DEVELOPMENT OF A HEATED
MULTILAYER SHEAR SENSOR
by
Todd Jerard Barber
B.S. Aero. Eng., Massachusetts Institute of Technology
(1988)
SUBMITTED TO THE DEPARTMENT OF
AERONAUTICS & ASTRONAUTICS
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF
MASTER OF SCIENCE
in Aeronautics & Astronautics
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
February 1991
©
Massachusetts Institute of Technology
Signature of Author ................... .. :..:....
Departm
S,
Certified by............
..
1990
.....
.
.......................... ........
of Aero
tics & Astronautics
/ ,,October
1990
............... . .............
Alan H. Epstein
Professor, A/eronautips & Astronautics
.. .-.........................
A ccepted by ....................................................... .. ....t- ..........
0........A..............
PHarold Y. Wachman, Chairman
Departmental Graduate Committee
Department of Aeronautics & Astronautics
MA$SACHUsETTS1STRUTE
OF TECHNlrV(iGY
FEB 19 1991
Aero
UBRARIES
DEVELOPMENT OF A HEATED
MULTILAYER SHEAR SENSOR
by
TODD JERARD BARBER
Submitted to the Department of Aeronautics & Astronautics
February, 1991 in partial fulfillment of the
requirements for the Degree of Master of Science in
Aerospace Engineering
ABSTRACT
An experimental study was carried out to test the feasibility of
using a double-layer heat transfer gauge for ultimate application
in determining the time-resolved behavior of the boundary layer,
passage shock, and possible separation point on a transonic
compressor rotor blade.
In particular, a gauge with equivalent
heater and sensor temperatures was tested, to see the effect of
cancelling the steady-state heat conduction into the substrate.
Tests were performed in a subsonic wind tunnel for steady
calibrations and in a shock tube for an unsteady step response.
For the steady flow case, the use of a controlled gauge allowed for
the calculation of the skin friction over a flat plate. Experimental
results agreed with theory within the accuracy of the experiment
at all but the lowest sensor overheat ratios.
Shock tube
predictions for the voltage change of the sensor across the shock
were generally good, except for one case tested. In both scenarios,
the theoretical model overpredicted the actual sensitivity of the
gauge to Mach number.
A new gauge geometry was designed for future compressor
testing, with tradeoff studies being performed for the parameters
under the control of the experimentalist. In particular, both fourelement and ten-element gauges were designed specifically with
compressor testing as the ultimate application.
Thesis Supervisor:
Title:
Dr. Alan H. Epstein
Professor of Aeronautics & Astronautics
ACKNOWLEDGEMENTS
The list of people who share this accomplishment with me is
truly enormous and it is my pleasure to recognize their efforts.
First and foremost, I would like to extend my deepest thanks to
Professor Alan Epstein for his uncanny experimental talents, his
extreme friendliness and approachability, and his faith in my
abilities through all the trials and tribulations of an experimental
thesis. His patience, understanding, and expertise will not be soon
forgotten.
The GTL support staff has eased my journey through graduate
life beyond comprehension. The efforts of Viktor Dubrowski, Roy
Andrew, Jim Nash, Bob Haimes, and Jerry Guenette have literally
saved months of aimless wandering.
Karen Hemmick, Holly
Rathbun, Nancy Clark, and Diana Park all have been indispensable
for the completion of this project. It is with a twinge of sadness
that I leave you all.
My fellow students in GTL have truly been an inspiration for
over two years now. There are so many who have helped me
through, not just in a technical sense. I would like to formally
thank Sasi Digavalli, Judy Pinsley, and Pete Silkowski for
brightening the interior of 31-256 with their friendship.
To
Martin Graf, my new friend and successor, I wish to extend a
special welcome and a heartfelt thank you for making my last
weeks at MIT as pleasant as possible. I offer my deepest respect
and thanks to Charlie Haldeman, the one student in GTL who was
never too busy to drop his work and solve my problems. To my
best friend in the GTL, Tonghuo Shang, I send a mixed message--a
happy 'thank you for everything and best wishes for you and
your wife' and a sad 'goodbye, buddy....'
