifetime-Based Methods
For the sinusoidal excitation light, the non-dimensional modulation frequency
and modulation depth can be selected to achieve the greatest sensitivity of the
gated intensity ratio to pressure defined as
Sp =
d ( I 2 /I 1 )
8ʌ Ȧ 2 IJ H
∂τ
=
dp
[ʌ (1 + Ȧ 2 IJ 2 ) + 2 H] 2 ∂p
.
(6.26)
The optimal modulation frequency for the maximum sensitivity is
(Ȧ IJ)op =
3 ≈ 1.732 .
(6.27)
For Ru(dpp) in GE RTV 118 that has the lifetime of 4.7 µs at the ambient
conditions, the optimal modulation frequency is 59 kHz.
The appropriate modulation depth H can also be selected according to certain
criteria for a balance between the pressure sensitivity and SNR. It is noted that the
off-phase intensity I 2 = ( Am IJ / 2 f )[ 1 − ( 2 H / ʌ )(1 + Ȧ 2 IJ 2 )−1 ] decreases as H
increases and the normalized off-phase intensity at the optimal modulation
frequency is I 2 /(I 2 )H =0 = 1 − H / 2ʌ . Since the SNR is proportional to
[ I 2 /(I 2 )H =0 ] 1 / 2 = ( 1 − H / 2π )1 / 2 , the SNR is a decreasing function of H in a
range of 0 ≤ H ≤ 1 . On the other hand, the normalized sensitivity S p at the
optimal modulation frequency, which is proportional to H / ( 2π + H ) 2 , is an
increasing function of H in a range of 0 ≤ H ≤ 1 . Therefore, the appropriate
modulation depth H of about 0.5 is chosen to achieve both a high SNR and good
pressure sensitivity.
The gated intensity integrals I1 and I2 are taken over the intervals from 0 to 1/2f
(0 to π in Ȧ t ) and 1/2f to 1/f (π to 2π in Ȧ t ). The time variable t in these
integrals is relative to the modulated excitation light. The integration is carried
out immediately after the measurement system receives a trigger signal that is
synchronized with the modulated excitation light. The trigger signal can be
provided by a photodiode sensing the excitation light or a driver for the
modulator. In practice, however, the trigger signal may have a time delay relative
to the excitation light. The time delay, although small, may significantly alter the
relation between I 2 / I 1 and pressure especially when the modulation frequency is
high. For the sinusoidally modulated excitation light E(t) = Am [ 1 + H sin( Ȧ t )] ,
if the trigger signal has a time delay ǻt , the gated intensity ratio is
I 2 /I 1 =
³
1/f + ǻt
1/2f + ǻt
I dt
³
1/2f + ǻt
ǻt
Idt =
ʌ − 2 H cos(ij ) cos( ij − Ȧ ǻt)
ʌ + 2 H cos(ij ) cos( ij − Ȧ ǻt)
,
(6.28)
where cos( ij) = 1 / 1 + ( Ȧ IJ)2 . For a typical PSP, Ru(dpp) in GE RTV 118,
Figure 6.9 shows the relation between I 2 / I 1 and p/p ref for different phase shifts
Ȧ ǻt , where the sinusoidal modulation frequency is 25 kHz and the modulation
depth is H = 1. It is clear that the behavior of the relation is significantly affected
6.2. Lifetime Measurement Techniques
127
by the phase shifts Ȧ ǻt and the curve is even no longer monotonous when the
phase shift is large. The similar change also occurs for the excitation light having
other waveforms like the square waveform. This change due to the trigger signal
delay was observed in experiments.
0.9
ω∆t = π/2
0.8
0.7
I2/I1
0.6
0.5
π/3
0.4
π/4
0.3
0
0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
P/Pref
Fig. 6.9. The gated intensity ratio I 2 / I 1 as a function of p/p ref at different phase shifts
Ȧ ǻt for Ru(dpp) in GE RTV 118 (T = 20oC and Pref = 1 atm), where the sinusoidal
modulation frequency is 25 kHz and the modulation depth H is one
Furthermore, the gated intensity ratio method can be applied to the pulse
excitation light; in this case, the luminescent intensity signal is
I (t) = Am exp( − t / IJ ) . For two gating intervals [ t 0 , t 1 ] and [ t 2 , t 3 ] where
t 3 > t 2 > t 1 > t 0 is assumed, the gated intensity ratio is
I 2 /I 1 =
³
t3
t2
I dt
³
t1
t0
Idt =
exp( − t 3 / IJ ) − exp( − t 2 / IJ )
.
exp( − t 1 / IJ ) − exp( − t 0 / IJ )
(6.29)
For the given gating intervals, the ratio I 2 / I 1 is only related to the lifetime. This
integration approach was used as an alternative to the time-resolved pulse
approach, which was called the time-resolved multiple-gate method by Goss et al.
(2000). Bell (2001) discussed an optimization problem of the gating parameters
( t 0 , t1 , t 2 , t 3 ) to achieve the maximum sensitivity in an ICCD camera system. In
a limiting but representative case where the time t g divides the two gating
intervals [ 0 , t g ] and [ t g , ∞ ] ( t 0 = 0 , t 3 → ∞ , t 1 = t 2 = t g ), we have
I 2 /I 1 =
exp( − t g / IJ )
1 − exp( − t g / IJ )
.
(6.30)
128
6. Lifetime-Based Methods
Although the above methods utilize two gating intervals, three gating intervals can
be similarly used and therefore two gated intensity ratios like I 1 / I 2 and I 1 / I 3
can be obtained. If the two gated intensity ratios have sufficiently different
dependencies to pressure and temperature for certain PSP, the surface pressure
and temperature distributions can be determined simultaneously from the gated
intensity ratio images.
6.3. Fluorescence Lifetime Imaging
6.3.1. Intensified CCD Camera
The structure of an intensified CCD (ICCD) system is illustrated in Fig. 6.10.
After being impacted by a photon, the photocathode creates photoelectrons that
are amplified by the micro channel plate (MCP); the amplified electrons are
converted back into photons by a phosphor screen. These photons are relayed to a
CCD by either a fiber-optic bundle or a relay lens; the CCD creates the
photoelectrons that are measured. The biggest advantage of ICCD is its ability of
gating that allows the luminescent lifetime imaging over a painted area.
Electronic shutter action can be produced by pulsing the MCP voltage and the
gain can be modulated by simply changing the voltage on the intensifier. Figure
6.11 illustrates the luminescent lifetime imaging method with an ICCD.
Photo
Cathode
Micro Channel
Plate
A
Phosphor
Screen
Fiber-Optic
Taper
CCD
A
A
Fig. 6.10. Structure of ICCD and multiple photon-electron conversions in ICCD
< I > =
I (t, r )
Image
Intensifier
I(t, r ) G (t)
1
T
INT
³
T INT
I ( t , r ) G ( t ) dt
0
CCD
G (t)
Fig. 6.11. Diagram of lifetime imaging with ICCD for modulated illumination
6.3. Fluorescence Lifetime Imaging
129
For the pulse excitation light, the gain function is typically a top-hat function or
a square function. The luminescent signal is gated in two different intervals
during an exponential decay of luminescence and the gated intensity ratio is
related to the luminescent lifetime by Eq. (6.29). This approach was employed for
PSP measurements by Goss et al. (2000), Bencic (2001), Bell (2001), Baker
(2001), and Mitsuo et al. (2002). Another approach uses the sinusoidal excitation
light combined with either the square gain function (Holmes 1998) or sinusoidal
gain function (Lakowicz and Berndt 1991). Consider the sinusoidally modulated
excitation light E(t) = Am [ 1 + H sin( Ȧ t )] and the corresponding luminescent
signal from PSP is I (t) = Am IJ [ 1 + H M eff sin(Ȧt − ij) ] , where the effective
amplitude modulation index is M eff = (1 + IJ 2 Ȧ 2 ) −1 / 2 = cos( ij ) . When the gain
function has a square-waveform, the gated intensity ratio is given by Eq. (6.25).
Instead of using the square function, Lakowicz and Berndt (1991) adopted the
sinusoidal gain function for modulating the intensifier. When the MCP is
sinusoidally modulated, the gain function of the detector is
G(t) = G0 [ 1 + m D sin(Ȧt − ș D ) ] , where G0 is the intensifier gain without
applying a modulating signal, m D is the gain modulation depth, and ș D is the
detector phase angle relative to the modulated illumination light. The CCD
collecting photons over an integration time actually serves as an integrator; thus,
the signal output from the CCD is represented by a time-averaged intensity over
an integration time TINT
<I>=
1
TINT
³
TINT
0
I ( t , r ) G( t ) dt = Am IJ G0 [ 1 + 0.5 M eff m D cos( ij − ș D ) ] .
(6.31)
To extract the phase angle or lifetime from the CCD output < I > , several values
of < I > are obtained by changing the detector phase angle ș D . Therefore, a
system of equations is given for eliminating Am and G0 . These equations can be
solved using least-squares method to determine the phase angle ij that is related
to the luminescent lifetime τ. In the simplest case where only two different
detector phase angles ș D1 and ș D2 are chosen, a ratio between the two timeaveraged intensities at ș D1 and ș D2 is
< I > ( șD 2 ) / < I > ( șD1 ) =
1 + 0.5 m D cos( ij ) cos( ij − ș D 2 )
.
1 + 0.5 mD cos( ij ) cos( ij − ș D 1 )
(6.32)
Once the parameters m D , ș D1 , and ș D2 are given, the ratio in Eq. (6.32) is only
related to the phase angle ij . Lakowicz and Berndt (1991) used three different
detector phase angles to recover the luminescent lifetime. One shortcoming of the
intensifier CCD camera is that the SNR may be reduced due to quantum losses
and additive noise in the multiple-step photon-electron transfer processes.
130
6. Lifetime-Based Methods
6.3.2. Internally Gated CCD Camera
An internally gated CCD camera is promising for luminescent lifetime imaging.
Fisher et al. (1999) developed a phase-sensitive CCD camera system for twodimensional imaging of concentrations of radical species in reacting flows such as
turbulent flames. They modified a commercial scientific-grade CCD camera to
perform phase-sensitive imaging as well as to reduce the level of integrated
background light. In fact, this internally gated CCD camera has the capability to
selectively integrate the time-varying luminescent intensity either in-phase or outof-phase with respect to the modulated excitation light. A ratio between the outof-phase and in-phase images is related to the luminescent lifetime, and thus a
pressure field can be obtained from a luminescent lifetime image.
Modern CCD cameras available for industrial machine vision or scientific uses
possess many of the features required to construct a phase-sensitive imaging
system. Most notably, the feature commonly referred to as ‘electronic shuttering’
can be suitably modified to serve phase sensitive imaging or lifetime imaging.
The CCD array architecture employed by cameras capable of performing
electronic shuttering is referred to as an interline transfer array shown in Fig. 6.12.
It consists of photodiodes separated by vertical transfer registers that are covered
by an opaque metal shield that prevents direct entry of photoelectrons. Charge
accumulated in the photosensors can be transferred either to the vertical registers
or discarded in the substrate by supplying a high voltage to the Read Out Gate
(ROG) or the Over Flow Drain (OFD) respectively.
In order to perform phase-sensitive imaging, charge shifting and storage in the
CCD must be synchronized with the light-source modulation signal. This requires
appropriate modification of the camera controller logic, and of the camera head
circuitry and logic. Based on the modulation waveform, a suitable control signal
will be generated, which raises the ROG voltage and lowers the OFD voltage
during the in-phase half of the cycle. The in-phase luminescent signal is thus
integrated into the vertical register. In the out-of-phase half of the modulation
cycle, the ROG and OFD voltages are reversed, thus dumping the out-of-phase
light into the substrate. This process is repeated for a number of cycles until the
full-well capacity of the vertical registers is utilized to maximize the SNR.
Finally, after the desired integration time (or the number of cycles) the
accumulated charge in the vertical registers can be read out through the horizontal
register using conventional frame transfer techniques. The out-of-phase image
o
can be similarly obtained, the only difference being the introduction of a 180
phase lag between the modulation signal and the control signal described above.
As pointed out before, a ratio between the out-of-phase and in-phase intensity
images, I 2 /I 1 , is a function of the phase angle or the luminescent lifetime;
therefore, a pressure field can be obtained from the luminescent lifetime image.
6.4. Lifetime Experiments
131
Fig. 6.12. Interline transfer CCD architecture and charge flow
6.4. Lifetime Experiments
Lachendro (2000) used a set-up shown in Fig. A2 in Appendix A for phase
calibration of PSP and TSP formulations at temperatures lower than –30°C, which
was capable of holding pressures down to 0.03 psi. In order to make phase
calibrations, LED arrays were used as a modulated excitation source; a blue LED
array was used for Ruthenium-based complexes and a green LED array for
Porphyrin-based luminophores. Each array consisted of seven LEDs arranged in a
hexagonal formation for more uniform illumination. The light from an LED array
was passed through an appropriate interference filter to eliminate unwanted
emission. A function generator was used to directly power and modulate the
arrays; the TTL signal from the function generator was used as an external
reference for a lock-in amplifier. After passing through a focusing lens, the
luminescent response of PSP (or TSP) was detected using a PMT fitted with an
interference filter centered at 620 nm and then was sampled by the lock-in
amplifier. A PC was used to acquire calibration data from the lock-in amplifier.
Figures 6.13-6.15 show phase calibration results for three PSP formulations:
Ru(dpp) in a silicone polymer with silica gel, PtTFPP in a silicone polymer with
silica gel, and PtTFPP in a porous polymer/ceramic(Al2O3) composite tape casting.
Figures 6.16-6.18 show phase calibration results for three TSP formulations:
PtTFPP, Ru(trpy)(C6F5-trpy)(NO3)2, and Ru(bipy)2(p-bipy)2 in DuPont
ChromaClear.
132
6. Lifetime-Based Methods
0
-5
Phase Shift (Degrees)
-10
-15
-20
-30οC
-20οC
-15οC
-10οC
-5οC
0οC
10οC
20οC
3rd Order
-25
-30
-35
-40
-45
-50
0
1
2
3
4
5
6
7
8
9
10 11
12 13
14
15
Pressure (psia)
Fig. 6.13. Phase calibration for PSP, Ru(dpp) in RTV 110 with Silica Gel.
Lachendro (2000)
From
0
-2
Phase Shift (Degrees)
-4
-6
-8
-10
-30οC
-18οC
-3οC
10οC
20οC
5th Order Fit
-12
-14
-16
-18
-20
-22
0
1
2
3
4
5
6
7
8
9
10 11
12
13 14 15
Pressure(psia)
Fig. 6.14. Phase calibration for PSP, PtTFPP in RTV 110 with Silica Gel. From Lachendro
(2000)
6.4. Lifetime Experiments
4
-50οC
-45οC
-40οC
-35οC
-30οC
-25οC
-20οC
ο
-15 C
-10οC
-5οC
0οC
5οC
10οC
15οC
20οC
25οC
0
-4
Phase Shift (Degrees)
133
-8
-12
-16
-20
-24
-28
-32
-36
-40
-44
0
1
2
3
4
5
6 7 8 9 10 11 12 13 14 15
Pressure (psia)
Fig. 6.15. Phase calibrations for PSP, PtTFPP in a porous polymer/ceramic(Al2O3)
composite tape casting. From Lachendro (2000)
0
-1
Phase Shift (degrees)
-2
-3
-4
-5
-6
-7
-8
-9
-10
-50 -45 -40 -35 -30 -25 -20 -15 -10 -5
Temperature (οC)
0
5
10 15 20
Fig. 6.16. Phase calibration for TSP, PtTFPP in DuPont ChromaClear. From Lachendro
(2000)
134
6. Lifetime-Based Methods
0
-2
Phase Shift (degrees)
-4
-6
-8
-10
-12
-14
-16
-18
-20
-50 -45 -40 -35 -30 -25 -20 -15 -10 -5
0
5
10 15 20
ο
Temperature ( C)
Fig. 6.17. Phase calibration for TSP, Ru(trpy)(C6F5-trpy)(NO3)2 in DuPont ChromaClear.
From Lachendro (2000)
2
0
Phase Shift (degrees)
-2
-4
-6
-8
-10
-12
-14
-16
-18
-50 -45 -40 -35 -30 -25 -20 -15 -10 -5
0
5 10 15 20 25
Temperature (oC)
Fig. 6.18. Phase calibration for TSP, Ru(bipy)2(p-bipy)2 in DuPont ChromaClear. From
Lachendro (2000)
Goss et al. (2000) evaluated the lifetime techniques based on several different
modulation/gating combinations such as the time-resolved multiple-gate method
for the pulse excitation, sine-square method, and square-square method. The
detectors used were ICCD, phase-sensitive interline-transfer CCD, and back-lit
CCD with a liquid-crystal shutter. A xenon strobe light and a Nd:YAG laser were
6.4. Lifetime Experiments
135
used as a pulse light source, while a LED array was used for the sinusoidal and
square-wave excitation. PSP tested was PtTFPP in a sol-gel binder. The gated
intensity ratio was measured as a function of pressure using the detectors with
different gating strategies. They found that the time-resolved multiple-gate
method had greater sensitivity to pressure than other lifetime methods and the
intensity-based (or radiometric) method. The square-square method had the
second best sensitivity to pressure. Figure 6.19 shows calibration results of the
gated intensity ratio for that PSP obtained with the ICCD employing the timeresolved multiple-gate method and square-square method. One of the problems
with the ICCD was a high noise level of the system; the rms variation of the gated
intensity ratio was as high as 3-5% even after binning.
1.8
1.6
Multiple-Gate Method
Square-Square Method
Gated Intensity Ratio
1.4
PtTFPP-sol-gel PSP
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0
20
40
60
80
100
Pressure (kPa)
Fig. 6.19. Calibration of the gated intensity ratio for PtTFPP-sol-gel PSP with ICCD using
the time-resolved multiple-gate method and square-square method. From Goss et al.
(2000)
Bell (2001) studied the time-resolved multiple-gate method for the pulse
excitation to optimize the gating parameters. He found that the gated intensity
ratio was not constant over a PSP-coated surface even at constant pressure and
temperature, and the variation was 0.5-3% depending on homogeneity of the
paint. This indicated that the lifetime was different at different locations even
when pressure and temperature are uniformly invariant over a surface. Earlier, in
laser-scanning PSP measurements, Torgerson et al. (1996) observed a variation of
o
about 0.5 in the phase angle (related to the lifetime) across a measurement
domain in the flow-off case where pressure and temperature were constant.
Similar to Bell’s observation on the gated intensity ratio, the spatial phase pattern
was repeatable, dependent on the location. Hartmann et al. (1995) also observed
similar results and attributed this phenomenon to microheterogeneity of the
polymer environment. The small lifetime or phase variation may not significantly
affect PSP measurements at higher Mach numbers, whereas it can introduce a
136
6. Lifetime-Based Methods
considerable error in low-speed PSP measurements. To correct this intrinsic
spatial variation of the lifetime, Torgerson et al. (1996) and Bell (2001) used raw
lifetime or phase distributions in the flow-off conditions as a reference, and took a
ratio between the wind-on and reference lifetime images (signals). Unfortunately,
this correction method defeats to certain degree the original purpose of using the
lifetime method to eliminate the wind-off reference. Bencic (2001) compared the
lifetime method with the intensity-based method for PSP measurements at high
viewing polar angles and in a shadowed region, and found that the lifetime-based
measurements achieved better results in these cases.
Mitsuo et al. (2002) studied the luminescent decay of a PtTFPP-based PSP
using a streak camera and found that the multiple-exponential decay of the paint
was sensitively dependent on pressure and temperature. This characteristic
allowed simultaneous determination of pressure and temperature from three gated
intensities obtained by an ICCD camera since two ratios between the three gated
intensities had sufficiently different dependencies on pressure and temperature.
They selected the first and third gating intervals ǻ T1 = 0 − 0.8 µs and
ǻ T3 = 30 − 82.8 µs. The gated intensity I 1 in ǻ T1 was almost independent from
both pressure and temperature, whereas the gated intensity I 3 in ǻ T3 was very
sensitive to pressure and temperature.
The second gating interval
ǻ T2 = 12 − 19.4 µs was chosen based on minimization of the pressure error due
to a small pertubation of the intensity ratio signal. Their calibration experiments
showed that pressure could be well described by polynomials of the gated
intensity ratios I 1 / I 2 and I 1 / I 3 with the temperature-dependent coefficients.
Using the calibration relations, they were able to obtain simultaneously the surface
pressure and temperature fields in a sonic impinging jet from the two gated
intensity ratio images. Recent tests by Watkins et al. (2003) used a new internally
gated interline transfer CCD camera to alleviate noise sources associated with
ICCD.
7. Uncertainty
7.1. Pressure Uncertainty of Intensity-Based Methods
7.1.1. System Modeling
Uncertainty analysis is highly desirable in order to establish PSP as a quantitative
measurement technique. Based on the Stern-Volmer equation, Sajben (1993)
investigated error sources contributing to the uncertainty of PSP, and found that
the uncertainty strongly depended on flow conditions and the surface temperature
significantly affected the final measurement results. Oglesby et al. (1995a)
presented an analysis of an intrinsic limit of the Stern-Volmer relation to the
achievable sensitivity and accuracy. Mendoza (1997a, 1997b) studied CCD
camera noise and its effect on PSP measurements and suggested the limiting Mach
number for quantitative PSP measurements. From a standpoint of system
modeling, Liu et al. (2001a) gave a general and comprehensive uncertainty
analysis for PSP.
The following uncertainty analysis focuses on the intensity-ratio method widely
used in PSP measurements. From Eq. (4.24), air pressure p can be generally
expressed in terms of the system’s outputs and other variables
Vref ( t, x ) p ref
A(T) p ref
p = U1
−
.
(7.1)
V( t' , x' ) B(T)
B(T)
The factor U1 in Eq. (7.1) is
U1 =
Ȇ c Ȇ f h( x' ) c( x' ) q0 ( t' , X' )
,
Ȇ c ref Ȇ f ref href ( x ) c ref ( x ) q0 ref ( t, X )
where x = (x, y)T and x' = (x' , y' )T are the coordinates in the wind-off and windon images, respectively, X = (X, Y, Z)T and X' = (X' ,Y' , Z' )T are the object space
coordinates in the wind-off and wind-on cases, respectively, and t and t’ are the
instants at which the wind-off and wind-on images are taken, respectively. Here,
the paint thickness h and dye concentration c are expressed as a function of the
image coordinate x rather than the object space coordinate X since the image
138
7. Uncertainty
registration error is more easily treated in the image plane. In fact, x and X are
related through the perspective transformation (the collinearity equations).
In order to separate complicated coupling between the temporal and spatial
variations of these variables, some terms in Eq. (7.1) can be further decomposed
when a small model deformation and a short time interval are considered. The
wind-on image coordinates can be expressed as a superposition of the wind-off
image coordinates and an image displacement vector ǻx , i.e., x' = x + ǻx .
Similarly, the temporal decomposition is t' = t + ǻt , where ǻt is a time interval
between the instants at which the wind-off and wind-on images are taken. If ǻx
and ǻt are small, a ratio between the wind-off and wind-on images can be
separated into two factors, Vref ( t, x )/V( t' , x' ) ≈ Dt (ǻt ) D x (ǻx )Vref ( t, x )/V( t, x ) ,
where
the
factors
Dt ( ǻt ) = 1 − ( ∂V / ∂ t )( ǻt)/V
and
D x (ǻx ) = 1 − ( ∇V ) • ( ǻx ) /V represent the effects of the temporal and spatial
changes of the luminescent intensity, respectively. The temporal change of the
luminescent intensity is mainly caused by photodegradation and sedimentation of
dusts and oil droplets on a surface. The spatial intensity change is due to model
deformation generated by aerodynamic loads. In the same fashion, the excitation
q0 ( t' , X' )/q0 ref ( t, X ) ≈
light
flux
can
be
decomposed
into
Dq0 (ǻt ) q0 ( t, X' )/q0 ref ( t, X ) ,
where
the
factor
Dq0 ( ǻt ) = 1 + ( ∂ q0 / ∂ t )( ǻt) / q0 ref represents the temporal variation in the
excitation light flux.
The use of the above estimates yields the generalized Stern-Volmer relation
Vref ( t, x ) p ref
A(T) p ref
−
,
(7.2)
p = U2
V( t, x ) B(T)
B(T)
where
U 2 = Dt (ǻt ) D x (ǻx ) Dq0 (ǻt )
Ȇ c Ȇ f h( x' ) c( x' ) q0 ( t, X' )
.
Ȇ c ref Ȇ f ref href ( x ) c ref ( x ) q0 ref ( t, X )
Without any model motion ( x' = x and X' = X ) and temporal illumination
fluctuation, the factor U2 is unity and then Eq. (7.2) recovers the generic SternVolmer relation. Eq. (7.2) is a general relation that includes the effects of model
deformation, spectral variability, and temporal variations in both illumination and
luminescence, which allows a more complete uncertainty analysis and a clearer
understanding of how these variables contribute the total uncertainty in PSP
measurements.
7.1.2. Error Propagation, Sensitivity and Total Uncertainty
According to the general uncertainty analysis formalism (Ronen 1988; Bevington
and Robinson 1992), the total uncertainty of pressure p is described by the error
propagation equation
7.1. Pressure Uncertainty of Intensity-Based Methods
M
[ var( ȗ i ) var( ȗ j )] 1/2
var (p)
=
S
S
ȡ
i
j ij
p2
ȗ iȗ j
i, j = 1
¦
where
between
ȡi j = cov( ȗ i ȗ j )/[ var( ȗ i ) var( ȗ j )] 1/2
the
variables
ȗi
and
,
139
(7.3)
is the correlation coefficient
ȗj,
var (ȗ i ) = < ǻȗ i >
2
and
cov (ȗ i ȗ j ) = < ǻȗ i ǻȗ j > are the variance and covariance, respectively, and the
notation < > denotes the statistical ensemble average. Here, the variables
{ȗ i , i = 1 M} denote a set of the parameters Dt (ǻt ) , D x (ǻx ) , Dq0 (ǻt ) , V ,
Vref , Ȇ c /Ȇ c ref , Ȇ f /Ȇ f ref , h / href , c / c ref , q0 /q0 ref , p ref , T , A, and B in Eq.
(7.2). The sensitivity coefficients S i are defined as S i = ( ȗ i /p )( ∂ p / ∂ ȗ i ) . Eq.
(7.3) becomes particularly simple when the cross-correlation coefficients between
the variables vanish ( ȡi j = 0 , i ≠ j ).
Table 7.1 lists the sensitivity coefficients, the elemental errors and their
physical origins. Many sensitivity coefficients are proportional to a factor
ϕ = 1 + [A(T) /B(T)] / (p / p ref ) . For Bath Ruth + silica-gel in GE RTV 118,
Figure 7.1 shows the factor 1 + [A(T) /B(T)] / (p / p ref ) as a function of p / p ref
for different temperatures, which is only slightly changed by temperature. The
temperature sensitivity coefficient is S T = −T [B' (T) + A' (T) p ref /p]/ B ( T ) ,
where the prime denotes differentiation respect with temperature. Figure 7.2
shows the absolute value of S T as a function of p / p ref at different temperatures.
After the elemental errors in Table 7.1 are evaluated, the total uncertainty in
pressure can be readily calculated using Eq. (7.3). The major elemental error
sources are discussed below.
140
7. Uncertainty
Table 7.1. Sensitivity coefficients, elemental errors, and total uncertainty of PSP
Variable
Sensi.
Coef.
ȗi
Elemental Variance
Physical Origin
var( ȗ i )
Si
1
D t (ǻt )
ij
[( ∂V / ∂ t )( ǻt)/V ] 2
2
D x (ǻx )
ij
[ (∂V/∂x ) ı x2 + (∂V /∂ y ) ı 2y ] V − 2
3
D q0 (ǻt )
[( ∂ q 0 / ∂ t )( ǻt)/q 0 ref ] 2
4
5
6
Vref
V
Ȇ c /Ȇ c ref
7
Ȇ f /Ȇ f ref
8
h / href
ij
ij
-ij
ij
ij
ij
9
c / c ref
ij
−2
[ (∂ c /∂ x ) ı x2 + (∂ c /∂ y ) ı 2y ] c ref
10 q 0 /q 0 ref
ij
( q0 ref )−2 ( ∇q0 ) • ( ǻX )
11
1
var( p)
p ref
12 T
13 A
14 B
15 Pressure
mapping
2
2
Temporal variation in luminescence
due to photodegradation and surface
contamination
Image registration errors for
correcting luminescence variation
due to model motion
Temporal variation in illumination
Photodetector noise
V ref G ! Ȟ B d
Photodetector noise
V G !Ȟ Bd
[ R2 /(R1 + R2 )] (ǻR1 /R1 )
2
2
var(Ȇ f /Ȇ f ref )
−2
[ (∂ h /∂ x ) ı x2 + (∂ h /∂ y ) ı 2y ] href
2
2
2
2
2
ST
var( T)
1 − ij var( A)
-1
var( B)
1
(∂ p/∂x )2 ı x2 + (∂p /∂y )2 ı 2y
and ( ∇ p )surf • ( ǻX )surf
2
Change in camera performance
parameters due to model motion
Illumination spectral variability and
filter spectral leakage
Image registration errors for
correcting thickness variation due to
model motion
Image registration errors for
correcting concentration variation
due to model motion
Illumination variation on model
surface due to model motion
Error in measurement of reference
pressure
Temperature effect of PSP
Paint calibration error
Paint calibration error
Errors in camera calibration and
pressure mapping on a surface of a
presumed rigid body
M
Total Uncertainty in Pressure
var (p)/ p 2 =
¦S
2
i
var( ȗ i )/ ȗ i
2
i =1
Note:
(1) ı x and ı y are the standard deviations of least-squares estimation in the image
registration or camera calibration.
(2) The factors for the sensitivity coefficient are defined as ij = 1 + [ A( T ) / B( T )]( p ref / p )
and S T = − [ T / B ( T )] [B' (T) + A' (T)(p ref / p ) ] .
7.1. Pressure Uncertainty of Intensity-Based Methods
141
3.0
T = 293 K
T = 313 K
T = 333 K
1 + (A(T)/B(T))(Pref/P)
2.5
2.0
1.5
1.0
0.5
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
P/Pref
Fig. 7.1. The sensitivity factor 1 + [A(T) /B(T)] / (p / p ref ) as a function of p / p ref at
different temperatures for Bath Ruth + silica-gel in GE RTV 118. From Liu et al. (2001a)
10
9
T = 293 K
T = 313 K
T = 333 K
|(dP/dT)(T/P)|
8
7
6
5
4
3
2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
P/Pref
Fig. 7.2. The temperature sensitivity coefficient as a function of p / p ref at different
temperatures for Bath Ruth + silica-gel in GE RTV 118. From Liu et al. (2001a)
7.1.3. Photodetector Noise and Limiting Pressure Resolution
The uncertainties in the outputs V and Vref from a photodetector (e.g. camera)
are contributed from a number of noise sources in the detector such as the photon
shot noise, dark current shot noise, amplifier noise, quantization noise, and pattern
142
7. Uncertainty
noise. When the dark current and pattern noise are subtracted and the noise floor
is negligible, the detector is photon-shot-noise-limited. In this case, the signal-tonoise ratio (SNR) of the detector is SNR = ( V / G ! ȞBd )1 / 2 , where ! is the
Planck’s constant, ν is the frequency, Bd is the electrical bandwidth of the
detection electronics, G is the system’s gain, and V is the detector output. The
uncertainties in the outputs are expressed by the variances var(V) = V G ! Ȟ Bd and
var(Vref ) = Vref G ! Ȟ Bd . In the photon-shot-noise-limited case in which the error
propagation equation contains only two terms related to V and Vref , the pressure
uncertainty is
ǻ p §¨ G Bd ! Ȟ ·¸
=
¨ V ref ¸
p
¹
©
1/ 2
ª
A( T ) p ref
«1 +
B( T ) p
«¬
ºª
p º
»
» «1 + A( T ) + B( T )
p ref »¼
»¼ ¬«
1/ 2
,
(7.4)
which holds for both CCD cameras and non-imaging detectors.
For a CCD camera, the first factor in the right-hand side of Eq. (7.4) can be
simply expressed by the total number of photoelectrons collected over the
integration time ( ∝ 1 / Bd ), n pe = V /( G ! ȞBd ) . When the full-well capacity of
the CCD camera is achieved, we obtain the minimum pressure difference that PSP
can measure from a single frame of image
( ǻp)min
1
=
p
(n pe ref )max
ª
p º
A(T) p ref º ª
»
«1 +
» «1 + A(T) + B(T)
p ref »¼
B(T) p »¼ ¬«
¬«
1/2
,
(7.5)
where (n pe ref )max is the full-well capacity of the camera in reference conditions.
When N images are averaged, the limiting pressure difference (7.5) is further
1/2
reduced by a factor N . Eq. (7.5) provides an estimate for the noise-equivalent
pressure resolution for a CCD camera. When (n pe ref )max is 500,000 electrons for
a CCD camera and Bath Ruth + silica-gel in GE RTV 118 is used, the minimum
pressure uncertainty ( ǻp)min / p is shown in Fig. 7.3 as a function of p / p ref for
different temperatures, indicating that an increased temperature degrades the
limiting pressure resolution.
Figure 7.4 shows
(n pe ref )max ( ǻp)min / p
as a
function of p / p ref for different values of the Stern-Volmer coefficient B(T) .
Clearly, a larger B(T) leads to a smaller limiting pressure uncertainty ( ǻp)min / p .
Figure 7.5 shows
(n pe ref )max ( ǻp)min / p
as a function of the Stern-Volmer
coefficient B(T) for different values of p / p ref . There is no optimal value of B in
this case.
Minimum pressure uncertainty (%)
7.1. Pressure Uncertainty of Intensity-Based Methods
143
0.40
0.36
0.32
T = 333 K
T = 313 K
0.28
T = 293 K
0.24
0.20
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
P/Pref
Fig. 7.3. The minimum pressure uncertainty ( ǻp)min / p as a function of p / p ref at
different temperatures for Bath Ruth + silica-gel in GE RTV 118. From Liu et al. (2001a)
7
(∆P)min/P [(npe ref)max]
1/2
6
5
B = 0.5
4
0.6
3
0.7
0.8
2
0.9
1
0.0
0.5
1.0
1.5
2.0
P/Pref
Fig. 7.4. The normalized minimum pressure uncertainty
(n pe ref )max ( ǻp)min / p as a
function of p / p ref for different values of the Stern-Volmer coefficient B(T) . From Liu
et al. (2001a)
144
7. Uncertainty
20
P/Pref = 0.2
(∆P)min/P [(npe ref)max]
1/2
0.5
15
1.0
1.5
10
2.0
5
0.0
0.2
0.4
0.6
0.8
1.0
B
Fig. 7.5. The normalized minimum pressure uncertainty
(n pe ref )max ( ǻp)min / p as a
function of the Stern-Volmer coefficient B for different values of p / p ref . From Liu et
al. (2001a)
7.1.4. Errors Induced by Model Deformation
Model deformation generated by aerodynamic loads causes a displacement
ǻx = x' − x of the wind-on image relative to the wind-off image. This
displacement leads to the deviations of the quantities D x (ǻx ) , h / href , c / c ref ,
and q0 /q0 ref in Eq. (7.2) from unity because the distributions of the luminescent
intensity, paint thickness, dye concentration and illumination level are not
spatially homogeneous on a surface. After the image registration technique is
applied to re-align the wind-on and wind-off images, the estimated variances of
these quantities are var[Dx (ǻx )] ≈ W ( V ) / V 2 , var( h / href ) ≈ W ( h ) /( href )2 ,
and
var( c / c ref ) ≈ W ( c ) /( c ref ) 2 .
The
operator
W( • )
is defined
as
W( • ) = (∂ /∂ x ) ı + (∂ /∂ y ) ı , where ı x and ı y are the standard deviations of
least-squares estimation for image registration.
The uncertainty in q0 ( X )/q0 ref ( X' ) is caused by a change in the illumination
intensity on a model surface after the model moves with respect to the light
sources. When a point on the model surface travels along the displacement vector
ǻX = X' − X in the object space, the variance of q0 /q0 ref is estimated by
2
2
x
2
2
y
2
var[q0 ( X ) / q0 ref ( X' )] ≈ ( q0 ref )−2 ( ∇q0 ) • ( ǻX ) . Consider a point light source
7.1. Pressure Uncertainty of Intensity-Based Methods
with unit strength that has a light flux distribution q0 ( X − X s ) = X − X s
145
−n
,
where n is an exponent (normally n = 2) and X − X s is the distance between the
point X on the model surface and the light source location X s . Thus, the
variance of q0 /q0 ref for a single point light source is var[q0 ( X ) / q0 ref ( X' )]
= n2 X − X s
−4
2
( X − X s ) • ( ǻX ) .
The variance for multiple point light
sources can be obtained based on the principle of superposition. In addition,
model deformation leads to a small change in the distance between the model
surface and the camera lens. The uncertainty in the camera performance
parameters due to this change is var(Ȇ c /Ȇ c ref ) ≈ [ R2 /(R1 + R2 )] 2 (ǻR1 /R1 )2 ,
where R1 is the distance between the lens and model surface and R2 is the
distance between the lens and sensor. For R1 >> R2 , this error is very small.
7.1.5. Temperature Effect
Since the luminescent intensity of PSP is intrinsically temperature-dependent, a
temperature change on a model during a wind tunnel run results in a significant
bias error in PSP measurements if the temperature effect is not corrected. In
addition, temperature influences the total uncertainty of PSP measurements
through the sensitivity coefficients of the variables in the error propagation
equation. Hence, the surface temperature on a model must be known in order to
correct the temperature effect of PSP. In general, the surface temperature
distribution can be measured experimentally using TSP or IR camera and
determined numerically by solving the motion and energy equations of flows
coupled with the heat conduction equation for a model. For a compressible
boundary layer on an adiabatic wall, the adiabatic wall temperature Taw can be
estimated using a simple relation
Taw / T0 = [ 1 + r( γ - 1)M 2 / 2 ] [ 1 + ( γ - 1)M 2 / 2 ] −1 ,
where r is the recovery factor for the boundary layer, T0 is the total temperature,
M is the local Mach number, and γ is the specific heat ratio.
