28th Aerodynamic Measurement Technology,Ground Testing, and Flight Testing Conference<br><i>i
25 - 28 June 2012, New Orleans, Louisiana
AIAA 2012-3014
Development of a Digital Fringe Projection Technique to Quantify Surface
Film/Rivulet Flows
Bin Wang1, William Lohry 2, Song Zhang3 and Hui Hu4()
Iowa State University, Ames, Iowa, 50011
Downloaded by Hui Hu on March 22, 2013 | http://arc.aiaa.org | DOI: 10.2514/6.2012-3014
A novel digital fringe projection (DFP) technique is developed to achieve non-intrusive
thickness measurements of wind-driven water droplet/rivulet flows in order to quantify the
unsteady surface water transport process pertinent to aircraft icing phenomena. The DFP
technique is based on the principle of structured light triangulation in a similar manner as a
stereo vision system but replacing one of the cameras for stereo imaging with a digital
projector. The digital projector is used to project a fringe pattern of known characteristics
onto a test object (i.e., a water droplet/rivulet on a test plate for the present study). Due to
the 3D shape profile of the test object, the fringe pattern is deformed seen from a perspective
different from the projection axis. By comparing the distorted fringe pattern over the test
object (i.e., the water droplet/rivulet on the test plate) and a reference fringe pattern on a
reference plane (i.e., the test plate only without the water droplet/rivulet), the 3D profile of
the test object with respect to the reference plane (i.e., the thickness distribution of the water
droplet/rivulet flow) can be retrieved quantitatively and instantaneously. The feasibility and
implementation of a DFP system is first demonstrated by measuring the thickness
distribution of a small flat-top pyramid over a test plate to evaluate the measurement
accuracy level of the DFP system. Then, the DFP system is applied to achieve time-resolved
thickness distribution measurements of a droplet/rivulet flow to quantify the transient
behavior of the water droplet/rivulet flow driven by boundary layer airflow over a test plate.
The dynamic shape change and stumbling runback motion of the wind-driven water
droplet/rivulet flow over the test plate are revealed clearly and quantitatively from the DFP
measurement results. Such information is highly desirable to elucidate underlying physics to
improve our understanding about the surface water transport process pertinent to glaze ice
formation and accretion over aircraft wings in atmospheric icing conditions
1
Introduction
I
CING is widely recognized as one of the most serious weather hazards to aircraft operations. Aircraft icing occurs
when small, super-cooled, airborne water droplets, which make up clouds and fog, freeze upon impacting a
surface which allows formation of ice (Mason 1971). The freezing can be completely or partially depending on how
rapidly the latent heat of fusion can be released into the ambient air. In a dry regime, all the water collected in the
impingement area freezes on impact to form rime ice. For a wet regime, only a fraction of the collected water
freezes in the impingement area to form glaze ice and the remaining water runs back and can freeze outside the
impingement area (Politovich 1989; Hu and Jin 2010). Because of its wet nature, glaze ice can form much more
complicated shapes which are very difficult to accurately predict, and the resulting ice shapes tend to substantially
deform the accreting surface with the formation of “horns” and larger “feathers” growing outward into the airflow.
Glaze ice is considered as the most dangerous type of ice. Glaze ice formation can severely decrease the airfoil
1
Graduate Student, Department of Aerospace Engineering.
Undergraduate Graduate Student, Department of Chemical and Biological Engineering.
3
Assistant Professor, Department of Mechanical Engineering.
4
Associate Professor, Department of Aerospace Engineering, AIAA Associate Fellow, Email: huhui@iastate.edu
2
1
Copyright © 2012 by Bin Wang, William Lohry, Song Zhang and Hui Hu . Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.
Downloaded by Hui Hu on March 22, 2013 | http://arc.aiaa.org | DOI: 10.2514/6.2012-3014
aerodynamic performance by causing large scale flow separation which produces dramatic increases in drag and
decreases in lift (Politovich 1989, Grent et al, 2000). The behavior of unfrozen water on an ice accreting surface can
directly and indirectly influence the shape of the resulting glaze ice accretion. The transport behavior of unfrozen
water prior to freezing has a direct impact on the shape of glaze ice due to its effect of redistributing the impinging
water mass. Current ice accretion models usually ignore the complicated details of the interaction among the
unfrozen surface water, the local airflow and ice and the ice phase transition, due to the lack of knowledge about the
microphysical phenomena. The surface water transport and surface roughness are usually treated in a simplistic or
heuristic manner, typically using correlations or simple decoupled models (Hansman & Turnock 1989; Otta &
Rothmayer 2009). The simplistic evaluation of surface roughness and surface water transport behavior, which omits
consideration of the detailed surface physics, is considered to be a significant factor in the poor agreement between
the predictions of the glaze ice accretion models and experimental results for glaze ice (Hansman &Turnock 1989;
Myers & Charpin 2004; Brakel et al. 2007).