The faculty in GTL, both permanent and visiting members, have
provided many useful technical hints throughout this project. In
particular, I greatly appreciate the efforts of Dr. Edward Greitzer,
Dr. Choon S. Tan, Dr. Mike Giles, and Dr. Peter Bryanston-Cross for
their timely advice.
Without the wonderful friendships I've enjoyed outside of GTL,
my journey through a master's degree would have been much
more difficult. I give a special thanks to Al, Aric, Ella, Emily,
Glenn, Greg, Gus, Iman, Jamie, John, Sam, Steve A., Thomas, Tricia,
Venkat, and Will. You are all the best. Notice I listed these
alphabetically, absolutely devoid of any favoritism.
I'm no
dummy--I want to keep my friends. I shall miss all of you so
very, very much.
I want to express my deepest gratitude to my family in Kansas.
To Mom, Dad, and Lea--thanks for being there for me for eighteen
years,
helping me to grow into a (more or less) well-adjusted
adult. It's too bad MIT has taken all of that away. Just kidding. I
love you all very much. Whatever my successes, I take along a
part of you.
Finally, I want to send my love across the miles to Lisa, the
most special person in my life. Your caring and support through
the darkest of days were the one thing that always kept me going.
I treasure all of our wonderful memories. Soon we will begin a
lifetime of memories together. Oh, and one more thing: Psyche,
silly willy...your sugar booger will be there soon!
TABLE OF CONTENTS
ABSTRACT
ACKNOWLEDGEMENTS
TABLE OF CONTENTS
LIST OF FIGURES
LIST OF TABLES
-v
CHAPTER 1: BACKGROUND AND INTRODUCTION
CHAPTER 2: THIN-FILM HEAT TRANSFER GAUGES: INTRODUCTION AND
OPERATIONI,
2.1 INTRODUCTION TO THIN-FILM HEAT TRANSFER GAUGES
--
19
2.2 OPERATING MODES OF THIN-FILM GAUGES
CHAPTER 3: THEORETICAL PREDICTIONS FOR UNSTEADY HEAT TRANSFER AND
23
MULTI-ELEMENT GAUGE DESIGN
3.1 MODELLING THE UNSTEADY SUBSTRATE HEAT CONDUCTION
3.2 PARALLEL VS. SERIES GAUGES
23
3.3 VOLTAGE PREDICTIONS FOR A MULTI-ELEMENT GAUGE
27
3.4 MULTI-LAYER MULTI-ELEMENT GAUGE DESIGN TRADEOFFS
29
3.4.1
Element spacing
--
3.4.2
Power considerations in gauge sizing
30
3.4.3
Tag resistance tradeoffs:
and plating
31
effects of 2D electrical conduction
CHAPTER 4: DESCRIPTION OF EXPERIMENTAL APPARATUS AND TEST
GAUGES
35
4.1 EXPERIMENTAL APPARATUS FOR THE SHOCK TUBE
35
4.1.1
Introduction and principle of operation
35
4.1.2
Data acquisition and triggering mechanism
36
4.1.3
Selection of diaphragm materials
38
4.2 EXPERIMENTAL APPARATUS FOR THE SUBSONIC WIND TUNNEL
39
4.3 DESCRIPTION OF TEST GAUGES
40
4.3.1
Probe supports for thin film gauges
41
4.3.2
The calibration of a
42
4.3.3
Feasibility of balancing non-standard resistors
44
CHAPTER 5: DATA REDUCTION AND ERROR ANALYSIS
47
5.1 DATA REDUCTION FOR THE SHOCK TUBE
47