7.1.6. Calibration Errors
The uncertainties in determining the Stern-Volmer coefficients A(T) and B(T) are
calibration errors. In a priori PSP calibration in a pressure chamber, the
uncertainty is represented by the standard deviation of data collected in replication
tests. Because tests in a pressure chamber are well controlled, a priori calibration
results usually show a small precision error. However, a significant bias error is
found when a priori calibration results are directly used for data reduction in wind
tunnel tests due to unknown surface temperature distribution and uncontrollable
146
7. Uncertainty
testing environmental factors. In contrast, in-situ calibration utilizes pressure tap
data over a model surface to determine the Stern-Volmer coefficients. Because
in-situ calibration correlates the local luminescent intensity with the pressure tap
data, it can reduce the bias errors associated with the temperature effect and other
sources, achieving a better agreement with the pressure tap data. The in-situ
calibration uncertainty, which is usually represented as a fitting error, will be
specially discussed in Section 7.3.
7.1.7. Temporal Variations in Luminescence and Illumination
For PSP measurements in steady flows, a temporal change in the luminescent
intensity mainly results from photodegradation and sedimentation of dusts and oil
droplets on a model surface. The photodegradation of PSP may occur when there
is a considerable exposure of PSP to the strong excitation light between the windoff and wind-on measurements. Dusts and oil droplets in air sediment on a model
surface during wind-tunnel runs; the resulting dust/oil layer absorbs both the
excitation light and luminescent emission on the surface and thus causes a
decrease of the luminescent intensity. The uncertainty in Dt (ǻt ) due to the
photodegradation and sedimentation can be collectively characterized by the
variance var[Dt ( ǻt )] ≈ [( ∂V / ∂ t )( ǻt)/V ] 2 . Similarly, the uncertainty in
Dq0 (ǻt ) , which is produced by an unstable excitation light source, is described by
var[Dq0 ( ǻt )] ≈ [( ∂q 0 / ∂ t )( ǻt)/q 0 ref ] 2 .
7.1.8. Spectral Variability and Filter Leakage
The uncertainty in Ȇ f /Ȇ f ref is mainly attributed to the spectral variability of
illumination lights and spectral leaking of optical filters. Possolo and Maier
(1998) observed the spectral variability between flashes of a xenon lamp; the
uncertainties in the absolute pressure and pressure coefficient due to the flash
spectral variability were 0.05 psi and 0.01, respectively. If optical filters are not
selected appropriately, a small portion of photons from the excitation light and
ambient light may reach a detector through the filters, producing an additional
output to the luminescent signal.
7.1.9. Pressure Mapping Errors
The uncertainty in pressure mapping is related to the data reduction procedure in
which PSP data in images are mapped onto a surface grid of a model in the object
space. It is contributed from the errors in camera resection/calibration and
mapping onto a surface grid of a presumed rigid body.
The camera
resection/calibration error is represented by the standard deviations ı x and ı y of
the calculated target coordinates from the measured target coordinates in the
7.1. Pressure Uncertainty of Intensity-Based Methods
147
image plane. Typically, a good camera resection/calibration method gives the
standard deviation of about 0.04 pixels in the image plane. For a given PSP
image, the pressure variance induced by the camera resection/calibration error is
2
2
var(p) ≈ (∂ p/∂ x ) ı x2 + (∂p /∂ y ) ı 2y .
The pressure mapping onto a presumably non-deformed model surface grid
leads to another deformation-related error because a model may undergo a
considerable deformation generated by aerodynamic loads in wind tunnel tests.
When a point on a model surface moves by ǻX = X' − X in the object space, the
pressure variance induced by mapping onto a presumed rigid body grid without
2
correcting the model deformation is var(p ) = ( ∇ p )surf • ( ǻX )surf , where (∇ p )surf
is the pressure gradient on the surface and ( ǻX )surf is the component of the
displacement vector ǻX projected on the surface in the object space. To
eliminate this error, a deformed surface grid should be generated for PSP mapping
based on optical model deformation measurements under the same testing
conditions (Liu et al. 1999).
7.1.10. Paint Intrusiveness
A thin PSP coating may slightly modify the overall shape of a model and produces
local surface roughness and topological patterns. These unwanted changes in
model geometry may alter flows over a model and affect the integrated
aerodynamic forces (Engler et al. 1991; Sellers 1998a). Hence, this paint
intrusiveness to flow should be considered as an error source in PSP
measurements. The effects of a paint coating on pressure and skin friction are
directly associated with locally changed flow structures and propagation of the
induced perturbations in flow; these local effects may collectively alter the
integrated aerodynamic forces. When a local paint thickness variation is much
smaller than the boundary layer displacement thickness, a thin coating does not
alter the inviscid outer flow. Instead of directly altering the outer flow, a rough
coating may indirectly result in a local pressure change by thickening the
boundary layer; coating roughness may reduce the momentum of the boundary
layer to cause early flow separation at certain positions. Therefore, the effective
aerodynamic shape of a model is changed and as a result the pressure distribution
on the model is modified; this effect is mostly appreciable near the trailing edge
due to the substantial development of the boundary layer on the surface.
Vanhoutte et al. (2000) observed an increment in the trailing edge pressure
coefficient relative to the unpainted model, which was consistent with an increase
in the boundary layer thickness at the trailing edge. For certain models such as
high-lift models, a coating may change the gap between the main wing and slat or
flap when the gap is small; thus, the pressure distribution on the model is locally
influenced. In addition, a coating may influence laminar separation bubbles near
the leading edge at low Reynolds numbers and high angles-of-attack. The
perturbations induced by a rough coating near the leading edge may enhance
148
7. Uncertainty
mixing that entrains the high-momentum fluid from the outer flow into the
separated region. The perturbations could be amplified by several hydrodynamic
instability mechanisms such as the Kelvin-Helmholtz instability in the shear layer
between the outer flow and separated region and the cross-flow instability near the
attachment line on a swept wing. Consequently, the coating causes the laminar
separation bubbles to be suppressed. Vanhoutte et al. (2000) reported this effect
that led to a reduction in drag.
Schairer et al. (1998a, 2002) observed that a rough coating on the slats slightly
decreased the stall angle of a high-lift wing. Also, they found that the empirical
criteria for ‘hydraulic smoothness’ and ‘admissible roughness’ based on 2D data
by Schichting (1979) were not sufficient to provide a satisfactory explanation for
their observation. Indeed, in 3D complex flows on the high-lift model, the effect
of the coating on the cross-flow instability and its interactions with the boundary
layer and other shear layers such wakes and jets are not well understood. Schairer
et al. (1998a, 2002) and Mebarki et al. (1999) found that a rough coating moved a
shock wave upstream and the pressure distribution was shifted near the shock
location. This change might be caused by an interaction between the shock and
the incoming boundary layer affected by the coating. In an attached flow at high
Reynolds numbers, a rough coating increases skin friction by triggering premature
laminar-turbulent transition and increasing the turbulent intensity in a turbulent
boundary layer (Mebarki et al. 1999; Vanhoutte et al. 2000). An increase in drag
due to a rough coating was observed in airfoil tests in high subsonic flows
(Vanhoutte et al. 2000). In fact, premature transition by coating roughness has
been often observed in TSP transition detection experiments (see Chapter 10).
Amer et al. (2001, 2003) reported that a very smooth coating on the upper surface
of a delta wing model at Mach 0.2 and a semi-span arrow-wing model at Mach 2.4
did not significantly change the drag coefficients of these models. Generally
speaking, the effect of a coating on aerodynamic forces highly depends on flows
over a specific model configuration; there is no universal conclusion on this
effect.
7.1.11. Other Error Sources and Limitations
Other error sources include the self-illumination and induction effect; there are
limitations in the time response and spatial resolution of PSP. The selfillumination is a phenomenon that the luminescent emission from one part of a
model surface reflects to another surface, thus distorting the observed luminescent
intensity at a point by superposing all the rays reflected from other points. It often
occurs on surfaces of neighbor components of a complex model (Ruyten 1997a,
1997b, 2001a; Le Sant 2001b). The self-illumination effect on calculation of
pressure and temperature are discussed in Section 5.3. Another problem is the
‘induction effect’ observed as an increase in the luminescent emission during the
first few minutes of illumination for certain paints; the photochemical process
behind it was explained by Uibel et al. (1993) and Gouterman (1997). In PSP
measurements in unsteady flows, the limiting time response of PSP, which is
7.1. Pressure Uncertainty of Intensity-Based Methods
149
mainly determined by oxygen diffusion process across a PSP layer (see Chapter
8), imposes an additional restriction on the accuracy of PSP measurements. The
spatial resolution of PSP is limited by oxygen diffusion in the lateral direction
along a paint surface. Considering a pressure jump across a point on a surface (a
normal shock wave), Mosharov et al (1997) gave a solution of the diffusion
equation describing a distribution of the oxygen concentration in a PSP layer near
the pressure jump point. According to this solution, the limiting spatial resolution
is about five times of the paint layer thickness.
7.1.12. Allowable Upper Bounds of Elemental Errors
In the design of PSP experiments, we need to give the allowable upper bounds of
the elemental errors for the required pressure accuracy. This is an optimization
problem subject to certain constraints. In matrix notations, Eq. (7.3) is expressed
as ı P2 = ı T A ı , where the notations are defined as ı P2 = var (p)/p 2 ,
A ij = S i S j ȡi j , and ı i = [ var( ȗ i ) ] 1/2 / ȗ i . For required pressure uncertainty ı P ,
we look for a vector ı up to maximize an objective function H = W T ı , where
W is the weighting vector. The vector ı up gives the upper bounds of the
elemental errors for a given pressure uncertainty ı P . The use of the Lagrange
multiplier method requires H = W T ı + Ȝ ( ı P2 − ı T A ı ) to be maximal, where λ
is the Lagrange multiplier. The solution to this optimization problem gives the
upper bounds
A −1 W
ı up =
ıP .
(7.6)
( W T A −1 W )1/2
For the uncorrelated variables with ȡi j = 0 (i ≠ j) , Eq. (7.6) reduces to
−1/2
·
§
(ı i )up = S i− 2 Wi ı P ¨¨
S −k 2 Wk2 ¸¸ .
(7.7)
¹
© k
When the weighting factors Wi equal the absolute values of the sensitivity
coefficients | S i | , the upper bounds can be expressed in a very simple form
¦
(ı i )up / ı P = N V−1 / 2 S i
−1
, ( i = 1, 2 , , N V )
(7.8)
where N V is the total number of the variables or the elemental error sources. The
relation Eq. (7.8) clearly indicates that the allowable upper bounds of the
elemental uncertainties are inversely proportional to the sensitivity coefficients
and the square root of the total number of the elemental error sources. Figure 7.6
shows a distribution of the upper bounds of 15 variables for PSP Bath Ruth +
silica-gel in GE RTV 118 at p / p ref = 0.8 and T = 293 K. Clearly, the
allowable upper bound for temperature is much lower than others, and therefore
the temperature effct of PSP must be tightly controlled to achieve the required
pressure accuracy.
150
7. Uncertainty
1.8
1.6
1.4
1.2
1
Dt (ǻt )
9
c / c ref
2
Dx (ǻx )
10
q0 /q0 ref
3
Dq0 (ǻt )
11
Pref
12
13
T
A
B
V
Vref
4
(ı i )up
1.0
ıP
0.8
5
0.6
6
Ȇ c /Ȇ c ref
14
7
Ȇ f /Ȇ f ref
15 Pressure mapping
8
h / href
0.4
0.2
0.0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Variable Index
Fig. 7.6. Allowable upper bounds of 15 variables for Bath Ruth + silica-gel in GE RTV 118
when p / p ref = 0.8 , and T = 293 K. From Liu et al. (2001a)
7.1.13. Uncertainties of Integrated Forces and Moments
The uncertainties of the integrated aerodynamic forces and moments can be
estimated based on their definitions. For example, the uncertainty in the lift is
1/ 2
∆FL / FL = FL−1 [ ∆
−1
L
≈F
³³
( ¦¦ ( n • l
p( n • l L )dS ] 2
L
∆S )i ( n • l L ∆S ) j < ∆ p i ∆ p j >
)
,
(7.9)
1/ 2
where n is the unit normal vector of a surface panel, ∆S is the area of the surface
panel, and l L is the unit vector of the lift. The correlation between the pressure
differences at the panel ‘i’ and panel ‘j’ is simply modeled by
< ∆ pi ∆ p j >= δ ij < ∆ pi >< ∆ p j > , where the Kronecker delta is δ ij = 1 for
i = j and δ ij = 0 for i ≠ j . Thus, the uncertainty in the lift can be estimated
based on the PSP uncertainty at all the surface panels, i.e.,
§
ǻF L / F L ≈ ¨
¨
©
N
¦ (n•l
i =1
L
2
i
2
2
PSP i
ǻS ) ( p i / FL ) ( ǻp / p )
·
¸
¸
¹
1/ 2
(7.10)
Similarly, the uncertainties in the pressure-induced drag and pichting moment are
estimated by
7.2. Pressure Uncertainty Analysis for Subsonic Airfoil Flows
§
ǻFD / FD ≈ ¨
¨
©
§
ǻM c / M c ≈ ¨
¨
©
N
¦ (n•l
D
2
i
2
2
PSP i
ǻS ) ( pi / FD ) ( ǻp / p )
i =1
·
¸
¸
¹
1/ 2
,
N
¦ [ n×( X − X
mc
2
i
151
2
2
PSP i
) ǻS ] ( p i / M c ) ( ǻp / p )
i =1
(7.11)
·
¸
¸
¹
1/ 2
, (7.12)
where l D is the unit vector of the drag and X mc is the assigned moment center.
7.2. Pressure Uncertainty Analysis
for Subsonic Airfoil Flows
PSP measurements on a Joukowsky airfoil in subsonic flows are simulated in
order to illustrate how to estimate the elemental errors and the total uncertainty
using the techniques described above. The airfoil and incompressible potential
flows around it are generated using the Joukowsky transform; the pressure
coefficients Cp on the airfoil in the corresponding subsonic compressible flows are
obtained using the Karman-Tsien rule. Figure 7.7 shows typical distributions of
the pressure coefficient and adiabatic wall temperature on a Joukowsky airfoil at
o
Mach 0.4 and AoA = 5 .
-8
-3
Cp
Temperature
-6
-2
-4
0
-2
Cp
-1
Taw - Tref (deg C)
AoA = 5 deg, Mach = 0.4
0
1
Joukowski Airfoil
2
2
0.0
0.2
0.4
0.6
0.8
1.0
x/c
Fig. 7.7. Typical distributions of the pressure coefficient and adiabatic wall temperature on
o
a Joukowsky airfoil at Mach 0.4, AoA = 5 , and Tref = 293 K
152
7. Uncertainty
Presumably, PSP, Bath Ruth + silica-gel in GE RTV 118, is used, which has
the Stern-Volmer coefficients A(T) ≈ 0.13 [ 1 + 2.82( T − Tref ) / Tref ] and
B(T) ≈ 0.87 [ 1 + 4.32( T − Tref ) / Tref ] over a temperature range of 293-333 K.
The uncertainties in a priori PSP calibration are ǻA/A = ǻB/B = 1% . We assume
that the spatial changes of the paint thickness and dye concentration in the image
plane are 0.5%/pixel and 0.1%/pixel, respectively. The rate of photodegradation
of the paint is 0.5%/hour for a given excitation level and the exposure time of the
paint is 60 seconds between the wind-off and wind-on images. The rate of
reduction of the luminescent intensity due to dust/oil sedimentation on the surface
is assumed to be 0.5%/hour.
In an object-space coordinate system whose origin is located at the leading
edge of the airfoil, four light sources for illuminating PSP are placed at the
locations X s1 = ( − c , 3c ) , Xs2 = ( 2c, 3c ) , X s3 = ( − c , − 3c ) , and Xs4 = ( 2c, − 3c ) ,
where c is the chord of the airfoil. For the light sources with unit strength, the
illumination flux distributions on the upper and lower surfaces are, respectively,
(q0 )up = X up - X s1
−2
+ X up - X s2
−2
and (q0 )low = X low - X s3
−2
+ X low - X s4
−2
,
where X up and X low are the coordinates of the upper and lower surfaces of the
airfoil, respectively. The temporal variation of irradiance of these lights is
assumed to be 1%/hour. It is also assumed that the spectral leakage of optical
filters for the lights and cameras is 0.3%. Two cameras, viewing the upper
surface and lower surface respectively, are located at ( c/2, 4 c ) and ( c/2, − 4c ) .
The pressure uncertainty associated with the photon shot noise can be estimated
by using Eq. (7.5). Assume that the full-well capacity of ( n pe )max = 350,000
electrons of a CCD camera is utilized. The numbers of photoelectrons collected in
a CCD camera are mainly proportional to the distribution of the illumination field
on the model surface. Thus, the photoelectrons on the upper and lower surfaces
( n pe )up = ( n pe )max ( q0 )up / max[( q0 )up ]
and
are
estimated
by
( n pe )low = ( n pe )max ( q0 )low / max[( q0 )low ] . Combination of these estimates with
Eq. (7.5) gives the shot-noise-generated pressure uncertainty distributions on the
surfaces.
Movement of the airfoil produced by aerodynamic loads is expressed by a
superposition of a local rotation (twist) and translation. A transformation between
the non-moved and moved surface coordinates X = ( X ,Y )T and X' = ( X ' ,Y ' )T
is X' = R( θ twist ) X + T , where R( θ twist ) is the rotation matrix, θ twist is the local
wing twist, and T is the translation vector.
Here, for θ twist = −1o and
T = ( 0.001c , 0.01 c )T , the uncertainty in q0 ( X )/q0 ref ( X' ) is estimated by
2
var[q0 ( X ) / q0 ref ( X' )] ≈ ( q0 ref )−2 ( ∇q0 ) • ( ǻX ) , where the displacement vector
is ǻX = X' − X . The pressure variance associated with mapping PSP data onto a
rigid body grid without correcting the model deformation is estimated by
7.2. Pressure Uncertainty Analysis for Subsonic Airfoil Flows
153
2
var(p ) = ( ∇ p )surf • ( ǻX )surf , where (∇ p )surf is the pressure gradient on the
surface and ( ǻX)surf = ( X' − X)surf is the component of the displacement vector
projected on the surface.
To estimate the temperature effect of PSP, an adiabatic model is considered at
which the wall temperature Taw is given by
Taw / T0 = [ 1 + r( γ - 1)M 2 / 2 ] [ 1 + ( γ - 1)M 2 / 2 ] −1 ,
where the recovery factor is r = 0.843 for a laminar boundary layer. Assuming
that the reference temperature Tref equals to the total temperature T0 = 293 K, we
can calculate a temperature difference ∆T = Taw − Tref between the wind-on and
wind-off cases. The adiabatic wall is the most severe case for PSP measurements
since the surface temperature on a metallic model is much lower than the adiabatic
wall temperature due to heat conduction to the model.
The total uncertainty in pressure is estimated by substituting all the estimated
elemental errors into Eq. (7.3). Figure 7.8 shows the pressure uncertainty
distributions on the upper and lower surfaces of the airfoil for different freestream
Mach numbers. It is indicated that the temperature effect of PSP dominates the
uncertainty of PSP measurements on an adiabatic wall. The uncertainty becomes
larger and larger as the Mach number increases because the adiabatic wall
temperature increases. The local pressure uncertainty on the upper surface is as
high as 50% at one location for Mach 0.7, which is caused by a local surface
o
temperature change of about 6 C.
In order to compare the PSP uncertainty with the pressure variation on the
airfoil, a maximum relative pressure variation on the airfoil is defined as
max ǻp
surf
/ p∞ = 0.5 γ M ∞2 max ∆C p . Figure 7.9 shows the maximum relative
pressure variation
max ǻp
surf
/ p∞
along with the chord-averaged PSP
uncertainty < ( ǻp/p)PSP > aw on the adiabatic airfoil at the Mach numbers of 0.050.7. The uncertainty < ( ǻp/p)PSP > ∆T =0 without the temperature effect is also
plotted in Fig. 7.10, which is mainly dominated by the a priori PSP calibration
error ǻB/B = 1% in this case. The curves max ǻp surf / p∞ , < ( ǻp/p)PSP > aw and
< ( ǻp/p)PSP > ∆T =0 intersect near Mach 0.1. When the PSP uncertainty exceeds
the maximum pressure variation on the airfoil, the pressure distribution on the
airfoil cannot be quantitatively measured by PSP. As shown in Fig. 7.9, because a
temperature change on a non-adiabatic wall is smaller, the PSP uncertainty for a
real wind tunnel model generally falls into the shadowed region confined by
< ( ǻp/p)PSP > aw and < ( ǻp/p)PSP > ∆T =0 .
The PSP uncertainty associated with the photon shot noise
< ( ǻp/p)PSP > ShotNoise is also plotted in Fig. 7.9. The intersection between
max ǻp
surf
/ p∞ and < ( ǻp/p)PSP > ShotNoise gives the limiting low Mach number
154
7. Uncertainty
( ~ 0.06 ) for PSP measurements in this case. The uncertainties in the lift ( FL )
and pitching moment ( M c ) are also calculated from the PSP uncertainty
distribution on the surface. Figure 7.10 shows the uncertainties in the lift and
pitching moment relative to the leading edge for the Joukowsky airfoil over a
o
range of the Mach numbers when the angle of attack is 4 . The uncertainties in the
lift and moment decrease monotonously as the Mach number increases since the
absolute values of the lift and moment rapidly increase with the Mach number.
0.6
Upper Surface
0.5
Uncertainty in P
M = 0.7
0.4
0.3
0.2
M = 0.5
0.1
M = 0.3
0.0
M = 0.1
0.0
0.2
0.4
0.6
0.8
1.0
x/c
(a)
0.06
Lower Surface
M = 0.7
Uncertainty in P
0.05
0.04
M = 0.5
0.03
0.02
M = 0.3
0.01
M = 0.1
0.0
(b)
0.2
0.4
0.6
0.8
1.0
x/c
Fig. 7.8. PSP uncertainty distributions for different freestream Mach numbers on (a) the
upper surface and (b) lower surface of a Joukowsky airfoil. From Liu et al. (2001a)
7.2. Pressure Uncertainty Analysis for Subsonic Airfoil Flows
155
1
Relative Error or Variation
Upper Surface
< ( ǻP/P)PSP > aw
max ǻP
surf
/ P∞
0.1
0.01
< ( ǻP/P)PSP > ∆T =0
< ( ǻP/P)PSP > ShotNoise
0.001
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Freestream Mach number
(a)
1
Relative Error or Variation
Lower Surface
max ǻP
0.1
surf
/ P∞
< ( ǻP/P)PSP > aw
0.01
< ( ǻP/P)PSP > ∆T =0
< ( ǻP/P)PSP > ShotNoise
0.001
0.0
(b)
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Freestream Mach number
Fig. 7.9. The maximum relative pressure change and chord-averaged PSP uncertainties as a
function of the freestream Mach number on (a) the upper surface and (b) the lower surface
of a Joukowsky airfoil. From Liu et al. (2001a)
156
7. Uncertainty
0.7
0.6
Lift
Pitching Moment
Uncertainty
0.5
0.4
0.3
0.2
0.1
0.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Freestream Mach Number
Fig. 7.10. Uncertainties in the lift and pitching moment of a Joukowsky airfoil as a function
of the freestream Mach number. From Liu et al. (2001a)
7.3. In-Situ Calibration Uncertainty
7.3.1. Experiments
As pointed out before, the use of a priori PSP calibration in large wind tunnels
often leads to a considerable systematic error since the surface temperature
distribution is not known and the illumination change on a surface due to model
deformation cannot be corrected by the image registration technique. The
systematic error is also related to uncontrollable environmental testing factors.
Therefore, in actual PSP measurements, experimental aerodynamicists are forced
to calibrate PSP in situ by fitting (or correlating) the luminescent intensity to
pressure tap data at a number of suitably distributed locations. In a sense, in-situ
PSP calibration eliminates the systematic error associated with the temperature
effect and the illumination change by absorbing it into an overall fitting error.
Kammeyer et al. (2002a, 2002b) assessed the accuracy of the Boeing
production PSP system by statistical analysis of comparison between PSP and
pressure transducers over a large numbers of data points. The Boeing PSP system
is a typical intensity-based system that uses eight CCD (1024×1024 or 512×512)
cameras for imaging, thirty lamps for illumination, and two IR cameras measuring
the surface temperature for correcting the temperature effect of PSP. The test
article was a 1/12th-scale model of a Cessna Citation that was instrumented with a
total of 225 pressure taps. The tests were conducted in the DNW/NLR HST wind
tunnel, a variable-density, closed circuit, continuous tunnel with slotted top and
bottom test section walls (12% open). The test section was 6.56 ft wide and was
7.3. In-Situ Calibration Uncertainty
157
configured to be 5.25 ft high. The cameras and lamps were mounted in the floor
and ceiling. A run consisted of a lift polar at each of several Mach numbers from
0.22 to 0.82. Two Reynolds numbers, 4.5 and 8.3 millions, were run. Fourteen
o
angles of attack were from –4 to 10 . Over 8300 visual images and over 2000 IR
images were obtained for 676 test points. The wind-off reference images were
acquired after the run when the fan had stopped in order to reduce the effect of the
model temperature distribution. Figure 7.11 shows a typical pressure distribution
on the model obtained by PSP.
Fig. 7.11. Typical pressure distribution obtained from PSP on a Cessna Citation model.
From Kammeyer et al. (2002a)
In-situ PSP calibrations were performed by utilizing 78 of 225 pressure taps for
each of the cameras. Figure 7.12 shows the variation of the in-situ calibration
slope (i.e. the Stern-Volmer coefficient B) as a function of test point throughout
the tests, where no temperature correction was applied. The variation does not
show an overall trend; the repeating pattern mirrors the pattern of the test
conditions, wherein sequential angles of attack were run for sequentially
increasing Mach numbers. The mean value of the slope is close to one, which is
approximately consistent with the paint characteristics given by a priori
calibration. The scatter is attributed to a number of factors, including the nonhomogeneous temperature distributions, temperature differences between the
wind-off and wind-on conditions, lamp intensity drift, and image registration
error.
The accuracy of the PSP system was directly assessed by comparing the
pressure value measured by a transducer/tap combination with that obtained from
PSP at the same tap location. After some problematic pressure data were
excluded, 130,391 comparisons from 221 taps and 676 wind-on test points were
used as an overall set of realizations for statistical analysis. The PSP data
158
7. Uncertainty
processing included in-situ calibration, but did not exercise the explicit
temperature correction. When examining the comparisons, the 78 taps were used
for in-situ calibration to provide residual comparisons, while other taps provided
truly independent comparisons. Figure 7.13 shows a histogram for the over set of
comparisons, where a Gaussian distribution with the same mean and standard
deviation is superimposed for comparison. Clearly, the distribution is nonGaussian. A robust estimate of the 68% confidence level gives an estimate of the
standard uncertainty of 0.29 psi, which corresponds to 0.0065 in Cp. Figure 7.14
shows the standard uncertainty as a function of the angle of attack for the right
wing. The behavior of the dependency of the uncertainty on the angle of attack
corresponds to wing deformation. This indicates that the error is associated with
the movement of the model in the non-homogenous illumination field, which
cannot be corrected by the image registration technique. Kammeyer et al. (2002a,
2002b) also studied temperature correction using the IR cameras. Two sets of
PSP data obtained before and after temperature correction were used to assess the
effectiveness of the temperature correction. Figure 7.14 shows the standard
uncertainty after the temperature correction as a function of the angle of attack.
The temperature correction was increasingly effective when the angle of attack
o
was larger than 2 ; it removed the spatial biases associated with the temperature
distribution on the model. Overall, the standard uncertainty, priori to the
temperature correction, was in the range 0.16-0.45 psi (0.04-0.1Cp); with the
temperature correction, it was in the range 0.17-0.35 psi (0.04-0.09Cp). The
significance of the work of Kammeyer et al. (2002a, 2002b) is that it identifies the
functional dependency of in-situ PSP calibration uncertainty on the testing
parameters such as the angle of attack and Mach number.
Fig. 7.12. Variation of PSP in-situ calibration slope throughout the tests on a Cessna
Citation model. From Kammeyer et al. (2002a)
7.3. In-Situ Calibration Uncertainty
159
Fig. 7.13. Histogram of the overall set of PSP errors compared with a Gaussian distribution
of the equivalent mean and standard deviation. From Kammeyer et al. (2002a)
Fig. 7.14. Standard uncertainty of PSP on the right wing of a Cessna Citation model as a
function of the angle of attack. From Kammeyer et al. (2002a)
7.3.2. Simulation
Inspired by the experimental study of Kammeyer et al. (2002a, 2002b), Liu and
Sullivan (2003) studied in-situ calibration uncertainty of PSP through a simulation
of PSP measurements in subsonic Joukowsky airfoil flows. It is assumed that insitu calibration uncertainty is mainly attributed to the temperature effect of PSP
and illumination change on a surface due to model deformation. The Joukowsky
airfoil and subsonic flows around it are generated using the Joukowsky transform
plus the Karman-Tsien rule as described in Section 7.2. An adiabatic model is
160
7. Uncertainty
considered that is coated with Bath Ruth + silica-gel in GE RTV 118. Four point
light sources for illuminating PSP and two cameras for imaging are placed at the
same locations as described in Section 7.2. The twist θ twist and bending T y of the
airfoil are a function of the angle of attack (AoA or α ) for a given Mach number
and Reynolds number. Based on previous wing deformation measurements
(Burner and Liu 2001), the typical linear relations θ twist = −0.113α (deg) and
T y = 0.022 α ( in ) are used over a certain range of AoA at a certain spanwise
location of a wing. Thus, a change of the illumination radiance on the airfoil
surface due to the deformation is estimated using a transformation of rotation and
translation for the airfoil moving in the given illumination field.
In simulation, the measured luminescent intensity (I) distribution of PSP in the
wind-on case (deformation case) is generated by
I
I ref 0
§ I ref
=¨
¨ I ref 0
©
·§
·
¸ ¨ A( T ) + B( T ) p ¸
¸¨
p ref ¸¹
¹©
−1
§ L
= ¨¨
© L0
−1
·§
p ·¸
¸ ¨ A( T ) + B( T )
,
¸¨
p ref ¸¹
¹©
where I ref 0 and I ref are the reference luminescent intensities (without wind) on
the non-deformed airfoil and deformed airfoil, respectively. It is assumed that
I ref 0 and I ref are proportional to the corresponding illumination radiance levels
L0 and L on the non-deformed airfoil and deformed airfoil, respectively. The
surface temperature T is substituted by the adiabatic wall temperature distribution
Taw , and the pressure distribution is given by the Joukowsky transform plus the
Karman-Tsien rule for subsonic flows. Therefore, the resulting luminescent
intensity distribution contains the effects of both the illumination change and
temperature variation on the surface.
Assuming that the wind-on image (I) is already re-aligned with the wind-off
image I ref 0 on the non-deformed airfoil by the image registration technique, in-
situ PSP calibration is made to correlate I ref 0 / I to p / p ref using the SternVolmer relation based on 104 virtual pressure taps on each of the upper and lower
surfaces. For a given AoA and Mach number, the histogram of in-situ calibration
error ∆p / p ref = ( p − pin − situ ) / p ref is found to be a near-Gaussian distribution,
where ∆p is a difference between the true pressure from the theoretical
distribution and the pressure converted from the luminescent intensity using insitu calibration. The standard deviation (std) of the probability density function is
dependent on AoA and Mach number. Figures 7.15 and 7.16 show the std of the
in-situ calibration error as a function of AoA for Mach 0.4 and as a function of the
o
Mach number for AoA = 5 , respectively. Figures 7.15 and 7.16 also show the
isolated effects of the temperature and illumination change on the std. The
behavior of the calculated std as a function of AoA is very similar to the
experimental results shown in Fig. 7.14. The concavity of the std as a function of
AOA in Fig. 7.15 is mainly attributed to the movement of the airfoil.
7.3. In-Situ Calibration Uncertainty
161
Figure 7.17 shows the simulated histogram for an overall sample set of
∆p / p ref (a total of 10920 samples) over the whole range of AoA and Mach
numbers, duplicating the experimental non-Gaussian distribution in Fig. 7.13
given by Kammeyer et al. (2002a, 2002b). The Gaussian distribution with the
same std is also plotted in Fig. 7.17 as a reference. In fact, for a union of sample
sets having near-Gaussian distributions with different the std values at different
AoA and Mach numbers, the distribution becomes non-Gaussian because more
and more samples accumulate near zero when forming a union of the sample sets.
The probability density function of a union of the N sample sets should be given
by a sum of the Gaussian distributions rather than the Gaussian distribution, i.e.,
N
N −1
¦ exp( − x
2
/ 2σ i2 ) / 2π σ i .
i =1
As shown in Fig. 7.17, this distribution correctly describes the simulated
histogram. Note that we should not confuse this case with the central limit
theorem that deals with a sum of independent random variables. Although the
simulation is made for an airfoil section of a wing, the in-situ calibration error for
a wing can be estimated by averaging the local results over the full wingspan;
therefore, the behavior of the error for a wing should be similar to that for an
airfoil.
0.012
Illumination change only
with constant temperature
Temperature effect only
without illumination change
Both temperature effect
and illumination change
std[(p - pin-situ)/pref]
0.010
0.008
0.006
0.004
0.002
0.000
Mach = 0.4
-5
0
5
10
15
AoA (deg)
Fig. 7.15. In-situ PSP calibration error as a function of the angle-of-attack (AoA) for Mach
0.4 in Joukowsky airfoil flows. From Liu and Sullivan (2003)
162
7. Uncertainty
0.004
Illumination change only
with constant temperature
Temperature effect only
without illumination change
Both temperature effect
and illumination change
std[(p - pin-situ)/pref]
0.003
0.002
0.001
0.000
AoA = 5 deg
0.25
0.30
0.35
0.40
0.45
0.50
0.55
0.60
0.65
Mach Number
o
Fig. 7.16. In-situ PSP calibration error as a function of the Mach number for AoA = 5 in
Joukowsky airfoil flows. From Liu and Sullivan (2003)
900
800
Sample Number
700
Sum of Gaussian
Distributions
600
500
400
Gaussian
Distribution
300
200
100
0
-0.01 -0.008 -0.006 -0.004 -0.002
0
0.002 0.004 0.006 0.008
0.01
∆p/pref
Fig. 7.17. Histogram of the overall set of in-situ PSP calibration errors in the whole ranges of
AoA and Mach numbers in Joukowsky airfoil flows. From Liu and Sullivan (2003)
7.4. Pressure Uncertainty of Lifetime-Based Methods
163
7.4. Pressure Uncertainty of Lifetime-Based Methods
7.4.1. Phase Method
The phase method for PSP measurements, as described in Chapter 6, determines
pressure by
§
·
−1 ¨ Ȧ IJ 0
¸
p = K SV
(7.13)
¨ tan ij − 1¸ ,
©
¹
where tan ij = Ȧ IJ = − Vc / Vs is uniquely related to the lifetime for a fixed
modulation frequency, and Vc = − Am IJ H M eff sin (ij ) and Vs = Am IJ H M eff cos (ij ) are
the DC components from the low-pass filters. The error propagation equation
gives the relative variance of pressure
var( K SV )
var( IJ 0 )
var (p)
var( T )
= S T2
+ S K2 SV
+ S IJ20
2
2
2
2
p
T
K SV
IJ0
.
(7.14)
2 var( V s )
2 var( Vc )
+ S Vs
+ SVc
Vs2
Vc2
The first term is the uncertainty related to temperature, the second is the
uncertainty in PSP calibration, the third is the error in the given reference lifetime,
and the last two terms are the uncertainties associated with the measurement
system composed of a photodetector and lock-in amplifier. The sensitivity
coefficients in Eq. (7.14) are
T ∂p
T ∂K SV 1 + K SV p T ∂τ 0
ST =
,
=−
+
p ∂T
K SV ∂T
K SV p τ 0 ∂T
S K SV =
K SV ∂p
= −1 ,
p ∂K SV
S IJ0 =
IJ0 ∂ p
= 1 + 1 /( K SV p ) ,
p ∂ IJ0
SVs =
Vs ∂ p
= 1 + 1 /( K SV p ) ,
p ∂ Vs
SVc =
Vc ∂ p
= − SVs .
p ∂ Vc
Compared to the intensity-based method discussed in Chapter 4, many error
sources associated with model deformation do not exist, which reflects the
advantage of the lifetime-based method. When the photon shot noise of the
detector dominates, the pressure uncertainty is mainly contributed by the last two
terms in Eq. (7.14). In the photon-shot-noise-limited case, the uncertainties in the
outputs of the detector and lock-in amplifier are var(Vs ) = | Vs |G ! Ȟ Bd and
164
7. Uncertainty
var(Vc ) = | Vc | G ! Ȟ Bd , where G is the system gain, Bd is the bandwidth of the
system, and ! is the Planck’s constant. Therefore, the photon-shot-noise-limited
pressure uncertainty is given by
∆p
p
§ GBd !ν ·
¸
¸
© | Vs | ¹
= ¨¨
1/ 2
§
· § 1 + K SV p ·
¨1 + 1 ¸ ¨1 +
¸
¨
ȦIJ 0 ¸¹
K SV p ¸¹ ¨©
©
1/ 2
.
(7.15)
The estimate Eq. (7.15) for the phase method is similar to Eq. (7.4) for the
intensity-based CCD camera system. The behavior of the pressure uncertainty as
a function of pressure and the Stern-Volmer coefficient B is similar to that shown
in Figs. 7.4 and 7.5.
7.4.2. Amplitude Demodulation Method
When the amplitude demodulation method is used, as indicated in Chapter 6,
pressure is given by
·
Ȧ IJ0
1 §
¨
(7.16)
p=
− 1 ¸¸ ,
2
2
1/ 2
¨
K SV © [ H ( Vmean / Vstd ) / 2 − 1 ]
¹
where Vmean and Vstd are the mean and standard deviation of the photodetector
output, respectively. Thus, the error propagation equation gives the relative
variance of pressure
var( K SV )
var( IJ 0 )
var (p)
var( T )
= S T2
+ S K2 SV
+ S IJ20
2
2
2
2
p
T
K SV
IJ0
.