Advancing the technology for safe and efficient aircraft operation in atmospheric icing conditions requires a better
understanding of the important micro-physical phenomena pertinent to aircraft icing phenomena. While several
studies have been carried out recently to simulate ice accretion on aircraft wings through icing wind tunnel testing or
using ‘‘artificial’’ iced profiles with various types and amounts of ice accretion to investigate the aerodynamic
performances of iced airfoils/wings (Bragg et al. 1986), very few fundamental studies were conducted to elucidate
underlying physics associated with aircraft icing phenomena. Many important micro-physical processes associated
with aircraft icing phenomena, such as transient behavior of surface water droplets/rivulet flows, unsteady heat
transfer process within icing water droplets/film flows, and phase change process of water droplets/film flows over
smooth/rough ice accreting surfaces, are still unclear (Hu and Huang, 2009; Hu and Jin 2010). Advanced
experimental techniques capable of providing accurate measurements to quantify important micro-physical
processes pertinent to aircraft icing phenomena such as transient behavior of surface water transport and interaction
among the unfrozen surface water, the local airflow and ice are highly desirable in order to elucidate the underlying
physics. In this study, we report the progress made in our recent effort to develop a novel Digital Fringe Project
(DFP) system to achieve non-intrusive thickness measurements of wind-driven water droplet/rivulet flows over test
surfaces as a function of time and space in order to elucidate underlying physics of unsteady surface water transport
process pertinent to glaze ice formation and accretion process over aircraft wings in atmospheric icing conditions..
2
Literature Review of the Film Thickness Measurement Techniques
Several measurement techniques have been developed in recent years to achieve non-intrusive thickness
distribution measurements of surface film/rivulet flows, which include fluorescence imaging based techniques;
density based techniques; stereoscopic imaging techniques; and structured light projection techniques. The technical
basis of the measurement techniques will be introduced briefly in this section. The advantages and the limitations of
the techniques for water film/rivulet thickness measurements in an icing environment for icing physics studies will
also be commented.
Laser Induced Fluorescence (LIF) technique is widely used for qualitative flow visualizations and quantitative
measurements of passive scalar distributions in fluid flows. In LIF, laser light is used to excite fluorescent tracers
premixed in fluid flows. Fluorescence images are acquired to provide useful information, either qualitatively or
quantitatively, about a fluid property of interest. Fluorescence imaging techniques have been used to conduct
thickness measurements of film flows. According to quantum theory (Pringsheim 1949), for a diluted solution and
unsaturated excitation, the acquired fluorescence intensity will be a function of the amount of the fluorescent tracer
molecules and fluid temperature. With a reasonable assumption of the tracer molecules being uniformly distributed
through a thin film flow, local film thickness will be proportional to the amount of the tracer molecules in the line of
sight of an image detector. Therefore, the thickness distribution of a thin film flow can be derived from the acquired
fluorescence images if the flow is under isothermal condition or the temperature distribution of the film flow is
known. Several studies have been conducted in recent years by using fluorescence imaging techniques to measure
the thickness distributions of thin film flows. For example, Liu et al. (1995) conducted an experimental study to
quantify the dynamic thickness variations of film flows due to the gravity-driven three-dimensional instabilities by
using LIF technique. Johnson et al (1997, 1999) developed a fluorescence imaging system to quantify the transient
behavior of thin film flows over flat surfaces under an isothermal condition. Essentially the same fluorescence
imaging approach has also been used recently by Lel et al., (2005), Chinnov et al., (2007), and Schagen et al., (2007)
to conduct thickness measurements in film flows at various experimental settings. It should be noted that the fluid
flows are usually required to be transparent in order to be able to use fluorescence imaging technique to achieve
2
Downloaded by Hui Hu on March 22, 2013 | http://arc.aiaa.org | DOI: 10.2514/6.2012-3014
quantitative film thickness distribution measurements. However, in an icing environment, water droplet/rivulet flows
over an icing accreting surface may become semi-transparent or even opaque. Furthermore, the LIF intensity is
usually also temperature dependent, and the temperature of water film/rivulet flows would vary significantly during
ice formation and accretion process. Therefore, it will be very difficult, if not impossible, to use LIF technique to
conduct quantitative film thickness measurements of water droplet/rivulet flows in an icing environment for icing
physics studies.
A density-based color light encoding technique was developed by Zhang et al. (1996) to measure free-surface
gradients of fluid flows, and successfully applied to measure the surface deformation due to near-surface turbulence.
For the measurements, an array of lenses were used to transform the rays of an optical light source into a series of
color-coded parallel light beams by passing the light through a group of two-dimensional color palettes at the focal
planes of the lens array. The parallel light beams were used to illuminate a free surface of water. The reflected rays
from the free surface were captured by a charge-coupled device (CCD) color camera located above the surface. The
slopes were derived from the color images after the calibration, and surface elevations were obtained by integrating
the slopes. Other density-based approaches include the diffusing light photography (Wright et al. 1996) employed to
investigate the free surface motion under a fully developed isotropic ripple turbulence and optical Schlieren
techniques used to qualitatively visualize the liquid-gas interface instabilities of a locally heated falling liquid film
(Kabov et al. 2002). It will be quite difficult, if not impossible; to use the density-based approaches to achieve
accurate thickness distribution measurements of water film/rivulet flows over an ice accreting surface since the
variations of the refraction index at the interface between water and ice and the thermally-induced density changes
in the water film/rivulet flows will affect the measurement results significantly.
A 3-D stereo system (called Wave Acquisition Stereo System, i.e., WASS in short) was developed by
Benetazzo (2006) to recover topographic information from a sequence of synchronous, overlapping video images by
utilizing binocular stereogrammetry. Two synchronized progressive scan cameras were used for data acquisition.