5.2 DATA REDUCTION FOR THE SUBSONIC WIND TUNNEL
50
5.3 ERROR ANALYSIS
54
CHAPTER 6: EXPERIMENTAL DATA AND COMPARISON OF DATA WITH
THEORY
58
6.1 SHOCK TUBE EXPERIMENTAL RESULTS
58
6.2 SUBSONIC WIND TUNNEL PROOF OF CONCEPT TESTING AND
EXPERIMENTAL RESULTS
6.3 SHOCK TUBE COMPARISON OF THEORY AND EXPERIMENT
60
61
6.4 SUBSONIC WIND TUNNEL COMPARISON OF THEORY AND
EXPERIMENT
63
CHAPTER 7: CONCLUSIONS AND RECOMMENDATIONS FOR FURTHER STUDY
66
BIBLIOGRAPHY
69
FIGURES
71
APPENDIX A: THERMAL TRANSPARENCY OF THE THIN FILM
161
APPENDIX B: OPTIMIZATION OF ELEMENT RESISTANCE FOR A GIVEN TOTAL
GAUGE RESISTANCE
167
APPENDIX C: TABLES OF FLOW PARAMETERS FOR THE TEN SHOCK TUBE
RUNS
173
APPENDIX D: VOLTAGE TRACES FOR SHOCK TUBE RUNS #6-#10
184
LIST OF FIGURES
CHAPTER 2
Figure 2.1:
Figure 2.2:
Figure 2.3:
Constant temperature anemometer feedback loop
Thin-film heat transfer gauge cross-section
Comparison of gauges and operating modes
CHAPTER 3
Figure 3.1:
Figure 3.2:
Figure 3.3:
Figure 3.4:
Figure 3.5:
Figure 3.6:
Figure 3.7:
Figure 3.8:
Figure 3.9:
Figure 3.10:
Figure 3.11:
Figure 3.12:
Figure 3.13:
Normalized unsteady substrate conduction vs. time
Normalized unsteady substrate conduction vs.
logl 0 (time)
Normalized unsteady substrate conduction vs. time;
effect of the glue layer
Normalized unsteady substrate conduction vs.
log 10 (time); effect of the glue layer
Comparison of parallel and series gauge geometries
Series to parallel gauge voltage ratio vs. number of
resistance elements
Sensor voltage vs. normalized shock position; ars =
1.2, laminar flow
Sensor voltage vs. normalized shock position; ars =
1.4, laminar flow
Sensor voltage vs. normalized shock position; ars =
1.2, turbulent flow
Sensor voltage vs. normalized shock position; ars =
1.4, turbulent flow
Sensor voltage change vs. temperature ratio: ars =
1.2, laminar flow
Sensor voltage change vs. temperature ratio: ars =
1.4, laminar flow
Sensor voltage change vs. temperature ratio: ars =
1.2, turbulent flow
9
Figure 3.14:
Figure 3.15:
Figure 3.16:
Figure 3.17:
Figure 3.18:
Figure 3.19:
Figure 3.20:
Figure 3.21:
Figure 3.22:
Figure 3.23:
Figure 3.24:
Figure 3.25:
Figure 3.26:
Figure 3.27:
Sensor voltage change vs. temperature ratio: ars =
1.4, turbulent flow
Oscillating shock on a multi-element gauge
Electric power dissipated vs. number ot elements:
= 0.342 2/square
Electric power dissipated vs. number of elements:
= 0.684 a/square
Electric power dissipated vs. number of elements:
= 1.378 a/square
Dissipated heat flux vs. overheat ratio
Dissipated to supplied power ratio vs. gauge
resistance; effect of n for fixed tag to element
resistance ratio
Dissipated to supplied power ratio vs. gauge
resistance; effect of tag to element resistance ratio
for a fixed n
Actual [2D] to expected [1D] resistance ratio vs.