(7.17)
var( Vmean )
var( Vstd )
2
+ SV2mean
+
S
Vstd
2
Vmean
Vstd2
The first term is the uncertainty related to temperature, the second is the
uncertainty in PSP calibration, the third is the error in the given reference lifetime,
and the last two terms are the uncertainties associated with the photodetector. The
sensitivity coefficients in Eq. (7.17) are
T ∂p
T ∂K SV 1 + K SV p T ∂τ 0
,
ST =
=−
+
p ∂T
K SV ∂T
K SV p τ 0 ∂T
S K SV =
S IJ0 =
IJ0 ∂ p
= 1 + 1 /( K SV p ) ,
p ∂ IJ0
§ 1 + K SV p ( 1 + K SV p )3
Vmean
∂p
= − ¨¨
+
p ∂( Vmean )
K SV p( ȦIJ 0 ) 2
© K SV p
V
∂p
= std
= − SVmean .
p ∂( Vstd )
SVmean =
SVstd
K SV ∂p
= −1 ,
p ∂K SV
·
¸,
¸
¹
7.4. Pressure Uncertainty of Lifetime-Based Methods
165
In the photon-shot-noise-limited case, the uncertainties in the detector outputs
are var(Vmean ) = Vmean G ! Ȟ Bd and var(Vstd ) = Vstd G ! Ȟ Bd . Thus the photon-shotnoise-limited pressure uncertainty is
∆p
p
§ GB d !ν ·
¸
¸
© V mean ¹
1/ 2
= ¨¨
ª 1 + K SV p ( 1 + K SV p ) 3 º
+
«
»
K SV p( ȦIJ 0 ) 2 ¼»
¬« K SV p
1/ 2
­
( ȦIJ 0 ) 2 º ½°
2ª
°
× ®1 +
» ¾
«1 +
H «¬ ( 1 + K SV p ) 2 ¼» °
°̄
¿
.
1/ 2
(7.18)
Figure
7.18(a)
shows
the
normalized
pressure
uncertainty
1/ 2
(ǻp/p)( Vmean / G ! Ȟ Bd )
as a function of p/p ref at different values of the SternVolmer coefficient B for Ȧ IJ 0 = 10 and H = 1 . Here, for a fixed temperature
T = Tref ,
we
use
the
following
= ( B / A )( p / p ref ) and A + B = 1 .
relations
K SV p = K SV p ref ( p / p ref )
Figure 7.18(b) shows the normalized
pressure uncertainty (ǻp/p)( Vmean / G ! Ȟ Bd )1 / 2 as a function of B at different
values of p/p ref for Ȧ IJ 0 = 10 and H = 1 . Interestingly, in this case, there is an
optimal
value
of
the
Stern-Volmer
coefficient
B
at
which
1/ 2
(ǻp/p)( Vmean / G ! Ȟ Bd ) is minimal. The optimal value of the Stern-Volmer
coefficient B varies between 0.7 and 0.9, depending on the value of pressure.
20
50
45
P/Pref= 0.2
10
(∆P/P)(Vmean/GBdhν)1/2
(∆P/P)(Vmean/GBdhν)1/2
40
15
B = 0.5
0.6
0.7
0.8
0.9
5
35
0.5
30
25
20
1.0
15
1.5
10
2.0
5
0
0
0.0
0.5
1.0
1.5
2.0
0.0
P/Pref
(a)
0.2
0.4
0.6
0.8
1.0
B
(b)
Fig. 7.18. The normalized pressure uncertainty (ǻp/p)( Vmean / G ! Ȟ Bd )1 / 2 in the
amplitude demodulation method with Ȧ IJ 0 = 10 and H = 1 as a function of p/p ref for
different values of the Stern-Volmer coefficient B, and a function of B for different values
of p/p ref
166
7. Uncertainty
7.4.3. Gated Intensity Ratio Method
In the gated intensity ratio method for the sinusoidally modulated excitation light,
pressure can be expressed as a function of the gated detector output ratio V2 / V1
−1 / 2
·
Ȧ IJ 0 § 2 H 1 + V2 / V1
1
¨
p=
− 1 ¸¸
−
.
(7.19)
¨
K SV © ʌ 1 − V2 / V1
K SV
¹
Therefore, the error propagation equation is
var( K SV )
var( IJ 0 )
var( V1 )
var( V2 )
var (p)
var( T )
= S T2
+ S K2 SV
+ S IJ20
+ SV21
+ SV22
2
2
2
p2
T2
K SV
V
V22
IJ0
1
(7.20)
where the sensitivity coefficients are
T ∂p
T ∂K SV 1 + K SV p T ∂τ 0
,
+
ST =
=−
p ∂T
K SV ∂T
K SV p τ 0 ∂T
S K SV =
K SV ∂p
= −1 ,
p ∂K SV
S IJ0 =
IJ0 ∂ p
= 1 + 1 /( K SV p ) ,
p ∂ IJ0
SV1 =
V1 ∂ p { π [1 + Ȧ 2 IJ 02 ( 1 + K SV p )−2 ] − 2 H }( 1 + K SV p )3
,
=
p ∂V1
2ʌ Ȧ 2 IJ 02 K SV p
V2 ∂ p
= − SV1 .
p ∂V2
In the photon-shot-noise-limited case, the uncertainties in the detector outputs
are var(V1 ) = V1 G ! Ȟ Bd and var(V2 ) = V2 G ! Ȟ Bd . Thus, the photon-shot-noiselimited pressure uncertainty for the gated intensity ratio method is
SV2 =
§ GB d !ν
= ¨¨
p © V1
∆p
·
¸
¸
¹
1/ 2
2π { π [1 + Ȧ 2 IJ 02 ( 1 + K SV p ) − 2 ] − 2 H } 1 / 2
2ʌ Ȧ 2 IJ 02
[1 + Ȧ 2 IJ 02 ( 1 + K SV p ) − 2 ] 1 / 2 ( 1 + K SV p ) 3
×
K SV p
.
(7.21)
Figure 7.19(a) shows the normalized pressure uncertainty (ǻp/p)( V1 / G ! Ȟ Bd )1 / 2
as a function of p/p ref at different values of the Stern-Volmer coefficient B for
Ȧ IJ 0 = 10 and H = 1 . Figure 7.19(b) shows the normalized pressure uncertainty
(ǻp/p)( Vmean / G ! Ȟ Bd )1 / 2 as a function of B at different values of p/p ref for
Ȧ IJ 0 = 10 and H = 1 . Similar to the amplitude demodulation method, there is an
optimal value of B (around 0.8) to achieve the minimal value of
(ǻp/p)( Vmean / G ! Ȟ Bd )1 / 2 . In general, to reduce the noise, the gated intensity
ratio method has to collect sufficient photons over a large number of cycles. For
7.4. Pressure Uncertainty of Lifetime-Based Methods
167
example, compared to a standard CCD camera system with an integration time of
1 second, a gated CCD camera with a modulation frequency of 50 kHz needs to
accumulate photons over 100,000 cycles to achieve the equivalently small
uncertainty. The accumulation of photons can be done automatically in a phase
sensitive camera.
15
(∆P/P)(V1/GBdhν)1/2
(∆P/P)(V1/GBdhν)1/2
4
3
B = 0.5
2
10
P/Pref= 0.2
0.5
5
0.6
1.0
1.5
2.0
0.7
0.8
0.9
0
1
0.0
0.5
1.0
P/Pref
(a)
1.5
2.0
0.0
0.2
0.4
0.6
0.8
1.0
B
(b)
Fig. 7.19. The normalized pressure uncertainty ( ∆p/p)( V1 / G ! Ȟ Bd )1 / 2 for the gated
intensity method using a sinusoid modulation with Ȧ IJ 0 = 10 and H = 1 as a function of
p/p ref for different values of the Stern-Volmer coefficient B, and a function of B for
different values of p/p ref
When the gated intensity ratio method is applied to the pulse excitation light,
pressure can be expressed as a function of the gated detector output ratio V2 / V1
p=
IJ0
V2 / V1
1
,
ln
−
t g K SV 1 + V2 / V1
K SV
(7.22)
where the time t g divides the two gating intervals [ 0 , t g ] and [ t g , ∞ ] . Thus,
we have the pressure uncertainty
var( K SV )
var( IJ 0 )
var( V1 )
var( V2 )
var (p)
var( T )
= S T2
+ S K2 SV
+ S IJ20
+ SV21
+ SV22
2
2
2
2
2
p
T
K SV
V1
V22
IJ0
(7.23)
where the sensitivity coefficients are
∂K SV
∂τ 0
T ∂p
T ª 1 + K SV p §
¨¨ K SV
−τ0
ST =
= 2 «
p ∂T K SV p «¬ τ 0
∂T
∂T
©
· ∂K SV
¸¸ +
∂T
¹
º
»,
»¼
168
7. Uncertainty
S K SV =
K SV ∂p
= −1 ,
p ∂K SV
S IJ0 =
IJ0 ∂ p
= 1 + 1 /( K SV p ) ,
p ∂ IJ0
SV1 =
τ0
V1 ∂ p
=−
1 − exp[ −( 1 + K SV p )( t g / τ 0 )] ,
p ∂V1
t g K SV p
SV2 =
V2 ∂ p
= − SV1 .
p ∂V2
{
}
In the photon-shot-noise-limited case, only the terms associated with V1 and
V2 remain in Eq. (7.23) and the uncertainties of the system outputs are
var(V1 ) = V1 G ! Ȟ Bd and var(V2 ) = V2 G ! Ȟ Bd . The photon-shot-noise-limited
pressure uncertainty for the time-resolved multiple-gate method is
§ GBd !ν
= ¨¨
p © V1
∆p
·
¸
¸
¹
1/ 2
1
1 − exp[ − ( 1 + K SV p )( t g / τ 0 )]
K SV p ( t g / τ 0 ) exp[ − 0.5( 1 + K SV p )( t g / τ 0 )]
. (7.24)
The factor V1 / G ! Ȟ Bd equals to the number of photoelectrons collected in the
first gating interval [ 0 , t g ] .
Figure 7.20(a) shows the normalized pressure
uncertainty (ǻp/p)( V1 / G ! Ȟ Bd )1 / 2 as a function of p/p ref at different values of
the Stern-Volmer coefficient B for a fixed gating time t g /IJ 0 = 0.2 , where the
relations K SV p = ( B / A )( p / p ref ) and A + B = 1 are imposed. Figure 7.20(b)
shows the normalized pressure uncertainty (ǻp/p)( Vmean / G ! Ȟ Bd )1 / 2 as a
function of B at different values of p/p ref for t g /IJ 0 = 0.2 . The optimal value of
the Stern-Volmer coefficient B is about 0.8-0.9. For t g /IJ 0 < 0.5 , the pressure
uncertainty ǻp/p remains small, but ǻp/p rapidly increases as t g /IJ 0 approaches
one.
7.5. Uncertainty of Temperature Sensitive Paint
169
15
4
(∆P/P)(V1/GBdhν)1/2
(∆P/P)(V1/GBdhν)
1/2
P/Pref= 0.2
3
B = 0.5
0.6
2
0.7
10
0.5
1.0
5
1.5
2.0
0.8
0.9
1
0
0.0
0.5
1.0
1.5
2.0
0.0
0.2
0.4
P/Pref
0.6
0.8
1.0
B
(b)
(a)
Fig. 7.20. The normalized pressure uncertainty ( ∆p/p)( V1 / G ! Ȟ Bd )1 / 2 for the gated
intensity method with a pulse excitation and t g /IJ 0 = 0.2 as (a) a function of p/p ref for
different values of the Stern-Volmer coefficient B, and (b) a function of B for different
values of p/p ref
7.5. Uncertainty of Temperature Sensitive Paint
7.5.1. Error Propagation and Limiting Temperature Resolution
In principle, the above uncertainty analysis for PSP can be adapted for TSP since
many error sources of TSP are the same as those of PSP. For simplicity, instead
of the general Arrhenius relation, we use an empirical relation between the
luminescent intensity (or the photodetector output) and temperature T for a TSP
uncertainty analysis (Cattafesta and Moore 1995; Cattafesta et al. 1998)
T − Tref = K T ln( I ref / I ) = K T ln( U 2 V ref / V ) ,
(7.25)
where K T is a TSP calibration constant with a temperature unit and U 2 is the
factor defined previously in Eq. (7.2) for the PSP uncertainty analysis. Without
model deformation and temporal illumination variation, the factor U 2 equals to
one. Eq. (7.25) can be used to fit TSP calibration data over a certain range of
temperature. The error propagation equation for TSP is
M
var( ȗ i ) var( K T )
K T2
var (T)
=
+
,
(7.26)
2
2
ȗ i2
K K2
(T − Tref )
(T − Tref ) i = 1
¦
170
7. Uncertainty
where the variables {ȗ i , i = 1 M} denote a set of the parameters Dt (ǻt ) ,
D x (ǻx ) , Dq0 (ǻt ) , V , Vref , Ȇ c /Ȇ c ref , Ȇ f /Ȇ f ref , h / href , c / c ref , and q0 /q0 ref
as defined in Section 7.1. The summation term in the right-hand side of Eq. (7.26)
include the errors associated with model deformation, unstable illumination,
photodegradation, filter leakage, and luminescent intensity measurements. The
last term in Eq. (7.26) is the TSP calibration error.
Similar to the uncertainty analysis for PSP, in the photon-shot-noise-limited
case without any model deformation, we are able to obtain the minimum
temperature difference that TSP can measure from a single frame of image
ª
§ T − Tref
( ǻT)min =
«1 + exp¨¨
(n pe ref )max «¬
© KT
)max is the full-well capacity of a CCD
KT
where (n pe ref
1/2
·º
¸» ,
(7.27)
¸»
¹¼
camera in the reference
conditions. The minimum resolvable temperature difference ( ǻT)min is inversely
proportional to the square-root of the number of collected photoelectrons, and
approximately proportional to the calibration constant K T . When (n pe ref )max is
o
500,000 electrons, for a typical Ruthenium-based TSP having K T = 37.7 C, the
minimum resolvable temperature difference ( ǻT)min is shown in Fig. 7.21 as a
o
function of T at a reference temperature Tref = 20 C. When N images are
averaged, the limiting temperature resolution given by Eq. (5.27) should be
1/2
divided by a factor N .
7.5.2. Elemental Error Sources
The elemental error sources of TSP have been discussed by Cattafesta et al.
(1998) and Liu et al. (1995c). Table 7.2 lists the elemental error sources,
sensitivity coefficients, and total uncertainty of TSP. The sensitivity coefficients
for many variables are related to ij = KT /(T − Tref ) . The elemental errors in the
variables Dt (ǻt ) , D x (ǻx ) , Dq0 (ǻt ) , V , Vref , Ȇ c /Ȇ c ref , Ȇ f /Ȇ f ref , h / href ,
c / c ref , and q0 /q0 ref can be estimated using the same expressions given in the
uncertainty analysis for PSP, which represent the error sources associated with
model deformation, unstable illumination, photodegradation, filter leakage, and
luminescence measurements. The camera calibration error and temperature
mapping error can be also estimated using the similar expressions to those for
PSP, i.e., var(T) ≈ (∂T/∂ x ) ı x2 + (∂T /∂ y ) ı 2y and var(T ) = ( ∇T )surf • ( ǻX )surf ,
2
2
2
where ı x and ı y are the standard deviations of least-squares estimation in image
registration or camera calibration. In order to estimate the TSP calibration errors,
the temperature dependency of TSP was repeatedly measured using a calibration
set-up over days for several TSP formulations (Liu et al. 1995c). Temperature
measured by TSP was compared to accurate temperature values measured by a
7.5. Uncertainty of Temperature Sensitive Paint
171
Minimum Temperature Difference (deg. C)
standard thermometer. Figure 7.22 shows histograms of the temperature
calibration error for EuTTA-dope and Ru(bpy)-Shellac TSPs, which exhibit a
near-Gaussian distribution. The standard deviation for EuTTA-dope TSP is about
o
o
0.8 C over a temperature range of 15-70 C. For Ru(bpy)-Shellac TSP, the
o
histogram has a broader error distribution having the deviation of about 2 C over a
o
temperature range of 20-100 C.
The temperature hysteresis introduces an additional error source for TSP,
which was reported in calibration experiments for a Rhodamine(B)-based coating
(Romano et al. 1989). The temperature hysteresis is related to the polymer
structural transformation from a hard and relatively brittle state to a soft and
rubbery one when temperature exceeds the glass temperature of a polymer. Since
the thermal quenching of luminescence in a brittle condition is different from that
in a rubbery state, the temperature dependency is changed after it is heated beyond
the glass temperature. To reduce the temperature hysteresis, TSP should be preheated to a certain temperature above the glass temperature before it is used as an
optical temperature sensor for quantitative measurements. It was found that for
both pre-heated EuTTA-dope and Ru(bpy)-Shellac paints the temperature
hysteresis was minimized such that the temperature dependency remained almost
unchanged in repeated tests over several days (Liu et al. 1995c).
0.18
0.16
0.14
0.12
0.10
0.08
0.06
0.04
-20
0
20
40
60
80
100
Temperature (deg. C)
Fig. 7.21. The minimum resolvable temperature difference as a function of temperature for
o
o
a Ruthenium-based TSP for (n pe ref )max = 500,000e, K T = 37.7 C , and Tref = 20 C
172
7. Uncertainty
0.4
1.0
EuTTA - dope paint
Ru(bpy) - Shellac paint
0
Gaussian with σ = 0.8 C
0.3
Frequency
Frequency
0.8
0.6
0.4
Gaussian with σ = 2 0C
0.2
0.1
0.2
0.0
0.0
-4
-3
-2 -1
0
1
2
3
Temperature error (deg. C)
(a)
4
-10 -8 -6 -4 -2 0 2 4 6
Temperature Error (deg. C)
8 10
(b)
Fig. 7.22. Temperature calibration error distributions for (a) EuTTA-dope TSP and (b)
Ru(bpy)-Shellac TSP, where σ is the standard deviation. From Liu et al. (1997b)
7.5. Uncertainty of Temperature Sensitive Paint
173
Table 7.2. Sensitivity coefficients, elemental errors, and total uncertainty of TSP
Variable
Sensi.
Coef.
ζi
Si
Elemental Variance
Physical Origin
var( ȗ i )
1
D t (ǻt )
ij
[( ∂V / ∂ t )( ǻt)/V ] 2
2
D x (ǻx )
ij
[ (∂V/∂x ) ı x2 + (∂V /∂ y ) ı 2y ] V − 2
3
D q0 (ǻt )
ij
[( ∂ q 0 / ∂ t )( ǻt)/q 0 ref ] 2
4
ij
V ref G ! Ȟ B d
Photodetector noise
5
6
Vref
V
Ȇ c /Ȇ c ref
-ij
ij
V G !Ȟ Bd
Photodetector noise
[ R 2 /(R 1 + R 2 )] 2 (ǻR1 /R1 ) 2
7
Ȇ f /Ȇ f ref
ij
var(Ȇ f /Ȇ f ref )
8
h / href
ij
−2
[ (∂ h /∂ x ) ı x2 + (∂ h /∂ y ) ı 2y ] href
9
c / c ref
ij
−2
[ (∂ c /∂ x ) ı x2 + (∂ c /∂ y ) ı 2y ] c ref
10
q0 /q0 ref
ij
( q0 ref )−2 ( ∇q0 ) • ( ǻX )
11
KT
1
var( K T )
Change in camera performance
parameters due to model motion
Illumination spectral variability and
filter spectral leakage
Image
registration
errors
for
correcting thickness variation due to
model motion
Image
registration
errors
for
correcting concentration variation due
to model motion
Illumination variation on model
surface due to model motion
Paint calibration error
12
Temperature
mapping
1
2
2
2
2
2
2
2
(∂T/∂x )2 ı x2 + (∂T /∂y )2 ı 2y
and ( ∇T )surf • ( ǻX )surf
2
Temporal variation in luminescence
due to photodegradation and surface
contamination
Image
registration
errors
for
correcting luminescence variation due
to model motion
Temporal variation in illumination
Errors in camera calibration and
temperature mapping on a surface of
a presumed rigid body
M
Total Uncertainty in Temperature
var (T)/ (T - Tref ) 2 =
¦S
2
i
var( ȗ i )/ ȗ i
2
i =1
Note:
(1) ı x and ı y are the standard deviations of least-squares estimation in the image
registration or camera calibration.
(2) The factor for the sensitivity coefficient is defined as ij = KT /(T − Tref ) .
8. Time Response
8.1. Time Response
of Conventional Pressure Sensitive Paint
8.1.1. Solutions of Diffusion Equation
The fast time response of PSP is required for measurements in unsteady flows,
which is related to two characteristic timescales of PSP. One is the luminescent
lifetime of PSP that represents an intrinsic physical limit for an achievable
temporal resolution of PSP. Another is the timescale of oxygen diffusion across a
PSP layer. Because the timescale of oxygen diffusion across a homogenous
polymer layer is usually much larger than the luminescent lifetime, the time
response of PSP is mainly determined by oxygen diffusion. In a thin homogenous
polymer layer, when diffusion is Fickian, the oxygen concentration [O2] can be
described by the one-dimension diffusion equation
∂ 2 [ O2 ]
∂ [O2 ]
,
(8.1)
= Dm
∂z2
∂t
where Dm is the diffusivity of oxygen mass transfer, t is time, and z is the
coordinate directing from the wall to the polymer layer. The boundary conditions
at the solid wall and the air-paint interface for Eq. (8.1) are
∂ [O2 ] / ∂ z = 0 at z = 0 ,
[O2 ] = [O2 ]0 f ( t ) at z = h ,
(8.2)
where the non-dimensional function f ( t ) describes a temporal change of the
oxygen concentration at the air-paint interface, [O2 ]0 is a constant concentration
of oxygen, and h is the paint layer thickness. The initial condition for Eq. (8.1) is
[O2 ] = [O2 ]0 f ( 0 ) at t = 0 .
(8.3)
Introducing the non-dimensional variables
n(t' , z' ) = [O2 ] / [O2 ]0 − f ( 0 ) , z' = z / h , t' = tDm / h 2 ,
(8.4)
we have the non-dimensional diffusion equation
176
8. Time Response
∂n ∂ 2 n
=
∂ t' ∂ z' 2
,
(8.5)
with the boundary and initial conditions
∂n / ∂ z' = 0 at z = 0 , n = g( t' ) at z' = 1 ,
n = 0 at t = 0 ,
(8.6)
where the function g( t' ) is defined as g ( t' ) = f ( t' ) − f ( 0 ) that satisfies the
initial condition g ( 0 ) = 0 .
Applying the Laplace transform to Eq. (8.5) and the boundary and initial
conditions Eq. (8.6), we obtain a general convolution-type solution for the
normalized oxygen concentration n(t' , z' )
n( t' , z' ) =
³
t'
g t ( t' −u ) W ( u , z' ) du .
0
(8.7)
In Eq. (8.7), the function g t ( t ) = d g( t ) / dt = df ( t ) / dt is the differentiation of
g(t) with respect to t and the function W ( t , z ) is defined as
W( t,z ) =
∞
¦
( −1 )k erfc(
1 + 2k − z
2 t
k =0
)+
∞
¦ ( −1 ) erfc(
k
1 + 2k + z
2 t
k =0
).
(8.8)
The derivation of Eq. (8.7) uses the following expansion in negative exponentials
[ 1 + exp( −2 s )] −1 =
∞
¦ ( −1 )
n
exp( −2n s ) , where s is the complex variable of
n =0
the Laplace transform. In particular, for a step change of the oxygen
concentration at the air-paint interface, after g t ( t ) = δ ( t ) is substituted into Eq.
(8.7), the oxygen concentration distribution in a paint layer is simply
n( t' , z' ) = W ( t' , z' ) , a classical solution given by Crank (1995) and Carslaw and
Jaeger (2000).
Instead of using the Laplace transform, Winslow et al. (2001) studied the
solution of the diffusion equation using an approach of linear system dynamics.
The special solutions for a step change and a sinusoidal change of oxygen were
used for PSP dynamical analysis by a number of researchers (Winslow et al. 1996,
2001; Carroll et al. 1995, 1996; Mosharov et al. 1997; Fonov et al. 1998). The
trigonometrical-series-type solution for a step change of oxygen given by Carroll
et al. (1996) is
[O2 ]( t , z ) − [O2 ] min
= 1−
[O2 ] max − [O2 ] min
∞
¦ [ A cos( λ z ) exp( −λ D
k
k
2
k
m
t )] ,
(8.9)
k =1
where Ak = −2( −1 )k /( hλk ) , λk = ( 2k − 1 )π /( 2h ) , [O2 ] max = [O2 ]( t , h ) , and
[O2 ] min = [O2 ]( 0 , z ) . Similarly, Winslow et al. (1996) used the trigonometricalseries-type solution for a sinusoidal change of oxygen
8.1. Time Response of Conventional Pressure Sensitive Paint
177
[O 2 ]( t , z ) − [O 2 ] 0 =
[O2 ] 1
4
∞
π¦
k =1
( 2k − 1 )π z
( −1 ) k − 1
cos[
] sin( ω t − β k ) cos( β k )
( 2k − 1 )
2h
(8.10)
where
β k = tan −1 [
4 h 2ω
].
π 2 ( 2 k − 1 ) 2 Dm
The constants [O2 ]0 and [O2 ]1 are given in the initial and boundary conditions
[O2 ]( 0 , z ) = [O2 ]0 and [O2 ]( t , h ) = [O2 ]0 + [O2 ]1 sin( ω t ) .
Mosharov et al. (1997) also presented the trigonometrical-series-type solution
of the diffusion equation in a similar form to Eq. (8.9) for a step change at a
surface. Note that they defined a coordinate system in such a way that the airpaint interface was at z = 0 and the wall was at z = h . For a sinusoidal change
of oxygen [O2 ]( t ,0 ) = [O2 ]0 + [O2 ]1 sin( ω t ) at the air-paint interface, they
gave a solution composed of two harmonic terms, i.e.,
[O2 ]( t , z ) = [O2 ]0 + [O2 ]1 [ X ( γ , z' ) sin( ω t ) + Y ( γ , z' ) cos( ω t )] ,
(8.11)
where γ = ( ω h 2 / Dm )1 / 2 is a non-dimensional frequency and z' = z / h is a nondimensional coordinate normal to the wall. The coefficients in Eq. (8.11) are
X ( γ , z' ) =
cosh[ 2 γ ( 1 − z' / 2 )] cos( γ z' /
2 ) + cos[ 2 γ ( 1 − z' / 2 )] cosh( γ z' /
2)
cosh( 2 γ ) + cos( 2 γ )
Y ( γ , z' ) =
sinh[ 2 γ ( 1 − z' / 2 )] sin( γ z' / 2 ) + sin[ 2 γ ( 1 − z' / 2 )] sinh( γ z' / 2 )
.
cosh( 2 γ ) + cos( 2 γ )
(8.12)
These trigonometrical-series-type solutions, which are often obtained using the
method of separation of variables, should be equivalent to the general
convolution-type solution Eq. (8.7) that is reduced in these special cases.
The solutions of the diffusion equation give a classical square-law estimate for
the diffusion timescale τdiff through a homogenous PSP layer,
τ diff ∝ h 2 / Dm .
(8.13)
The square-law estimate is actually a phenomenological manifestation of the
statistical theory of the Brownian motion. Interestingly, this estimate is still valid
even when the diffusivity of a homogeneous polymer is concentration-dependent.
The 1D diffusion equation with the concentration-dependent diffusivity can be
178
8. Time Response
reduced to an ordinary differential equation by using the Boltzmann’s
transformation ξ = z /( 2t 1 / 2 ) ; hence, the solution for the concentration
distribution can be expressed by this similarity variable (Crank 1995). Clearly,
the Boltzmann’s scaling indicates that the timescale for any point to reach a given
concentration is proportional to the square of the distance (or thickness).
Using the solution of the diffusion equation for a step change of pressure,
Carroll et al. (1997) estimated the mass diffusivity Dm for oxygen in a typical
silicon polymer binder and gave D m = 1.23 − 1.88 × 10 −9 m 2 /s over a temperature
range of 9.9-40.2 C. The values of D m = 3.55 × 10 −9 m 2 /s for the pure polymer
o
Poly(dimethyl Siloxane) (PDMS) and D m = 1.2 × 10 −9 m 2 /s for PDMS with 10%
fillers were also reported (Cox and Dunn 1986; Pualy 1989). For a 10 µm thick
polymer layer having the diffusivity D m = 10 −10 − 10 −9 m 2 /s , the diffusion
timescale is in the order of 0.1-1 s. Therefore, a conventional non-porous polymer
PSP has slow time response, and it is not suitable to unsteady pressure
measurements.
8.1.2. Pressure Response and Optimum Thickness
Schairer (2002) studied the pressure response of PSP based on the solution Eq.
(8.11) of the diffusion equation given by Mosharov et al. (1997). In a simpler
notation, the luminescent intensity integrated over a paint layer is expressed as
I(t) = C
³
h
0
exp( − β z )
dz ,
a + k [ O 2 ]( t , z )
(8.14)
where β is the extinction coefficient for the excitation light, C is a proportional
constant, and a and k are the coefficients. In the quasi-steady case, the indicated
pressure by PSP is
p PSP ( t ) = [ I ref / I ( t ) − A ] / B ,
(8.15)
where the Stern-Volmer coefficients are determined from steady-state calibration
of PSP. As shown in Eq. (8.15) coupled with Eqs. (8.11), (8.12) and (8.14), the
indicated pressure p PSP ( t ) is a non-linear function of the true pressure that
sinusoidally varies with time, p( t ) = p0 + p1 sin( ω t ) , although the diffusion
equation is linear. However, if the amplitude of the unsteady pressure is small
compared to the mean pressure ( p1 << p0 ), the PSP response can be linearized
and it is given by
p PSP ( t ) = p0 PSP + p1PSP sin( ω t + φ )
,
(8.16)
= p0 + p1 [ α ( γ ) sin( ω t ) + β ( γ ) cos( ω t )]
where
8.1. Time Response of Conventional Pressure Sensitive Paint
α( γ ) =
β(γ ) =
δ ln( 10 )
1 − 10
−δ
δ ln( 10 )
1 − 10
−δ
³
³
1
0
1
0
179
10 −δ η X ( γ ,η )dη
10 −δ η Y ( γ ,η )dη .
(8.17)
The quantity δ = β h /ln(10) represents the optical thickness of the paint layer.
The unsteady amplitude ratio and phase shift are given by
p1PSP / p1 = α 2 + β 2
φ = tan −1 ( β / α ) .
(8.18)
Figure 8.1 shows the attenuated amplitude ratio p1 PSP / p1 at different frequencies
for δ / h = 0.01 µm −1 and D m = 10 3 µm 2 /s .
The paint thickness affects both the frequency response and the signal-to-noise
ratio (SNR) of PSP. As the thickness increases, the luminescent signal from PSP
and thus the SNR increase, whereas the frequency response of PSP decreases as a
result of the attenuation of the unsteady amplitude ratio. Hence, there exists an
optimum thickness that balances the two conflicting requirements to achieve both
high frequency response and SNR. Considering the unsteady luminescent signal
I ( t ) = I 0 + I 1 sin( ω t ) , Schairer (2002) introduced the unsteady signal amplitude
I 1 = I 0 α 2 + β 2 and then the unsteady SNR, SNR' = I 1 / I 0 = I 0 α 2 + β 2 .
Figure 8.2 shows the normalized SNR' as a function of the relative thickness
h / h(-1.25dB) , where h(-1.25dB) is the thickness that corresponds to 1.25dB
( p1 PSP / p1 = 0.866 ) attenuation of the unsteady amplitude ratio as illustrated in
Fig. 8.1.
Thus, an empirical estimate for the optimum thickness is
hop / h(-1.25dB) ≈ 1 that corresponds to the maximum value of the normalized
SNR' . As shown in Fig. 8.3, the optimum thickness hop ≈ h(-1.25dB) decreases
with the unsteady pressure frequency for a given diffusivity and relative optical
thickness. Figure 8.3 indicates that the optimum thickness is less than 5 µm for
D m < 16 × 10 3 µm 2 /s when the pressure frequency is 100 Hz. For such a thin
paint layer, the absolute SNR ( ∝ I 0 ) is so low that accurate measurement of the
luminescent emission becomes difficult. This indicates that a conventional
polymer-based PSP is not suitable to unsteady measurements.
When an unsteady pressure variation is no longer small, the non-linear effect of
PSP response is appreciable, and the waveform of the PSP signal is distorted. In
this case, recovery of the true unsteady pressure from the distorted signal is nontrivial. Assuming that the oxygen concentration is uniform across a thin paint
layer, we substitute p PSP ( t ) ≡ p = [ O2 ] S −1φ O−21 into Eq. (8.15) and use the
general solution Eq. (8.7) for [ O2 ] , where S is the oxygen solubility of the
binder and φ O2 is the mole fraction of oxygen in air. Thus, at the air-paint
180
8. Time Response
interface ( z' = z / h = 1 ), we obtain a Voltera-type integral equation for the
function g t ( t ) = d g( t ) / dt = df ( t ) / dt
º
1 ª I ref
− A» − f ( 0 ) =
«
B p 0 ¬« I ( t )
¼»
³
t'
0
g t ( t' −u )W ( u ,1 ) du ,
(8.19)
where p0 = [ O2 ] 0 S −1φ O−21 is the initial pressure amplitude. In principle, after Eq.
(8.19) is solved for
f ( t ) , the unsteady pressure can be recovered, i.e.,
p( t ) = p0 f ( t ) . However, since the non-dimensional time variable t' = tDm / h 2
in Eq. (8.19) contains the diffusion timescale τ diff = h 2 / D m , recovery of the true
unsteady pressure is affected by the local paint thickness unlike steady-state PSP
measurements where the effect of the thickness is, at least theoretically speaking,
eliminated by the intensity ratio procedure.
Fig. 8.1. The unsteady amplitude ratio as a function of the paint thickness for
δ / h = 0.01 µm −1 and D m = 10 3 µm 2 /s . From Schairer (2002)
8.1. Time Response of Conventional Pressure Sensitive Paint
181
Fig. 8.2. The normalized SNR’ as a function of the relative paint thickness for
δ / h = 0.01 µm −1 and D m = 10 3 µm 2 / s . From Schairer (2002)
Fig. 8.3. The optimum thickness as a function of the unsteady pressure frequency for
δ / h = 0.01 µm −1 . From Schairer (2002)
182
8. Time Response
8.2. Time Response of Porous Pressure Sensitive Paint
8.2.1. Deviation from the Square-Law
Compared to a conventional homogeneous PSP, a porous PSP has a much shorter
diffusion time ranging from 18 µs to 500 µs due to enlarged air-polymer interface
(Sakaue and Sullivan 2001; Sakaue et al. 2002a).
Interestingly, recent
measurements of the response time for three polymers, GP197, GP197/BaSO4
mixture and Poly(TMSP), show that the classical square-law estimate Eq. (8.13)
does not hold for a porous PSP (Teduka 2001; Asai et al. 2001). As shown in Fig.
8.4, measurements gave the power-law relations for the diffusion timescale
τ diff ∝ h 1.83 for GP197, τ diff ∝ h 1.07 for GP197/BaSO4 mixture, and τ diff ∝ h 0.29
for Poly(TMSP) at 313.1 K. For a porous anodized aluminum (AA) surface, the
power-law relation is τ diff ∝ h 0.573 (Sakaue 1999; Sakaue and Sullivan 2001). For
the GP197 silicone polymer, the power-law exponent is close to 2 as predicted by
the classical estimate for a homogenous polymer film. However, the power-law
exponent for the porous materials GP197/BaSO4 mixture, Poly(TMSP), and AAPSP is significantly smaller than 2. In addition, Figure 8.5 shows that the powerlaw exponent for the polymer Poly(TMSP) linearly increases with temperature
over a temperature range of 293.1-323.1 K. In order to understand the time
response of a porous PSP, from a standpoint of phenomenology, Liu et al. (2001b)
derived the expressions for the effective diffusivity and diffusion timescale of a
porous layer.
τ diff ∝ h 1.83
Time constant, msec
1000
100
GP197
τ diff ∝ h 1.07
GP197/BaSO4
10
τ diff ∝ h 0.29
poly(TMSP)
1
τ diff ∝ h 0.573
0.1
AA-PSP
0.01
1
10
Thickness, micron
Fig. 8.4. The power-law relationship between the response time and coating thickness for
three polymers GP197, GP197/BaSO4 mixture and Poly(TMSP) at 313.1 K, and AA
surface at about 300K. Experimental data are from Teduka (2001), Asai et al. (2001), and
Sakaue (1999)
8.2. Time Response of Porous Pressure Sensitive Paint
183
0.5
Power-law exponent
0.4
0.3
0.2
0.1
0.0
290
295
300
305
310
315
320
325
Temperature, K
Fig. 8.5. The exponent of the power-law relation between time-scale and coating thickness
for the polymer Poly(TMSP) as a function of temperature. Experimental data are from
Teduka (2001) and Asai et al. (2001)
8.2.2. Effective Diffusivity
Diffusion in a porous material can be considered as a diffusion problem in a twophase system made up of one disperse phase and one continuous polymer or other
material. In PSP, the disperse phase is composed of numerous pores filled with
air. Figure 8.6 shows a typical scanning electron microscopic (SEM) image of an
anodized aluminum (AA) surface for PSP. Consider an element of a porous
polymer layer of the length l, width l, and thickness h, as shown in Fig. 8.7. The
coordinate z is normally directed to the polymer layer from the upper surface of
the layer. First, we assume that many cylindrical (tube-like) pores are distributed
and oriented in the z-direction in the element. The effective radius and depth of a
pore are denoted by rpore and h pore , respectively. The radius of a pore is much
larger than the size of a molecule of oxygen. In general, the depth of a pore is
smaller than or equal to the layer thickness, i.e., h pore ≤ h . For simplicity of
expression, the normal directional derivative of the oxygen concentration [O2 ] at
the air-polymer interface is denoted by
∂ [O2 ]
.
(8.20)
v n (z) =
∂n
184
8. Time Response
20nm ~ 100nm micropore
(a): SEM picture.
(b): Schematic.