Image analysis techniques were used for retrieving water surface elevation fields spatially and temporally from CCD
image sequences. A remarkable feature of the stereo imaging method is its capability to measure surface
discontinuities (Tsubaki and Fujita, 2005). The measurable length-scales were found to depend on the pixel
resolution, the triangulation accuracy, and the acquisition frame rate. The accuracy of the technique depends on the
geometry of the stereo rig, and the camera resolution. The distance between the cameras and the inclination angle of
the camera’s lines of sight were also found to affect the measure uncertainty in the 3-D surface shape measurements
strongly. The performance of the stereo imaging of waves would also degrade with the increased distance between
the cameras and the water surface.
More recently, Moisy et al. (2008) developed a non-intrusive optical method for the measurements of the
instantaneous topography of the interface between two transparent fluids. This method is based on the analysis of
the refracted image of a random dot pattern visualized through the interface. The apparent displacement field
between the refracted image and a reference image obtained when the surface is flat was determined using a Digital
Image Correlation (DIC) algorithm. A numerical integration of this displacement field, based on a least square
inversion of the gradient operator, was used to reconstruct the instantaneous surface height, allowing for a good
spatial resolution with a low computational cost. The main limitations of the method are: (i) it is not able to detect
changes in the mean surface height; (ii) it is extremely sensitive to slight vibrations; (iii) It is unable to determine the
displacement field for strong curvature and/or large surface-pattern distance. The limitations are usually
unacceptable for achieving accurate thickness distribution measurements of water film/rivulet flows over an ice
accreting surface for icing physics studies.
Another category of measurement approach capable of achieving non-intrusive thickness measurements in
film/rivulet flows is called structured light technique. This technique relies on actively projecting light with known
patterns onto an object, and extracts 3D surface shape of the object from the images of the light patterns captured
from one or more points of view (Salvi et al. 2010). Structured light techniques have been applied very successfully
in many fields including 3D sensing; object recognition; robotic control; industrial inspection of manufactured parts;
stress/strain and vibration measurements; biometrics; biomedicine; dressmaking and visual media. Structured light
techniques are also capturing increasing attention of the fluid dynamics community in recent years. For example,
Cazabat et al. (1990) used a technique to project equally spaced fringes to reconstruct the thickness profiles of thin
spreading films in order to investigate the characteristics of climbing film flows driven by temperature gradients.
Grant et al. (1990) employed a projection moiré method to measure water waves to investigate the wave-structure
interactions for safer and more cost-effective design of offshore structures. Zhang and Su (2002) applied a fringe
projection technique to reconstruct the vortex shape at a free surface. Pouliquen and Forterre (2002) employed a
3
similar method to record the time evolution of the free surface deformation of a dense granular flow. More recently,
Cochard and Ancey (2008) designed a digital fringe projection system to measure the time-evolution of the surge
downstream an inclined plate due to the dam break. Cobelli et al. (2009) also conducted an experimental study to
measure the free surface deformations of a water flow by using a digital fringe projection system.
Downloaded by Hui Hu on March 22, 2013 | http://arc.aiaa.org | DOI: 10.2514/6.2012-3014
The digital fringe projection (DFP) technique described in this study is a special structured light technique. It
has the merits of lower cost, higher speed, and easier to develop, which has been a very active research topic within
the past decades (Geng 1996, Huang et al. 1999, 2002, Zhang et al. 2002, Zhang and Su 2002, Pan et al. 2005,
Zhang et al. 2006, Zhang and Huang 2006, Zhang and Yau 2006, 2007, Fechteler et al. 2007, Guo and Huang 2008,
Wang et al. 2009, Li et al. 2010, Liu et al. 2010, Nguyen 2011, Gong and Zhang 2011). In the context that follows,
the technical basis of the DFP technique will be described briefly at first. The feasibility and implementation of the
DFP technique will be demonstrated by measuring the thickness (height) distribution of a flat-top pyramid with a
known height distribution. The DFP measurement results are compared with the nominal height distribution of the
pyramid quantitatively in order to evaluate the measurement uncertainty of the DFP system. Finally, the DFP
technique was applied to achieve time-resolved thickness distribution measurements of wind-driven droplet/rivulet
flow to quantify the transient behavior of the droplet/rivulet flow driven by boundary layer airflow over a test plate
to improve our understanding about the surface water transportation process pertinent to aircraft icing phenomena.
3.
Technical Basis of Digital Fringe Projection (DFP) Technique
As described above, DFP technique is a special kind of the structured light projection method, which is based
on the projection of structured light patterns varying sinusoidally in the light intensity. While the structured light
project technique is similar to a stereoscopic imaging method, it uses a projector to replace one of the cameras need
for the stereoscopic imaging method (Salvi et al., 2010). As for all the triangulation-based methods, the height
information can be recovered by identifying the corresponding pairs from two different views (Geng, 2011).
Instead of using laser interference to generate fringe, the DFP technique used in the present study generates
fringe patterns through a digital image processing procedure. Compared with laser interference based technology,
the major advantages of using a DFP technique are: (1) no speckle noise. Instead of using a coherent light source,
white light can be used for this technology. Therefore, the implications associated with using the coherent light
source do not exist; (2) the profile of the fringe patterns can be accurately controlled by using an digital image
processing procedure; and (3) the phase shift error caused by mechanical devices is also eliminated since the phase
shift is generated digitally.