width to length ratio of rectangular tag
Plate to element resistance ratio vs. number of
elements; material= copper; effect of a of plate
material
Plate to element resistance ratio vs. number of
elements; material= gold; effect of a of plate
material
Plate to element resistance ratio vs. number of
elements; effect of plate material for a given plate
thickness
Four-element gauge design
Ten-element gauge design
CHAPTER 4
Figure 4.1:
Figure 4.2:
Figure 4.3:
Shock tube experimental apparatus
Shock tube configuration: before burst
Shock tube configuration: x-t diagram after burst
Figure 4.4:
Shock tube configuration: pressure and temperature
profiles with streamwise direction after burst
Figure 4.5:
Maximum data acquisition time vs. shock Mach
number
Figure 4.6:
Mean and deviation break pressures for shock tube
diaphragm materials
Mean and deviation Mach numbers for shock tube
Figure 4.7:
diaphragm materials
Figure 4.8:
Shock speed percentage error vs. Mach number
Figure 4.9:
Subsonic wind tunnel experimental apparatus
Figure 4.10: Single-layer sensor shock tube probe support
Figure 4.11: Double-layer sensor shock tube probe support
Figure 4.12: Subsonic wind tunnel flat plate probe support
Figure 4.13: Flat plate leading edge profile geometry
Figure 4.14: Test material resistance vs. test material
temperature
Figure 4.15: Sensor resistance vs. sensor temperature: the value
of as; brass support
Figure 4.16: Heater resistance vs. heater temperature: the value
of ah; brass support
Figure 4.17: Sensor resistance vs. sensor temperature: the value
of as; anodized aluminum support
Figure 4.18: Heater resistance vs. heater temperature: the value
of ah; anodized aluminum support
Figure 4.19: Subsonic tunnel sensor resistance vs. sensor
temperature for as
Figure 4.20: Subsonic tunnel heater resistance vs. heater
temperature for ahl
Figure 4.21: Subsonic tunnel sensor resistance vs. sensor
temperature for as2
Figure 4.22: Subsonic tunnel heater resistance vs. heater
temperature for ah2
Figure 4.23: Anemometer output voltage vs. sensor cold
resistance for a fixed control resistance
Figure 4.24: Anemometer output voltage vs. sensor overheat
ratio resistance for a fixed cold resistance
Figure 4.25:
Figure 4.26:
Sensor to ambient temperature ratio vs. heater to
ambient temperature ratio for a passive sensor test
Balanced-gauge voltage vs. sensor overheat ratio in
zero flow
CHAPTER 5
Figure 5.1:
Percentage error vs. error-producing source for a
typical flow condition
CHAPTER 6
Unsteady voltage traces vs. time: single-layer
sensor, low Mach number trials
Unsteady voltage traces vs. time: single-layer
Figure 6.2:
sensor, intermediate Mach number trials
Figure 6.3:
Unsteady voltage traces vs. time: single-layer
sensor, high Mach number trials
Figure 6.4:
Unsteady voltage traces vs. time: double-layer
gauge, low Mach number trials, heater passive, #1
Figure 6.5:
Unsteady voltage traces vs. time: double-layer
gauge, intermediate Mach number trials, heater
passive, #1
Figure 6.6:
Unsteady voltage traces vs. time: double-layer
gauge, high Mach number trials, heater passive, #1
Figure 6.7:
Sensor voltage vs. mass flux: turbulent flow
calibration curves
Figure 6.8:
Sensor voltage vs. mass flux: laminar flow
calibration curves
Figure 6.9:
Heater voltage vs. mass flux: turbulent flow
calibration curves
Figure 6.10: Heater voltage vs. mass flux: laminar flow
calibration curves
Figure 6.11: Sensor voltage vs. Mach number: experimental and
theoretical output for single-layer sensor, brass
probe support
Figure 6.1:
Figure 6.12:
Figure 6.13:
Figure 6.14:
Figure 6.15:
Figure 6.16:
Figure 6.17:
Figure 6.18:
Figure 6.19:
Figure 6.20:
Figure 6.21:
Figure 6.22:
Sensor voltage vs. Mach number: experimental and
theoretical output for double-layer gauge, brass
probe support, heater passive, #1
Sensor voltage vs. Mach number: experimental and
theoretical output for double-layer gauge, brass
probe support, heater passive, #2
Sensor voltage vs. Mach number: experimental and
theoretical output for double-layer gauge, brass
probe support, heater active
Percent difference of theoretical and experimental
voltage for a heater active vs. a heater passive case
Sensor voltage vs. Mach number: experimental and
theoretical output for double-layer gauge, anodized
aluminum probe support, heater active, ars = 1.06, t
= 0.8 ms
Sensor voltage vs. Mach number: experimental and
theoretical output for double-layer gauge, anodized