Fig. 8.6. SEM image and schematic of an anodized aluminum (AA) surface. From Sakaue
(1999)
Fig. 8.7. Element of a porous binder layer
The effective diffusivity Dmeff of the porous polymer layer with many
cylindrical pores is given by a balance equation between the mass transfer through
the apparent homogenous upper surface and the total mass transfer across the airpolymer interface, i.e.,
2
2
Dmeff l 2 v n ( 0 ) = Dm ( l 2 − N poreπ r pore
)v n ( 0 ) + Dm N poreπ r pore
v n ( h pore )
+ Dm N pore 2π rpore
³
h pore
0
,
v n ( z )dz
(8.21)
where N pore is the total number of the pores in the element and Dm is the
diffusivity of the polymer continuum. The integral term in Eq. (8.21) is the total
mass transfer across the peripheral surface of the pores in the element. Thus, the
effective diffusivity Dmeff is given by
2
Dmeff / Dm = 1 + [ v n ( h pore ) / v n ( 0 ) − 1 ] N pore π r pore
l −2
+ N pore 2π r pore l −2 v n−1 ( 0 )
³
h pore
0
v n ( z )dz
.
(8.22)
8.2. Time Response of Porous Pressure Sensitive Paint
185
In a simplified case where v n (z) = const . across the thin layer, Eq. (8.22) becomes
−1
D meff / D m = 1 + 2 aV r pore
h,
(8.23)
2
h pore l −2 h −1 is the volume fraction of the cylindrical pores
where aV = N pore π r pore
in the polymer layer. Eq. (8.23) indicates that an increase of the effective
diffusivity is proportional to the volume fraction of the pores and a ratio between
the polymer layer thickness and the radius of the pore. Eq. (8.23) for Dmeff is
valid only for an ideal porous polymer layer with the straight cylindrical pores
oriented normally. Nevertheless, this model can be generalized for real porous
polymers where topology of the pores is often highly complicated.
For more realistic modeling, the topological structure of a pore is considered as
a highly convoluted and folded tube in a polymer layer while the cross-section of
the tube remains unchanged. The integral in Eq. (8.22) should be replaced by an
integral along the path of a highly convoluted tube-like pore. In this case, the
concept of the fractal dimension should be introduced because the length of a
highly convoluted tube is no longer proportional to the linear length scale of the
tube in the z-direction (e.g. h pore ) (Mandelbrot 1982). According to the lengthd
/2
fr
area relation for a fractal path, the integral along the path is proportional to A pore
fr
or h pore
, where d fr ( 1 ≤ d fr < 2 ) is the fractal dimension of the path of a pore
d
2
and A pore ∝ h pore
is the characteristic area covering over the path.
speaking, the fractal dimension represents the degree of complexity of
pathway. In order to take the fractal nature of pores into account, Eq.
generalized using a Riemann-Liouville fractional integral of the order
(Nishimoto 1991)
Loosely
the pore
(8.22) is
d fr , i.e.,
2
Dmeff / Dm = 1 + [ v n ( h pore ) / v n ( 0 ) − 1 ] N pore π r pore
l −2
+ N pore 2π rpore l −2 v n−1 ( 0 )
³
h pore
0
v n ( z )( dz )
d fr
.
(8.24)
1− d
Note that a unitary constant with the dimension [ m fr ] is implicitly embedded
in the third term in the right-hand side of Eq. (8.24) to make Eq. (8.24)
dimensionally consistent. This dimensional constant is implicitly contained in all
the results derived from Eq. (8.24). In a simplified case where v n (z) = const .
across a thin layer, a generalized expression for Dmeff is
D meff
Dm
= 1+
−1
2 aV r pore
§ h pore
¨
Γ ( 1 + d fr ) ¨© h
·
¸
¸
¹
d fr − 1
h
d fr
,
(8.25)
where Γ ( 1 + d fr ) is the gamma function. Here, h pore is interpreted as a linear
length scale of a convoluted tube in the z-direction and aV is the volume fraction
186
8. Time Response
of the apparent cylindrical pores. Eq. (8.25) clearly shows that the effective
d
diffusivity Dmeff is not only proportional to h fr , but also related to the porosity
−1
and h pore / h . For d fr = 1 , Eq. (8.25) is simply reduced to
parameters aV r pore
Eq. (8.23) for the straight cylindrical pores.
8.2.3. Diffusion Timescale
For a porous polymer layer where diffusion is Fickian under some microscopic
assumptions (Cunningham and Williams 1980; Neogi 1996), the diffusion
equation Eq. (8.1) is still a valid phenomenological model as long as the
diffusivity Dm is replaced by the effective diffusivity Dmeff . Hence, an estimate
for the diffusion timescale of a porous PSP layer is
h 2 / Dm
.
(8.26)
τ diff ∝
d fr −1
−1
§ h pore ·
2 aV rpore
d fr
¨
¸
h
1+
Γ ( 1 + d fr ) ¨© h ¸¹
Eq. (8.26) as a generalized form of Eq. (8.13) clearly illustrates how the fractal
−1
dimension d fr and the porosity parameters aV r pore
and h pore / h affect the
−1
<< 1 or h pore / h << 1 , Eq. (8.26)
response time of a porous PSP. For aV rpore
naturally approaches to the classical square-law estimate Eq. (8.13) for a
homogenous polymer layer.
−1
On the other hand, for aV rpore
>> 1 and h pore / h ≈ 1 , another asymptotic
estimate for τ diff is a simple power-law as well
τ diff ∝ h 2 −d fr / Dm .
(8.27)
The estimate Eq. (8.27) is asymptotically valid for a very porous polymer layer.
The exponent in the power-law relation between the response time τ diff and
thickness h deviates from 2 by the fractal dimension d fr due to the presence of
the fractal pores in the polymer layer. The relation Eq. (8.27) provides an
explanation for the experimental finding that the exponent q in the power-law
relation τ diff ∝ h q is less than 2 for a porous PSP. In addition, this relation can
serve as a useful tool to extract the fractal dimension of the tube-like pores in a
very porous polymer layer from measurements of the diffusion response time. For
example, the fractal dimension d fr of a pore in the polymer Poly(TMSP) is
d fr = 1.71 , while for GP197/BaSO4 mixture the fractal dimension d fr is close to
one. In addition, based on the experimental results shown in Fig. 8.5, we know
that the fractal dimension d fr for Poly(TMSP) linearly decreases with
temperature in a temperature range of 293.1-323.1 K. This implies that the
geometric structure of a pore in Poly(TMSP) may be altered by a temperature
8.3. Measurements of Pressure Time Response
187
change. Note that the diffusivity Dm of oxygen mass transfer is also temperaturedependent, but it is independent of the coating thickness h. Therefore, the
experimental results in Fig. 8.5 mainly reflect the temperature effect on the
geometric structure of pores in the polymer rather than the diffusivity.
Table 8.1. Response times and luminescent lifetimes of PSPs
Paint
Thickness
(µm)
Lifetime
(µs)
LPSF1 (pyrene)
PSPL2 (pyrene)
PSPL4 (pyrene)
PSPF2 (pyrene)
PF2B (Ru(dpp))
2
20
13
PF2B (Ru(dpp))
PF2B (Ru(dpp))
PF2B (Ru(dpp))
PtOEP/polymer
15
25
35
19
PtOEP/GP197
PtOEP/GP197
PtOEP/GP197
Ru(dpp)/RTV
Ru(dpp)/RTV
Ru(dpp)/RTV
Ru(dpp)/RTV
Ru(dpp)/PDMS
PtOEP/GP197
PtOEP/copolymer
H2TFPP/silica
H2TFPP/TLC
luminophore/AA
22
26
32
6
11
16
20
4-5
-
50
50
50
5
5
5
5
5
50
50
1.4 s
1.6 s
2.4 s
22.4 ms
58.6 ms
148 ms
384 ms
3-6 ms
2.5 s
0.4 s
1.5-10 ms
25 µs
18-90 µs
Ru(dpp)/FIB and
alumina
PtTFPP/FIB and
alumina
PtTFPP/porous
ceramic
Ru(dpp)/AA
Ru(dpp)/TLC
-
5
<500 µs
-
50
<500 µs
-
50
60 µs
Ponomarev &
Gouterman (1998)
Ponomarev &
Gouterman (1998)
Scroggin (1999)
-
5
5
80 µs
70 µs
Sakaue et al. (2001)
Sakaue et al. (2001)
Response
time
Comments
References
5
5 ms
0.2 s
0.172 s
0.1-2.6 ms
0.48 s
Borovoy et al. (1995)
Fonov et al. (1998)
Fonov et al. (1998)
Fonov et al. (1998)
Carroll et al. (1996b)
5
5
5
50
0.88 s
1.2 s
2.4 s
0.82 s
OPTROD formulation
OPTROD formulation
OPTROD formultation
OPTROD formulation
McDonnell Douglas (MD)
formulation
MD formulation
MD formulation
MD formulation
concentrated luminophore near
outer surface of the binder
silica with a binder
depended on the luminophore
and anodization processes
approached the apparatus
response time
approached the apparatus
response time
Carroll et al. (1996b)
Carroll et al. (1996b)
Carroll et al. (1996b)
Carroll et al. (1996b)
Carroll et al. (1996b)
Carroll et al. (1996b)
Carroll et al. (1996b)
Winslow et al. (1996)
Winslow et al. (1996)
Winslow et al. (1996)
Winslow et al. (1996)
Hubner et al. (1997)
Baron et al. (1993)
Baron et al. (1993)
Baron et al. (1993)
Baron et al. (1993)
Mosharov et al. (1997)
8.3. Measurements of Pressure Time Response
The fast time response of PSP was achieved by Baron et al. (1993) using a
commercial porous silica thin-layer chromatography (TLC) plate as a binder; the
observed response time of this PSP was less than 25 µs. Although this fragile PSP
cannot be practically used for wind tunnel testing, Baron’s work suggest that a
short response time of PSP can be obtained using a porous material as a binder.
Mosharov et al. (1997) reported that the response time of anodized aluminum
188
8. Time Response
(AA) PSP was in a range of 18-90 µs, depending on a luminophore and on some
features of an anodization process. Asai et al. (2001, 2002) also measured the
response time of an AA-PSP with Ru(dpp) as a luminophore using a pressure
chamber with a solenoid type valve. According to Jordan et al. (1999b), a sol-gelbased PSP achieved the frequency response of as high as 6 kHz. Ponomarev and
Gouterman (1998) and Scroggin et al. (1999) developed binders by mixing hard
particles with polymers to increase the degree of porosity. Ponomarev and
Gouterman found that increasing the number of hard particles above a critical
pigment volume concentration drastically shortened the response time. Table 8.1
summarizes the response times of some PSP formulations along with their
luminescent lifetimes.
Solenoid valve type switching has been used to generate a step change in
pressure for measurements of the response time of PSP by a number of
researchers (Engler 1995; Carroll et al. 1995, 1996; Winslow et al. 1996;
Mosharov et al. 1997; Fonov et al. 1998). Figure 8.8 shows a typical pressure
jump apparatus used by Asai et al. (2002) for testing the time response of PSP.
This apparatus had a small test chamber connected directly to a fast opening valve
having a time constant of a few milliseconds. Sample plates used in this apparatus
were typically aluminum coupons coated with PSP. Figure 8.9 shows the time
response of the luminescent intensity for several PSP formulations using PtOEP as
a probe molecule in binders GP197, AA, and Poly(TMSP) to a step change in
pressure from vacuum to the atmospheric pressure. The pressure signal from a
kulite® pressure transducer was also shown in Fig. 8.9 as a reference. The PSP
based on GP197 was very slow and its time constant was in the order of seconds.
Figure 8.10 shows the thickness effect on the time response of PtOEP in GP-197
to a step change of pressure (Carroll et al. 1996). In contrast, AA-PSP had the
sub-millisecond time response, and Poly(TMSP)-PSP had a comparable response
time to AA-PSP since Poly(TMSP) having a very large free volume is very
porous. The time constant of Poly(TMSP)-PSP was about a few milliseconds.
Jordan et al. (1999b) conducted frequency response experiments of sol-gel-based
PSP using a speaker driver producing an oscillating pressure wave, and achieved
the frequency response as high as 6 kHz. For a porphine-based PSP on a silica-gel
TLC plate, Sakamura et al. (2002) utilized Cassegrain optics to detect a periodic
pressure fluctuation of about 1 kHz in a chapped impinging air jet. The
aforementioned measurements indicate that a high porosity is required to achieve
the high time response of PSP. This viewpoint was examined by Asai et al.
(2001) for a mixture of GP-197 with hard particles of BaSO4. Figure 8.11 shows
the reduced response time to a step change of pressure with elevating the
concentration of BaSO4 as a result of an increased porosity. Asai et al (2001) also
noticed that a fast-responding porous PSP usually had lower temperature
sensitivity.
8.3. Measurements of Pressure Time Response
Light Guide
from Xe Lamp
Pressure
Transducer
Bandpass Filter
for Excitation Light Photomultiplier
Tube (PMT)
Sharp Cut Filter
PSP
Sample
Solenoid
Valve
Dichroic Filter
Vacuum or
Atmosphere
Bandpass Filter
for Luminescence Emission
Fig. 8.8. Schematic of a pressure jump apparatus. From Asai et al. (2002)
1.0
0.0
-1.0
-2.0
Kulite(ref)
-3.0
-4.0
0
50
100
150
200
250
300
350
400
time, msec
(a)
1.5
1.4
GP197
1.3
1.2
1.1
1.0
0
50
100
150
200
250
300
350
400
time, msec
(b)
1.0
0.8
Anodized
0.6
0.4
0.2
0.0
0
(c)
50
100
150
200
250
time, msec
Fig. 8.9. (cont.)
300
350
400
189
190
8. Time Response
1.0
0.9
poly(TMSP)
0.8
0.7
0.6
0.5
0.4
0
50
100
150
200
250
300
350
400
time, msec
(d)
Fig. 8.9. Time response of several PSPs to a step change in pressure, (a) kulite sensor
(reference), (b) GP197-PSP, (c) AA-PSP, and (d) poly(TMSP)-PSP, where PtOEP is used a
probe molecule. From Asai et al. (2002)
1.2
(P - Pmin)/(Pmax - Pmin)
1.0
0.8
0.6
Pressure transducer
22 µm paint
26 µm paint
32 µm paint
0.4
0.2
0.0
0
1
2
3
4
Time (second)
Fig. 8.10. Time response of PtOEP in GP197 to a step change of pressure, depending on
the paint thickness. From Carroll et al. (1996)
8.3. Measurements of Pressure Time Response
191
1.2
1.0
0.8
increasing particle numbers
0.6
BaSO4:GP197=0g:1g
0.4
BaSO4:GP197=0.5g:1g
0.2
BaSO4:GP197=2g:1g
0.0
transducer
-0.2
-1
0
1
2
3
4
time, sec
5
6
7
8
Fig. 8.11. Effect of the BaSO4 particle concentration in the polymer GP-197 on the time
response of BaSO4/GP197 PSP at 313.1 K. From Asai et al (2001)
Another apparatus for creating a step pressure change is a shock tube (Sakaue
et al. 2001; Teduka et al. 2000). A shock tube can generate a pressure rise in a
few microseconds, and therefore it is a good device for testing a porous PSP
having a response time less than a millisecond. Figure 8.12 shows a schematic of
a simple shock tube for testing the time response of PSP (Sakaue et al. 2001). The
shock tube had a 55×40 mm cross-section, a 428 mm long driver section, and a
485 mm long driven section. An aluminum foil diaphragm was burst by a
pressure difference between the driver and driven sections, where the driver
pressure was one atmospheric pressure. A pressure transducer (PCB Piezotronics
model 103A11), which was connected to a 2 mm diameter pressure tap on the
shock tube wall, was used to measure the unsteady reference pressure. Absolute
pressures were measured using an Omega pressure transducer connected to the
driven section. PSP was applied to a 25.4 mm square aluminum block flush
mounted to the shock tube wall. The reference pressure transducer and PSP
sample were mounted 300 mm from the diaphragm. A 532-nm laser was used as
an illumination source for PSP and the laser spot size was about 2 mm on the
sample surface. The luminescent emission from PSP was collected by a PMT
through a long pass filter (> 570 nm) and the readout voltage from the PMT was
acquired using a LeCroy oscilloscope. The response time of the PMT was about 2
µs. The time resolution of the apparatus was also limited by the laser spot size.
The laser spot size d spot and the shock velocity u s gives the limiting detectable
pressure rising time t lim it = d spot / u s (about 3-5 µs) for this setup.
192
8. Time Response
steady absolute
pressure transducer
driven section (low pressure, p1) driver section (atmosphere, p4)
unsteady pressure transducer
PSP
flow directions
vacuum
diaphragm
PMT
green laser
oscilloscope
Fig. 8.12. Schematic of a simple shock tube setup for testing PSP time response. From
Sakaue (1999)
AA-PSP
pressure tap
theoretical calculation
pressure (kPa)
100
80
incident normal shock
60
40
reflected normal shock
20
0.0
0.3
0.6
0.9
1.2
1.5
time (ms)
Fig. 8.13. Pressure data obtained from AA-PSP with a thickness of 9 µm and pressure
transducer compared with theoretical calculation. From Sakaue (1999)
Figure 8.13 shows typical pressure signals from a Ru(dpp) AA-PSP (9 µm
thick) and the pressure transducer along with the theoretical pressure jumps
associated with the incident and reflected normal shock waves. This AA-PSP was
able to follow the sharp pressure rises after the incident and reflected shock waves
passed through the laser-illuminated spot. Figure 8.14 shows the normalized
pressure signals from the AA-PSP with different thickness values (4.3, 9.0, 13.2,
and 27.2 µm). It was found that the diffusion response time of this AA-PSP
8.3. Measurements of Pressure Time Response
193
followed the power-law relation τ diff ∝ h 0.573 . Figure 8.15 shows a comparison of
the time response of four PSP formulations to a step change of pressure. These
formulations used the same probe molecule Ru(dpp) with four different binders:
AA, TLC, polymer/ceramic (PC), and conventional polymer RTV. The response
times of AA-PSP and TLC-PSP were in the order of ten microseconds, whereas
the conventional RTV-PSP had a much longer response time (in the order of
hundred milliseconds). In addition, it was found that PC-PSP had a longer
response time (about 1 ms) than the thicker but more porous TLC-PSP. For a very
porous PSP, the porosity of a binder had more pronounced influence on the time
response of PSP than the binder thickness. This is consistent with the theoretical
analysis presented in Section 8.2.
normalized pressure
1.2
1.0
0.8
l = 4.3 µm, τ = 34.8 µs
l = 9.0 µm, τ = 70.9 µs
l = 13.2 µm, τ = 80.0 µs
l = 27.2 µm, τ = 102 µs
0.6
0.4
0.2
0.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
time (ms)
Fig. 8.14. Normalized pressure response of AA-PSP with different values of the paint
thickness l. From Sakaue (1999)
normalized pressure
1.2
1.0
0.8
0.6
AA-PSP4
TLC-PSP
polymer/ceramic PSP
0.4
0.2
0.0
0.0
(a)
0.2
0.4
time (ms)
Fig. 8.15. (cont.)
0.6
0.8
194
8. Time Response
normalized pressure
1.2
1.0
0.8
0.6
0.4
polymer PSP
0.2
0.0
0
(b)
50
100
150
200
250
300
350
400
time (ms)
Fig. 8.15. Comparison of the time response among (a) porous Ru(dpp)-based PSPs (AAPSP, TLC-PSP, and PC-PSP) and (b) conventional polymer PSP Ru(dpp) in RTV. From
Sakaue (1999)
8.4. Time Response of Temperature Sensitive Paint
Similar to PSP, TSP has two characteristic timescales: the luminescent lifetime
and the thermal diffusion timescale. The luminescent lifetimes of EuTTA-dope
and Ru(bpy)-Shellac TSPs at room temperature are about 0.5 ms and 5 µs,
respectively. The time response of EuTTA-dope TSP is intrinsically limited by its
long luminescent lifetime, while Ru(bpy)-Shellac TSP has a much shorter
luminescent lifetime. Overall, the time response of TSP is strongly dependent
upon the boundary conditions of heat transfer in a specific application. Based on
the transient solution of the heat conduction equation, the thermal diffusion time
for a thin TSP coating is in the order of h 2 / α T , where h is the coating thickness
and α T is the thermal diffusivity of TSP. In a convection-dominated case, the
thermal diffusion time can also be expressed as hk / α T hc , where k is the thermal
conductivity and hc is the convective heat transfer coefficient. In general, the
thermal diffusion time is much larger than the luminescent lifetime for many TSP
formulations, and therefore thermal diffusion limits the time response of TSP. In
contrast to PSP where oxygen diffusion always obeys the no-flux condition at a
solid boundary, heat transfer to the substrate through a non-adiabatic wall
inevitably affects the thermal time response of TSP in actual experiments. Hence,
the timescale of TSP depends on not only the thermal conductivity of the paint
itself, but also the boundary conditions in a specific heat transfer problem for TSP
application. To measure the time response of TSP to a rapid change of
temperature, Liu et al. (1995c) conducted experiments of pulse laser heating on a
metal film and step-like jet impingement cooling.
8.4. Time Response of Temperature Sensitive Paint
195
8.4.1. Pulse Laser Heating on Thin Metal Film
We consider short-pulse laser heating on a thin metal film to determine the
thermal diffusion timescale of TSP applied to the film. The heat conduction
equation for this problem is
∂θ
= αT ∇ 2θ ,
∂t
(8.28)
where θ = T − Tin is a temperature change of the film from an initial temperature
Tin and α T is the thermal diffusivity of the metal film. The Lapalce operator in
Eq. (8.28) is defined as ∇ 2 = ∂ 2 / ∂r 2 + r −1 ∂ / ∂r + ∂ 2 / ∂ z 2 , where r is the radial
distance from the center of a hot spot heated by a laser and z is the coordinate
normal to the metal film directing from the heated side to other side. The initial
temperature Tin is assumed to be the ambient temperature. After heated by a laser
pulse, the film is cooled down due to natural convection on both the sides of the
metal film. When the surface temperature of the metal film decreases fast enough
along the radial direction from the center of the hot spot (i.e., rθ → 0 as r → ∞ ),
we introduce a spatially averaging operator
< θ >2 =
2π
Aeff
³
∞
0
rθ dr
,
(8.29)
where Aeff is the effective area of the hot spot. Hence, applying the spatially
averaging operator to Eq. (8.28), we have the unsteady 1D heat conduction
equation
∂ 2 < θ >2
∂ < θ >2
= αT
.
(8.30)
∂ z2
∂t
The initial and boundary conditions for Eq. (8.30) are
< θ > 2 ( z , 0 )= 0,
∂ < θ > 2 ( 0, t )
= Plaser δ ( t ) − hc < θ > 2 ( 0 , t )
∂z
∂ < θ > 2 (η m , t )
−k
= hc < θ > 2 ( η m , t )
∂z
−k
(8.31)
where hc is the average heat transfer coefficient of natural convection, k is the
thermal conductivity, δ(t) is the Dirac-delta function, η m is the metal film
thickness, and Plaser represents the strength of the pulse-laser heat source. There
are two physical processes involved: rapid heating of the film by the laser pulse
and relatively slow cooling process due to natural convection. At the beginning,
since the film is heated in a very short time interval, the natural convection terms
in the boundary conditions can be neglected; thus, the problem is simplified for
the rapid heating process. For a thin metal film ( η m << 1), application of the
Laplace transform Θ ( z , s ) = La( < θ > 2 ) to Eqs. (8.30) and (8.31) yields
196
8. Time Response
Θ ( η m ,s ) =
2 Plaser α T
exp( − s / α T η m )
k s
1 − exp( −2 s / α T η m )
≈
Plaser α T
exp( − η m s / α T ) ,
k ηm s
(8.32)
where s is the complex variable in the Laplace transform. The inverse Laplace
transform leads to an asymptotic expression for the laser heating when t is small
< θ >2 =
Plaser α T
erfc( τ 1 / t ) .
kη m
(8.33)
The characteristic timescale for the laser heating is τ 1 = η m2 /( 4α T ) .
For the slow cooling process due to natural convection after the pulse-laser heat
source ceases, we introduce an additional average operator across the metal film
< θ >3 =
1
ηm
³
ηm
0
< θ > 2 dz .
(8.34)
Applying the operator Eq. (8.34) to Eq. (8.30) leads to a simple lumped model for
the cooling process
d < ș >3
2α h
α P į(t)
= − T c < ș > 3 + T laser
.
dt
Șm k
k Șm
(8.35)
The solution to Eq. (8.35) is
< θ >3 =
Plaser α T
exp( − 2t / τ 2 ) .
kη m
(8.36)
Eq. (8.36) describes an exponential decay of the averaged temperature, which
gives the characteristic timescale τ 2 = kη m /( 2α T hc ) for the cooling process due
to natural convection.
Obviously, for the problem of pulse laser heating on a thin film, there are the
fast timescale τ 1 = η m2 /( 4α T ) and slow timescale τ 2 = kη m /( 2α T hc ) . The time
response of Ru(bpy)-Shellac TSP to a rapid temperature rise was tested by
utilizing short pulse laser heating on a 25-µm thick steel film. Figure 8.16 is a
schematic of the experimental set-up. One side of the steel film was heated by a
pulse laser beam with a 8-ns duration from a Nd:YAG laser (532 nm at an 800-mJ
maximum output) through a focusing lens. The opposite side of the steel film was
coated with a 10-µm thick Ru(bpy)-Shellac TSP illuminated by a 457-nm blue
beam from a 1-mW Argon laser at the hot spot. The response of the luminescent
emission from TSP to pulse laser heating was detected using a PMT, and the
signal was acquired using an oscilloscope (Tektronix TDS 420). The surface
temperature was calculated from the luminescent intensity using a priori
calibration relation for TSP. Figure 8.17 shows a typical transient response of the
surface temperature to pulse laser heating on the steel film. The surface
8.4. Time Response of Temperature Sensitive Paint
197
temperature increases rapidly after heating at the film and then decays due to
natural convection. To estimate the response times, the asymptotic solutions Eq.
(8.33) and Eq. (8.36) were used to fit the experimental data. The response time of
TSP for the laser heating process was τ 1 = 0.25 ms, while the time constant for
the cooling process by natural convection was τ 2 = 12.5 ms.
532 nm pulse green beam
YAG Laser
lens
25 microns thick steel foil
painted side
550 nm LP filter
457 nm blue beam
PMT
Argon laser for
illumination
Fig. 8.16. Schematic of a pulse laser heating setup for testing TSP time response. From Liu
et al. (1997b)
<T - Tin> (deg. C)
25
paint measurement
16erfc[(τ1/t)0.5], τ1 = 0.25 ms
16exp(-2t/τ2), τ2 = 25 ms
20
15
10
5
0
-5
0
5
10
15
20
25
time (ms)
Fig. 8.17. Temperature response of Ru(bpy)-Shellac TSP to pulse laser heating on a steel
foil. From Liu et al. (1997b)
198
8. Time Response
8.4.2. Step-Like Jet Impingement Cooling
Sudden fluid jet impingement to TSP coated on a hot body, which produces a
rapid decrease of the surface temperature, can be used for testing the time
response of TSP. A lumped heat transfer model gives an approximate solution for
a temporal evolution of the temperature on a paint layer during step jet
impingement cooling
T − Tmin
= exp( − t / τ 3 ) ,
(8.37)
Tin − Tmin
where Tin is the initial temperature of the paint and Tmin is the minimum
temperature of the paint that is asymptotically reached as t → ∞. The timescale
for this cooling process is τ 3 = kh /( α T hc ) , where hc is the average heat transfer
coefficient of the impinging jet and h is the paint thickness.
Figure 8.18 shows an experimental setup for step jet impingement cooling. A
475-nm blue laser beam was used for illumination at the impingement point. The
luminescent intensity was measured using a PMT and then was converted into
temperature using a priori calibration relation. To achieve a small response time,
a sub-zero temperature impinging Freon jet generated by a Freeze-it£ sprayer was
utilized, where a mechanical camera shutter was used as a valve to control issuing
of the jet. After the shutter opened within 1 ms, the Freon jet impinged on the
o
surface of a hot soldering iron (about 100 C) which was coated with a 19-µm thick
Ru(bpy)-Shellac TSP. Figure 8.19 shows a rapid decrease of the surface
o
temperature on the thin paint coating to the minimum temperature of about 44 C.
The measured timescale τ 3 of TSP for this cooling process was 1.4 ms. Cool air
impingement jet was also tested; the measured timescales were 16 ms and 25 ms
for 19 µm and 38 µm thick Ru(bpy)-Shellac TSP coatings, respectively.
Hot body
550 nm LP filter
paint
457 nm blue beam
PMT
jet
Argon laser for
illumination
Fig. 8.18. Schematic of a step-like jet impingement cooling setup for testing TSP time
response
8.4. Time Response of Temperature Sensitive Paint
199
1.5
(T - Tmin)/(Tmax - Tmin)
exp(- t/τ), τ = 1.4 ms
Ru(bpy)-Shellac paint
1.0
0.5
0.0
0
5
10
Time (ms)
Fig. 8.19. Temperature response of Ru(bpy)-Shellac TSP to step-like Freon jet
impingement cooling
9. Applications of Pressure Sensitive Paint
9.1. Low-Speed Flows
9.1.1. Airfoil Flows
PSP measurements are challenging in low-speed flows where a change in air
pressure is very small. The major error sources, notably the temperature effect,
image misalignment and CCD camera noise, must be minimized to obtain
acceptable quantitative pressure results at low speeds. Brown et al. (1997, 2000)
made baseline PSP measurements on a NACA 0012 airfoil at low speeds (less
than 50 m/s). The experiments systematically identified the major error sources
affecting PSP measurements at low speeds and developed the practical
procedures for minimizing these errors. After all efforts were made to reduce
the errors, reasonably good pressure results were obtained at speeds as low as 10
m/s.
Brown (2000) conducted three sets of tests (Cases I, II and III) with
increasingly improved instrumentation arrangement and data processing. All the
tests were made in The NASA Ames Research Test Facility Wind Tunnel
having a 12-in high, 12-in wide and 24-in long test section. The Mach number
ranged from 0.02 to 0.4. PSP measurements were conducted on an unswept
stainless steel NACA 0012 airfoil with a 3-in chord and 9-in span. The airfoil
was mounted vertically, and there is a 1.5-in gap between the airfoil’s edges and
the top/bottom of the test section. Sixteen mid-span pressure taps (0.048-in
diameter) were machined into the upper surface of the airfoil. Each test case
was conducted consistently using the same test equipment. Images were
obtained using a 14-bit Photometrics CH250 CCD camera with a Melles Griot
filter (650±20 nm) attached to a 50-mm Nikor lens. Data were collected on a
PC using associated Photometrics imaging software. Two Electrolite UV lamps
provided illumination for PSP. Pressure tap measurements were performed with
differential pressure meters connected to the airfoil via Tygon tubing. The
airfoil was coated with FIB-7 basecoat and PtTFPP/FIB-7 PSP developed by the
University of Washington. The white basecoat provided surface scattering to
enhance the luminescent emission received by the camera. Application of the
basecoat and PSP was performed using a commercial spray air gun. The
202
9. Applications of Pressure Sensitive Paint
basecoat was lightly buffed to reduce surface roughness. The sufficiently thick
PSP topcoat applied to the basecoat was insured to be as uniform as possible.
After completing the PSP application, a hot-air gun was used to raise PSP above
o
its glass transition temperature of about 70 C. This annealing process reduced
the temperature sensitivity of PSP.
The first set of tests (Case I) provided useful PSP testing experience to identify
the potential problems. The airfoil was secured onto the tunnel test section with
o
the angle of attack of 5 . The camera and two UV lamps were secured onto a rigid
double U-frame surrounding the test section mounted on the ground floor by bolts,
which were approximately 18 inches away from the test section. The camera
viewed perpendicularly the airfoil on which ten registration marks were placed for
image registration. The total thickness of the basecoat and PSP was about 34 µm
and the roughness of PSP was about 2.6 µm. The tests were run at 10, 20, 30, 40
and 50 m/s. For each tunnel run period, the tunnel settling temperature was
recorded just priori to and just after image acquisition. The temperature change
o
was within 0.17 C during a single period of image acquisition, depending on the
flow velocity. The typical results for a speed of 30 m/s and the angle of attack of
o
5 are shown in Figs. 9.1-9.3. Figure 9.1 is the in-situ Stern-Volmer plot for PSP
obtained using pressure tap data, indicating a large variation and a poor correlation
between the luminescent intensity and pressure. The corresponding PSP image is
shown in Fig. 9.2, where flow is from left to right. Although the low-pressure
region near the leading edge is visible in the PSP image, apparent striation patterns
and granular features corrupt the quality of the PSP data. This random spatial
noise can be clearly seen in the chordwise pressure distribution at the mid-span, as
shown in Fig. 9.3. The PSP data at speeds of 10, 20, 40 and 50 m/s had similar
noise patterns.
Several problems were identified that might contribute to the large spatial
noise. First, scratches on the tunnel plexiglass wall caused the streaky patterns.
Secondly, PSP suffered from a considerable thickness variation due to poor
application of the paint. The effect of the surface roughness could not be
completely corrected using the image registration technique for the non-aligned
wind-off and wind-on images. The third problem was related to model motion
with respect to the lamps. Since the lamps were fixed on the ground floor, the test
section underwent a lateral oscillation estimated to be on the order of 10 Hz
relative to the lamps. If the model moved in a non-homogenous illumination field,
the effect of the motion could not be corrected using the image registration
technique. Also, this problem exaggerated the second problem associated with the
surface roughness. Note that these problems might not be serious for PSP
measurements in high subsonic, transonic and supersonic flows.
In Case II tests, a new test section plexiglass wall was installed to replace the
scratched one. The model was cleaned and repainted carefully; thus, the
roughness of the PSP layer was reduced to 0.89 µm from 2.6 µm in Case I. In
order to reduce the relative motion between the model and lamps, a new mounting
structure for the camera and lamps was designed and constructed, which was
secured to the test section rather than the ground floor. Therefore, the lateral and
vertical shifts in the image plane due to the motion were reduced to 0.43 and 0
pixels from 2.41 and 1.9 pixels in Case I, respectively. In addition, to reduce the
9.1. Low-Speed Flows
203
temperature change between the wind-off and wind-on images, the experimental
procedure was revised such that the tunnel was run for one hour and the wind-off
image was taken immediately after the wind-on image. In this way, the
temperature distribution on the model in the wind-off case was close to that in the
wind-on case. Figures 9.4-9.6 show results obtained in Case II tests for a speed of
o
30 m/s and the angle of attack of 5 . The in-situ Stern-Volmer plot in Fig. 9.4 has
a better linearity and an improved correlation with the pressure tap data. The PSP
image in Fig. 9.5 is also considerably improved, clearly showing not only a correct
chordwise pressure profile, but also the 3D effect near the airfoil edges. The
pressure tap gutter lines are also visible in the image since the gutter line epoxy
has a different thermal conductivity from the stainless steel such that a small
temperature difference exists. As shown in Fig. 9.6, the chordwise pressure
distribution at the mid-span clearly shows a reduced noise level compared to the
corresponding result in Case I.
In Case III tests, careful application of PSP led to a further reduction of the
paint roughness to 0.46 µm. To increase the statistical redundancy in image
registration, all 16 pressure taps were used in images as registration marks, in
addition to the original eight registration marks applied to the paint surface. For
better in-situ calibration of PSP, 32 ‘virtual pressure taps’ located at 10 pixels
above and below the spanwise location of the actual taps were created and used in
images under the assumption of two-dimensionality of flows near the mid-span.
As shown in Fig. 9.7, it was found that the use of the additional virtual taps
provided an accuracy of 10% better than that achieved by using the actual taps
only in least-squares estimation for in-situ calibration. The results of Case III tests
o
are shown in Figs. 9.7-9.9 for a speed of 30 m/s and the angle of attack of 5 .
Overall, the results indicate the improved quality of the PSP data and a reduced
noise level compared to Case II.
The valuable lessons learned from this study of low-speed PSP measurements
are summarized as follows. (1) Vibration and model movement with respect to
cameras and lamps must be minimized to reduce the image registration error. (2)
The temperature-induced errors must be minimized. Not only the tunnel test
section, but also the model surface should reach a stable equilibrium state of
temperature priori to acquisition of the wind-on images. It is highly suggested that
the wind-off image should be acquired immediately after the corresponding windon image as soon as the tunnel is shut down. (3) The quality of application of both
the basecoat and PSP topcoat to a surface is critical and the paint roughness must
be minimized to obtain good results at low speeds. (4) In-situ PSP calibration
utilizing a sufficient number of pressure taps is required to eliminate the
systematic errors and obtain quantitative results. (5) Image registration is critical
to reduce the spatial noise. (6) Scientific-grade CCD cameras (14 and 16 bits)
should be used, and averaging a large number of images should be performed to
reduce the photon shot noise and other random noises. Note that some of the
above procedures for controlling the error sources are not generally applicable to
large production wind tunnels.
204
9. Applications of Pressure Sensitive Paint
Fig. 9.1. In-situ calibrated Stern-Volmer plot in Case I for 30 m/s and α = 5
o
Fig. 9.2. Calibrated PSP image in Case I for 30 m/s and α = 5 . From Brown (2000)
o
Fig. 9.3. Chordwise pressure profile at mid-span in Case I for 30 m/s and α = 5
o
9.1. Low-Speed Flows
Fig. 9.4. In-situ calibrated Stern-Volmer plot in Case II for 30 m/s and α = 5
205
o
Fig. 9.5. Calibrated PSP image in Case II for 30 m/s and α = 5 . From Brown (2000)
o
Fig. 9.6. Chordwise pressure profile at the mid-span in Case II for 30 m/s and α = 5
o
206
9. Applications of Pressure Sensitive Paint
Fig. 9.7. In-situ calibrated Stern-Volmer plot in Case III for 30 m/s and α = 5
o
Fig. 9.8. Calibrated PSP image in Case III for 30 m/s and α = 5 . From Brown (2000)
o
Fig. 9.9. Chordwise pressure profile at the mid-span in Case III for 30 m/s and α = 5
o
9.1. Low-Speed Flows
207
9.1.2. Delta Wings, Swept Wings, and Car Models
PSP measurements on delta wings, swept wings and car models at low speeds
were performed at ONERA in France and DLR in Germany to optimize their
paint formulations, hardware and software for low-speed measurements (Engler
et al. 2001a). It is realized that PSP measurements at low speeds require the
accuracy of 0.1% over a pressure range of 800-1000 mb. This accuracy is
difficult to achieve using a typical PSP with a temperature sensitivity of 1%/K
because a temperature change of 0.1 K could produce an error as large as a
required pressure resolution. Furthermore, the accuracy of PSP is further
reduced due to the camera noise and variation of the excitation intensity during a
test run. The most common procedure to deal with the temperature effect is
application of in-situ calibration to correlate the local luminescent intensity to
the corresponding pressure tap data under an assumption that the temperature
distribution on a model is uniform. In this case, the temperature-induced error is
absorbed into an overall fitting error in in-situ calibration. Even though some
systematic errors are removed, it is impossible for this procedure alone to reduce
the error to a level equivalent to that caused by a temperature change of 0.1 K on
a non-uniform thermal surface in wind tunnel tests. After investigating lowspeed PSP measurements in large production wind tunnels at NASA Ames, Bell
et al. (1998) pointed out that the most significant errors were due to the
temperature effect of PSP and model motion. Therefore, a better solution is the
combined use of in-situ calibration with a temperature-insensitive PSP. An
illumination field should be measured in order to correct both the spatial and
temporal excitation variations on a surface. Furthermore, a large number of
images (up to 64) should be averaged to reduce the camera noise.