Fig.1: Schematic of a digital fringe projection system
Figure 1 shows the schematic of the typical setup of a DFP system. A digital projector is used to project fringe
patterns of known characteristics onto a test object (i.e., a water droplet/rivulet flow over a test plate for the present
study). Due to the 3-D surface shape of the test object, the projected fringe patterns will be deformed seen from a
perspective different from the projection axis. The projection unit (D), image acquisition unit (E), and the three-
4
dimensional object (B) form a triangulation base. If the corresponding points between the camera (A) and the
projector (C) are identified through a calibration procedure, 3-D surface shape of the object can be obtained through
an analysis of triangulation (∆ABC). In such a system, the correspondence is usually established by analyzing the
phase of the structured patterns (fringe patterns) through fringe analysis techniques. More specifically, by comparing
the phase differences between the distorted fringe patterns (i. e., with the water droplet/rivulet flow over the test
plate for the present study) and a reference fringe pattern on a reference plane (i.e., the test plate only without the
water droplet/rivulet flow), the 3D surface shape of the test object with respect to the reference plane (i.e., thickness
distribution of the water droplet/rivulet flow) can be determined quantitatively.
3.1
Fourier transform based fringe analysis technique
As described in Takeda et al. (1982) and Takeda & Mutoh (1983), a typical fringe pattern recorded by a camera
for DFP measurements can be expressed generally as signals with spatial carrier frequencies ⁄ modulated in both
)and amplitude (
), as given by the following Fourier series expansion
phase (
Downloaded by Hui Hu on March 22, 2013 | http://arc.aiaa.org | DOI: 10.2514/6.2012-3014
(
)
(
with:
(
∑
)
(
)
)
(
⁄ )
(1)
[
(
)]
(2)
(
) represents amplitude modulation due to the light source and
where, j is the imaginary unit,
) contains the desired 3D shape
inhomogeneous surface reflectivity of the test object. The phase (
information of the test object (i.e., the shape of the water droplet/rivulet for the present study), p is the fringe pitch
on the reference plane. The zero frequency intensity value corresponds to the background intensity variation over the
field of view. Since the phase carries information about the 3D shape to be measured, the strategy would be to
) out from the intensity signal.
separate the phase (
) distribution
By using discrete Fourier Transform in spatial domain, the Fourier spectra of the intensity (
) and (
) would vary very slowly compared with
captured at a certain instant can be obtained. Since (
the spatial frequency of the fringe given by ⁄ for most cases, all the spectra can be well separated from each
other. A filtering operation can be performed to single out the spectrum of the fundamental frequency component,
and compute its inverse Fourier transform to obtain a complex signal as written below
̂(
)
(
{[
)
⁄
)]}
(
(3)
The same signal processing can also be done for the reference fringe image to obtain
̂(
)
(
)
{[
⁄
(
)]}
(4)
Then the phase difference between the deformed fringe image (i.e., the case with the water droplet/rivulet flow over
the test plate) and the reference image (i.e., the case without the water droplet/rivulet over the test plate) can be
calculated from a new signal as given below
̂(
) ̂(
)
(
) (
)
{[
(
)]}
(5)
(
)
(
)
(
) is the phase difference
where indicates complex conjugate of the signal, and
between the deformed fringes over the object and the reference fringes. The phase difference can be computed from
the ratio between the imaginary and real part of the new signal as written below
(
)
{
[ ̂(
) ̂(
)]⁄
[ ̂(
) ̂(
)]}
(6)
It should be noted that the phase map calculated from the arctangent function given above is wrapped in the
range of [–
], thus, the phase map is also called the wrapped phase map. An additional step called phase
unwrapping needs to be applied in order to obtain a continuous phase map. The phase unwrapping step is essentially
finding the 2π jumps from neighboring pixels, and removing them by adding or subtracting an integer number of 2π
5
to the corresponding point (Ghiglia and Pritt 1998). In other words, the phase unwrapping algorithm is to determine
integer number k(x,y) so that
(
)
(
)
(
)
(7)
(
) is the unwrapped phase map. Once the unwrapped phase map is known, the 3-D coordinates
Here
can then be recovered using the unwrapped phase, assuming that the system is properly calibrated (Zhang and
Huang 2006).
Downloaded by Hui Hu on March 22, 2013 | http://arc.aiaa.org | DOI: 10.2514/6.2012-3014
3.2
Phase-to-height conversion algorithm
As described above, the obtained unwrapped phase map contains the height information, Z(x,y), of the measured
object (i.e., the shape of the water droplet/rivulet flow over the test plate for the present study); 3-D surface shape
can be extracted from the unwrapped phase map if the DFP system is calibrated. To convert the phase map to height
distribution, the relationship between the height and the phase must be established. Figure 2 shows the schematic
the diagram of the proposed DFP system for phase-to-height conversion. A reference plane with height 0 in the zdirection is used as the reference for subsequent measurement (i.e., the surface of test plate for the present study).