aluminum probe support, heater active, ars = 1.08, t
= 0.8 ms
Sensor voltage vs. Mach number: experimental and
theoretical output for double-layer gauge, anodized
aluminum probe support, heater active, ars = 1.11, t
= 0.8 ms
Sensor voltage vs. Mach number: experimental and
theoretical output for double-layer gauge, anodized
aluminum probe support, heater active, ars = 1.06, t
= 1.27 ms
Sensor voltage vs. Mach number: experimental and
theoretical output for double-layer gauge, anodized
aluminum probe support, heater active, ars = 1.08, t
= 1.27 ms
Sensor voltage vs. Mach number: experimental and
theoretical output for double-layer gauge, anodized
aluminum probe support, heater active, ars = 1.11, t
= 1.27 ms
Shock tube pressure pulse: expanded time scale
Figure 6.23: Experimental to theoretical skin friction ratio
actual mass flux for turbulent flow
Figure 6.24: Experimental to theoretical skin friction ratio
actual mass flux for laminar flow
Figure 6.25: Skin friction coefficient vs. Mach number for
turbulent flow: experiment vs. theory
Figure 6.26: Skin friction coefficient vs. Mach number for
laminar flow: experiment vs. theory
Figure 6.27: Experimental to theoretical skin friction ratio
true mass flux: ars 1 = 1.02, ars2 = 1.04
Figure 6.28: Experimental to theoretical skin friction ratio
true mass flux: ars 1 = 1.02, ars2 = 1.06
Figure 6.29: Experimental to theoretical skin friction ratio
true mass flux: ars = 1.02, ars2 = 1.08
Figure 6.30: Experimental to theoretical skin friction ratio
true mass flux: ars 1 = 1.04, ars2 = 1.06
Figure 6.31: Experimental to theoretical skin friction ratio
true mass flux: ars 1 = 1.04, ars2 = 1.08
Figure 6.32: Experimental to theoretical skin friction ratio
true mass flux: arsi = 1.06, ars2 = 1.08
VS.
vs.
vs.
vs.
vs.
vs.
vs.
vs.
APPENDIX B
Figure B.1:
Figure B.2:
Optimum tag to element resistance ratio vs. number
of elements
Optimum element resistance vs. number of elements
APPENDIX D
Figure D.1:
Figure D.2:
Unsteady voltage traces vs. time: double-layer
gauge, low Mach number trials, heater passive, #2
Unsteady voltage traces vs. time: double-layer
gauge, intermediate Mach number trials, heater
passive, #2
Figure D.3:
Figure D.4:
Figure D.5:
Figure D.6:
Figure D.7:
Figure D.8:
Figure D.9:
Figure D.10:
Figure D.11:
Figure D.12:
Figure D.13:
Figure D.14:
Unsteady voltage traces vs. time: double-layer
gauge, high Mach number trials, heater passive, #2
Unsteady voltage traces vs. time: double-layer
gauge, low Mach number trials, heater active, brass
support
Unsteady voltage traces vs. time: double-layer
gauge, intermediate Mach number trials, heater
active, brass support
Unsteady voltage traces vs. time: double-layer
gauge, high Mach number trials, heater active, brass
support
Unsteady voltage traces vs. time: double-layer
gauge, low Mach number trials, heater active,
anodized aluminum support, ars = 1.06
Unsteady voltage traces vs. time: double-layer
gauge, intermediate Mach number trials, heater
active, anodized aluminum support, ars = 1.06
Unsteady voltage traces vs. time: double-layer
gauge, high Mach number trials, heater active,
anodized aluminum support, ars = 1.06
Unsteady voltage traces vs. time: double-layer
gauge, low Mach number trials, heater active,
anodized aluminum support, ars = 1.08
Unsteady voltage traces vs. time: double-layer
gauge, intermediate Mach number trials, heater
active, anodized aluminum support, ars = 1.08
Unsteady voltage traces vs. time: double-layer
gauge, high Mach number trials, heater active,
anodized aluminum support, ars = 1.08
Unsteady voltage traces vs. time: double-layer
gauge, low Mach number trials, heater active,
anodized aluminum support, ars = 1.11
Unsteady voltage traces vs. time: double-layer
gauge, intermediate Mach number trials, heater
active, anodized aluminum support, ars = 1.11
Figure D.15:
Unsteady voltage traces vs. time: double-layer
gauge, high Mach number trials, heater active,
anodized aluminum support, ars = 1.11
LIST OF TABLES
Table 3.1:
Table C.1:
Table C.2:
Table C.3:
Table C.4:
Table C.5:
Table C.6:
Table C.7:
Table C.8:
Table C.9:
Gauge design system parameters for the four-element
and ten element gauges
Comparison of predicted and measured shock speeds
for the shock tube: shock tube familiarity testing with
heavy duty aluminum foil only
Comparison of predicted and measured shock speeds
for the shock tube: shock tube familiarity testing with
a variety of diaphragm materials
Comparison of predicted and measured shock speeds