Engler et al. (2001a) tested three Pyrene-based PSP formulations for lowspeed measurements. One was the B1 PSP developed by OPTROD in Russia, in
which a pressure-insensitive reference dye was added to correct the excitation
variation when performing a ratio between the pressure and reference emissions.
The temperature sensitivity of the B1 PSP was 0.5%/K which could not be
neglected when a high accuracy for pressure measurements was required.
Another was the PyGd PSP developed at ONERA, containing Pyrene as a
pressure-sensitive dye and a gadolinium oxysulfide as a reference component.
The two components absorbed the ultraviolet excitation light and emitted the
luminescence at different wavelengths. Besides its high sensitivity to pressure,
the PyGd PSP displayed a very low temperature sensitivity of 0.05%/K because
the temperature sensitivity of the reference component was almost the same as
Pyrene and thus an intensity ratio between the two components compensated the
temperature effect of Pyrene. Therefore, this paint was suitable to low-speed
PSP measurements. The PdGd PSP, developed at ONERA mainly for transonic
flows, was also tested to evaluate its feasibility and accuracy of measurements at
low speeds. This paint was a mixture of PSP and TSP, containing a pressuresensitive component Palladium octaethylporphine (PdOEP) and a temperaturesensitive component Gadolinium oxysulfide having a temperature sensitivity of
1.5%/K.
208
9. Applications of Pressure Sensitive Paint
Illumination system used was a Mercury light filtered in a UV range
(325±15nm or 340±35nm) and a xenon-flash lamp equipped with four optical
outputs with 25-Hz repetition rate (308 nm); the lights were connected to liquid
light guides to illuminate models. Cooled CCD cameras (512×512, 1024×1024 or
1340×1300 pixels) with back illuminated detectors were used. A filter holder was
placed in the front of the lens or the CCD chip. The filters separated the emitted
lights from the pressure component (430-510 nm) and from the reference
component (615-625 nm). For the PdGd paint, the third filter was required for the
temperature-sensitive component at 480-520 nm. The exposure time was typically
1-30 seconds, depending on the illumination source, camera, and size of a test
section. Filter-shifting device and two-camera system were developed to acquire
the pressure and reference images.
Preliminary measurements at low speeds were made on a delta wing to identify
the major error sources and evaluate the performance of different paints (B1,
PyGd and PdGd) under the same flow conditions. The delta wing with a 500-mm
chord and a swept angle of 75° was successively painted with the three PSPs. The
model was mounted in the ONERA low-speed research wind tunnel having a test
section of 1-m diameter and the maximum speed of 50 m/s. The model was
equipped with 47 pressure taps used to assess the accuracy of PSP. Ten images
for each filter setting (blue or red filter) were taken using the CCD cameras
(512×512 and 1340×1300 pixels) for frame averaging.
0
pressure taps
-4
Fig. 9.10. The pressure coefficient Cp map obtained using the PyGd PSP on a delta wing at
25 m/s. From Engler et al. (2001a)
Figure 9.10 shows a typical image of the pressure coefficient C p on the 75°o
delta-wing obtained using the PyGd PSP at 25 m/s and the angle of attack of 32 .
The leading-edge vortex signature was clearly visualized on the model and the
secondary vortices were distinguished from the primary vortices. Figure 9.11
shows the distributions of C p obtained using the B1, PyGd and PdGd PSPs at the
chordwise station equipped with pressure taps, where the error bars of 1 mb
(0.0145 psi) indicate the accuracy of PSP measurements. The results obtained
9.1. Low-Speed Flows
209
using the PyGd PSP are in good agreement with the pressure tap data and less
noisy compared to those given by the B1 and PdGd PSPs. This is due to not only
much higher luminescent emission from the PyGd PSP, but also very low
temperature sensitivity of the PyGd PSP. Spatial averaging was applied to the
PSP data over a 3-pixel-radius circle around each pixel. Since a 3-pixel radius in a
512×512-pixel camera corresponded to a larger area on the surface, spatial
averaging on the image plane was more effective for the 512×512-pixel camera,
which was evidenced by a reduced noise level of the results. Since the PdGd PSP
was a mixture of PSP and TSP, the temperature fields were also obtained,
indicating a temperature increase of 0.2 K on the wing surface from the left to
right. Moreover, by comparing the TSP images taken before and after the test, a
temperature increase of 1.6 K was observed in a test run of 30 minutes due to the
heat dissipated by the motor of the wind tunnel. Other researchers also measured
the pressure distributions on delta wings using PSP at low speeds (Morris 1995;
Shimbo et al. 1997; Le Sant et al. 2001a; Verhaagen et al. 1995). The flow over a
delta wing is particularly suitable to testing the capability of PSP at low speeds
since there is a relatively large pressure change induced by the leading edge
vortices on the upper surface.
0.5
0
-0.5
-1
Cp
-1.5
-2
Kp 400
512x512, radius=3
1340x1300, radius=3
-2.5
-3
-150
-100
-50
0
50
100
150
100
150
y (mm)
(a)
1
0.5
0
-0.5
cp
-1
-1.5
-2
Kp 400
512x512, radius=3
-2.5
1340x1300, radius=3
-3
-150
(b)
-100
-50
0
y (mm)
Fig. 9.11. (cont.)
50
210
9. Applications of Pressure Sensitive Paint
2
1.5
1
0.5
0
Cp
-0.5
-1
-1.5
-2
Kp 400
512x512, radius=3
1340x1300, radius=3
-2.5
-3
-150
(c)
-100
-50
0
50
100
150
y (mm)
Fig. 9.11. Comparison of PSP measurements with pressure tap data on a delta wing at the
chordwise location x = 400 mm at 25 m/s, (a) PyGd PSP, (b) B1 PSP, (c) PdGd PSP. From
Engler et al. (2001a)
Measurements on swept wings were performed in the Low-Speed-Wind-Tunnel
(LSWT) of Daimler-Chrysler Aerospace at Bremen in German. This Eiffel-type
wind tunnel with a 2.1×2.1 m test section was operated in a range of velocities
from 30 to 75 m/s. Images were acquired at 10 minutes after the tunnel was
turned on to stabilize flow temperature and minimize the temperature effect on
PSP. During the tests, all ambient light sources were covered and the test section
was painted black to minimize reflection of the luminescent light on the walls.
After preliminary tests on a swept constant-chord half-wing model to examine the
performance of the PSP system, PSP measurements were made on an Airbus A340
half-model. Figure 9.12 shows the wing of the Airbus model coated with different
paints including ‘Göttingen Dyes’ (GD) PSPs and B1 PSP of OPTROD. A large
number of pressure taps on the wing were available for comparison. Figure 9.13
shows a raw blue image of the wing of the Airbus model illuminated with a 308nm diffuse lamp when the integration time of the CCD cameras was 32 s for 16
images acquired. The GD146 PSP gave the most sensitive signal. Figure 9.14
shows a comparison of PSP measurements with pressure tap data along a chord at
the spanwise location AB indicated in Fig. 9.13 on the Airbus model at 60 m/s and
o
the angle of attack of 16 . Figure 9.15 shows a similar comparison between PSP
and pressure taps for the wing/slat configuration of a swept constant-chord halfwing model at 60 m/s and the angle-of-attack of 16°. The resolution of
∆C p = 0.02 was achieved on the swept wings at 60 m/s.
9.1. Low-Speed Flows
211
Fig. 9.12. Airbus A340 half model tested with different PSPs. From Engler et al. (2001a)
Fig. 9.13. Raw blue image obtained using two separate CCD cameras and a 308-nm lamp
for excitation, where the integration time for 16 images was 32 seconds. From Engler et al.
(2001a)
Fig. 9.14. Comparison of PSP and pressure tap data at 60 m/s and the angle of attack of 16
along the line A-B on the Airbus A340 half model. From Engler et al. (2001a)
o
212
9. Applications of Pressure Sensitive Paint
Fig. 9.15. Comparison of PSP and pressure tap data for the wing/slat configuration of a
o
swept constant-chord half-wing model at 60 m/s and the angle of attack of 16 . From
Engler et al. (2001a)
Engler et al. (2001a) and Aider et al. (2001) measured the pressure distributions
on car models at low speeds. The models were a Daimler Benz and a PSA
Peugeot Citroen (900 mm long, 400 mm wide and 350 mm high). The tests were
conducted in the ENSMA’s T4P low-speed wind tunnel at Poitiers in France and
in the Daimler Benz wind tunnel at Sindelfingen in Germany. The maximum
velocity of these tunnels was 65 m/s and the free-stream turbulence intensity was
less than 1%. Figure 9.16 shows typical PSP data mapped onto a CFD grid of the
Daimler Benz model, where 64 raw images were averaged to reduce the camera
noise. The total time to acquire all the wind-on and wind-off images was longer
than one hour since the powerful 308-nm light sources were not available for these
tests and a long integration time for the camera was required. Fortunately, the
static temperature of flows in the wind tunnels was stable enough such that an
error produced by a long-time temperature shift in the tunnels was small. Figure
9.17 shows a comparison between PSP and pressure tap data along the centerline
of the Daimler Benz model. The absolute pressure accuracy of about 1 mb
(0.0145 psi) was achieved after a large number of images were averaged. Figure
9.18 presents a comparison between PSP and pressure taps on the rear window of
the PSA Peugeot Citroen model at 40 m/s along the left-hand sideline A and the
centerline C equipped with pressure taps. In this case, the absolute pressure
accuracy was better than 1 mb. There was an interesting difference between the
pressure distributions along the sideline A and centerline C. There was only one
pressure minimum point along the centerline C through the roof/window junction.
In contrast, two pressure minimum points existed along the sideline A, which
corresponded to the roof/window junction and a vortex system around the car,
respectively. PSP was able to visualize the pressure signatures associated with
complex flow patterns that were completely missed in pressure tap data such as a
pressure peak between the two pressure minimum points along the sideline A.
9.1. Low-Speed Flows
213
0.4
Cp
0.2
0.0
-0.2
-0.4
-0.6
-0.8
-1.0
Fig. 9.16. Pressure image mapped onto a surface grid of the Daimler Benz model with
arrangement of pressure taps at 60 m/s. From Engler et al. (2001a)
Cp
0.4
0.2
0.0
-0.2
10 mb
-0.4
-0.6
PSP
PSI
-0.8
-1.0
0.0
0.5
x/l
1.0
Fig. 9.17. The pressure coefficient distribution obtained from PSP compared with pressure
tap data at the centerline on the Daimler Benz model at 60 m/s. From Engler et al. (2001a)
1.006
1.004
1.002
C
P (bar)
1.000
0.998
0.996
C
0.994
A
0.992
A
0.990
0.988
0.986
200
250
300
350
400
450
500
X (mm)
Fig. 9.18. Comparison of PSP with pressure tap data along the sideline A and centerline C
on the rear window of the PSA Peugeot Citroen model at 40 m/s. From Engler et al.
(2001a)
214
9. Applications of Pressure Sensitive Paint
9.1.3. Impingement Jet
Torgerson et al. (1996) conducted PSP experiments in a low-speed impinging jet
to determine the limiting pressure difference that can be resolved using a laser
scanning system combining an optical chopper or acoustic-optic modulator with a
lock-in amplifier. They tested three PSP formulations, Ru(dpp) in GE RTV 118,
PtTFPP in model airplane dope and PtTFPP/Green-Gold in dope. Ru(dpp) in GE
RTV 118 had a relatively low temperature sensitivity of 0.78%/°C compared to
1.8%/°C for PtTFPP-dope PSP. PtTFPP/Green Gold in dope was a twoluminophore PSP where Green Gold served as a pressure-insensitive reference
dye. They compared the intensity ratio method, phase method and two-color ratio
method to evaluate their feasibility for low-speed PSP measurements. The paint
was coated on a white Mylar film attached on an aluminum impingement surface
that was located at 10 mm away from a 5-mm diameter nozzle. A laser beam
modulated by an optical chopper provided illumination for PSP at 457 nm. A 0.2mm laser spot was scanned across the impingement plate. The luminescent
emission was detected using a PMT through a long-pass filter (>600 nm). The
PMT signal was input into a lock-in amplifier connected with a PC either to
reduce the noise for intensity-based measurements or to extract the phase angle for
phase-based measurements. For Ru(dpp) in GE RTV 118, a typical chopping
frequency was 500 Hz with a lock-in time constant set to 200 ms. Pressure was
calculated from the intensity ratio and the phase angle after five scan ensembles
were averaged. Figure 9.19 shows the pressure distributions on the impingement
plate converted from the intensity ratio of Ru(dpp) in GE RTV 118, where the
lateral coordinate is normalized by the nozzle diameter. These results indicated
that the laser scanning system, working with Ru(dpp) in GE RTV 118, was able to
measure an absolute pressure difference as low as 0.05 psi with a reasonable
accuracy. However, it was found that the PtTFPP-dope PSP exhibited a stronger
temperature effect distorting significantly the pressure distribution near the shear
layer region of the impinging jet.
Phase measurements in the wind-off case for Ru(dpp) in GE RTV 118 and
PtTFPP in dope led to a somewhat surprising finding that the phase angle showed
a repeated variation or pattern over a scanning range even when pressure and
temperature were uniformly constant.
The phase variation introduced a
considerable error in low-speed PSP measurements although it might not be
significant for PSP application to high-speed flows. The phase variation was
attributed to microheterogeneity of a polymer environment around a probe
molecule that locally altered the luminescence and quenching behavior. To
correct this intrinsic pattern of the phase angle (or lifetime), a ratioing process is
still needed. Similarly, for the two-luminophore paint PtTFPP/Green-Gold in
dope, a two-color intensity ratio was not constant over a scanning range because
the two dyes were not homogeneously mixed into the binder. In this case, a ratioof-ratios of the signals was used to remove this effect.
9.2. Subsonic, Transonic, and Supersonic Wind Tunnels
215
0.5
y/d = 2
0.4 psi
0.2 psi
0.1 psi
0.05 psi
0.4
∆P, psi
0.3
0.2
0.1
0.0
-0.1
-1
0
1
Location, x/d
Fig. 9.19. Pressure distributions in a low-speed impinging jet obtained using a laser
scanning system. From Torgerson et al. (1996)
9.2. Subsonic, Transonic, and Supersonic Wind Tunnels
Most PSP measurements were conducted in high subsonic, transonic and
supersonic flows since PSP is most effective in a range of the Mach numbers from
0.3 to 3.0. Experiments on various aerodynamic models with PSP in large
production wind tunnels have been made at three NASA Research Centers
(Langley, Ames and Glenn), the Boeing Company at Seattle and St. Louis, AEDC,
and Wright-Patterson in the United States. Also, PSP has been widely used in
wind tunnels at TsAGI in Russia (Bukov et al. 1993, 1997; Troyanovsky et al.
1993; Mosharov et al. 1997), British Aerospace and DERA in Britain (Davies et
al. 1995; Holmes 1998), DLR in Germany (Engler et al. 1995, 1997a, 2001b),
ONERA in France (Lyonnet et al. 1997), and NAL in Japan (Asai 1999). Besides
predominant applications of PSP in external aerodynamic flows, PSP has been
used to study supersonic internal flows with complex shock wave structures in
turbomachinery (Cler et al. 1996; Lepicovsky 1998; Lepicovsky et al. 1997;
Taghavi et al. 1999; Lepicovsky and Bencic 2002). This section describes typical
PSP measurements in subsonic, transonic and supersonic flows.
9.2.1. Aircraft Model in Transonic Flow
Engler et al. (2001b) measured the pressure distributions and aerodynamic loads
on an AerMacchi M-346 Advanced Trainer Aircraft model at the angles of attack
from -4° to 36° and the angles of sideslip from -13° to 13° over a Mach number
range of 0.6-0.95. Their experiments represented a good example of PSP
216
9. Applications of Pressure Sensitive Paint
application to a complex model with flaps, air brakes, rudders and ailerons in a
production wind tunnel, which utilized a two-luminophore PSP, eight CCD
cameras and 16 fiber optics illumination heads. In addition, control of PSP
hardware and interface with a standard wind tunnel data acquisition/processing
system became an operational issue in a production wind tunnel.
Experiments were conducted in the industrial wind tunnel with a 1.8×1.8 m
test-section at DNW-HST in Amsterdam, The Netherlands. The AerMacchi M346 advanced trainer aircraft model had a 1.2-m length and a 1.0-m span. Figure
9.20 shows a surface grid and a painted model with exchangeable flaps, air brakes,
rudders and ailerons. Since a total of 19 configurations were tested, 20 additional
model parts were painted besides the basic model. All the parts of the complex
model were illuminated and captured by CCD cameras placed around it in order to
measure the aerodynamic effects at high angles-of-attack and angles of sideslip for
maneuvers influenced by flaps, air brakes, rudders and ailerons. To overcome the
problems of shadows and inhomogeneous illumination for excitation, the Pyrenebased two-luminophore B1 PSP from OPTROD was employed. In addition, since
this PSP had weak temperature dependency, the error due to the temperature effect
could be reduced.
rudder
horizontal
aileron
tails
ou tboard
droop
inboard
dr oop
variable flaps
(a)
(b)
Fig. 9.20. The AerMacchi M-346 advanced trainer aircraft model, (a) surface grid, (b) PSP
coated model. From Engler et al. (2001b)
As shown in Fig. 9.21, at each of four observation directions, an UV light
source connected to four 20-m long optic fibers; thus, a total of 16 fiber optics
heads connected with four UV light sources illuminated the whole model from all
the four directions. Eight cooled 12-bit CCD cameras were used for image
acquisition. At each observation direction, a twin-CCD-camera unit with different
filters was used to acquire in parallel the pressure signal at 450-550 nm (blue) and
reference signal at 600-650 nm (red). Figure 9.21 shows a twin-CCD-camera unit
and illuminator heads installed on the wall of the test-section. The use of the twinCCD-camera unit eliminated a filter-shifting device that could not be immune
9.2. Subsonic, Transonic, and Supersonic Wind Tunnels
217
from unsteadiness of the light sources. In this arrangement of cameras and lights,
the exposure time was typically 15 seconds for a camera placed at 1 m away from
the model.
As PSP was integrated into a standard wind tunnel measurement system,
accurate and rapid acquisition and transmission of data became an important issue
to decrease the wind tunnel run time. An automatic trigger and data exchange
system was used. After acquisition of a set of ‘blue’ and ‘red’ images by the four
twin-CCD-camera units (eight CCD cameras), a TTL ready signal from the PSP
system was sent to the wind tunnel control/data system, and the flow parameters
and model attitudes were adjusted and recorded for next run. After the above
process was completed, a TTL trigger signal from the tunnel control/data system
activated all the cameras and lights for new PSP measurements.
Given limited illumination sources (16 illuminator heads) for the complex
model, shadows were inevitably generated mainly by vertical rudders on the
fuselage and horizontal tails. The effect of shadows was largely eliminated using
the ratio-of-ratios approach for the pressure (blue) and reference (red) images in
the wind-on and wind-off cases (four images in total). In some areas without PSP
like registration markers, screws and damaged spots, pressure was given by a
proper interpolation scheme from PSP data around these areas.
Fig. 9.21. PSP system including twin-CCD-camera units, fiber optics illuminators,
computers for data/image acquisition. From Engler et al. (2001b)
Figures 9.22 and 9.23 show the distributions of the pressure coefficient Cp on
the upper surface of the model for the clean configuration and the configuration
o
with positive and negative ailerons at Mach 0.6 and the angle-of-attack of 14 . It
218
9. Applications of Pressure Sensitive Paint
can be seen that the pressure distribution is significantly altered from one
configuration to another. The pressure distributions along the lines on the wings
indicate a symmetric pressure field with respect to the model centerline for the
clean wing configuration, in contrast to the asymmetric one for the configuration
with the positive and negative ailerons. Figure 9.24 shows a typical pressure field
mapped onto a 3D grid of the model. PSP data were first mapped onto the upper,
lower, left and right parts of the model grid, and then these parts were merged into
a complete 3D surface of the model. From the 3D PSP data on the model surface,
Engler et al. (2001b) calculated the coefficients of the normal force (CN), pitching
moment (CPM), rolling moment (CRM), wing root torsion moment (CTM),
outboard droop hinge moment (ODHM), and horizontal tail normal force (CNHT).
Figure 9.25 shows the aerodynamic force and moment coefficients obtained from
PSP along with data given by a balance at Mach 0.95 on the configuration with the
leading edge droop set to zero. In Fig. 9.25, D1 denotes the data obtained by a
six-component balance during PSP tests and D2 denotes balance measurements on
the same model without PSP in previous wind tunnel tests. The PSP-derived
aerodynamic loads were in reasonable agreement with the balance data except for
the horizontal tail normal force. Previous balance data indicated the existence of
the forebody side force at high angles-of-attack, which was caused by the
asymmetric boundary layer separation and vortex system. In these cases, PSP
indeed showed the asymmetric pressure fields on the wings.
0
Cp
0.
1
-1.5
-2
Cp
600
700
800
700
800 x 900
x 900
0
0.
-1
1.5
-2
600
Fig. 9.22. The pressure coefficient (Cp) distributions along the lines on the upper surface on
the model for the clean configuration at Mach 0.6 and the angle of attack of 14°. From
Engler et al. (2001b)
9.2. Subsonic, Transonic, and Supersonic Wind Tunnels
219
0
Cp
0.5
-1
-1.5
-2
600
700
800 x 900
0
Cp
-0.5
-1
-1.5
-2
600
700
800
x
900
Fig. 9.23. The pressure coefficient (Cp) distributions along the lines on the upper surface on
the model for the configuration with the positive and negative ailerons at Mach 0.6 and the
angle of attack of 14°. From Engler et al. (2001b)
Fig. 9.24. Typical pressure distribution mapped onto a surface grid of the model. From
Engler et al. (2001b)
220
9. Applications of Pressure Sensitive Paint
M= 0.95
M=0.95
(a) Aircraft normal force coefficient
M= 0.95
(b) Aircraft pitching moment coefficient.
M= 0.95
(c) Aircraft rolling moment coefficient
(d) Wing root torsi on moment coefficient
M= 0.95
(e) Outboard droop hinge moment coefficient
M= 0.95
(f) Horizontal tail normal force coefficient
Fig. 9.25. The coefficients of aerodynamic loads obtained from PSP compared with the
force balance data. From Engler et al. (2001b)
9.2. Subsonic, Transonic, and Supersonic Wind Tunnels
221
9.2.2. Supercritical Wing at Cruising Speed
Using porphyrin-based PSPs (FIB, Uni-Coat, Sol-gel, FEM, and PAR paints),
Mebarki and Le Sant (2001) studied the pressure fields on the supercritical wing
of a Dash 8-100 aircraft model at the cruising Mach number 0.74. Experiments
were conducted in a blow-down pressurized tri-sonic wind tunnel at the Institute
for Aerospace Research (IAR) of National Research Council (NRC) in Canada.
At Mach 0.74, the total pressure of flow was changed from 1.4 bar to the
maximum value of 3.1 bar, and accordingly the unit Reynolds number from 18.7
to 49 millions/m. The duration of a run depended on the Mach number and total
pressure p0. At Mach 0.74, the run duration varied from 11 seconds at Rec =
6
6
8.51×10 and p0 = 3.14 bar to 37 seconds at Rec = 3.81×10 and p0 = 1.41 bar,
where Rec is the Reynolds number based on the mean chord. The start-up time to
establish stable flow was 2 seconds. The supercritical wing without a nacelle had
a zero swept angle at the 60% chord line. The steel wing with an aluminum half
fuselage was mounted on an external sidewall balance. The overall length,
wingspan and mean chord of the model were 1.73, 1.1 and 0.203 m, respectively.
The airfoil sections were designed to sustain extensive laminar flow on the
surface. The wing was equipped with four rows of 32 pressure taps (stations A, B,
C and D), which were located at 11%, 27%, 35% and 57% of the wingspan,
respectively.
The ceiling of the test section was equipped with 20 optical windows. To
provide fairly uniform and stable illumination, 16 cooled green halogen lamps
(Iwasaki JY 1562 GR/N/CG 50W) with filters (color filter KOPP 4-96) were used
for all the PSP formulations since they used the same porphyrin molecule
(PtTFPP) as a probe. A 12-bit CCD Photometrics camera (1024×1024 pixels) and
an Infrared Agema 900 camera (136×272 pixels) were mounted in the plenum
shell. The CCD camera, equipped with two interference filters (Andover 650FS40
and Melles Griot 03FIB014) in parallel, recorded the luminescent emission of PSP
from the wing root (station A) to approximately 85% of the wingspan. The
infrared camera focused on three rows of taps (from station B to D), thus covering
30% of the wingspan. Of the porphyrin-based (PtTFPP) PSP formulations used,
the PAR PSP from IAR and FEM PSP from NASA Langley were not
commercially available, and three other paints, the FIB PSP, Sol-gel PSP and UniCoat PSP, were commercially produced by Innovative Scientific Solutions Inc.
(ISSI) in Dayton, Ohio.
Figure 9.26 shows a comparison of pressure results obtained using the FIB PSP
with the pressure tap data at the spanwise stations B (27% wingspan) and C (35%
6
wingspan) for four angles of attack at Mach 0.74 and Rec = 3.8×10 , where in-situ
calibration was applied. An average error in Cp was about 0.02, corresponding to
1.4% of the full pressure range at those locations. Figure 9.27 shows the
distributions of Cp along with the corresponding temperature distributions obtained
using an infrared camera for the angles of attack of 0, 1, 3 and 5 degrees at Mach
6
0.74 and Rec = 3.8×10 . A shock across which a rapid change of pressure occurred
o
can be clearly identified in these PSP images. At the angle of attack of 5 , the
wedge-like patterns at the spanwise stations C and D can be observed in the PSP
images, which are associated with flow separation triggered by surface
222
9. Applications of Pressure Sensitive Paint
imperfections near the leading edge of the wing. Fluorescent oil flow
visualization on the surface confirmed this observation. As shown in Fig. 9.27,
infrared thermography visualizes a surface temperature change induced by the
flow separation at these stations and indicates that small turbulent wedges are
generated by surface imperfections at the angles of attack of 0, 1 and 3 degrees.
However, these turbulent wedges did not significantly alter the pressure
distributions. In addition, using the Uni-Coat PSP, they studied the Reynolds
number effect on the pressure distribution on the wing.
Mebarki and Le Sant (2001) evaluated the accuracy of PSP measurements at
Mach 0.74 for all the PSP formulations through in-situ calibration. Table 9.1
summarizes the accuracy of the PSP results in terms of the absolute difference in
Cp and the percentage error (%FS) over the full-scale range of Cp that is defined as
the maximum range of Cp measured during a run on the wing upper surface by 39
pressure taps. The exposure times of the camera used for the PSP formulations are
also listed in Table 9.1, depending on the luminescent intensity of a particular
paint. Generally speaking, the accuracy was fairly good for all the PSPs at
different Reynolds numbers despite their different temperature sensitivities,
because a temperature variation over the wing chard during a run was relatively
o
small (less than 2 C).
Table 9.1. Absolute and relative accuracy of PSP formulations in Cp
PSP
UniCoat
Sol-gel
FIB
FEM
PAR
M = 0.74, Rc = 3.8 mil
t (ms)
%FS
∆Cp
50
0.04
3.2
M = 0.74, Rc = 8.5 mil
t (ms)
%FS
∆Cp
75
0.10
8.4
125
500
500
250
250
1000
1000
500
0.04
0.02
0.02
0.03
2.8
1.4
1.7
2.2
0.04
0.03
0.04
0.03
Station C
Station B
-1.6
-1.6
o
α=0
α=1o
α=3o
o
α=5
-1.4
-1.2
α =0 o
α =1 o
o
α =3
α =5 o
-1.4
-1.2
-1
CP
-1
CP
3.1
2.7
3.3
2.6
-0.8
-0.8
-0.6
-0.6
-0.4
-0.4
-0.2
-0.2
0.2
0.6
0.4
x/c
0.8
0.2
0.6
0.4
0.8
x/c
Fig. 9.26. Comparison of PSP results (lines) obtained using the FIB PSP with pressure tap
6
data (circles) at M = 0.74 and Rec = 3.8×10 . From Mebarki and Le Sant (2001)
9.2. Subsonic, Transonic, and Supersonic Wind Tunnels
Cp
¯ FLOW
223
T (deg. C)
a =0o
-0.2
-0.4
a =1o
-0.6
-0.8
a =3
o
-1
-1.2
a =5o
-1.4
B
C
D
-1.6
Fig. 9.27. The distributions of the pressure coefficient Cp on the wing upper surface
obtained with the FIB PSP and the corresponding temperature distributions obtained using
6
an infrared camera at M = 0.74, Rec = 3.8×10 , and AoA = 0, 1, 3 and 5 degrees. From
Mebarki and Le Sant (2001)
9.2.3. Transonic Wing-Body Model
Shimbo et al. (2000) conducted PSP measurements on an 8%-scaled model of the
Mitsubishi MU-300 business jet at the Mach numbers 0.6-0.8 and the angles-ofattack 0-4.6 degrees in the 2-m transonic wind tunnel at the National Aerospace
Laboratory (NAL) in Japan. The main objective of their tests was to examine the
feasibility of PSP combined with TSP for correcting the temperature effect of
PSP. The model was equipped with 32 pressure taps in four rows on the upper
surface of the starboard wing. A water-cooled 14-bit CCD camera (1008×1018
pixels) attached with optical filters was used. A xenon lamp was used as an
excitation light source and the light was introduced through optic fibers to light
reflectors. Each light reflector had an optical filter such that only the UV light
went through for paint excitation. The classical PSP, PtOEP in GP-197, was
applied on the upper surface of the starboard wing for pressure measurements,
whereas a typical TSP, EuTTA in PMMA, was applied on another wing for
temperature measurements. Since the emission peaks of both PSP and TSP were
close in the emission spectra, the luminescent intensity from both PSP and TSP
were acquired on the same image using the CCD camera mounted on the ceiling
of the test section. Assuming the flow symmetry with respect to the model
centerline, Shimbo et al. (2000) used the temperature distributions on one of the
wings obtained by TSP to correct the temperature effect of PSP on another wing.
224
9. Applications of Pressure Sensitive Paint
Figure 9.28 shows typical pressure fields on the wing surface obtained using a
combination of PSP and TSP at Mach 0.75 for the angles of attack of 2.3 and 4.7
degrees. A shock on the wing is clearly seen in the PSP images. For a
quantitative comparison, the pressure distributions obtained using a combination
of PSP and TSP and in-situ calibration at four spanwise locations are shown in
Fig. 9.29 along with the corresponding pressure tap data for Mach 0.75 and the
angle of attack of 2.3. In this example, a combination of PSP and TSP was able to
give reasonable pressure results without utilization of any pressure tap data for
correcting the temperature effect.
(a) M = 0.73, AoA = 2.3 deg.
(b) M = 0.75, AoA = 4.7 deg.
Fig. 9.28. Typical pressure fields on the Mitsubishi MU-300 business jet model obtained
using a combination of PSP and TSP at Mach 0.73 and α = 2.3 and 4.7 degrees. From
Shimbo et al. (2000)
9.2. Subsonic, Transonic, and Supersonic Wind Tunnels
y/s=0.19
Cp
-1
-1.5
-1
-0.5
-0.5
0
0
0
20
40 60
x/c [%]
80
100
y/s=0.55
Cp
0
-1.5
-1
-1
-0.5
-0.5
0
0
20
40 60
x/c [%]
20
80
100
0
40 60
x/c [%]
80
100
80
100
y/s=0.85
Cp
-1.5
0
y/s=0.32
Cp
PSP/TSP
in situ
o tap
-1.5
225
20
40 60
x/c [%]
Fig. 9.29. Comparison between PSP (lines) and pressure tap data (circles) for the
Mitsubishi MU-300 business jet model at Mach 0.73 and α = 2.3 deg. PSP data were
obtained using a combination of PSP and TSP as well as in-situ calibration. From Shimbo
et al. (2000)
9.2.4. Laser Scanning Pressure Measurement on Transonic Wing
Torgerson (1997) demonstrated a phase-based laser scanning system for PSP
measurements on a transonic airfoil in the Boeing Company model transonic wind
tunnel. A 10% thick airfoil having a sharp leading edge and a small amount of
camber was used, which was equipped with 19 pressure taps along the upper
surface for a comparison with PSP data. The airfoil was coated with a Rutheniumbased PSP. The scanning system had a small air-cooled argon-ion laser for
excitation and a PMT as a detector. The blue laser beam was modulated using an
electro-optic modulator before scanning over the airfoil surface with a computercontrolled mirror, enabling the PMT signal to be processed using a two-phase
lock-in amplifier. Both the phase and intensity signals were recorded during
scanning over the airfoil such that a comparison between the intensity and phase
methods could be made. Figure 9.30 shows a typical pressure distribution at
Mach 0.8, indicating that both the phase and intensity methods compared
favorably with the pressure tap data after in-situ calibration was applied.
Nevertheless, phase-based measurements had the advantage that the wind-off data
were not required.
226
9. Applications of Pressure Sensitive Paint
12
Intensity
Phase
Pressure taps
Pressure, psia
10
M=0.80
8
6
4
0.0
0.2
0.4
0.6
0.8
1.0
x/c
Fig. 9.30. Pressure distribution on a transonic airfoil obtained using a laser scanning system
based on the phase and intensity methods. From Torgerson (1997)
9.2.5. Boundary Layer Control in Supersonic Inlets
Bencic (2002) applied PSP to boundary layer control experiments in supersonic
inlets through mass removal in the 1×1 foot Supersonic Wind Tunnel at NASA
Glenn. The tests investigated shock/boundary-layer interactions that caused a
reduction in the inlet performance due to boundary layer separation. As shown in
Fig. 9.31, the test setup consisted of a porous boundary layer control device
replacing a wind tunnel sidewall panel. The boundary layer bleed used a pressure
difference generated by a suction plenum mounted to the backside of the porous
surface to remove the low momentum fluid in the boundary layer.
The bleed control panels were painted with a silicone-based Ruthenium PSP
(Boeing PF2B).
Reference images were taken at reduced pressure of
approximately 12 kPa since this facility had the capability to be brought to near
vacuum conditions quickly. The reduced reference pressure was used because it
was in the range of pressures measured on the porous plates during wind tunnel
operation. A constant exposure time was used for both the wind-off and wind-on
images, producing images that filled about 80% of the full-well capacity of the
CCD camera. Each image was ensemble average of eight frames to further reduce
the photon shot noise. Reduction of the acquired data was performed using the
intensity-based method plus in-situ calibration based on data from 16 pressure taps
located in the painted sections. Typical PSP images are shown in Figs. 9.32, 9.33
and 9.34 for three surface bleed configurations C1, C6 and C3 that denote the
standard 90° bleed hole configuration, the pre-conditioned 90° bleed hole
configuration and the 20° inclined bleed hole configuration, respectively (Willis et
9.2. Subsonic, Transonic, and Supersonic Wind Tunnels
227
al. 1995). Each image was acquired at a nominal tunnel speed of Mach 2.0 under
the similar conditions of the total mass flow through the bleed hole regions.
The PSP images show the surface pressure normalized by the wall static
pressure measured upstream of the fenced porous plate insert. The orifice and row
interactions, which were clearly evident in these figures, were undetectable with
conventional pressure tap instrumentation. The significant result from this test
was the performance increase of 50% in removing mass by the pre-conditioned
90° configuration compared to the standard 90° orifice as reported by Willis et al.
(1995). This increase was due to a combination of flow turning and the pressure
gradient acting across the flush inlet. The performance differences between these
configurations can be seen as larger pressure excursions as noted by the change in
lower scale in Figs. 9.32, 9.33 and 9.34. The more efficient configurations in
Figs. 9.33 and 9.34 generally showed a higher level of interaction between
adjacent rows compared to the standard 90° configuration in Fig. 9.32. The PSP
measurements had an error of 0.3 kPa or less in these examples. A systematic
shift was found between PSP and pressure tap data in the bleed hole region
compared to the solid region upstream and downstream of the porous region. This
shift was due to a temperature difference in the aluminum insert plate caused by
the airflow through the orifice holes. Clearly, simultaneous full-field temperature
measurements (TSP or infrared thermography) are needed to compensate for the
temperature sensitivity of PSP to minimize the errors associated with the effect.
The experiments of Bencic (2002) represent a typical PSP application to
complicated geometric configurations in turbomachinery flows. PSP provides a
powerful diagnostic tool for turbomachinery flows with complex shock wave
structures where a pressure field cannot be mapped with conventional techniques
in a high spatial resolution. PSP has been used for pressure measurements in
narrow supersonic channel, shock/wall interaction, stator vanes, transonic fan
cascade, mixer-ejector nozzles, and jet/flow interaction (Lepicovsky and Bencic
2002; Taghavi et al. 1999; Lepicovsky 1998; Lepicovsky et al. 1997; Cler et al.
1996; Everett et al. 1995). However, confined spaces by multiple surfaces in
turbomachinery cause significant inter-reflection of the luminescent light between
neighboring surfaces and this self-illumination complicates the data processing to
extract correct values of pressure on these surfaces. So far, a correction scheme
for the self-illumination was made only for simple geometric configurations such
as a corner between two planes. For complex geometry in turbomachinery, an
efficient numerical scheme for correcting the self-illumination effect have to be
developed based on an accurate model for the bi-directional reflectance
distribution function of PSP (see Section 5.3).