The arbitrary point M in the captured image corresponds to point N in the projected image, and point D on the object
surface (i.e., on the free surface of the droplet/rivulet flow for the present study). From the projector’s point of view,
phase D on the object surface has the same phase value as A on the reference plane, that is, A= D. While from
the point of view of the CCD camera, point D on the object surface images is at the same pixel as point C on the
reference plane. The phase difference between point C on the reference plane and point D on the object can be
expressed as: CD= CA= C- A. Assume the distance between point M and point N is d, and the reference plane is
parallel to the device with a distance s between them. By analyzing the similar relationship between ∆MND and
∆CAD, we can get:
d
s  BD
s


1
CA
BD
BD
(8)
In DFP measurements, the distance s is usually much larger than
Z ( x, y )  BD 
BD , therefore, the equation can be simplified as:
s
ps
CA 
CA
d
2d
(9)
d
CCD
M
N DMD
I
P
Capture
direction
s
Project
direction
Optical
axis
Optical
axis
Object
D
z
Reference plane A B F O C
Fig. 2: Schematic diagram of the phase-to-height conversion
6
Here p is the distance per fringe on the reference plane. From above equation, it can be seen that a linear
relationship between the phase difference, CA, and the height information, Z ( x, y ) , can be obtained. Therefore,
the 3D surface shape of the test object (i.e., thickness distribution of the water droplet/rivulet flow over the test plate
for the present study) can be determined quantitatively by measuring the phase difference between the distorted and
reference images.
Downloaded by Hui Hu on March 22, 2013 | http://arc.aiaa.org | DOI: 10.2514/6.2012-3014
3.3
Binary defocusing technique
While a conventional DFP system may work well for static or quasi-static 3D shape measurements, there are
several technical problems need to be solved in order to achieve time-resolved measurements to quantify the
transient behavior of wind-driven water droplets/rivulet flows over smooth/rough surface for icing physics studies.
They are: the precise synchronization problem, the nonlinearity problem, and the maximum speed limit problem
(Lei and Zhang 2010). The core of a digital-light-processing (DLP) projector is a digital micro-mirror device
(DMD). Each micro-mirror can rotate between + θL (ON) and – θL (OFF). The grayscale value of each pixel is
realized by controlling the ON time ratio: for an 8-bit system, 0% ON time represents 0, 50% ON time means 128,
and 100% ON time is 255. Therefore, a DLP projector produces a grayscale value by time modulation. As a result,
for a conventional DFP system where the sinusoidal fringe patterns are fed to the projector, the camera must be
precisely synchronized with projector in order to correctly capture the projected patterns. A conventional DMD is
usually fed with an intensity value of 0 or 255, it will remain its status (without flipping ON/OFF) during the period
of channel projection. If binary (0s and 255s) instead of sinusoidal structured patterns are used, it will permit the use
of an arbitrary exposure time for the camera. However, as described above, sinusoidal fringe patterns are required in
order to perform 3D surface shape measurements by using DFP technique. To resolve this dilemma, a flexible
method has been developed recently for sinusoidal fringe generation by defocusing binary structured ones (Lei and
Zhang 2009). When a projector is fed with binary structured patterns and their focal length is changed, the projected
structured patterns will be deformed: the pattern starts with focused binary images and gradually deformed to be
sinusoidal ones. This technique also eliminates another major problem of the conventional DFP technique: the
nonlinearity of the projector. Even though numerous nonlinearity calibration approaches have been developed, it
remains difficult for a conventional projector to generate ideal sinusoidal patterns. Since the binary defocusing
technique only requires two intensity values, the nonlinearity problem does not present in nature. In addition,
because of the use of 1-bit binary patterns, it has the potential for super-high-speed 3-D shape imaging. In the
present study, the binary defocusing technique, instead of using 8-bit sinusoidal patterns, was used to generate
sinusoidal fringe patterns for DFP measurements, which can significantly increase the temporal resolution of the
DFP measurements.
3.4
Calibration procedure to determine the phase-to-height conversion relationship
As described above, the 3D shape of the test object (i.e., the thickness distribution of the water droplet/rivulet
flow over the test plate for the present study) can be obtained by measuring the phase differences between the
deformed fringe image (i.e., the cases with water droplet/rivulet over the test plate) and the reference image (i.e., the
case without water droplet/rivulet over the test plate). A calibration procedure was conducted to determine the
relationship between the phase difference and the height information for the phase-to-height conversion.
Figure 3 shows the schematic set-up of the calibration procedure employed in the preset study. A binary
blank/white fringe image was generated artificially by using MATLAB software on a host computer. A portable
digital projector (Dell M109S DLP SVGA Projector) was used to project the binary fringe image onto a test plate
(100mm×100mm in size), which is about 1200mm away from the projector. The test plate was mounted on the top
of a vertical translation stage, and the height of the vertical translation stage (i.e., the position of the test plate along
Z-direction) can be adjusted by using a micrometer drive with a resolution of 10µm. In the present study, the focal
plane of the digital projector was adjusted to be off the test plate in order to use the binary defocusing technique
described above to generate sinusoidal fringe patterns on the test plate. A progressive scan CCD camera
(DMK21BU04, Imaging Source Corp.) was used to acquire the images of the projected fringe patterns on the test
plate. The acquired images were stored on the host computer for DFP image processing.
During the calibration procedure, by adjusting the height of vertical translation stage, the test plate was moved
at 10 parallel positions in Z-direction (i.e., 10 different height values) at an interval of 0.5mm. The image of the
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Downloaded by Hui Hu on March 22, 2013 | http://arc.aiaa.org | DOI: 10.2514/6.2012-3014
sinusoidal fringes on the test plate was acquired at each pre-determined position (i.e., with different height). Then,
the acquired fringe images were processed by using the Fourier-transform-based fringe analysis technique described
above to calculate the phase shift of the fringes (i.e., the phase difference from the origin position with Z=0) on the
test plane due to the height change. Figure 4 shows the derived phase difference of the projected fringes as the test
plate was moved away from its original position (i.e. at different heights). It can be seen clearly that the relationship
between the height and the phase difference of the fringes can be fitted to a linear function well, as predicted
theoretically by Equation (9). The linear relationship derived from calibration procedure was used for the phase-toheight conversion in DFP measurements to be described in the next sections.