for the shock tube: diaphragm material testing
Comparison of predicted and measured shock speeds
for the shock tube: heat transfer data recorded for a
single-layer sensor (#1)
Comparison of predicted and measured shock speeds
for the shock tube: heat transfer data recorded for a
single-layer sensor (#2)
Comparison of predicted and measured shock speeds
for the shock tube: heat transfer data recorded for a
homemade double-layer gauge with the heater run
passively
Comparison of predicted and measured shock speeds
for the shock tube: heat transfer data recorded for a
homemade double-layer gauge with the heater run
actively
Comparison of predicted and measured shock speeds
for the shock tube: heat transfer data recorded for a
turbine double-layer gauge on anodized aluminum
with the heater run actively; ars = 1.06
Comparison of predicted and measured shock speeds
for the shock tube: heat transfer data recorded for a
turbine double-layer gauge on anodized aluminum
with the heater run actively; ars = 1.08
Table C.10:
Comparison of predicted and measured shock speeds
for the shock tube: heat transfer data recorded for a
turbine double-layer gauge on anodized aluminum
with the heater run actively; ars = 1.11
CHAPTER 1
BACKGROUND AND INTRODUCTION
A hot-film or hot-wire probe is a useful diagnostic tool for
making steady or time-resolved measurements in a given flow.
The hot-film seems particularly well-suited for making
measurements in the boundary layer of a rotating compressor (as
in a modern gas turbine axial-flow machine) due to its proven
technology, ability to withstand centrifugal stresses, absence of
interaction with the flow field, high frequency response, and its
The structure of the boundary
capacity for spatial resolution.
layer, possible separation point, and the oblique passage shock on
a compressor rotor blade is largely unknown, particularly in an
A correctly designed and calibrated thin-film
unsteady sense.
gauge may be able to be used to directly verify and measure
This dictates the
these phenomena in a compressor test rig.
design of a thin-film heat flux gauge specifically for that purpose.
In particular, it is postulated [Epstein, Gertz, Owen, and Giles]
that vortex shedding in upstream compressor blade wakes drives
an observed 15 kHz oscillation of the oblique passage shock. This
was inferred from a bimodal velocity histogram from
A shock oscillation
experimental laser anemometry data.
amplitude of 0.5 mm was proposed to explain the observations. It
is desired to verify this amplitude and frequency of oscillation for
The thin-film heat transfer gauge
the passage shock directly.
offers the experimentalist a means to do so.
In addition, a low frequency ( 350 Hz) oscillation is inferred in
the experimental measurements as well. It is postulated that this
is due to an oscillation of a separation point on the suction surface
of the rotor blade. Again , thin-film heat transfer technology may
offer a direct measurement of this phenomenon, confirming the
Also of interest is the
indirect observations previously made.
location of a possible transition point in the boundary layer on the
The success of a computational code (CFD
compressor blade.
model) for a turbomachine component hinges on knowledge of the
correct location of the transition point from laminar to turbulent
flow. In short, a well-designed thin-film heat transfer gauge may
provide the mean and time-resolved flow structure in a transonic
compressor rotor passage.
Such a thin-film gauge would need to be designed with all of
the above criteria in mind. In particular, a double-layer multielement heat transfer gauge has been developed [Epstein,
Guenette, Norton, and Yuzhang] that satisfies many of the
requirements above.
Proof of concept testing and preliminary
calibrations may be performed on these readily available gauges.
Ultimately, a gauge with a geometry tailored to the application
(mapping the unsteady flow structure on a compressor rotor
blade) should be designed, calibrated, and tested on a compressor
simulation rig. It is the aim of this work to perform experiments
on readily available thin-film gauges to obtain predictions for the
sensor voltage changes as a function of the flow properties in the
test. In particular, steady-state and time-resolved testing should
both be performed for a wide variety of flow Mach numbers,
controlled gauge temperatures, and operating modes (described
subsequently).