228
9. Applications of Pressure Sensitive Paint
Fig. 9.31. Test setup of a bleed control panel as a boundary layer control device. From
Bencic (2002)
Fig. 9.32. Normalized surface pressure map P/Ps on the control panel with a standard
multiple 90° bleed hole configuration, where Ps is the wall static pressure measured
upstream of the fenced porous plate insert. Tunnel flow is from left to right. From Bencic
(2002)
9.2. Subsonic, Transonic, and Supersonic Wind Tunnels
229
Fig. 9.33. Normalized surface pressure map P/Ps on the control panel with a multiple preconditioned 90° bleed hole configuration, where Ps is the wall static pressure measured
upstream of the fenced porous plate insert. Tunnel flow is from left to right. From Bencic
(2002)
Fig. 9.34. Normalized surface pressure map P/Ps on the control panel with a multiple 20°
inclined bleed hole configuration, where Ps is the wall static pressure measured upstream of
the fenced porous plate insert. Tunnel flow is from left to right. From Bencic (2002)
230
9. Applications of Pressure Sensitive Paint
9.3. Hypersonic and Shock Wind Tunnels
PSP application in hypersonic flows is more difficult because high enthalpy of
flows may produce such a large temperature increase on a model that the
temperature effect of PSP is overwhelming. Since hypersonic wind tunnels are
usually short-duration tunnels, a very thin PSP coating is required not only to
sustain high skin friction, but also to achieve a short response time. However, the
luminescent emission from a very thin PSP layer is weak and thus a low SNR
becomes a problem. The short run-time limits the exposure time of a CCD camera
to collect photons and further reduces the possibility of improving the SNR.
Kegelman et al. (1993) conducted PSP measurements on a 1/6-scale Pegasus
launch vehicle model and a shock/boundary-layer interaction model in the NASA
Langley Mach 6 High Reynolds Number Tunnel. The McDonnell Douglas PSP
and TSP were used in their tests. The pressure distributions obtained using PSP
on the Pegasus model were in qualitative agreement with the Navier-Stokes code
results over most of the wing. However, considerable discrepancies between the
PSP data and CFD results were observed near the leading edge and wing tip where
high temperature generated by aerodynamic heating exceeded the workable
temperature range of the paint. Quantitative PSP results, which were compared
favorably with the pressure tap data, were obtained on the surface of a flat-plate
model on which an oblique shock impinged; the accuracy of about 0.1 psia was
reported.
Using fast-responding PSP formulations, Troyanovsky et al. (1993) carried out
semi-quantitative PSP visualization in shock/body interaction in a Mach 8 shock
tube with a duration of 0.1 s. Borovoy et al. (1995) measured the pressure
distribution on a cylinder at Mach 6 in a shock wind tunnel with a duration of 40
ms, and achieved reasonable agreement with the theoretical solution and pressure
transducer measurements. Jules et al. (1995) used a McDonnell Douglas PSP to
study shock/boundary-layer interaction over a flat-plate/conical-fin configuration
at Mach 6, showing a systematic shift compared to pressure tap measurements.
Hubner et al. (1997, 1999, 2000, 2001) measured the pressure distributions on a
wedge and an elliptic cone at Mach 7.5 in the Calspan hypersonic shock tunnel
with a run-time of 7-8 ms. To reduce the temperature effect of PSP, they applied
PSP directly on the metal model surface rather than a white basecoat. However,
for a very thin layer of PSP without a white basecoat, the luminescent intensity of
PSP was so low that only 5-12% of the CCD full-well capacity was utilized. Buck
(1994) discussed simultaneous temperature and pressure measurements on dyed
ceramic models using luminescent materials in hypersonic wind tunnels.
9.3.1. Expansion and Compression Corners
Nakakita et al. (2000) used anodized aluminum (AA) PSP to measure the
pressure fields on the expansion corner and compression corner models at Mach
10 in the NAL Middle Scale Shock Tunnel with a duration of 30 ms. More
recent measurements in shock tunnels were made using AA-PSP on a wing-body
model, a hemisphere and scramjet inlet models (Nakakita and Asai 2002;
9.3. Hypersonic and Shock Wind Tunnels
231
Sakaue et al. 2002b). AA-PSP with a probe molecule Ru(dpp) was used since it
had a very short response time of about 30–100 µs. Furthermore, because AAPSP on aluminum models was binder-free and pure aluminum models had high
thermal conductivity, an increase of the surface temperature was relatively small
o
(less than 2 C) in most parts of the model during a run in the shock tunnel. The
NAL Middle Scale Shock Tunnel had the total temperature of 1180 K, total
pressure of 3.4 MPa, Pitot pressure of 7800 Pa, Mach number of 10.4, and
5
Reynolds number 1.6×10 based on the 0.1-m model span. Figure 9.35 shows an
optical system for illumination and measurements, which was set at the front of
an optical window of a vacuum tank and 1.3 m away from the model. A highly
stable continuous xenon lamp (fluctuation of the light intensity was much
smaller than 1%) was used as an illumination light source and the illumination
light was transmitted through a light guide and projected onto the model by a
lens at the exit of the light guide. A cooled 14-bit CCD camera (Hamamatsu
C4880-07) attached with an image intensifier (Hamamatsu C6245MOD) was
used to detect the luminescent emission from PSP. The intensifier enhanced the
capability of the camera to measure weak luminescence in a short exposure time
at the cost of introducing additional noise. The spatial resolution of the CCD
camera was originally 1008×1018 pixels. However, after 2×2 binning was
applied to reduce the shot noise and readout noise, the spatial resolution was
reduced to 504×509 pixels. To separate the illumination light from the
luminescent emission, a band-pass filter (460±50nm) was placed between the
exit of the light guide and the condenser lens transmits; another band-pass filter
(600-800nm) was mounted in the front of the intensifier to eliminate the
illumination light projected to the CCD camera. The exposure time for the
camera was 20 ms.
Figure 9.36 shows the expansion corner and compression corner models made
of pure aluminum. Both models had an upstream plane connected to a
downstream plane. The expansion corner model had the downstream plane
o
deflecting outward 15 relative to the upstream one, whereas the compression
o
corner model had the downstream plane having a 30 ramp against the upstream
one. There were six pressure taps connected Kulite (XCS-093-5A) pressure
transducers on each model to provide reference pressure data for comparison.
The expansion corner model was tested at the angles of attack of 10, 20, 30 and
40 degrees. Figure 9.37 shows a typical PSP image and a Schlieren image along
with a comparison plot of PSP data with pressure tap data at the angle of attack
o
of 40 . In Fig. 9.37, the horizontal axis is the coordinate along the model surface
normalized by the length of upstream plane Lp and the vertical axis is the local
pressure normalized by the Pitot pressure P02. PSP data were in good agreement
with the pressure tap data. On the expansion corner model, the flow field on
each plane can be considered as a 2D wedge-flow where pressure on the surface
is constant. As shown in Fig. 9.37, the pressure distributions are nearly uniform
on the upstream and downstream planes. The Schlieren images indicate a shock
wave at the leading edge and an expansion fan at the corner of the model. The
compression corner model was also tested at the angles of attack of 0, 10, 20,
and 30 degrees. Figure 9.38 shows a typical PSP image, a Schlieren image, and
a pressure distribution plot for the compression corner at the angle of attack of
232
9. Applications of Pressure Sensitive Paint
o
30 . The Schlieren image indicates a much more complicated flow field
including shock/boundary-layer interaction and shock/shock interaction on the
compression corner model. The high-pressure region was associated with
shock/shock interaction near the corner. Again, PSP data were in good
agreement with the pressure tap data.
Fig. 9.35. Optical system for PSP measurements and calibration in the NAL Middle Scale
Shock Tunnel (viewing from the ceiling). From Nakakita et al. (2000)
9.3. Hypersonic and Shock Wind Tunnels
233
=
>
Fig. 9.36. Experimental models: (a) Expansion corner model and (b) Compression corner
model. From Nakakita et al. (2000)
234
9. Applications of Pressure Sensitive Paint
PSP (3runs)
Pressure Transducer (3runs)
P/P02 (P02=8,000Pa)
0.8
0.6
0.4
0.2
0.0
-0.5
0.0
0.5
1.0
X/Lp
1.5
2.0
2.5
Fig. 9.37. PSP image, Schlieren photograph, and pressure distribution on the expansion
o
corner model at Mach 10 and the angle of attack of 40 . From Nakakita et al. (2000)
9.3. Hypersonic and Shock Wind Tunnels
P/P02 (P 02=8,000Pa)
1.4
235
PSP (3runs)
Pressure Transducer (3runs)
1.2
1.0
0.8
0.6
0.4
0.2
0.0
-0.5
0.0
0.5
1.0
X/Lp
1.5
2.0
2.5
Fig. 9.38. PSP image, Schlieren image, and pressure distribution on the compression corner
o
model at Mach 10 and the angle of attack of 30 . From Nakakita et al. (2000)
236
9. Applications of Pressure Sensitive Paint
9.3.2. Moving Shock Impinging to Cylinder Normal to Wall
Asai et al. (2001) demonstrated the feasibility of Ru(dpp) AA-PSP for timeresolved unsteady pressure measurements in the NAL 0.44 m Hypersonic Shock
Tunnel. Figure 9.39 is a schematic of the experimental setup for the shock tube
tests. A circular block of a 12 mm diameter was installed vertically in the center
of a PSP-coated part flush mounted on the shock tube wall. Calibration of PSP
was made by adjusting the test section pressure prior to running the shock tube.
Full-field measurements were acquired using a CCD camera with an intensifier
that can be gated at successive instants after incidence of a moving shock wave.
Illumination for PSP was provided by a flash lamp. Sequential images were
obtained from 475 to 530 µs in an interval of 5 µs. The camera gating time was
set at 10 µs. Figure 9.40 shows a time sequence of images of an unsteady pressure
field induced by a moving shock wave interacting with the stationary circular
block, where the shock speed was 610 m/s. Because the observation window flush
mounted on the surface of the tube acted like a 2D concave lens, the images were
compressed vertically so that a circular section of the cylinder looked like an
ellipse. As shown in Fig. 9.40, a curved high-pressure region induced by the
reflected shock was formed in the front of the block after the incident plane shock
impinged to the block. At the same time, a part of the incident shock continued
traveling downstream after it was deflected, and the expansion waves were
generated. A pair of symmetric vortices, which are visualized as the low-pressure
regions in Fig. 9.40, formed and grew behind the circular block.
PSP coating model with BAR Shock tube
36.95mm
73.9mm
Xenon flash lamp
Optical window
Dichroic Beam Splitter
Optical fiber
Image Intensifier
Flash lamp driver
Cooled CCD camera
Fig. 9.39. Schematic of an experimental setup for time-resolved PSP measurements in a
shock tube. From Asai et al (2001)
9.4. Cryogenic Wind Tunnels
237
Fig. 9.40. Sequential images of unsteady pressure field induced by interaction between a
moving shock wave and a circular cylinder block, where the speed of the shock is 610 m/s
and the interval between two images is 5 µs. From Asai et al (2001)
9.4. Cryogenic Wind Tunnels
PSP measurements were made in cryogenic wind tunnels where the oxygen
concentration in the working nitrogen gas is extremely low and temperature is as
low as 90 K (Asai et al. 1997a; Upchurch et al. 1998). The development of
cryogenic PSP formulations was motivated by the needs of global pressure
measurement techniques in large-scale pressurized cryogenic wind tunnels such as
the National Transonic Facility (NTF) at NASA Langley and the European
Transonic Wind Tunnel (ETW). Asai et al (1997a) developed a binder-free PSP
coating on an anodized aluminum surface and measured the surface pressure
distributions on a 14% thick circular-arc bump model in a small cryogenic wind
tunnel in the National Aerospace Laboratory (NAL) in Japan. PSP data were in
good agreement with pressure tap data at 100 K over a range of the Mach numbers
of 0.75-0.84. However, the methodology of coating on an anodized surface
cannot be applied to stainless steel models typically used in cryogenic wind
tunnels. Upchurch et al. (1998) developed a polymer-based cryogenic PSP that
could be universally applicable to all types of surfaces including stainless steel and
this paint was successfully demonstrated in pressure measurements on an airfoil in
the 0.3-m cryogenic tunnel at NASA Langley. Asai et al. (2000, 2002) also
presented a polymer-based cryogenic PSP formulation applied to cryogenic wind
tunnels and short-duration shock tunnels, which was based on a polymer named
Poly(TMSP) having extremely high gas permeability. This PSP can be dissolved
238
9. Applications of Pressure Sensitive Paint
into a solvent and applied using an airbrush to any model surface including
stainless steel in contrast to AA-PSP only applicable to aluminum or aluminum
alloy. Hitherto, cryogenic PSP measurements have not been conducted in NTF
and ETW due to safety concerns on injection of a small amount of air (oxygen)
into the tunnels. Therefore, small cryogenic tunnels are more suitable to
preliminary pioneering experiments since they are more adaptable and relatively
inexpensive to run.
Asai et al. (2000, 2002) described application of Poly(TMSP)-based PSP and AAPSP data to a circular-arc bump model and a delta wing model in the 0.1-m Transonic
Cryogenic Wind Tunnel at NAL. Figure 9.41 is a schematic of the tunnel operated by
controlling both liquid nitrogen injection and gaseous nitrogen exhaust. A small
amount of air was injected just downstream of the test section, and the oxygen
concentration in flow was measured from sampled exhaust gas using a Zirconia (ZrO2)
sensor. The oxygen concentration was varied from near zero to 2000 ppm by
adjusting the flow rate of the injected air. Figure 9.42 is a schematic of the optical
setup for experiments. The model mounted on the sidewall was viewed through a 70mm diameter window on the opposite sidewall.
A 300-watt xenon lamp with a band-pass filter (400±50nm) was used for
illumination. A dichroic mirror (550 nm) was used to separate the luminescent
emission of PSP from the excitation light. A 14-bit cooled CCD digital camera with a
band-pass filter (650±20 nm) placed before the lens was used for luminescence
measurements. As shown in Fig. 9.43, a 2D bump model and a clipped delta wing
were used for experiments. The cross-section of the aluminum bump model was a
14% circular arc having the chord length of 50 mm. The bump model was equipped
with 16 pressure taps at the mid-span. The Poly(TMSP)-PSP were coated in two 8mm wide strips on the surface using an airbrush, while other two strips were anodized
to make AA-PSP using a method developed by Sakaue et al. (1999). The stainless
o
steel delta wing model had a 65 -sweep angle and a sharp leading edge, on which an
array of eight taps was installed at 80% of the 60-mm model chord. The model was
o
strut-mounted on the sidewall at the angle of attack of 20 . The Poly(TMSP)-PSP was
applied to the whole upper surface of the delta wing using an airbrush.
Fig. 9.41. Schematic of the NAL 0.1 m Transonic Cryogenic Wind Tunnel. From Asai et
al. (2002)
9.4. Cryogenic Wind Tunnels
239
Fig. 9.42. Schematic of an optical setup for PSP measurements in the NAL 0.1 m Transonic
Cryogenic Wind Tunnel. From Asai et al. (2002)
50mm
Pressure Taps
(0.3mm x 16)
(47.563)
65deg
Removable Strip
48
60
5
8 static pressure taps at x/c=80%
(a)
(b)
Fig. 9.43. (a) Circular-arc bump model, and (b) 65-degree sweep delta wing model for
cryogenic PSP measurements. From Asai et al. (2002)
In experiments, the Mach number was set at either 0.4 or 0.82, and the total
temperature and pressure in the tunnel were maintained at 100 K and 190 kPa,
respectively. The oxygen concentration was varied up to 1000 ppm. Figure 9.44
shows in-situ calibration results for Poly(TMSP)-PSP at the total temperature Tt =
100 K and [O2] = 1000 ppm, indicating the linear Stern-Volmer relation between
the luminescent intensity ratio Iref/I and the relative pressure p/pref. Since the model
surface was fairly isothermal in cryogenic flows, a single calibration curve was
used for data reduction on the entire surface of the model. Figure 9.45 shows the
240
9. Applications of Pressure Sensitive Paint
pressure distribution obtained using in-situ calibration on the bump model at Mach
0.82 and Tt = 100 K, where the image at Mach 0.4 was used as a reference image
since the tunnel could not run below that speed. The PSP-derived pressure data
were in good agreement with the pressure tap data after in-situ calibration is
applied. It was found that the use of a priori calibration did not produce results
consistent with the pressure tap data because the slope of a priori calibration curve
was twice as large as that of the in-situ calibration curve. For the delta wing
model, the raw images were taken at Mach 0.4 and 0.75, the total temperature Tt =
100 K, and the oxygen mole fraction [O2] = 997 ppm. Figure 9.46 presents a ratio
of the wind-on image at Mach 0.75 to the reference image at Mach 0.4, visualizing
the leading edge vortices. The primary and secondary separations were clearly
observed. Figure 9.46 also shows the spanwise distributions of the intensity ratio
I/Iref on the wing at four chordwise locations. The intensity ratio profiles were
noisy because the intensity difference between the images at Mach 0.4 and 0.75
was relatively small. The PSP measurements on the delta wing were basically
qualitative.
1.0
y=0.3557x + 0.6408
0.9
0.8
J JJ
JJ
J
J J
J
J
J
J
J
J
J
M=0.82
Mach
= 0.82
PtPt=190kPa
= 190 kPa
TtTt=100K
= 100 K
[O2]=1000ppm
[O2]
= 1000 ppm
0.7
0.6
0.4
J
0.5
0.6
0.7
0.8
0.9
1.0
P/Pref
Fig. 9.44. In-situ calibration for Poly(TMSP) PSP at the total temperature Tt = 100 K and
[O2] = 1000 ppm. From Asai et al. (2002)
9.4. Cryogenic Wind Tunnels
241
-1.0
-0.5
J
J
J
JJ
J
J
J
J
0.0
J
J
J
JJ
J
J
J
0.5
TAPS
CRYO-PSP
1.0
0.0
0.2
0.4
x/c
0.6
0.8
1.0
Fig. 9.45. The pressure coefficient distribution on the bump model obtained using
cryogenic PSP compared with pressure tap data at Mach 0.82. From Asai et al. (2002)
Fig. 9.46. Intensity ratio image of a delta wing and spanwise intensity distributions at 20,
40, 60, and 80% chords for M = 0.75, Tt = 100 K, Pt = 190 kPa and [O2] = 997 ppm. From
Asai et al. (2002)
242
9. Applications of Pressure Sensitive Paint
9.5. Rotating Machinery
PSP is a promising technique for measuring the surface pressure distributions on
high-speed rotating blades in turbomachinery where conventional techniques are
particularly difficult to use. Using a laser scanning system, Burns and Sullivan
(1995) measured the pressure distributions on a small wooden propeller at a
rotational speed of 3120 rpm and a TRW Hartzell propeller at a rotational speed of
2360 rpm. Mosharov et al. (1997) obtained the pressure distributions on
propellers using a CCD camera system with a pulse light source. PSP
measurements on helicopter rotor blades were carried out at TsAGI (Bukov et al.
1997; Mosharov et al. 1997) and NASA Ames (Schairer et al. 1998b). Navarra et
al. (1998) obtained pressure images on a rotor blade using an ICCD camera
system. Hubner et al. (1996) suggested a lifetime imaging method for PSP
measurements on a rotating object based on detecting the luminescent decay traces
of a rotating painted surface on a CCD camera. Here, we describe two typical PSP
measurements on rotating blades where a laser scanning system and a CCD
camera system were used respectively.
9.5.1. Laser Scanning Measurements
Using a laser scanning system, Liu et al. (1997a) and Torgerson et al. (1997, 1998)
performed PSP measurements on rotor blades in a high-speed axial flow
compressor (the Purdue Research Axial Fan Facility) and an Allied Signal F109
turbofan engine. They used Ru(dpp) in GE RTV 118 mixed with silica gel
particles as PSP and Ru(bpy) in Shellac as TSP. PSP and TSP were coated on
blades by dipping them into the paints, resulting in about 20-µm thick coatings.
Figure 9.47 is a schematic of a laser scanning system used for PSP and TSP
measurements in the compressor facility where optical access is very limited. An
air-cooled Argon laser with the filtered output at 488 nm was used as an
illumination source; the laser was mounted upstream of the inlet contraction. The
laser beam focused by a lens passed between upstream inlet guide vanes and
illuminated rotor blades in a 1-mm diameter spot. Using a computer-controlled
scanning mirror, a laser spot scanned across 21 spanwise (radial) locations along
each blade. As a blade rotated and cut the laser beam, the beam illuminated the
painted blade across its chord, and at least 100 data points were obtained across
the chord, depending on the rotational speed of the blade. The luminescent
emission from the paints was detected using a PMT attached with a long-pass
filter for eliminating the excitation light. Data were acquired using a PC with a
12-bit A/D converter operating at the maximum rate of 500,000 samples/s. The
pressure and temperature distributions were calculated using a priori calibration
relations for both PSP and TSP.
9.5. Rotating Machinery
Computer Controlled
Scanning Mirror
243
Variable inlet Guide Vanes
Compressor Rotor
Long Pass Filter
Photomultiplier Tube
Argon-ion Laser
(488 nm)
Inlet Contraction
Fig. 9.47. Laser scanning system for PSP and TSP measurements in a high-speed axial flow
compressor with very limited optical access. From Liu et al. (1997a)
Figure 9.48 shows typical raw intensity signals from PSP and TSP on the
suction surface of the painted blades at the rotational speeds of 1000, 13500 and
17000 rpm. As the rotational speed increased, the luminescent intensity of TSP
decreased due to the increased surface temperature. A change in the luminescent
intensity distribution of PSP was mainly caused by a pressure variation on the
surface. In particular, a rapid decrease in the luminescent intensity, which
occurred in a region from the 90th to 100th data point (0.6 to 0.67 chord) at 17,000
rpm, corresponded to a large pressure jump generated by a shock. The
luminescent signal at the lowest speed of 1000 rpm was used as the reference
intensity (nearly wind-off). Figure 9.49 shows the temperature distributions on
the suction surface at 50% span at different rotational speeds. The temperature
distributions appeared to be flat over a large portion of the chord, and the mean
temperature increased with the rotational speed due to friction heating. The
o
highest temperature on the blade surface was about 43 C at the speed of 17800
rpm. The pressure distributions on the surface were obtained using a priori
calibration relation of PSP where the temperature effect of PSP was corrected
based on the TSP data. Figures 9.50, 9.51 and 9.52 show the chordwise
distributions of the relative pressure p/p0 at 25%, 50%, and 75% spans for different
rotational speeds, where p0 is the upstream stagnation pressure (one atmosphere
pressure in this case). The formation of a shock was evidenced by an abrupt
increase in the pressure distributions at the speeds of 17000 and 17800 rpm. As
the rotational speed increased, the shock became stronger and its location moved
downstream. Figure 9.53 shows a composite representation of the pressure and
temperature distributions mapped onto a surface grid of blade at the speed of
17800 rpm.
244
9. Applications of Pressure Sensitive Paint
3000
Luminescent intensity (counts)
PSP
TSP
2500
2000
1000 rpm
1500
1000
500
17000 rpm
13500 rpm
0
0
50
100
150
200
250
300
data point
Fig. 9.48. Raw PMT signals from PSP and TSP at three rotational speeds of 1000, 13500,
and 17000 rpm. From Liu et al. (1997a)
60
R = 5 in (midspan)
temperature (deg. C)
55
50
increase of rotational speed
45
40
35
30
25
20
15
0.0
0.2
0.4
0.6
0.8
1.0
x/c
Fig. 9.49. Chordwise surface temperature distributions at 50% span at different rotational
speeds of 10000, 13500, 14750, 16000, 17000, and 17800 rpm. From Liu et al. (1997a)
9.5. Rotating Machinery
1.3
1.1
1.0
p/p0
25% span
10,000 rpm
14,500 rpm
16,000 rpm
17,000 rpm
17,800 rpm
1.2
0.9
0.8
0.7
0.6
increasing rpm
0.5
0.0
0.2
0.4
0.6
0.8
1.0
x/c
Fig. 9.50. PSP-derived pressure distributions at 25% span. From Liu et al. (1997a)
1.3
1.1
1.0
p/p0
50% span
10,000 rpm
14,500 rpm
16,000 rpm
17,000 rpm
17,800 rpm
1.2
0.9
0.8
0.7
0.6
increasing rpm
0.5
0.0
0.2
0.4
0.6
0.8
1.0
x/c
Fig. 9.51. PSP-derived pressure distributions at 50% span. From Liu et al. (1997a)
245
246
9. Applications of Pressure Sensitive Paint
1.3
14,500 rpm
16,000 rpm
17,000 rpm
17,800 rpm
1.1
1.0
p/p0
75% span
10,000 rpm
1.2
0.9
0.8
0.7
0.6
increasing rpm
0.5
0.0
0.2
0.4
0.6
0.8
1.0
x/c
Fig. 9.52. PSP-derived pressure distributions at 75% span. From Liu et al. (1997a)
Fig. 9.53. Pressure and temperature distributions on compressor blades at the speed of
17800 rpm. From Torgerson et al. (1998)
9.5. Rotating Machinery
247
9.5.2. CCD Camera Measurements
Using a CCD camera system, Bencic (1997, 1998) conducted full-field PSP and
TSP measurements on rotating blades of a 24-inch diameter scale-model fan in the
NASA Glenn 9×15 ft low speed wind tunnel at rotational speeds as high as 9500
rpm. PSP measurements with a CCD camera on high-speed rotating blades
presented challenging problems, such as limited optical access to the entire surface
of blades, very short light duration for sufficient illumination, detection of weak
luminescence from high-speed rotating blades, and quantitative measurements
without standard instrumentation for in-situ calibration of PSP.
A 25%-scale model fan used for experiments was a single rotation, ultra high
bypass fan. Two blades were painted, one with a proprietary Boeing TSP and
other with a Boeing PSP (PF2B) on a white primer basecoat. Figure 9.54 shows
o
the painted fan blades installed 180 apart in the fan test rig. The traditional
intensity-based method was used for both PSP and TSP, requiring two images for
each of the paints to determine the pressure and temperature fields. Nine black
targets were applied to both PSP and TSP painted blades for image registration.
Both PSP and TSP were illuminated at wavelengths centered at 450 nm with
multiple filtered and focused xenon flash quartz lamps with a 2-3 µs flash
duration. The flash duration was short enough to freeze the motion of the blades
with minimal blurring. Note that a 2-µs flash duration roughly corresponded to
0.5-mm blurring on blades at the highest speed.
Fig. 9.54. PSP and TSP painted blades mounted in an ultra-high bypass ratio fan rig. From
Bencic (1997)
Bencic (1997, 1998) used a 14-bit cooled scientific CCD camera (512×512
pixels) that was fitted with a 200-mm lens attached with a band-pass filter around
600 nm for both PSP and TSP. Image acquisition and pulsed excitation were
synchronized with the position of the rig using a trigger signal from a magnetic
speed sensor. Using a delayed trigger signal, blade motion could be stopped
o
anywhere in a full rotation of 360 . Therefore, a PSP blade image was acquired
248
9. Applications of Pressure Sensitive Paint
o
and then, by delaying the trigger signal in a 180 phase angle, a TSP image was
o
taken since the PSP and TSP coated blades were installed 180 apart, as shown in
Fig 9.54. Images were acquired and integrated over two hundred revolutions
under excitation of multiple flashes while the camera shutter was kept open until
achieving an acceptable CCD well capacity.
Two wind-off reference images and two data images of TSP and PSP were
taken at each fan operating condition of interest. TSP images were used to correct
the temperature effect of PSP. Figures 9.55 and 9.56 show, respectively, the
temperature images and pressure images at the test points 4950B, 5800B, 7450B
and 7875B that correspond to the speeds of 4950, 5800, 7450 and 7875 rpm,
o
respectively. The surface temperature change on the blade was as large as 20 C
under the operating conditions. TSP visualized flow separation occurred
approximately at 75% span and 60% chord at the test points 7450B and 7875B.
Fig. 9.55. Temperature fields on the TSP-coated blade at four rig speeds of 4950, 5800,
7450 and 7875 rpm. From Bencic (1997)
9.6. Impinging Jets
249
Fig. 9.56. Normalized pressure fields on the PSP-ccoated blade at four rig speeds of 4950,
5800, 7450 and 7875 rpm. From Bencic (1997)
9.6. Impinging Jets
Using PSP and TSP complemented with Schlieren flow visualization, Crafton et
al. (1999) studied subsonic jets and sonic under-expanded jets impinging on a flat
plate at an oblique incidence angle from a converging nozzle. Results were
o
obtained on two geometric configurations at the impingement angles of 10 and
o
20 and the impingement distances of 3.8 and 4.5 diameters of the jet, respectively.
The jet velocity was varied from Mach 0.3 to Mach 1.0. PSP was used to measure
the pressure distributions, and TSP to measure the distributions of temperature and
the heat transfer coefficient on the impingement surface. Figure 9.57 shows the jet
and impingement plate configuration. The jet facility consisted of a 5-in diameter
by 12-in long settling chamber with a 1.5-in radial inlet and a 5-mm diameter
o
nozzle with a 15 convergence angle. The settling chamber was instrumented with
a J-type thermocouple to monitor the total temperature of the jet; the total pressure
was set using a regulator and monitored using a 0.2 psi resolution Heise pressure
gauge. Compressed air was supplied to the nozzle from an air compressor system.
The impingement plate was an 8-in high, 12-in long and 1.5-in thick aluminum
plate.
The normalized geometric impingement distance (H/D) and the
impingement angle (θ) were varied independently to produce multiple
o
o
impingement configurations. The impingement angles of 20 and 10 were tested,
o
where 90 corresponded to normal impingement. The geometric impingement
distance (H) was four jet diameters. The coordinate system (S,Y) on the
impingement plate was defined in such a way that the origin coincided with the
250
9. Applications of Pressure Sensitive Paint
geometric impingement point, the S-coordinate was along the surface of the
impingement plate in the mainstream direction, and the Y-coordinate was along
the surface of the impingement plate in the cross-mainstream direction.
Air inlet
0.5 cm nozzle
Impingement
distance
Impingement
plate
H
θ
Plenum
Internal
diffuser
Geometric
impingement point
Impingement angle
Fig. 9.57. Schematic of an obliquely impinging jet test facility. From Crafton et al. (1999)
In experiments, Ru(dpp) in RTV was used as PSP and Ru(bpy) in model
airplane dope was used as TSP. PSP and TSP, coated on the surface of the
impingement plate, were excited to luminesce by a blue LED array at 460 nm.
The luminescent emission, filtered using a long-pass optical filter (>570 nm) to
eliminate the excitation light, was detected using a 16-bit Photometrics CCD
camera. A ratio between the flow-on and flow-off reference images was
converted to pressure or temperature using a priori calibration relations. The
temperature distribution on the impingement surface in a sonic jet is shown in Fig.
o
9.58 for H/D = 3.8, θ = 10 and p0/pa = 2.7, where pa is the atmospheric pressure.
o
The surface temperature varied by less than 0.5 C from the region outside of the
influence of the jet to any location inside the region of jet impingement. This
temperature difference would result in an error of about 0.1 psi in PSP
measurements if the temperature effect of PSP was not corrected. Figure 9.59
o
shows the pressure distribution obtained using PSP at H/D = 3.8, θ = 10 and p0/pa
= 2.7. The pressure pattern associated with shock cells in the sonic jet was clearly
visualized. The pressure on the impingement plate varied by more than 8 psi,
suggesting that the temperature-induced PSP measurement error was less than 3%
of the full range of pressure. Figure 9.60 shows the streamwise pressure
distributions for different total pressures (p0/pa) of the jet at the impingement
o
o
angles of 10 and 20 . The subsonic pressure distributions showed a single
pressure peak at the stagnation point. This peak pressure location changed with
the impingement angle. The first pressure peak in the multi-peak pressure
distributions of the sonic impinging jet coincided with the single peak in the
subsonic pressure distributions. The first pressure peak corresponded to the
stagnation point. In these cases, the first pressure peak location (the stagnation
point) was always found somewhere upstream (toward the nozzle) of the
geometric impingement point. In fact, the deviation of the stagnation point from
the geometric impingement point is an intrinsic property of the non-orthogonal
viscous stagnation flow (Dorrepaal 1986; Liu 1992). Theoretically, this deviation
o
decreases to zero as the impingement angle approaches to 90 . Crafton et al.
9.6. Impinging Jets
251
(1999) discussed a correlation of the peak pressure location with the geometric
impingement point, which was related to the impingement distance H and the
impingement angle θ. An insight into the multi-peak pressure distribution was
gained by Schlieren flow visualization. Figure 9.61 shows a composite
representation of the streamwise pressure distribution and Schlieren image for the
o
sonic jet impinging at 10 . The locations of the shock waves corresponded to the
pressure peaks on the impingement surface.
301
po/pa 2.71
H/D 3.8
12 θ
10o
300.8
10
300.4
8
300.2
6
300
S/D
14
300.6
4
299.8
2
299.6
0
299.4
-2
299.2
299
-5
0
5
Y/D
Temperature [K]
Fig. 9.58. Temperature distibution on the impingement surface of a sonic jet. From Crafton
et al. (1999)
19
po/pa 2.71
H/D 3.8
12 θ
10o
14
18
17
S/D
10
8
16
6
15
4
14
2
13
0
12
-2
11
-5
0
Y/D
5
Pressure [psia]
Fig. 9.59. Pressure distribution on the impingement surface of a sonic jet. From Crafton et
al. (1999)
252
9. Applications of Pressure Sensitive Paint
19
θ = 10, H/D = 3.8
Pressure [psia]
18
po/pa 1.07
po/pa 1.14
po/pa 1.27
17
po/pa 1.55
16
po/pa 2.10
po/pa 2.71
15
14
13
12
-4
0
4
8
12
16
S/D
19
θ = 20, H/D = 4.5
Pressure [psia]
18
po/pa 1.07
po/pa 1.14
po/pa 1.27
17
po/pa 1.55
16
po/pa 2.10
po/pa 2.71
15
14
13
12
-4
0
4
8
12
16
S/D
Fig. 9.60. Streamwise pressure distributions along the axis of symmetry. From Crafton et
al. (1999)
po/pa 2.71
H/D 3.8
θ
10o
Fig. 9.61. Composite representation of the streamwise surface pressure distribution with the
corresponding Schlieren image for a sonic jet. From Crafton et al. (1999)
9.6. Impinging Jets
253
Using the same impinging jet facility running under different geometry and
flow conditions, Guille (2000) conducted PSP and TSP measurements for a direct
comparison of an intensity-based CCD camera system with a fluorescent lifetime
imaging (FLIM) system developed by the Defense Evaluation and Research
Agency (DERA) in Britain (Holmes 1998). The FLIM system consisted of an
array of modulated LEDs, a phase-sensitive CCD camera, a modulation control
box with an analog-to-digital converter, and a PC for image acquisition and
processing. The CCD full-well capacity was limited to 80,000 electrons. The
camera can be modulated up to 300 kHz with a 95% modulation depth. The
control box contained a computer-controlled frequency source, 12-bit A/D
converter, computer interface, and modulation electronics. The image readout rate
was limited by the data rate of the link between the control box and computer.
The LED array, which was used as a modulated light source, was composed of
2
100 blue LEDs. The illumination output was 7 W/m at a distance of 50 cm. The
fluctuation of the lamp was 0.1% per hour under laboratory conditions after a
warm-up period of 5 minutes. The modulation frequency for the FLIM system
was set to 150 kHz in their experiments. Figures 9.62 and 9.63 show the
temperature distributions and pressure coefficient distributions obtained by the
intensity-based CCD camera system and FLIM system, respectively, where the
coordinates were normalized by the nozzle diameter (D). The pressure coefficient
Cp was defined as C p = ( p − p atm ) / q exit , where q exit is the dynamical pressure of
the jet at the exit. The intensity-based CCD camera system and FLIM system
gave at least qualitatively consistent results. The results from the FLIM system
were much noisier perhaps due to relatively high photon shot noise although it had
an advantage of requiring no reference image.
300
300
299
298
298
0
296
295
5
297
0
s /D
s /D
297
296
295
5
294
294
293
10
0
b/D
293
10
292
292
-5
(a)
299
-5
-5
-5
5
T(K)
0
b/D
5
T(K)
(b)
Fig. 9.62. Temperature distributions obtained using (a) the intensity-based CCD camera
system and (b) the FLIM system. From Guille (2000)
254
9. Applications of Pressure Sensitive Paint
0.12
0.12
-5
0.1
-5
0.1
0.06
0
0.04
0.08
0
0.06
s /D
s /D
0.08
0.04
5
0.02
5
0
0.02
0
10
-0.02
10
-5
0
b/D
-0.02
5
-5
Cp
(a)
0
b/D
5
Cp
(b)
Fig. 9.63. The distribution of Cp obtained using (a) the intensity-based CCD camera system
and (b) the FLIM system. From Guille (2000)
Sakaue et al. (2001) utilized an oscillating nitrogen impinging jet generated by
a miniature fluidic oscillator to test the time response of several porous PSP
formulations: anodized aluminum (AA) PSP, thin-layer chromatography (TLC)
PSP and polymer/ceramic (PC) PSP. The frequency response of AA-PSP, TLCPSP and PC-PSP measured previously in a shock tube was 12.2 kHz, 11.4 kHz
and 3.95 kHz, respectively. Figure 9.64 shows Schlieren images visualizing the
flow structures of an unsteady nitrogen jet from a fluidic oscillator.
0° phase
180° phase
fluidic
oscillator
hot wire
Fig. 9.64. Schlieren images of jet oscillation from a fluidic oscillator. From Sakaue et al.
(2001)
Figure 9.65 is a schematic of the experimental setup for oscillating jet
experiments. A porous PSP sample was placed under a fluidic oscillator in
parallel to the nozzle centerline. A blue LED array was used as an excitation light
source and a Photometrics 12-bit CCD camera (512×752 pixels) was used to
capture PSP images through a long-pass filter (>580 nm). The excitation light
source was pulsed and synchronized with flow oscillation through a pulse
generator based on the flow structure signature sensed by a miniature microphone.
A light pulse width was 12 µs, corresponding to 6% of a flow oscillation period
9.6. Impinging Jets
255
when the fluidic oscillator was operated at 5 kHz. By controlling a trigger delay
in the pulse generator, flow images at different phases were obtained. Figure 9.66
shows the luminescent intensity ratio images visualizing the flow structures of the
impinging nitrogen jet at different phases obtained using AA-PSP, TLC-PSP and
PC-PSP. The flow structures visualized by all three PSPs were similar to those
observed in the Schlieren images. TLC-PSP images and AA-PSP images were
captured in the total exposure times of 10 s and 11 s (50,000 and 55,000 light
pulses), respectively. AA-PSP provided the sharpest images of the flow
structures, indicating a high frequency response.