Fig. 3: Experimental setup for calibration
Fig. 4: Calibration curve to determine the phase-to-height conversion coefficient
8
4.
Application of DFP Technique to measure 3-D shape of a mini pyramid.
(a). Reference images without pyramid.
(b). Deformed fringe image with pyramid
(c). Wrapped phase map of the deformed image
(d). The phase difference map
8
Thickness distribution
(mm)
Nominal Height
Measurement Data
0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50
6
Height (mm)
Downloaded by Hui Hu on March 22, 2013 | http://arc.aiaa.org | DOI: 10.2514/6.2012-3014
In order to demonstrate the feasibility and implementation of the DFP technique described above for achieving
height distribution measurement of a test object, an experiment was conducted to apply the DFP technique to
measure 3-D shape (i.e., the thickness distribution) of a mini flat-top pyramid. A mini pyramid with the nominal
dimension of 4.7 mm in height, 15.0mm×15.0 mm in base and 45.0-degree slopes at four sides was used as the
target object for the demonstration experiment. The same experimental setup as that used for the calibration
procedure was used for the demonstration experiment with the mini pyramid sitting at the center of the test plate.
4
2
0
-2
0
100
200
300
400
500
600
Horizental Position (pixel)
(e). Derived height distribution of the pyramid
(f). The measured height vs. nominal height
Fig. 5: DFP measurement of a mini flat-top pyramid
Figure 5 shows the typical measurement result along with the acquired DFP raw images to measure the height
distribution of the mini pyramid. As shown in Fig. 5(a), before the mini pyramid was placed on the test plate, the
image of a set of straight fringes, which were projected onto the test plate by using the digital projector, was
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acquired as the reference image for the DFP measurements. As shown clearly in Fig. 5(b), the straight fringes were
found to be deformed greatly when the mini pyramid was placed on the test plate. By using the Fourier based fringe
analysis technique described above; a phase map of the fringes can be derived for both the acquired reference image
and the deformed fringe image. Figure 5(c) shows the phase map of the deformed fringe image. As described above,
since the phase map calculated from the arctangent function given in Equation (8) is wrapped in the range of
[–
], the phase map is called the wrapped phase map. Following the work described in Ghiglia and Pritt (1998),
a phase unwrapping step was used in the present study to reconstruct an unwrapped phase map of the fringes by
adding or subtracting an integer number of 2π to the corresponding point. Based on the quantitative comparison of
the unwrapped phase map of the deformed fringe image to that of the reference image without mini pyramid on the
test plate, the distribution of the phase change due to the existence of the mini pyramid on the test plate can be
derived, which is shown in Fig. 5(d). Then, with the phase-to-height conversion curve shown in Fig 4, the height
distribution of the mini pyramid can be determined, which is presented in Fig. 5(e).
Since the nominal height distribution of the pyramid is known, the measurement accuracy of the DFP system
can be assessed based on the quantitative comparison of the measured height distribution to the nominal height of
the pyramid. Figure 5(f) shows the quantitative comparison of the measured height against the nominal height of the
pyramid along a horizontal line passing the center of the pyramid. It can been seen clearly that, while the measured
height profile of the pyramid was found to agree with the nominal height values reasonably well in general, some
discrepancies (i.e., measurement errors) between the measured and nominal values were also seen clearly from the
quantitative comparison, especially in the regions with sharp change in object geometry (i.e., the sharp boundary of
the mini pyramid). For example, the DFP measurement was found to have relatively large measurement
uncertainties on the flat top of the pyramid. As shown in Fig. 5, since only three fringe was found on the flat top of
the pyramid, the relatively large measurement errors on the top of the pyramid are believed to be closely related to
the poor spatial resolution of DFP measurements in the region (i.e., the pitch of the projected fringes used for the
DFP measurement may be too large compared to the small flat top of the pyramid). It should be noted that, the
selection of the fringe pitch is a trade-off between the competing demands of the high spatial-resolution and good
image quality of the fringes for DFP measurements. A systematic study is planned to examine the effects of the
pitch of the projected fringes as well as other system parameters on the accuracy of the DFP measurements. In order
to put a number in perspective to assess the measurement uncertainty of the DPF measurement given in the presents
study, the root-mean-square of the measurement errors in the measurement window given in Fig. 5 was calculated,
which was found to be about 0.16mm. The value is about 3% of the nominal height of the pyramid.
6.
Application of DFP technique to quantify the transient behavior of wind-driven water droplet/rivulet
flows over a test plate.
The DFP technique was also used to achieve time-resolved thickness distribution measurements of a water
droplet/rivulet flow to quantify the transient behavior of the water droplet/rivulet flow driven by boundary layer
airflow over a test plate to elucidate the underlying physics of the unsteady surface water transportation process
pertinent to glaze ice formation and accretion over aircraft wings.