Theoretical predictions for these output voltage
changes should be compared with the actual experimental
observations for consistency.
In addition, a candidate gauge
design for the compressor testing should be presented, after a
tradeoff study is performed for the various gauge parameters that
are determined by the designer.
CHAPTER 2
THIN-FILM HEAT TRANSFER GAUGES:
INTRODUCTION AND OPERATION
2.1 INTRODUCTION TO THIN-FILM HEAT TRANSFER GAUGES
The use of single thin-film heat transfer gauges as a flow
sensor, via constant temperature anemometry, is a familiar
concept [Blackwelder]. The principle of operation is identical to
that of a hot-wire anemometer, which is a very popular diagnostic
tool.
A constant temperature anemometer is an electronic
feedback loop that will maintain a resistor (called the "probe" or
"gauge") at a certain resistance value set by the operator. There
exists an approximately linear relationship between resistance
and temperature:
Rh = Rc [1 + a(Tg - To)]
(2.1)
where Rh is the hot resistance (equal to the control resistance), Rc
is the cold resistance (the resistance of the gauge at To), Tg is the
gauge operating temperature, To is the ambient or reference
temperature, and a is the coefficient of thermal resistivity of the
thin-film material.
The ratio of the hot to the cold resistance
Rh/Rc is known as the resistive overheat ratio (ar), or the overheat
ratio for short.
Therefore, a constant temperature anemometer
loop fixes a gauge to be at a temperature Tg which is higher than
ambient temperature (since ar>l). See Figure 2.1 for a schematic
of the anemometer bridge loop employed.
A standard TSI anemometer unit, model 1050A, was throughout
testing.
In a hot-wire anemometer, the heat provided (via a
current) to the gauge is dissipated into the surrounding flow via
As the flow speed
the heat transfer process of forced convection.
is increased, for example, the convection of heat away from the
hot-wire to the flow is increased; therefore, more current needs
to be provided to the gauge to maintain it at the elevated
This change can be seen by monitoring the
temperature Tg.
voltage value across the gauge. Since the temperature (and hence
resistance) of the gauge is a constant and the current has
voltage value across the gauge will increase
increased, the
accordingly. In fact, if a reasonable relation can be obtained for
the forced convection as a function of velocity, it is possible to use
the hot-wire anemometer as a velocity meter, since the
temperature of the hot wire is known.
The arguments of the preceding paragraph hold for a hot-film
In
anemometer as well, but additional complications exist.
particular, due to the geometric nature of thin-film gauges, forced
convection is not the only heat transfer mechanism of importance.
A thin-film gauge consists of a thin (approximately 1000 A) film
of metal (in this case, pure nickel) mounted on an insulating layer
of kapton (a polyimide material) called a substrate. The kapton
thickness is many times greater than that of the thin nickel film.
Figure 2.2 represents a schematic of a cross section of a typical
gauge (not to scale). Heat conduction into the substrate allows for
another means for heat to be transferred from the heated film,
and has indeed been observed in practice.
2.2 OPERATING MODES OF THIN-FILM GAUGES
A comparison of the gauges used (in cross-section) and their
operating modes can be seen in Figure 2.3. In the case of the
shock tube,
the test article represents the shock tube probe
support. For the single-layer gauge, the kapton is bonded directly
to the test article. For the double-layer gauge, the lower resistor
(which acts as a heater) is bonded between the kapton and the
test article. Since the heater is bonded intimately with the probe
support, it is imperative that the probe support be a nonconducting material.
This lead to the requirement that the
aluminum probe support be anodized.
In the heater passive
mode, the bottom thin-film resistor is not controlled in a constant
temperature anemometer loop. This is in contrast to the heater
active mode, in which both the sensor and the heater are
controlled in separate anemometer loops.
Experimental results
utilizing these three operating modes will be presented later.
The off-design condition of balancing both the heater and the
sensor to different constant temperatures was not investigated. It
was determined that such a configuration was not stable, due to
the fact that the resistor operating at lower temperature by the
anemometer loop would have its temperature increased beyond
its operating temperature due to heat conduction from the resistor
operating at higher temperature.