N2 gas supply
pulse generator
fluidic oscillator
microphone signal
triggered pulse
(triggering LED)
microphone
blue LED
pulsed illumination
porous PSP
PSP
long pass filter
oscillating jet
CCD
Fig. 9.65. Schematic of an oscillating jet impingement setup. From Sakaue et al. (2001)
1.0
0.8
0.6
0.4
0.2
0.0
(a) TLC-PSP
1.0
0.8
0.6
0.4
0.2
0.0
(b) AA-PSP
1.0
0.8
0.6
0.4
0.2
0.0
(c) PC-PSP
Fig. 9.66. Intensity ratio images of jet oscillation from a fluidic oscillator. From Sakaue et
al. (2001)
256
9. Applications of Pressure Sensitive Paint
9.7. Flight Tests
Using PtOEP in silicone resin, McLachlan et al. (1992) measured the surface
pressure distributions on a fin attached to the underside of an F-104 fighter jet in
flight. A self-contained data acquisition system was installed inside the fin, which
consisted of an 8-bit digital video camera and an UV lamp triggered remotely to
excite PSP. PSP was applied to a Plexiglas panel mounted flush with the fin. The
luminescent emission from PSP was transmitted through the Plexiglas into the fin
where it was subsequently recorded by the video camera. Two tests were flown at
night at the Mach numbers 1.0-1.6 at altitudes between 30,000 and 33,000 ft.
Pressure taps mounted on the fin were used to calibrate PSP in-situ. Results
showed a favorable comparison to the pressure tap data at the Mach numbers
greater than 1.3, and the accuracy of about ±0.24 psi was reported. Houck et al
(1996) performed flight tests using PSP on a Navy A-6 Intruder where PSP was
painted on an Mk76 practice bomb. The data acquisition system consisted of a
battery-operated strobe light for excitation that was synchronized with a Nikon 50mm film camera used to measure the luminescent emission. This system was selfcontained and mounted onto a bomb rack adjacent to the practice bomb. Three
night flights were flown at altitudes between 5,000 and 10,000 ft at the Mach
numbers 0.4-0.82. After flight, the negative films were developed and digitized
by projecting them onto a 14-bit CCD camera. No in-situ calibration was done
such that only qualitative results were presented and the temperature effect was
unable to be accounted for. Using a similar film camera system, Fuentes and Abitt
(1996) measured the pressure distributions on a Clark-Y airfoil mounted
underneath the wing of a Cessna 152 aircraft. In general, issues associated with
film developing and processing make film-based systems more difficult for
quantitative measurements.
Using a portable 2D phase-based laser-scanning lifetime system, Lachendro et
al. (1998, 2000) conducted in-flight PSP measurements on a wing of a Raytheon
Beechjet 400A aircraft. Flight conditions were chosen to produce such a wing
pressure distribution that could be easily detected by the laser scanning system.
Thus, two flight conditions were considered: (1) 31,000 ft and Mach 0.75, and (2)
21,000 ft and Mach 0.69. These Mach numbers represented the maximum cruise
Mach number obtainable at the respective altitudes. Also, pressure data in the
above flight conditions were available from a flight test previously conducted by
Mitsubishi Heavy Industries (MHI). Since this aircraft was a derivative of the
Mitsubishi-designed Diamond II, it had been extensively studied in flight and
wind tunnel testing (Shimbo et al. 1999). The previous data were used to validate
the feasibility and accuracy of in-flight PSP measurements. The minimum and
maximum pressures and temperatures from both numerical calculations and MHI
flight tests were used as the design boundaries for selecting proper PSP and TSP
formulations for in-flight tests. A total of six in-flight tests were made. Three
tests were conducted at Purdue University on a university-owned and -operated
Beechjet 400A aircraft; three other tests were performed at Raytheon Aircraft
Company in Wichita, Kansas on a Beechjet 400A aircraft designated solely for inflight testing. In order to make in-flight PSP measurements, a lifetime-based or
phase-based technique is more suitable because this technique does not require
9.7. Flight Tests
257
reference signal (or image) used in conventional intensity-based systems and
therefore it is not affected by wing and fuselage deformation. The lifetime-based
technique is also insensitive to the ambient light from the Moon and stars.
Additionally, the system must be able to collect data over a large distance. In the
tests conducted by Lachendro et al. (1998, 2000), PSP and TSP measurements
were made at distances greater than 16 feet away from the photodetector. To
improve the SNR, a coherent light source such as a laser should be used. A
compact laser scanning system was specially designed for phase-based PSP and
TSP measurements at large distances.
The laser scanning system was designed to be as small as possible so as to
easily fit inside the aircraft. In addition, it was built to be robust and allow easy
modification to optical arrangement. The laser scanning system consisted of
scanning/positioning and data acquisition parts. Two 5-in diameter Velmex
programmable rotary tables were mounted orthogonally to each other via an
aluminum angle bracket. Mounted onto the vertical stage was an 8×5 in
aluminum backing plate that served as the mounting surface for the laser scanning
system plate. This allowed the scanner to position the laser spot on a wing. The
rotary stages were controlled through the serial port of a PC using a Velmex’s
NFS-90 stepper motor controller. A LabVIEW interface program allowed for
generation of a series of points distributed across a wing surface, and then a
surface grid formed by these points could be scanned repeatedly by the system
with a minimal deviation of the points from one scan to another. The angular
positioning resolution was ±0.0125° and the corresponding position resolution was
±1 mm at a distance of 16 feet.
Figure 9.67 shows the laser scanning system plate mainly comprised of a
UniPhase solid-state Nd:YAG laser (532 nm and 50 mW), a PMT, and an electrooptic (E-O) modulator with a driver. Data acquisition hardware is shown in Fig.
9.68. For phase-based measurements, a laser beam was passed through the E-O
modulator (Lasermetrics model 3079FW) for modulation. The input beam to the
E-O modulator was polarized using two Glan-Thompson polarizers. The first
polarizer was placed at the output of the laser to control the intensity, whereas the
second polarizer mounted at the end of the E-O modulator controlled the depth of
modulation. The beam was then passed through a Melles Griot 6X beam
expander/focuser, allowing for tightly focusing the scanning spot at a distance
greater than 1 m. The luminescent emission from PSP was collected through a 3in convex lens (f-number 1.86) and then was focused through a spatial aperture
located in the front of a long-pass filter (> 570 nm). The filtered emission was
passed into a PMT (Hamamatsu Model HC-120), and the PMT output was
sampled by a 16-bit A/D converter in a lock-in amplifier (EG&G model 5302).
The two-channel lock-in amplifier was capable of simultaneously measuring the
magnitude and phase of the luminescent signal. Data from the lock-in amplifier
was acquired through the GPIB interface into a PC using a LabVIEW program
that coordinated positioning of the scanning system with data acquisition. The
luminescent intensity and phase were recorded at each specified location of the
laser spot on the wing surface and saved for subsequent data analysis.
258
9. Applications of Pressure Sensitive Paint
E-O
Modulator
Polarizing
Optic
Linear
Traverse
6X Beam
Expander/ Focuser
Laser Path
Gimballed
Mirrors
Focusing
Lens
P.M.T
.
Polarizing
Optic
1/4 20 Optical
Breadboard
Longpass
Filter
Spatial
Aperture
532nm, 50mW,
Nd: YAG Laser
Fig. 9.67. Laser scanning system plate for flight test. From Lachendro (2000)
Scanning Head
D.C./A.C. Inverters
Outlet Strips
24V D.C.
Ni-Cad Battery
G.P.I.B
EO Modulator Lock-in Amplifier
Driver
Serial
Laptop
Rotary Stage
Controller
P.M.T. & Laser
Power Supplies
Fig. 9.68. Data acquisition hardware of a laser scanning system for flight tests. From
Lachendro (2000)
Four PSP formulations, Ru(dpp) PSP and three PtTFPP PSPs in different
binders, were developed for in-flight tests. These paints were chosen based on
their overall performance in a pressure range of 1-7 psi and a temperature range of
–50 to 0°C. PtTFPP in the FEM co-polymer binder was much less temperaturesensitive than other paints. Due to photosensitivity of the paints, they were
applied to the wing only just before a flight after the wing was cleaned with an
ethanol-based solvent. For the first flight test, two PSPs and one TSP were used
and sprayed separately onto 75-in long and 3-in wide strips on an adhesive-backed
monocoat film. As illustrated in Fig. 9.69, the strips wrapped around the leading
edge and positioned streamwise to the trailing edge. For the other three flight
tests, as shown in Fig. 9.69, the painted strips were placed at 31%, 55% and 85%
spans that corresponded to the locations in the MHI flight test. At each location,
PSP and TSP strips were placed side by side.
9.7. Flight Tests
259
532nm Nd: Yag laser
scanning from cabin window
Mylar strips coated
with PSP and TSP
η=0.
85
55
η=0.
.311
η==00.3
η
Fig. 9.69. PSP and TSP installation for flight tests. From Lachendro (2000)
Somewhat unexpectedly, Lachendro et al. (1998, 2000) found a considerable
temperature variation across the wing chord that was caused by wing fuel tanks
warmed by moving fuel and relatively cooled stringers. Due to poor temperature
sensitivity of TSP over the testing temperature range, the temperature effect of
PSP could not be corrected based on TSP data. Instead, they had to use a simple
heat transfer model to estimate the mean temperature on the wing in the flight
conditions. The chordwise pressure distributions were obtained at 31%, 55% and
85% span. Figure 9.70 shows the pressure coefficient Cp given by PSP at 21,000
ft and Mach 0.69 compared to the existing MHI fight test data. The distribution of
Cp was calculated from a priori calibration relation of PSP using the mean wing
temperature of –5°C estimated based on a heat transfer model. It was noted that
the first data point near the leading edge in the MHI flight test data was likely
erroneous and it could be disregarded. Near the trailing edge after x/c = 0.75, the
PSP data were significantly lower than the MHI flight test data. This was because
the mean temperature of –5°C used for PSP data reduction over the whole wing
section led to an underestimated value of Cp at the thin trailing edge that was
actually colder than the middle portion of the wing. Since the temperature
variation caused by moving fuel was not large at 21,000 ft, the PSP data in this
case did not exhibit a significant pattern produced by the temperature variation
across the wing section.
260
9. Applications of Pressure Sensitive Paint
-1.4
ο
-1.2
PSP T=-5 C
MHI Flight
Test Data
-1.0
-0.8
-0.6
-0.4
Cp
-0.2
0.0
0.2 0.0
0.4
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
x/c
0.6
0.8
Fig. 9.70. The distribution of Cp obtained by Ru(dpp)-based PSP at 21000 ft and Mach 0.69
compared with the MHI flight test data. From Lachendro (2000)
9.8. Micronozzle
PSP is a molecular sensor that can be used for global pressure measurements in
MEMS devices. Huang et al. (2002) used PSP to measure the pressure
distribution in a Mach 3 micronozzle fabricated with a high-accuracy CNC
machine. Generally, an imaging system for PSP (or TSP) applied to MEMS
devices must use an optical microscope and a close-up lens with a CCD camera to
achieve a sufficiently high spatial resolution. In experiments, Ru(dpp) was used
as a probe luminphore mixed with RTV as the binder dissolved in
dichloromethane. Using a CCD camera with a close-up lens, a spatial resolution
of 12 µm was achieved. Figure 9.71 is a schematic of the experimental setup for
PSP measurements in a micronozzle. The micronozzle was connected to a
vacuum pump, and one valve was used to control pressure at the micronozzle exit
and another valve to change the inlet pressure from the atmosphere. Two pressure
transducers were used to monitor the pressure signals at the micronozzle inlet and
exit. Figure 9.72 shows a schematic of the micronozzle and a typical pressure
image in the supersonic regime in the micronozzle where the total pressures at the
nozzle inlet was 11.45 psi and the estimated Reynolds number based on the nozzle
diameter was about 8000. Figure 9.73 shows a comparison of the PSP data with
an inviscid flow solution for local pressure and Mach number. The PSP data are
in agreement with the inviscid flow solution in the convergent and throat regions
of the nozzle. However, the Mach number obtained by PSP in the downstream
region after the nozzle was significantly lower than that predicted by the inviscid
flow solution after the Mach number reached 2.5. This discrepancy may be due to
the significant boundary-layer growth that was not taken into account in the
inviscid flow solution.
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9. Applications of Pressure Sensitive Paint
3.5
Inviscid Analysis
PSP Data
Mach Number and P/Po
3.0
Mach Number
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2.0
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1.0
0.5
p/p0
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10. Applications of Temperature Sensitive Paint
10.1. Hypersonic Flows
The global surface heat transfer distributions on a waverider model at Mach 10
were measured by Liu et al. (1994b, 1995b) using EuTTA-dope TSP. The
experiments were conducted in the Hypervelocity Wind Tunnel No. 9 at the Naval
Surface Warfare Center (NSWC), a blow-down facility operating at the Mach
Numbers of 8, 10, 14 and 16.5 with the corresponding maximum Reynolds
numbers per foot of approximately 50 ×10 6 , 20×10 6 , 3.8×10 6 and 3.2×10 6 ,
respectively. The test cell diameter was 5 feet and the length was over 12 feet,
which allowed for testing of large model configurations. Tunnel 9 used nitrogen
as the working gas. The waverider model had an overall length of 39 inches, a
span of 16.2 inches and a base height of 6.8 inches. The model was fabricated in
eight parts. The body consisted of four sections manufactured from 6061-T6
aluminum. The nose, both leading edges, and the main cavity cover plate were
manufactured from 17-4 PH stainless steel. Surface static pressures were
measured at 32 locations on the model with Kulite pressure transducers (Model
XCW-062-5A). Measurements of surface temperature rise were made using
Medtherm model TCS-E-10370 coaxial thermocouples. A 0.1-mm-thick white
Mylar layer covered the lower half of the windward side of the model from the
centerline to the outboard edge. EuTTA-dope TSP (about 10 µm thick) was
brushed on the Mylar layer. Ultraviolet illumination to excite the paint was
provided by four 40-watt fluorescent black lights. Two CCD video cameras,
viewing the front and back of the model separately, were used to image the TSPcoated surface. The analytical and numerical analyses of heat transfer on a thin
insulating layer on a semi-infinite metallic body gave an estimate of required
thickness of the insulating layer (about 0.1 mm). It was also proven that the
discrete Fourier law was reasonably accurate as a simple heat transfer model for
calculating heat flux from time-dependent TSP measurements in this case.
The experiment was run at the freestream Mach number of 10, average total
o
pressure of 1300 psia and average total temperature of 1840 R. The wind tunnel
run time was 2.3 seconds. The angle of attack was set at 10 degrees. Figure 10.1
shows windward side heat transfer maps of the lower half of the waverider (58%
of the total length is shown in the images) at 0.37, 0.57, 0.77, 1.04 and 1.24
seconds after the wind tunnel started to run. The gray intensity bar in Fig. 10.1
2
denotes heat flux in kW/m . The bright regions represent high heat transfer and
264
10. Applications of Temperature Sensitive Paint
dark regions low heat transfer. In these maps, the low heat transfer region (dark
region) downstream of the leading edge corresponds to laminar flow. Transition
from laminar to turbulent flow can be easily identified as an abrupt change from
low to high heat transfer. Also observed was a movement of the transition line
toward the leading edge as the laminar region diminished when the surface
temperature increased with time. Figure 10.2 shows typical temporal evolutions
of heat transfer obtained by TSP at the locations near the thermocouples. The heat
transfer history obtained by TSP was in agreement with that given by the
thermocouples at these locations.
Fig. 10.1. Sequential heat transfer maps of the windward side of the waverider model at
Mach 10. From Liu et al. (1995b)
10.1. Hypersonic Flows
120
120
Thermocouple at T3G
80
60
40
60
40
20
0
0
1
Time (sec)
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3
0
120
2
q (kW/m )
60
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40
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0
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60
0
2
3
80
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Time (sec)
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Thermocouple at T5G
100
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0
1
Time (sec)
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Thermocouple at T4G
Paint
100
2
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80
20
0
Thermocouple at T7G
Paint
100
Paint
2
q (kW/m )
2
q (kW/m )
100
265
0
1
Time (sec)
2
3
Fig. 10.2. History of heat transfer at four locations on the windward surface of the
waverider model at Mach 10. From Liu et al. (1995b)
Hubner et al. (2002) applied TSP with a high-speed imaging system to measure
full-field surface heat transfer rates on a 25°/55° indented cone model in shortduration hypersonic flows. Tests were performed in the 48-inch hypersonic shock
tunnel (HST) and the LENS I tunnel facilities at the Calspan-University of Buffalo
Research Center (CUBRC). Nominal test conditions ranged between the Mach
numbers 9.5 and 11.1 and the Reynolds numbers 140,000 and 300,000 per meter
with run times less than 10 ms. The indented cone model had the back diameter
of 0.262 m. The model was fitted with a sharp-nose cap (0.194 m long) or a
blunt-nose cap (6.4 mm radius). Over sixty platinum thin-film heat transfer
gauges were aligned along a ray on the model. Additional gauges were installed
azimuthally along the flare (aft) cone near the region of shock/boundary-layer
interaction. TSP and an insulating layer were applied to 50% of the model for the
HST tests and 25% of the model for the LENS I tests.
TSP used Ru-phen as an active sensing molecule. While Ru-phen itself
exhibited oxygen quenching and hence pressure sensitivity, the luminophor was
dissolved into an oxygen-impermeable polyurethane binder. TSP was applied
over a white polyurethane insulating layer, and both were sprayed using
conventional aerosol/airbrush equipment. The nominal TSP thickness and
insulator thickness were 5-10 µm and 100-150 µm, respectively (+/-5 µm). Both
266
10. Applications of Temperature Sensitive Paint
TSP and the insulating binders were polyurethane, thus exhibiting similar thermal
characteristics. The average thermal conductivity and diffusivity of the insulator
-7
2
were 0.48 W/(K-m) and 2.7×10 m /s, respectively, in a temperature range of 293323 K. The required insulating layer thickness was estimated to be the order of
100 microns for a run time of 10 ms based on a 1D transient heat transfer analysis
assuming a step change in the heat transfer rate on a semi-infinite body. By
minimizing the TSP thickness relative to the insulator thickness (while still
achieving viable intensity measurements), the shortest time constant of TSP was
achieved.
TSP was excited using a photographic xenon flash unit. Ultraviolet to blue
excitation filters and orange-red emission filters were required to separate the
luminescent emission from the excitation light. A combination of two Schott
glass filters was utilized to filter the xenon flash excitation. For emission filtering,
a 650 nm interference filter (80 nm bandpass) was used in conjunction with a
high-pass Schott glass filter. A fast-framing CCD camera system was used,
allowing on-chip framing rates from 15 to 1,000,000 frames per second (fps) with
a frame capacity of 17 frames. The practical framing rates for the measurement
system used at the CUBRC facilities were 100 to 5000 fps, depending on the
duration of a test run, the desired sampling rate, and the ability to effectively
detect the emission from TSP in short exposures. The advantage of the flexible
framing rate was the ability to choose from a single long-exposure image or
several short-exposure images during a single tunnel test. The frames were stored
on the chip until all 17 frames were acquired, then data were transferred to a PCinstalled frame grabber card. The CCD camera had a full-well capacity of
220,000 electrons and a readout noise of 70 electrons. The effective spatial
resolution per frame was 248 by 248 pixels.
Figure 10.3 shows a typical Schlieren image of the flow field around the
indented cone model. Visible was the intersection of the forebody shock and the
aftbody (flare) shock.
There was a separation region induced by the
shock/boundary-layer and shock/shock interactions. The flow separation existed
over the leading cone, and the flow reattached over the flare cone. Figure 10.4 is
an in-situ calibrated heat transfer image for the model with the sharp-nose cap at
Mach 9.6 and Re = 270,000 per meter in the LENS I tsets. The image shows a
stabilized axisymmetric pattern although the asymmetric flow appeared in the
transient stage of the onset of flow. Clearly present were the separated (violet)
and shock/boundary layer interaction (yellow-red) regions.
Where flow
separation was present, the corresponding surface heat transfer rate was low
(violet). Figure 10.5 shows the centerline heat transfer distributions obtained from
TSP and gauge measurements. The relative rms calibration error of TSP
measurements with the gauge measurements was 15%, which was mainly due to
the high-frequency unsteadiness in the flow.
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268
10. Applications of Temperature Sensitive Paint
surface heating. The first image taken just prior to the onset of flow indicates
uniform temperature. The following two images, acquired while the tunnel
conditions rose to the desired freestream conditions, show the flare shock
impingement just aft of the intersection of the leading and flare cones.
Afterwards, the separation region grew upstream and the shock impingement
moved downstream. As time increased, the separated region and shock
impingement boundary appeared to become stable and axisymmetric. Figure 10.7
shows the corresponding heat transfer results calculated from the time-dependent
intensity ratio data along the centerline of the model. First, the intensity-ratio data
was converted to temperature using a priori TSP calibration, and the heat transfer
rate was calculated using a transient heat transfer model when the thermal
properties of the coating were given. The heat transfer model was based on a
solution of the 1D heat conduction equation for a semi-infinite layer. Note that
some useful solutions of the heat conduction equation were given by Schultz and
Jones (1973) for the determination of the heat transfer rate in short-duration tunnel
testing. As shown by the thin line in Fig. 10.7, although the trend matched that of
the gauge measurements, the values of the heat transfer rate obtained by this
approach were over-predicted by 20 to 50%. This bias error might be due to the
differences between a priori TSP calibration experiments and actual experiments
(such as test set-up differences that led to spectral leakage, background
illumination, etc.), and uncertainties associated with the thermal properties of the
TSP and insulator. In-situ calibration with gauge measurements can account for
this bias error. When the intensity ratio data was calibrated with the gauge data
(thick line), excellent agreement was achieved. Besides the indented cone model,
Hubner et al. (2001) also measured the temperature distributions on an elliptic
cone lifting body in short-duration hypersonic flows. Recently, Matsumura et al.
(2002) and Schneider et al. (2002) used TSP to detect heat transfer signatures
induced by streamwise vortices shed from roughness elements on hypersonic
models in the Ludwieg tubes.
Fig. 10.6. Time-dependent intensity-ratio measurements on the sharp-nose indented cone in
the 48-in HST at Mach 11.0 and Re = 140,000 per meter. Images are shown at successive 1
ms intervals (actual acquisition rate was 2000 fps). From Hubner et al. (2002)
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270
10. Applications of Temperature Sensitive Paint
relative-intensity ratio could be used to determine temperature based on a priori
calibration relation without using a wind-off reference image. In fact, this kind of
thermographic phosphor was a two-color TSP. A three-color CCD camera was
used to acquire red, green and blue images even though only red and green images
were used for phosphor thermography. An estimated error in phosphor
o
o
thermography was about 3 C over a temperature range of 22-170 C, and the total
uncertainty in heat transfer measurements in typical hypersonic tunnels was less
than 10%.
Liquid crystal (LC) thermography has been applied to heat transfer
measurements in hypersonic flows (Jones and Hippensteele 1988; Babinsky
and Edwards 1996). Compared to polymer-based TSPs and thermographic
phosphors, thermochromic liquid crystals have a relatively narrow bandwidth
o
of temperature sensitivity (typically 32-42 C). Currently, there are two
implementation methods of LC for extracting quantitative heat transfer
information. The first approach is to use LC with a very narrow bandwidth of
about half a degree C. When a transient change in temperature occurs on a
model surface during a run in a short-duration tunnel, temperature at which a
single color of LC appears (usually yellow) is visualized most likely in a
narrow strip or contour moving on the surface. The temporal evolution of the
strip or contour with the specific temperature on the surface is recorded in a
series of images, and then the heat transfer rate on the surface can be
estimated based on certain transient heat transfer model. The instrumentation
for the narrow-band approach is simple with a CCD video camera attached
with a band-pass filter. The spatial resolution of measurement is limited by
the frame rate of the camera. An alternative is the wide-band approach that
utilizes the full range of colors (or hue) displayed by LC over a wider range of
temperature, which allows global heat transfer mapping using a single image
frame if the temperature-sensitive range of LC covers a temperature change
experienced on the whole surface. Using this approach, Babinsky and
Edwards (1996) obtained reasonable results of the heat transfer flux with the
o
total uncertainty of 7% on a cylinder/15 -flare model in hypersonic flows.
o
Note that the wide-band of LC (about 10 C) is, in fact, not wide compared to
the usable temperature ranges of polymer-based TSPs and thermographic
phosphors.
10.2. Boundary-Layer Transition Detection
TSP was utilized as a technique for visualizing flow transition (Campbell et al.
1992; Campbell 1993; McLachlan et al. 1993b; Cattafesta et al. 1995; Asai et al.
1997b, 1997c). Since convection heat transfer is much higher in turbulent flow
than in laminar flow, TSP can visualize a surface temperature difference between
the laminar and turbulent flow regions. Typically, at low speeds, model (or flow)
needs to be heated or cooled to generate a temperature change across the transition
line. However, at higher Mach numbers, artificial heating is not necessary
because friction heating is able to produce a significant temperature difference
between the laminar and turbulent flow regions. Using EuTTA-dope TSP,
10.2. Boundary-Layer Transition Detection
271
Campbell et al. (1992, 1993) visualized transition patterns on a Boeing symmetric
airfoil and a symmetric NACA 654-021 airfoil in a low-speed wind tunnel and
determined the dependency of the transition location on the angle of attack. In
o
their experiments, the airfoil models were pre-heated to about 50 C with a spot
lamp prior to a run to produce a sufficient temperature difference between the
turbulent and laminar flow regions by subsequent convection cooling. McLachlan
et al. (1993b) reported a similar transition detection experiment for a NACA64A010 airfoil using a proprietary TSP. Asai et al. (1997b) used a EuTTA-based
TSP to visualize transition on a 10-degree cone model at the Mach numbers 1.62.5 in a quiet supersonic wind tunnel.
Transition detection was made using EuTTA-dope TSP for a trapezoidal wing
(Trap Wing) semispan model at the Mach numbers 0.15-0.25 and Reynolds
6
6
numbers 3.5×10 -15×10 over a range of the angles of attack from -4° to 36° in the
NASA Ames 12-Ft Pressure Wind Tunnel (Burner et al. 1999). The transition
detection system consisted of three scientific-grade cooled CCD cameras, several
flash UV lights for illumination, and a computer for data processing. EuTTAdope TSP was coated on white paint stripes along the main wing, slat, and trailing
edge flap of the upper wing surface. The white basecoat was used to enhance
surface scattering and increase the luminescence emission from TSP. TSP was
applied only on the slat and the first 20% of chord on the main wing and flap since
previous testing of this model in the Langley 14×22 Ft tunnel had shown that
transition would always occur upstream of these locations. TSP data were
obtained with the three cameras viewing the slat, flap, and wingtip of the model.
The following data acquisition procedure was used. The tunnel was first run for
an extended period, without cooling, to raise the temperatures of the flow and the
model. Reference images of the ‘hot’ model were taken at several different angles
of attack (AoA). The cooling system was then activated, and ‘run’ images were
taken over the same AoA sequence while the flow cooled. The cooling sequence
generally required 2-3 minutes during which the flow temperature dropped at
about 5 °R/minute. Internal model temperatures, measured with thermocouples,
lagged the flow by from 2°R (slat) to 10°R in the main wing. Figure 10.8 shows a
typical transition image of the slat and main wing of the Trap Wing in the landing
configuration at the angle of attack of 24°, Mach 0.15, and the total pressure of 1
atm. Bright regions in the image were hot relative to dark regions. The slat was
dark relative to the main wing because its smaller mass allowed it to follow more
rapidly the drop in the flow temperature. Since the flow cooled the model,
boundary layer transition was indicated by a sharp decrease in brightness in the
image. This effect was seen clearly on the main wing where transition occurred at
10-15% chord except in the turbulent wakes behind the slat brackets.
Using a Ruthenium-based TSP, Cattafesta et al. (1995b, 1996) conducted
transition detection on several 3D models over a wide speed range in the NASA
Langley Supersonic Low-Disturbance Tunnel. Figure 10.9 shows a heat transfer
image mapped onto the half of the CFD model surface grid of a swept-wing
model, visualizing transition on the model at Mach 3.5. The bright region
corresponded to the turbulent boundary layer where the heat transfer rate was
higher than that in the laminar boundary layer. The onset of transition was
demarcated in the image as a bright parabolic band on the wing where the cross-
272
10. Applications of Temperature Sensitive Paint
flow instability mechanism dominated the transition process. No transition was
observed near the centerline of the model because near the symmetric plane of the
model the stability was mainly controlled by the Tollmien-Schlichting instability
mechanism that was weaker than the cross-flow instability mechanism.
Fig. 10.8. Transition image of the upper surface of the Trap Wing model at the angle of
attack of 24° and Mach 0.15. From Burner et al. (1999)
10.2. Boundary-Layer Transition Detection
273
Y (mm)
X (mm)
Z (mm)
Fig. 10.9. Heat transfer image of transition on a half of a CFD grid of a swept-wing model
at Mach 3.5. From Cattafesta et al. (1996)
Cryogenic TSP formulations, originally developed at Purdue University, were
used to detect transition on airfoils in the 0.1-m transonic cryogenic wind tunnel at
the National Aerospace Laboratory (NAL) in Japan and the 0.3-m cryogenic wind
tunnel at NASA Langley. In the NAL tests, two TSP formulations, Ru(trpy)GP197 and Ru(VH127)-GP197, were used by Asai et al. (1996, 1997c) in a
temperature range of 90-150 K for two NACA 64A012 airfoil models made of
white glass ceramic (MACOR®) and stainless steel. The stainless steel model
was covered with a thin white Mylar insulating layer to achieve a larger surface
temperature variation. In these tests, the total temperature varied from 90 to 150
K, the Mach number from 0.4 to 0.7, and the Reynolds number based on the chord
from 2.2 to 8.5 millions. In order to enhance a temperature difference across the
transition line, Asai et al. (1996, 1997c) employed both a transient method of
rapidly changing the freestream temperature and a steady internal heating method.
A rapid change of the freestream temperature was achieved by injecting liquid
nitrogen into the tunnel; the maximum temperature drop was about 7.5 K in 10
seconds. The CCD camera system used for cryogenic TSP transition detection
was the same as that for cryogenic PSP measurements at NAL described in
Chapter 9. Figure 10.10 shows a typical luminescent intensity ratio image of
Ru(VH127)-GP197 TSP on the stainless steel NACA 64A012 airfoil model
covered with a Mylar film at Mach 0.4 and the total temperature of 150 K, where
flow was from left to right. Bright and dark regions represented high and low heat
transfer, respectively. A turbulent wedge generated by a small roughness element
placed near the leading edge was clearly visible as well as the natural transition
line near 70% chord. Quantitatively, the surface temperature was calculated from
the luminescent intensity using a priori calibration relation. Figure 10.11 shows
the normalized chordwise surface temperature distributions at the natural and
forced transition locations on the stainless steel model, where the total temperature
was rapidly changed from 150 to 142.5 K by injecting liquid nitrogen to the
tunnel. Natural transition was shown as a sudden decrease in the chordwise
274
10. Applications of Temperature Sensitive Paint
temperature distribution. Figure 10.12 shows transition images on the stainless
steel airfoil model for different Reynolds numbers based on the chord at Mach 0.4.
Using several cryogenic TSPs, Popernack et al. (1997) also detected boundarylayer transition on a laminar-flow airfoil model in the NASA Langley 0.3-m
cryogenic wind tunnel. A typical transition image on this airfoil is shown in Fig.
10.13, clearly visualizing a number of turbulent wedges tripped by surface
roughness and the natural transition location. Transition detection on a swept
wing was recently made using cryogenic TSP in the European Transonic Wind
Tunnel (ETW) (Fey et al. 2003).
Fig. 10.10. Relative luminescent intensity image indicating transition on a NACA 64A012
airfoil at Mach 0.4 in the NAL 0.1 m transonic cryogenic wind tunnel, responding to a
decrease in the total temperature from T01 = 150 K to T02 = 142.5 K. From Asai et al.
(1996)
1.2
natural transition
(Ts - T02)/(T01 - T02)
1.0
0.8
0.6
forced transition
0.4
0.2
0.0
0.2
0.4
0.6
0.8
1.0
x/c
Fig. 10.11. Normalized chordwise surface temperature distributions in natural and forced
transition regions on a NACA 64A012 airfoil at Mach 0.4 obtained from Figure 10.10.
From Asai et al. (1996)
10.3. Impinging Jet Heat Transfer
275
Fig. 10.12. Transition images of a NACA 64A012 airfoil in the NAL 0.1 m transonic
cryogenic wind tunnel for different Reynolds numbers at Mach 0.4. From Asai et al.
(1996)
Fig. 10.13. Transition image on a laminar-flow airfoil model in the NASA Langley 0.3 m
cryogenic wind tunnel (flow from right to left). From Popernack et al. (1997)
10.3. Impinging Jet Heat Transfer
Using TSP complemented with hot-wire sensors and smoke visualization
technique, Liu and Sullivan (1996) studied the relationship between heat transfer
and flow structures in an acoustically excited impinging jet. Figure 10.14 is a
schematic of a variable-speed air jet facility and the coordinate system. The
facility consisted of two settling chambers. Air from a motor-driven centrifugal
blower entered the first rectangular settling chamber (254×533×483 mm) and then
passed through the second chamber that actually was a 178-mm long cylinder tube
of a 48 mm diameter. A 25-mm long contoured nozzle was mounted at the end of
the tube. The nozzle exit diameter D was 12.7 mm and the contraction ratio was
5.2. A loudspeaker attached to the opposite side of the first chamber to the nozzle
induced organ-pipe resonance in the chamber, producing axisymmetric and planewave excitation at the jet exit. To measure the local convection heat transfer
coefficient, air jet impinged on a 0.0254-mm thick, 115-mm wide and 130-mm
long stainless steel sheet that was heated by passing an electric current of 25
276
10. Applications of Temperature Sensitive Paint
Amperes. The sheet was stretched tautly by springs over two 12.5-mm diameter
aluminum rods that also served as electrodes, and deformation of the sheet due to
jet impingement was negligibly small. Given the uniform heat flux Qs from the
heated sheet surface and the measured surface temperature Ts of the heated sheet,
the convection heat transfer coefficient h = Qs /( Ts − T∞ ) and the Nusselt number
Nu = h D / k were calculated, where T∞ was the ambient temperature and k was
the thermal conductivity of air.
To measure the surface temperature Ts, EuTTA-dope TSP (about 10 µm thick)
was coated on a 0.05-mm thick white Mylar film attached on the backside
(relative to the jet impingement side) of the stainless steel sheet. A UV lamp was
used to illuminate TSP. The luminescent intensity images were taken by a CCD
viedo camera and digitized using a frame grabber with a spatial resolution of
512×512 pixels. The monochromatic excitation affected flow structures and
therefore changed the heat transfer rate on the impingement surface. Figure 10.15
shows the 2D Nusselt number (Nu) distributions of the impinging jet at the
excitation frequencies 950 Hz and 1750 Hz and without excitation for H/D =
1.125 and ReD = 12300. The natural frequency of the jet was 1750 Hz and the
subharmonic frequency was 950 Hz. Clearly, the 2D heat transfer distribution
was sensitive to the excitation frequency particularly in the wall-jet region. The
transverse heat transfer distributions in the excited impinging jet for H/D = 1.125
are shown in Fig. 10.16, compared to the unexcited impinging jet. At the natural
frequency of 1750 Hz, the local heat transfer coefficient in the wall-jet region (1<
r/D <2) was considerably enhanced by excitation compared to the unexcited
impinging jet. In contrast, at the subharmonic frequency of 950 Hz, the local heat
transfer coefficient was reduced in the wall-jet region. Near the stagnation-point
flow region (-1< r/D <1), the monochromatic excitation did not significantly
affect the time-averaged heat transfer coefficient. In the wall-jet region, the heat
transfer enhancement or reduction by excitation was related to the development of
the large-scale vortical structures that were studied using smoke flow visualization
coupled with hot-wire and hot-film measurements. When the excitation frequency
was close to the natural frequency of the impinging jet, intermittent vortex pairing
occurred, producing chaotic ‘lump eddies’ that contained a great deal of smallscale random turbulence. The random vortical structures enhanced the local heat
transfer. When the forcing was near the subharmonic of the natural frequency,
stable vortex pairing was promoted; resulting strong large-scale well-organized
vortices induced unsteady separation of the boundary layer in the wall-jet region
and caused a reduction in the local heat transfer coefficient. This experimental
study demonstrated that TSP, complemented with other experimental techniques,
provided an effective tool for study of basic fluid mechanics and heat transfer
problems.
10.3. Impinging Jet Heat Transfer
heated steel sheet
277
air flow
painted side
nozzle
loudspeaker
CCD Camera
electrode
UV lamp
spring
VCR
PC
rectangular chamber
(a)
H
D
y
O
r
(b)
Fig. 10.14. Experimental set-up: (a) Jet facility and TSP system, (b) Coordinate system.
From Liu and Sullivan (1996)
(a)
Fig. 10.15. (cont.)
278
10. Applications of Temperature Sensitive Paint
(b)
(c)
Fig. 10.15. Nusselt number distributions of the excited impinging jet for H/D = 1.125 and
ReD = 12300 at different excitation frequencies: (a) 950 Hz, (b) 1750 Hz and (c) unexcited.
From Liu and Sullivan (1996)
70
60
50
Nu
40
Unexcited
fe = 950 Hz
30
fe = 1750 Hz
20
-3
-2
-1
0
1
2
3
r/D
Fig. 10.16. Transverse Nusselt number distributions of the excited impinging jet for H/D =
1.125 and ReD = 12300 at different excitation frequencies. From Liu and Sullivan (1996)
10.3. Impinging Jet Heat Transfer
279
Using EuTTA-dope TSP, through an optical microscope and a close-up lens
attached with a CCD camera, Huang et al. (2002) measured the surface
temperature distributions in impinging micro-jets. The tested micro-jets were a
single jet of a 200-µm diameter, a multi-jet with 19 holes of a 200-µm diameter,
and a multi-jet with 19 tubes of a 100-µm inner diameter. The experimental setup
arrangement of micro-jet impingement was similar to that used by Liu and
Sullivan (1996). Figure 10.17 shows a typical temperature map in the impinging
multi-jet with 19 holes of a 200-µm diameter for H/D = 19.05, where the
Reynolds number based on the diameter was about 300. Figure 10.18 shows the
temperature distributions along the centerline of the multi-jet for three
impingement distances from the surface.