Figure 6 shows the schematic diagram of the experimental setup used in the present study to implement the DFP
technique to quantify the wind-driven surface droplet/rivulet flows. The DFP measurements were performed in a
low-speed wind tunnel located at Aerospace Engineering Department of Iowa State University. The digital
projector, the CCD camera and a flat test plate were arranged in the same manner as those used for the calibration
procedure described above. The test plate was flush mounted on the bottom surface of the test section of the wind
tunnel. The temperature of the test plate can be adjusted by using a water bath Circulator (Neslab RTE-211). Since
the objective of the present study is to demonstrate the feasibility and implementation of the DFP system for
thickness measurements of wind-driven droplet/rivulet flows, the test plate was kept in room temperature (i.e.,
T=23.0 OC, therefore, no ice formation) during the experiments. Water was employed as the working liquid in the
present study. Following the work of Cabelli et al. (2009), a small amount of white liquid dye was added into the
water in order to enhance the contrast of the projected fringes onto the free surfaces of the water droplet/rivulet for
DFP measurements. Driven by the incoming boundary layer airflow, the water droplet on the test plate would
deform and run back to form film/rivulet flows. It is used to simulate the surface water transportation process during
glaze ice formation and accretion process over aircraft wings, i.e., after impinging onto the surface of aircraft wings,
tiny supper-cold water droplets would aggregate to form larger droplets/rivulets and run back upon the pushing of
the boundary layer airflow during glaze ice formation and accretion process.
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Fig. 6: Experimental setup to quantify unsteady wind-driven droplet/rivulet flows
(a). DFP raw image
(b). Wrapped phase map
(c). Unwrapped phase map
(d). Derived height distribution
Fig. 7: DFP measurement result of a water droplet over a flat plate
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(a). t = t0+ 0.0s
(b). t = t0+ 3.0s
(c). t = t0+ 6.0s
(d). t = t0+ 8.0s
Fig. 8: Time sequence of the DFP measurement results to quantify the evolution of a wind-driven water
droplet/rivulet flow over a flat plate.
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Figure 7 shows an example of the DFP measurements of a water droplet with the size about 10.0 mm in
diameter on the test plate. The DFP measurements were conducted before the wind tunnel was turned on. As
expected, the water droplet was found to be round-sphere-cap shape on the test plate, which was can be seen clearly
from the raw DFP image, the wrapped and unwrapped phase maps as well as the measured thickness distribution of
the water droplet.
Based on the time sequence of the DFP measurements, the contact line moving velocity of the droplet/rivulet
flow over the test plate can be determined. Figure 9 shows the time evolution of the measured moving velocities of
the contact line at the front lobe and rear ends of the droplet/rivulet flow. It can be seen clearly that, even though the
boundary layer airflow was kept in constant during the experiments, the runback motion of the wind-driven
droplet/rivulet flow over the test plate was quite unsteady. The droplet/rivulet flow was found to stumble over the
test plate, instead of moving smoothly and continuously.
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Moving speed of the contact line (mm/s)
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Figure 8 shows the time sequences of the DFP measurements to reveal the dynamic shape change of the water
droplet on the test plate after the wind tunnel was turned on with the free stream velocity of the airflow V  = 10.0
m/s. While the images at the left are the acquired raw DFP images, which were taken at a frame rate of 60Hz, the
right figures show the corresponding thickness distributions based on the DFP measurements. As shown clearly in
the raw DFP images, the projected straight fringe patterns would be deformed dynamically in corresponding to the
dynamic shape change of the water droplet/rivulet flow driven by the boundary layer airflow. The DFP
measurement results revealed clearly that, as the water droplet run back upon the pushing of the boundary layer
airflow, a tail of the droplet would leave behind the moving droplet to form a thin film over the test plate. The shape
of the water droplet was found to change from round-sphere-cap to sand-dune-shape, and finally to become a thin
film/rivulet flow spreading out over the test plate.
rear end of the droplet/rivulet
front end of the droplet/rivulet
15
10
5
0
-5
0
1
2
3
4
5
6
7
8
9
Time (s)
Fig. 9: The contact line moving velocity of the front lobe and rear end of the wind-driven droplet/rivulet flow
The dynamic shape change and stumbling runback motion of the droplet/rivulet flow over the test plate can be
seen more clearly and quantitatively from the time evolution of the central line profile of the droplet/rivulet flow,
which are given in Fig. 10. As shown in the figure, the contact line of the droplet/rivulet was found to move very
slowly or almost do not move at all at the beginning (i.e., t < 4.5s), while the free surface of the droplet/rivulet was
found to deform dramatically to change its shape from round-sphere-cap to sand-dune-shape. The front lobe of the
deformed droplet/rivulet was found to “skip” downstream suddenly at the time of t  4.5s, and the contact line
moving velocity of the droplet/rivulet was found to increase rapidly corresponding to the “skip” motion, as revealed
quantitatively in clearly Fig. 9. Then, the droplet/rivulet was found to rest in its new position for a while (i.e., the
contact line moving velocity of the droplet/rivulet became quite small again at 5.5<t<7.0s) before it “skips” again to
run back further downstream. It should be noted, upon the pushing of the boundary layer airflow, wave structures
were found to form on the free surface of the droplet/rivulet flow, which propagate from the front lobe back to the
rear end of the droplet/rivulet flow. Then, the water was found to slosh back to the front lobe to push the
droplet/rivulet lurches forward. As shown clearly in Fig. 9, the moving velocity of the contact line at the front lobe
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of the droplet/rivulet was always found to be greater than that at the rear end of the droplet/rivulet. It indicates that
the wind-driven droplet/rivulet was spreading out over the test plate, as expected.
Fig. 10: The time evolution of the wind-driven droplet/rivulet flow over the test plate
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Based on the measured thickness distribution and wet surface area of the droplet/rivulet flow over the test plate,
the total volume (thereby, mass) of the water droplet/rivulet flow over the test plate can also be determined. The
time evolution of the measured total volume (thereby, mass) of the water droplet/rivulet is also shown in Fig.11. As
expected, the total volume (thereby, mass) of the water droplet/rivulet over the test plate was found to be decrease
monotonically due to evaporation. Since a larger wet surface area of the droplet/rivulet flow over the test plate
would promote a stronger evaporation of the water droplet/rivulet flow, as a result, the evaporation rate (i.e., the
volume decrease rate ) of the droplet/rivulet flow was found to become more significantly as the wet surface area of
the droplet/rivulet over the test plate increases.
Wet Surface Area (S/So), Droplet/Rivulet Volume (V/Vo)
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The time evolution of the wet surface area, i.e., the spreading area of the droplet/rivulet over the test plate, can
also be determined based on the time-resolved DFP measurement results. Figure 11 shows the measured wet
surface area of the droplet/rivulet flow as a function of time, which can be used to quantify the spreading extent of
the wind-driven droplet/rivulet flow over the test plate. It can be seen clearly that the wet surface area of the
droplet/rivulet flow over the test plate would increase with time monotonically, as expected. Interestingly, instead
of increasing smoothly and continuously, the wet surface area was found to increase with an interesting feature of
step jumping. The step jumping feature was found to be closely related to the stumbling motion of the wind-driven
droplet/rivulet flow as described above, i. e., each “skip” of droplet/rivulet flow in the stumbling runback process
would cause a step jumping to increase the wet surface area of the droplet/rivulet flow.
2.5
V/Vo
S/So
2.0
1.5
1.0
0.5
0
1
2
3
4
5
6
7
8
9
Time (s)
Fig. 11: The time evolution of the measured wet surface area and total volume of the wind-driven droplet/rivulet
flow over the test plate.
Conclusions
In the present study, a novel digital fringe projection (DFP) technique was developed to achieve non-intrusive
thickness measurements of wind-driven water droplet/rivulet flows over test surfaces as a function of time and space
in order to elucidate underlying physics of unsteady surface water transport process pertinent to glaze ice formation
and accretion process over aircraft wings in atmospheric icing conditions. The DFP technique developed in the
present study is a special kind of structured light projection method for 3D surface shape measurement. It is based
on the principle of structured light triangulation in a similar manner as a stereo vision system but replacing one of
the cameras for stereo imaging with a digital projector. The digital projector was used to project fringe patterns of
known characteristics onto a test object (i.e., a water droplet/rivulet flow for the present study). Due to the 3D
surface shape of the test object, the projected fringe patterns would be deformed seen from a perspective different
from the projection axis. By comparing the phase differences between the distorted fringe patterns over the test
object (i. e., the water droplet/rivulet flow) and a reference fringe pattern on a reference plane (i.e., the test plate
only without the water droplet/rivulet flow), the 3D surface shape of the test object with respect to the reference
plane (i.e., the thickness distribution of the water droplet/rivulet flow) was retrieved quantitatively and
instantaneously.
The feasibility and implementation of the DFP system was first demonstrated by measuring the thickness
distribution of a small flat-top pyramid over a test plate. The DFP measurement results were compared with the
15
nominal height distribution of the pyramid quantitatively in order to evaluate the measurement uncertainty of the
DFP system. With the parameter settings of the DPF system used in the present study, the measurement uncertainty
of the DFP system was found to be less than 160µm, which is about 3% of the nominal height of the flat-top
pyramid.
Downloaded by Hui Hu on March 22, 2013 | http://arc.aiaa.org | DOI: 10.2514/6.2012-3014
After carefully calibrated and validated, the DFP system was applied to achieve time-resolved thickness
distribution measurements of a wind-driven water droplet/rivulet flow to quantify the transient behavior of the
surface water droplet/rivulet flow driven by boundary layer airflow over a test plate. The dynamic shape change and
stumbling runback motion of the wind-driven water droplet/rivulet flow over the test plate were revealed clearly and
quantitatively in the terms of the thickness distribution, contact line moving velocity, wet surface area over the test
plate and the evaporation rate of the droplet/rivulet flow as a function of time. Such quantitative information is
highly desirable to elucidate the underlying physics of the unsteady surface water transport process pertinent to
glaze ice formation and accretion over aircraft wings in atmospheric icing conditions. A better understanding of the
wind-driven surface water transport process can lead to improved icing accretion models for more accurate
prediction of glaze ice formation and accretion on aircraft wings as well as development of effective anti-/de-icing
strategies tailored for safer and more efficient operation of aircraft in cold weather.
Acknowledgments
The research work was partially funded by National Aeronautical and Space Administration (NASA) - Grant
number NNX12AC21A with Mr. Mark Potapczuk as the technical officer. The support of National Science
Foundation (NSF) under award number of CBET-1064196 with Dr. Sumanta Acharya as the program manager is
also gratefully acknowledged.
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