Fig. 10.17. Surface temperature distribution of the impinging multiple-micro-jet at H/D =
19.05. From Huang et al. (2002)
Fig. 10.18. Surface temperature distributions along the centerline of the multiple-micro-jet
at three impingement distances. From Huang et al. (2002)
280
10. Applications of Temperature Sensitive Paint
10.4. Shock/Boundary-Layer Interaction
Liu et al. (1995a) used EuTTA-dope TSP to measure the heat transfer rate in
several typical shock/turbulent-boundary-layer interacting flows: sweptshock/boundary-layer interaction, flows over rearward- and forward-facing steps,
and incident shock/boundary-layer interaction.
TSP allowed quantitative
measurements of heat transfer in complex 3D separated flows induced by
shock/boundary-layer interaction. The experiments were carried out in a blowdown supersonic wind tunnel with a test cross-section of 44×56 mm at Purdue
University. The test models were mounted on the floor of the test section that was
about 33 cm downstream of the nozzle throat. The tests were performed at Mach 2.5,
the total pressure of 2.9 atm. and the total temperature of 295 K. The incoming
boundary layer on the floor of the test section was fully turbulent. The incoming
turbulent boundary-layer thickness (δ ) in the test section was about 4.6 mm and the
5
Reynolds number Reδ based on it was 1.3×10 . A thin insulating layer covered the
aluminum test section floor and surface of aluminum models that were thermally
attached to the floor using high thermal conductivity grease. The insulating layer was
composed of a 0.07-mm thick Scotch brand packing tape and 0.05-mm thick white
Mylar film. TSP was applied on the surface of the white insulating layer. The
purpose of using the insulating layer was two-fold. First, light scattering from the
white layer significantly enhanced the luminescent intensity viewed by a camera.
Secondly, the thin insulating layer produced a sufficient temperature difference
across it such that a simple data reduction model could be used to calculate the heat
transfer rate. Two UV lamps were used to excite the paint. A steady-state heat
transfer model was used to calculate the heat flux q s from the measure surface
temperature, and then the Stanton number St = q s / ρ ∞ u ∞ c p ( Taw − Ts ) was
evaluated, where ρ∞ and u∞ are the freestream density and velocity of air flow,
respectively, cp is the specific heat of air at a constant pressure, and Taw is the adiabatic
wall temperature.
An example was swept-shock/turbulent-boundary-layer interaction. As shown
in Fig. 10.19, an attached planar shock generated by a sharp fin interacted with the
incoming turbulent boundary layer on the floor, which produced complicated 3D
flow separation. Previously, Settles and Lu (1985) suggested that except in the
inception region near the leading edge of the fin, local physical quantities such as
pressure and heat transfer rate on the floor approached a quasi-conical
symmetrical state in which these quantities remained invariant along a ray from a
virtual conical origin. Several heat transfer measurements were made in the quasiconical symmetry region using conventional heat transfer sensors distributed
discretely along a fixed arc (Lee and Settles 1992; Rodi and Dolling 1992). Here,
TSP was used to obtain a global heat transfer map in the inception region where
the flow lacked the presumed quasi-conical symmetry and the heat transfer rate
significantly changed along the radial direction. Figure 10.20 shows a typical heat
o
5
transfer image in the inception region of the 10 fin at M∞ = 2.5 and Reδ = 1.3×10 .
In the image, bright and dark regions correspond to high and low heat transfer,
2
respectively, and the intensity scale bar represents the heat transfer flux in kW/m .
o
The viewing polar angle of the camera was about 60 . The arrow indicates the
10.4. Shock/Boundary-Layer Interaction
281
incoming flow direction and the length of the arrow in the image corresponds to 10
mm in the actual length scale in the streamwise direction.
The primary separation line was identified, and the highest heat transfer region
was located in the neighborhood of the fin. Figure 10.21 presents the distributions
of the relative Stanton number St/Str along four circular arcs with different radial
distance R from the leading edge of the fin, where Str is the reference Stanton
number in the undisturbed boundary layer upstream of the leading edge. As R
increased, the distributions of the heat transfer rate tended to approach an
asymptotic profile near the fin while the asymptotic tendency was not quite
evident near the inviscid shock location. When the maximum relative Stanton
number Stmax/Str was taken as a characteristic quantity, as shown in Fig. 10.22, it
was found that Stmax/Str increased with the non-dimensional radial distance R/δ and
approached the value measured previously using thin-film sensors by Lee and
Settles (1992) in the quasi-conical symmetry region. Therefore, the asymptotic
behavior of the heat transfer rate measured by TSP in the inception region
supported the concept of the quasi-conical symmetry. Heat transfer measurements
were also made using TSP for other shock/boundary-layer interactions such as
rearward and forward facing steps and incident shock/boundary-layer interaction;
comparisons of TSP measurements with previous results obtained by conventional
techniques for these flows were discussed by Liu et al. (1995a).
y
Sharp fin
U
α
x
O
β
R
z
Floor
Fig. 10.19. Fin geometry and coordinate system in swept shock/boundary-layer interaction.
From Liu et al. (1995a)
Fig. 10.20. Heat transfer image in swept shock/boundary-layer interaction at Mach 2.5.
2
The intensity scale bar represents heat flux in kW/m . From Liu et al. (1995a)
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10.5. Laser Spot Heating and Heat Transfer Measurements
283
convection heat transfer was determined from the surface temperature response
measured using TSP. Figure 10.23 is a general layout of the laser spot heating
heat transfer system with TSP (LSH-TSP) that consisted of three sub-systems, one
for temperature measurement and two for surface heating. The temperature
measurement system was composed of an excitation laser, TSP, a band-pass filter
and a photo-detector (PMT). The role of the temperature measurement subsystem was to measure the luminescent intensity and thus the surface temperature
at a target point. The heating system was composed of a heating laser, an
insulating layer and an absorbing layer, which created a local heat flux to the
surface that was necessary to make heat transfer measurements. Note that Mayer
et al. (1997) proposed a similar technique that used laser heating and an IR camera
(rather than TSP) for wall-shear stress measurements based on the relationship
between local heat transfer and shear stress.
The temperature measurement sub-system was very similar to the laser
scanning TSP system. A solid-state, diode pumped Nd:YLF laser with a
frequency doubling crystal produced a 50-mW beam at 532 nm, which served as
an excitation source for TSP. This beam was reflected off of a glass slide to
reduce the power to approximately 2 mW. Excitation of TSP at this power level
resulted in a significant luminescent signal while preventing excessive
photodegradation of TSP by the excitation laser. The excitation beam was
focused at a point of interest on the model surface. The luminescent emission
from TSP was gathered by a collection lens and focused through a band-pass filter
to a PMT. The PMT detected the luminescent intensity of TSP that was then
converted to temperature using a priori TSP calibration relation. The heating subsystem was composed of a solid-state, diode pumped Nd:YLF laser which
produced a 200-mW beam at 1064 nm (infrared) and optics to direct the beam at
the surface. This wavelength was much longer than both the absorption and
emission bands of a Ru(bpy)-based TSP used in their research, and any reflected
IR radiation was effectively filtered by a band-pass filter. This beam was focused
onto the absorbing layer on the surface that absorbed the radiation and heated up.
The absorbing layer was another important element of this system. Figure
10.24 shows an idealized model surface that was first coated with an insulator and
then a thin absorbing layer. The material of the absorbing layer absorbed
radiation from the heating laser, causing the temperature of the absorbing layer to
rise. The temperature gradient between the absorber and the TSP layer on the top
resulted in heat conduction from the absorber to TSP. The heat generated in the
absorbing layer and conducted through TSP was released through convection heat
transfer at the TSP surface. Two absorbing layers were investigated. The first
was a dark surface that absorbed IR radiation simply due to its color. Several dark
surfaces such as fine-grit polishing paper and magnetic tape proved to work well
as an absorber. The second option was an IR dye (IR26 from Lambdachrome
Laser Dyes) that absorbed strongly at 1 µm. A small portion of the absorbed
energy was re-emitted at a longer wavelength, but the majority of the energy went
into heating up the absorbing layer. The laser dye can be mixed with a polymer
applied as a separate layer, or mixed directly with TSP. Since adding the IR dye
to TSP did not change the temperature sensitivity of TSP and it also simplified
coating process, this option was chosen in their experiments.
284
10. Applications of Temperature Sensitive Paint
As shown in Fig. 10.23, the excitation and heating lasers were combined into a
single, co-linear beam using a glass slide. The combined beam was focused at a
target location on the model surface using a single lens. Since the optical path
length between the focusing lens and the model surface varied during
experiments, the optical system was designed with a large depth of field. In
practice, alignment of the two spots over the whole surface of interest was ensured
through visual inspection of a scan grid. Figure 10.25 shows the spectral
arrangement of the components of the LSH-TSP system. The emission spectra of
the lasers and IR dye did not overlap with the emission spectrum of the Ru(bpy)based TSP.
Excitation Laser (532 nm)
Glass
Scanning
Mirror
PMT
Heating Laser (1064 nm)
Band-Pass
Filter
V∞
Absorbing
Layer
Painted Model
Fig. 10.23. Schematic of laser-spot-heating-TSP (LSH-TSP) system. From Campbell et al.
(1998)
Heating Laser
Heat conduction from
absorbing layer to TSP
Convection to Flow
TSP Layer
TS
Absorbing Layer
TAB
Insulating Layer
Model Surface
Fig. 10.24. Idealized surface model for the LSH-TSP system. From Campbell et al. (1998)
Normalized Spectral Characteristics
10.5. Laser Spot Heating and Heat Transfer Measurements
1
Ru(bpy) Abs.
Heating Laser
0.8
285
IR 26
Ems.
BP Filter
0.6
Green Laser
0.4
IR 26
Abs.
Ru(bpy)
Ems.
0.2
0
400
600
800
1000
Wavelength (nm)
1200
1400
Fig. 10.25. Spectral arrangement for the LSH-TSP system. From Campbell et al. (1998)
Campbell et al. (1998) calculated the convection heat transfer coefficient hc
from a transient temperature history of the heated surface. Initially, temperature
on the whole surface was equal to the ambient temperature. Activating the
heating laser caused local temperature to rise and the luminescent intensity of TSP
to decrease. The luminescent intensity of TSP continued to decrease until it
reached a steady state when the input heat flux by the heating laser was balanced
by the heat loss due to convection in flow and conduction into the model. A
similar cycle was associated with the surface temperature response upon
deactivation of the heating laser. In this case, the surface temperature decreased
and the luminescent intensity increased until the surface temperature was equal to
the ambient temperature. A simple lumped capacitance model of the surface
indicated that the time constant of the cooling cycle was a function of the heat
transfer coefficient. Since the heating laser was turned off, the solution was
independent of the input heat flux, eliminating one unknown in data reduction.
Figure 10.26 is a schematic of the surface used for a transient analysis of the
cooling surface. The lumped capacitance analysis gives a solution for a temporal
evolution of the surface temperature Ts at a heated spot
§ t
§ t
·
θ Ts − T∞
=
= exp¨¨ − (1 + τ C )¸¸ = exp¨¨ −
θ i Ti − T∞
© τh
¹
© τh
1 ··
§
¨¨ 1 + ¸¸ ¸¸ ,
Bi ¹ ¹
©
(10.1)
where the time constant is defined as τ h = ρ c L / hc , the constant C = k / ρ c L2
is a correction term for heat conduction to the insulating layer, Bi = hc L / k is the
Biot number, Ti is the initial surface temperature (the ambient temperature), and
T∞ is the freestream temperature. In Eq. (10.1), ρ, c, and L are the density,
specific heat, and thickness of the insulating layer, respectively.
286
10. Applications of Temperature Sensitive Paint
Heated Spot
V∞, T∞
Heat Loss
(Convection)
− h (TS − T∞ )
Measurement
Location
L
Heat Loss
(Conduction)
−k
∂T
∂n
Substrate
TSP and
Absorber
Insulating
Layer
Fig. 10.26. Schematic of transient heat transfer analysis. From Campbell et al. (1998)
In order to determine the convection heat transfer coefficient hc , the surface
was first heated to a steady state and then the surface temperature response was
recorded after the heating laser was turned off. The natural log of the nondimensional temperature was plotted versus time and the slope of the resulting
curve was evaluated using the following relation
§ 1
·
§ T − T∞ ·
¸ = −t ¨ + C¸.
ln ¨¨ s
¨
¸
¸
©τ h
¹
© Ti − T∞ ¹
(10.2)
The slope was a sum of two terms: the time constant τ h that was a function of the
heat transfer coefficient hc and the heat conduction term C. The conduction term
C was experimentally determined for a given test configuration by making flowoff measurements. In such a case, the convection heat transfer due to natural
convection was several orders of magnitude lower than the heat conduction into
the model surface. Hence, the surface temperature response gave the conduction
term at a location, and the heat conduction term was equal to the log-slope of the
non-dimensional temperature response for a flow-off scan. This value was used to
adjust the log-slope of flow-on scan data to account for the heat conduction effect.
According to the transient model, higher heat transfer would be expected to
produce a small time constant τ h . Figure 10.27 shows typical responses of the
surface temperature to a pulsed laser heating at two different Reynolds numbers in
an impinging jet. The steady-state temperature was higher at lower Reynolds
numbers due to lower convection heat transfer. At higher Reynolds numbers, the
steady state was reached much sooner and the time constant was smaller due to
higher convention heat transfer. Figure 10.28 shows the natural log of the nondimensional temperature response θ / θ i for the first 0.5 seconds of the cooling
cycle. The log-plots exhibited a linear behavior and the increased slope (the
absolute value) with the Reynolds number, and demonstrated the sensitivity of the
slope to the heat transfer rate. In preliminary tests, using the LSH-TSP system,
Campbell et al. (1998) measured the Nusselt number distributions in an impinging
jet at different Reynolds numbers and gave reasonable results.
10.5. Laser Spot Heating and Heat Transfer Measurements
287
Surface Temperature Change (°C)
50
ReD =5,700
40
30
ReD =23,000
ReD =5,700
20
ReD =23,000
10
0
0
1
2
3
4
5
6
Time (s)
7
8
9
10
Fig. 10.27. Surface temperature response to pulsed laser heating in an impinging jet. From
Campbell et al. (1998)
0
Ln(θ/θi)
-0.1
-0.2
ReD
5,700
15,000
23,300
-0.3
-0.4
0
0.1
0.2
0.3
Time (s)
0.4
0.5
Fig. 10.28. Natural log-plot of the non-dimensional surface temperature response at three
Reynolds numbers in an impinging jet. From Campbell et al. (1998)
Campbell et al. (1998) presented application of the LSH-TSP system to more
o
complex flows. Quantitative measurements were made on a 75 swept delta wing
model using the LSH-TSP system in a region that was also visualized by TSP with
a CCD camera at the same conditions, as shown in Fig. 10.29a. Figure 10.29b
shows a map of the heat transfer coefficient hc in this region at the angle of attack
o
of 25 . Another experiment was performed for quantitative heat transfer
measurements in an intersection of a strut and a wall that often occurred in air
vehicles (e.g. the wing/body and stator/wall junction). Figure 10.30 shows
schematically the primary horseshoe vortex developed around the base of a strut
that influences the heat transfer distribution on the wall. A strut with a NACA
0015 airfoil cross-section and a 48-in chord was positioned vertically in the
Boeing subsonic wind tunnel at Purdue University and it spanned the 48-in height
of the test section. The flow velocity was about 90 ft/s and the Reynolds number
288
10. Applications of Temperature Sensitive Paint
was about 2.5 millions based on the chord. Another relevant length scale for this
flow was the strut thickness of 7.2 in, and the Reynolds number based on it was
about 350,000. The LSH-TSP system was used to measure the heat transfer rate
on the large model in a large wind tunnel since heating the entire wall would be
impractical. Figure 10.31 shows a map of the Stanton number on the surface
around the strut. The heat transfer results were computed using the transient heat
transfer model with heat conduction correction. The location on the surface was
normalized by the approaching boundary layer displacement thickness δ * = 0.5
in. The largest variation in heat transfer appeared near the leading edge of the
strut. There was a region of decreased heat transfer due to decelerating flow and
local flow separation caused by the presence of the strut. Near the strut, heat
transfer was enhanced by the primary horseshoe vortex that transported fluid
outside the boundary layer to the wall.
(a)
h (W/m2-°C)
0
120
110
-0.1
100
% Span
-0.2
90
80
-0.3
70
-0.4
60
50
-0.5
40
-0.6
30
20
-0.7
0.6
(b)
0.7
0.8
0.9
% Chord
Fig. 10.29. (a) TSP visualization with a CCD camera, and (b) quantitative heat transfer
measurements using the LSH-TSP system on a 75-degree swept delta wing at the angle of
o
attack of 25 in low-speed flow. From Campbell et al. (1998)
10.6. Hot-Film Surface Temperature in Shear Flow
289
y
Incident
Boundary
Layer
u(y)
Horseshoe Vortex
Strut
Endwall
z
Line of Separation
x
Fig. 10.30. Schematic of strut/endwall junction flow. From Campbell et al. (1998)
St
0
5 x 10-3
4.5 x 10-3
Z / δ*approach
5
4 x 10-3
10
3.5 x 10-3
15
3 x 10-3
2.5 x 10-3
20
2 x 10-3
-15
-10
-5
0
X / δ*approach
5
10
Fig. 10.31. Stanton number distribution around the strut obtained using the LSH-TSP
system at 90 ft/s and the Reynolds number of about 2.5 millions based on the chord of the
strut. From Campbell et al. (1998)
10.6. Hot-Film Surface Temperature in Shear Flow
Through an optical magnification system, a very high spatial resolution can be
achieved in TSP measurements on a small object. Liu et al. (1994a) used EuTTAdope TSP to measure a surface temperature field on a commercial flush-mounted
hot-film sensor (TSI 1237) in a flat-plate turbulent boundary layer. As shown in
Fig. 10.32, the sensor had a 0.127-mm streamwise length and a 1-mm spanwise
length. TSP was applied to the hot-film sensor by dipping. Figure 10.33 shows
the experimental set-up used for this study. The sensor was mounted flush with the
surface of a flat plate with a 1:6 elliptical nose (the leading edge) that was installed in
a low-speed blow-down wind tunnel at Purdue University. The sensor was located
290
10. Applications of Temperature Sensitive Paint
0.37 m downstream from the leading edge of the plate. The freestream velocity was
26 m/s in the experiments. A roughness band near the plate leading edge was used to
produce artificial flow transition such that the boundary layer was fully turbulent
downstream. The sensor was operated at a low overheat ratio of 1.07, where the cold
resistance of the sensor was 5.14 Ω. The luminescent intensity images were
obtained using a CCD video camera through an optical magnification system. The
streamwise and spanwise surface temperature distributions were computed from
the luminescent intensity images using a priori calibration relation.
Figure 10.34 shows the non-dimensional streamwise surface temperature
distributions at three spanwise locations, where Z is the spanwise coordinate, L is
the streamwise length, w is the half-span width, and Tm is the maximum surface
temperature. Liu et al (1994a) also derived the analytical solutions for a uniformtemperature (UT) film and uniform heat source (UHS) film on an adiabatic wall in
shear flow for a comparison with TSP measurements. These solutions are also
plotted in Fig. 10.34 as references. The temperature distributions on the TSI hotfilm sensor appeared to be nearly symmetric and largely deviated from the
theoretical distributions of the UT and UHS films on an adiabatic wall. This
deviation was mainly due to the dominant effect of heat conduction to the glass
substrate and the streamwise diffusion effect (the finite Peclet number effect) that
were neglected in the analytical solutions. This result indicated that the TSI hotfilm sensor had a large heat loss to the substrate that might limit the frequency
response of the sensor. The measured spanwise temperature distribution on the
TSI hot film is shown in Fig. 10.35 along with a theoretical temperature
distribution given by a simple lumped model for comparison. As shown in Fig.
10.35, the theoretical distribution was in good agreement with the experimental
data for the sensor in a region of ⏐Z⏐/w < 1.2. Outside of this region, the
theoretical distribution underestimated the surface temperature since the lumped
model neglected heat conduction into the substrate along the spanwise direction at
the tips of the sensor.
Stainless steel tube
Epoxy
Glass base
Platinum film
Gold lead
3.2 mm 2.5 mm
1.5 mm
Fig. 10.32. Configuration of the TSI 1237 hot-film sensor
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Appendix A. Calibration Apparatus
For PSP, the relationship between the luminescent intensity (or lifetime) and
air pressure is determined by calibration. Figure A1 shows a simple apparatus
for calibration of PSP (Burns 1995). A PSP coating is applied to an aluminum
block (1.5×1.5×0.625 cm) that is thermally anchored using high thermal
conductivity grease to a Peltier heater/cooler controlling the surface
temperature of the block. A thermometer inserted in the aluminum block near
the painted surface is used to measure the temperature of the paint sample.
The PSP sample on the block is placed inside a pressure chamber with an
optical access window. Pressure inside the chamber is controlled and
measured using a pressure transducer. An illumination light, typically from a
UV lamp, LED array or laser, passes into the chamber through the window
and excites the paint sample. The luminescent emission from the paint sample
is collected with a lens, filtered by a long-pass or band-pass optical filter, and
projected onto a photodetector like a photodiode, photomultiplier tube (PMT)
or CCD camera. The photodetector output over a range of pressures and
temperatures is acquired with a PC, where the dark current is subtracted from
the intensity output. Therefore, a relation between the luminescent intensity
and pressure is determined over a range of temperatures; the calibration data
are typically fit using the Stern-Volmer equation for different temperatures.
For lifetime or phase calibrations, a pulsed or modulated excitation light
should be used.
The set-up in Fig. A1 can be used for TSP calibration when the surface
temperature of a TSP coating on the aluminum block is varied over a range of
o
–15 to 150 C by controlling the Peltier heater/cooler while the chamber
pressure is kept constant.
Thus, a calibrated relation between the
luminescence intensity and temperature is obtained, which is typically
represented by the Arrhenius plot over a certain temperature range. Note that
an oven for calibrating fluorescent temperature sensors was described by
Crovini and Fernicola (1992). This simple apparatus can be adapted for TSP
calibration down to cryogenic temperatures (Campbell et al. 1994). In this
o
case, a TSP sample is thermally anchored to a copper bar cut at an angle of 45
at its top that rests in a container filled with liquid nitrogen. The sample
temperature near the temperature of liquid nitrogen can be achieved due to
heat conduction from liquid nitrogen to the sample through the copper bar. To
prevent condensation of moisture from forming on the paint sample, the
sample is purged with dry nitrogen gas. Using this apparatus, Campbell et al.
(1994) examined the temperature dependencies of the luminescent intensity
for many TSP formulations.
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Appendix A. Calibration Apparatus
Fig. A2. Calibration chamber for cryogenic PSP and TSP. From Erausquin (1998)
315
Appendix B. Recipes of Typical Pressure
and Temperature Sensitive Paints
Recipes of Three PSP Formulations
(1) Ru(ph2-phen) or Ru(dpp) in RTV
Ingredients: 4 mg of Bathophen Ruthenium Chloride [Ru(ph2-phen) or Ru(dpp)],
25 ml of dichloromethane, 7.5 ml of GE RTV 118, 2 g silica gel particles.
Directions: Dissolve Ru(ph2-phen) in the solvent dichloromethane, add silica gel
particles and then GE RTV 118, and stir until fully dissolved.
(2) PtTFPP in RTV
Ingredients: 6 mg of platinum meso-tetra(pentafluorophenyl)porphyrin (PtTFPP),
25 ml of dichloromethane, 7.5 ml of GE RTV 118, 2 g silica gel particles.
Directions: Dissolve PtTFPP in the solvent dichloromethane, add silica gel
particles and then GE RTV 118, and stir until fully dissolved.
(3) PtTFPP in FEM (NASA Langley)
Ingredients: 5.3 mg platinum meso-tetra(pentafluorophenyl)porphyrin (PtTFPP)
(120 ppm), 12 g Polytrifluorethyl-co-isobutyl methacrylate (TFEM/IBM), 37.5 g
Solvent DuPont 3602S, 3.6 g Solvent DuPont 3979S or 3696S.
Directions: Dissolve the TFEM/IBM in the DuPont solvents, add PtTFPP, and stir
until dissolved, and adjust the viscosity of the solution to 10.5 cp with the 3602S
solvent. Allow the paint to cure at the room temperature for about 20 minutes
before heating to 65°C for one hour.
318
Appendix B. Recipes of Typical Pressure and Temperature Sensitive Paints
Recipes of Two TSP Formulations
(1) Ru(bpy) in Clear Coat
Ingredients: 6 mg of tris(2,2’-bipyridyl) ruthenium [Ru(bpy)], 20 ml of
automobile Urethane Clear Coat (DuPont ChromaClear), 5 ml of activator, 10 ml
dichloromethane.
Directions: Dissolve Ru(bpy) in the solvent dichloromethane, sonicate for 5
minutes, add urethane clear, shake and sonicate. Just before painting (within 5
minuets) add the activator, shake and sonicate for 1 minute. Acetone is used as a
solvent to clean up the paint.
(2) EuTTA in Dope
Ingredients: 12 mg Europium (III) Thenoyltrifluoroacetonate (EuTTA), 20 ml
model airplane dope, 20 ml dope thinner.
Directions: Mix EuTTA with the dope thinner, shake and then sonicate for a few
minutes. Add the dope, shake and sonicate. Acetone is used as a solvent to clean
up the paint.
Appendix C. Vendors
Chemicals
(1) Frontier Scientific, Inc. (former Porphyrins Products)
P.O. Box 31, Logan, Utah 84323-0031, USA
Tel: (435) 753-6731, E-mail: sales@frontiersci.com, Web: www.frontiersci.com
Products: Pt(III) meso-tetra(Pentafluorophenyl)porphine (PtTFPP) (PSP probe),
Pt(II) Octaethylporphine (PtOEP) (PSP probe)
(2) Sigma-Aldrich
3050 Spruce St., St. Louis, MO 63103, USA
Tel: 800-325-3010, Web: www.sigmaaldrich.com
Products: Tris(2,2’-bipyridyl)ruthenium(II) chloride hexahydrate [Ru(bpy)] (TSP
probe), Dichlorotris(1,10-phenanthroline)ruthenium(II) [Re(ddp)] (PSP probe),
Pyrene (PSP probe)
(3) Gelest, Inc.
11 East Steel Road, Morrisville, PA 19067, USA
Tel: (215)-547-1015, E-mail: info@gelest.com, Web: www.gelest.com
Products: Europium III Thenoyltrifluoroacetonate (EuTTA) (TSP probe)
(4) GFS Chemicals, Inc.
P.O. Box 245, Powell, OH 43065, USA
Tel: (877)-534-0795, E-mail: sales@gsfchemicals.com, Web:
www.gfschemicals.com
Products: Terpyridine ruthenous dichloride [Ru(trpy)] (TSP probe),
Ruthenium bis(4,4’,5,5’-tetramethyl-2,2-bipyridine)(2,2’:6’,2”-terpyridine)
[Ru(tmb)2(trpy)] (TSP probe), Ruthenium bis(2,2’-bipyridine)(2,2’:6,2”terpyridine) [Ru(bypy)2(trpy)] (TSP probe), 1,10-phenanthroline ruthenous
chloride [Ru(phen)3Cl2] (TSP probe), Tris(2,2’-bipyridine) ruthenous dichloride,
hydrate [Ru(bypy)] (TSP probe), Tris(bathophenanthroline) ruthenium dichloride
[Ru(bath)] (PSP probe)
320
Appendix C. Vendors
(5) Innovative Scientific Solutions, Inc.
2766 Indian Ripple Road, Dayton, OH 45440-3638, USA
Tel: (937)-429-4980, E-mail: solutions@innssi.com, Web: www.innssi.com
Products: Unicoat PSP, FIB-based PSP top coat and base coat, PtTFPP sol-gel
PSP, and Ru sol-gel PSP
Cameras
(1) Roper Scientific, Inc.
3660 Quakerbridge Road, Trenton, NJ 08619, USA
Tel: (609)-587-9797, E-mail: info@roperscientific.com, Web:
www.roperscientific.com
Products: high-performance CCD cameras for scientific and technical applications
(2) PixelVision
10500 SW Nimbus Avenue, Tigard, OR 97223-4310, USA
Tel: (503)-431-3210, E-mail: info@pvinc.com, Web: www.pvinc.com
Products: high-performance CCD cameras for scientific and technical applications
(3) Hamamatsu Corporation (USA)
360 Foothill Road, Bridgewater, NJ 08807-0910, USA
Tel: (908)-231-0960, E-mail: usa@hamamatsu.com, Web: www.hamamatsu.com
Products: digital CCD cameras and other photonics equipment
Color Plates
The following pages contain color plates of figures that are shown in black and
white in the text to reduce the cost of reproduction.
Fig. 1.6. PSP image for the F-16C model at Mach 0.9 and the angle-of-attack of 4 degrees.
From Sellers (2000).
Fig. 7.11. Typical pressure distribution obtained from PSP on a Cessna Citation model.
From Kammeyer et al. (2002a).
Fig. 9.8. Calibrated PSP image in Case III for 30 m/s and α = 5 . From Brown (2000).
o
Fig. 9.13. Raw blue image obtained using two separate CCD cameras and a 308-nm lamp
for excitation, where the integration time for 16 images was 32 seconds. From Engler et al.
(2001a).
Fig. 9.16. Pressure image mapped onto a surface grid of the Daimler Benz model with
arrangement of pressure taps at 60 m/s. From Engler et al. (2001a).
Fig. 9.24. Typical pressure distribution mapped onto a surface grid of the AerMacchi M346 advanced trainer model. From Engler et al. (2001b).
Fig. 9.27. The distributions of the pressure coefficient Cp on the wing upper surface
obtained with the FIB PSP and the corresponding temperature distributions obtained using
6
an infrared camera at M = 0.74, Rec = 3.8×10 , and AoA = 0, 1, 3 and 5 degrees. From
Mebarki and Le Sant (2001).
Fig. 9.28. Typical pressure fields on the Mitsubishi MU-300 business jet model obtained
using a combination of PSP and TSP at Mach 0.73 and α = 2.3 and 4.7 degrees. From
Shimbo et al. (2000).
Fig. 9.32. Normalized surface pressure map P/Ps on the control panel with a standard
multiple 90° bleed hole configuration, where Ps is the wall static pressure measured
upstream of the fenced porous plate insert. Tunnel flow is from left to right. From Bencic
(2002).
Fig. 9.33. Normalized surface pressure map P/Ps on the control panel with a multiple preconditioned 90° bleed hole configuration, where Ps is the wall static pressure measured
upstream of the fenced porous plate insert. Tunnel flow is from left to right. From Bencic
(2002).
322
Color Plates
Fig. 9.34. Normalized surface pressure map P/Ps on the control panel with a multiple 20°
inclined bleed hole configuration, where Ps is the wall static pressure measured upstream of
the fenced porous plate insert. Tunnel flow is from left to right. From Bencic (2002).
Fig.9.37. PSP image on the expansion corner model at Mach 10 and the angle of attack of
o
40 . From Nakakita et al. (2000).
Fig.9.38. PSP image on the compression corner model at Mach 10 and the angle of attack
o
of 30 . From Nakakita et al. (2000).
Fig. 9.53. Pressure and temperature distributions on compressor blades at the speed of
17800 rpm. From Torgerson et al. (1998).
Fig. 9.55. Temperature fields on the TSP-coated blade at four rig speeds of 4950, 5800,
7450 and 7875 rpm. From Bencic (1997).
Fig. 9.56. Normalized pressure fields on the PSP-ccoated blade at four rig speeds of 4950,
5800, 7450 and 7875 rpm. From Bencic (1997).
Fig. 9.63. The distribution of Cp obtained using (a) the intensity-based CCD camera system
and (b) the FLIM system. From Guille (2000).
Fig. 9.72. Pressure distribution in a micronozzle at the total pressure of 11.45 psi. From
Huang et al. (2002).
Fig. 10.4. Heat transfer rate results for the sharp-nose indented cone model in LENS I with
an 8 ms delay from flow onset at Mach 9.6 and Re = 270,000 per meter. Color scale ranges
2
2
from violet = 0 W/cm to red = 100 W/cm . From Hubner et al. (2002).
Fig. 10.17. Surface temperature distribution of the impinging multiple-micro-jet at H/D =
19.05. From Huang et al. (2002).
Color Plates
323
Fig. 9.8.
Fig. 1.6.
Fig. 9.13.
Cp
0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
-1.0
Fig. 7.11.
Fig. 9.16.
324
Color Plates
(a) M = 0.73, AoA = 2.3 deg.
Fig. 9.24.
Fig. 9.28.
+F
¯ FLOW
a =0o
-0
-0
a =1
o
-0
-0
a =3
o
-1
-1
a =5
o
-1
Fig. 9.32.
-1
Fig. 9.27.
Color Plates
Fig.9.38.
Fig. 9.33.
Fig. 9.53.
Fig. 9.34.
Fig. 9.55.
Fig.9.37
325
326
Color Plates
Fig. 9.72.
Fig. 9.56.
0.12
0.1
-5
s/D
0.08
0.06
0
0.04
5
0.02
10
-0.02
0
-5
0
b/D
Fig. 10.4.
5
Cp
(a)
0.12
-5
0.1
0.08
0
s /D
0.06
0.04
5
0.02
0
10
-0.02
-5
(b)
Fig. 9.63.
0
b/D
5
Cp
Fig. 10.17.
Index
absorption and emission spectra, 36,
40, 42, 43, 47
aerodynamic forces and moments,
150, 218
airfoil flows, 151, 159, 201, 273
amplitude demodulation method,
121, 164
amplitude modulation index, 116,
121
anodized aluminum (AA), 50, 182,
184, 188, 192, 230, 236, 238
Arrhenius relation, 8, 20, 31
bidirectional reflectance distribution
function (BRDF), 98, 100
Biot number, 285
boundary-layer control, 226
calibration, 33, 131, 313
camera calibration, 82, 92
car models, 212
CCD camera, 3, 67, 70, 217
centroid, 103
collinearty equations, 83
compressibility effect, 107
cryogenic paints, 50, 237, 273
cryogenic wind tunnels, 237, 273
deformation surface grid, 112
delta-wing, 207, 239, 288
diffusion equation, 175, 195
diffusion timescale, 177, 182, 186,
187
direct linear transformation (DLT),
85
directional dependence, 69
effective diffusivity, 183
elemental error sources, 139, 170
error propagation, 138, 163, 164,
166, 167, 169
Euler orientation angles, 83
EuTTA, 48, 318
excitation, 15, 18, 62
excited states, 15
exterior orientation parameters, 84
filter leakage, 146
fixed pattern noise, 71
flight tests, 256
fluorescence, 15
fluorescence
lifetime
imaging
(FLIM), 128
fractal dimension, 185
gated intensity ratio method, 123,
130, 134, 166
hot-film, 289
hypersonic flows, 230, 263
ideal pressure sensitive paint, 56,
106
image registration, 76, 102
inlets, 226
in-situ calibration, 5, 156
intensified CCD camera (ICCD),
128, 236
intensity ratio method, 69, 75, 137
interior orientation parameters, 84
internally gated CCD camera, 130
Laplace transform, 176, 195
laser heating, 195, 282
laser scanning system, 6, 74, 225,
242, 282
lens distortion, 84
lifetime, 17, 19, 26, 35, 45, 115,
163, 256
lifetime method, 115
limiting pressure resolution, 142,
153
limiting temperature resolution, 170
low-speed airfoil flow, 201
luminescence, 15
328
Index
luminescent intensity (radiance), 61,
65
impinging jet, 198, 214, 249
impinging jet heat transfer, 275
Jablonsky energy-level diagram, 16
Joukowsky airfoil, 151, 159
jet impingement cooling, 198
Karman-Tsien rule, 108
micronozzle, 260
model deformation, 76, 112, 137,
158, 160
multiple-luminophore paint, 54
noise floor, 71
non-Gaussian distribution, 158, 160
Nusselt number, 276
optimization method, 87
oxygen diffusion, 24, 175, 182
oxygen quenching, 17, 18, 19, 24
paint intrusiveness, 147
perspective center, 82
phase angle, 116, 131
phase method, 119, 163
Phong model, 99
phosphorescence, 15
photodetector response, 68
photon shot noise, 71, 142
platinum porphyrins, 35
porous pressure sensitive paint, 24,
50, 182, 230, 236
Prandtl-Glauert rule, 108
PtOEP, 12
PtTFPP, 36, 317
pressure-correction method, 107
pressure sensitive paint (PSP), 2, 11,
18, 24, 34, 137, 175, 201
pressure mapping error, 146
principal distance, 83
principal point, 83
pyrene, 42
Riemann-Liouville fractional
integral, 185
radiance, 61, 62, 65, 92, 95
radiative energy transport, 62, 65
radiometric response function, 92
rotating machinery, 242, 247
Ru(bpy), 47, 318
Ru(dpp), 40, 317
Ru-pyrene, 57
Ru(trpy), 52
schlieren, 234, 235, 252, 267
self-illumination, 95, 148
shock, 191, 221, 223, 226, 230, 236,
243, 250, 266
shock/boundary-layer
interaction,
230, 280
shock tube, 192, 230, 236, 263
solenoid valve, 188
spectral variability, 146
square law, 177, 182
Stanton number, 280
Stern-Volmer relation, 3, 21, 23, 26,
28, 30, 138
Stern-Volmer coefficients, 3, 21, 23,
26, 28, 30, 138
subsonic flows, 107, 151, 215
supercritical wing, 221
supersonic flows, 226, 271, 280
swept-wing, 210, 223, 271
temperature effect, 145, 149
temperature hysteresis, 171
temperature sensitive paint (TSP), 8,
31, 45, 169, 263
thermal diffusion, 194
thermal quenching, 31
thermochromic liquid crystal, 49,
270
thermographic phosphor, 49, 269
time response, 175, 182, 187, 194
transition, 263, 270
transonic flow, 215, 221, 223, 237,
256,
turbomachinery, 227, 242
uncertainty, 137
upper bounds of elemental errors,
149
videogrammetric model deformation
technique (VMD), 112
view factor, 95
volume fraction, 185
waverider, 263