Once this elevated temperature
is realized in the lower temperature resistor, no means can be
provided to reduce the temperature of this resistor back to its
operating point (i.e., no mechanism exploiting the Peltier effect
exists for these standard anemometer units and probes). This is
due to the fact that positive current can only be injected into the
gauges by the anemometer unit and increases in current
correspond to increases in temperature of the resistor.
Control resistances were set on the anemometer unit using both
an external 5:1 bridge and the resistance decades, depending on
the resistance value of the probe used. Control resistances less
than 50 ohms may be set directly with the resistance decades on a
1:1 bridge, while control resistances greater than 50 ohms must
be set using the external control resistor feature on the 5:1 bridge.
A simple internal rewiring procedure described in the TSI
operating manual allows a toggle between these two methods of
External control resistors are
setting the control resistances.
constructed from potentiometers and standard circuit resistors in
series. With this design, the overheat ratio can be changed by
A circuit resistor is used in series
adjusting the potentiometer.
with the potentiometer to allow the use of a lower resistance
potentiometer, which gives better controllability on setting the
overheat ratio.
2.2-
CHAPTER 3
THEORETICAL PREDICTIONS FOR UNSTEADY HEAT
TRANSFER AND MULTI-ELEMENT GAUGE DESIGN
3.1 MODELLING THE UNSTEADY SUBSTRATE HEAT CONDUCTION
Various models were tried for the cases of non-zero heat
conduction into the substrate. A first attempt at modelling this
problem was made by assuming that the support was a good
thermal conductor and the temperature at the junction between
This
the substrate and probe support was ambient temperature.
lead to substrate conduction values well over three orders of
magnitude higher than the convection changes seen across the
From this model, the theoretical voltage output change
shock.
across the shock was predicted to be no more than 20 mV. Actual
output voltage changes across the shock were typically 200-300
mV. Clearly, this model is not sufficient to explain the operation
of the device. Rather, an unsteady model must be formulated. It
is hoped that this model could demonstrate a much lower value
for the conduction into the substrate at the time of data
acquisition. In all models employed here, it is assumed that the
thermal properties within the thin-film gauge itself can be
This is
ignored without substantially affecting the output.
presumed to be a good assumption due to the low thickness of the
nickel film (i.e., the film appears thermally transparent due to its
size). This is shown to be the case in Appendix A, which solves
the steady conduction solution for the case where the thermal
properties of the thin-film are not ignored.
The following unsteady heat transfer problem was solved to
investigate the time-dependant behavior of the substrate heat
conduction:
23.
a
atJ
a2T 2
aT2
(3.1)
` 1 ax2 = at
"2 =
K2
at(3.2)
subject to the following boundary conditions:
1. T1(O,t)= T* [= Ts-To] = constant
2. Tl(8,t)= T2(8,t)
aT1
3. k1 ax (8,t) = k2
aT2
x (8,t)
4. T2 (0o, t) = 0
5. Tl(x,O)= 0
6. T2(x,O)= 0
Here, k is the thermal conductivity, 8 is the thickness of the
substrate, and K is the thermal diffusivity. The subscript 1 refers
to the kapton layer and the subscript 2 refers to the brass probe
support. This readily solved via Laplace transform techniques. In
particular, it is found that the temperature in the brass support is
represented by:
T2 (x,t) = T*(1-0) £1 [e
-q2(x+2i8) e-(q l-q2)8 0ii
e
(x+2i)
2
i=O
-2iql8]
.
(3.3)
where q2 and 3 are defined as follows:
s
K2
q2
1
with
defined
below
as:
with y defined below as:
".4.
(3.4)
(3.5)
plclk1
p k
Y=
(3.6)
P2c2k2
In (3.6), p represents the material density and c represents the
material specific heat.
The individual terms in (3.3) may be
evaluated [Carslaw and Jaeger] using the following relation:
£-1 [e
2 X]
s
where erfc(
as follows:
[]
= erfc
(3.7)
L2
) denotes the complimentary error function defined
z
erfc(z) = 1 - erf(z) = 1 - 2
e-t2d t
(3.8)
This is a common function in unsteady heat transfer problems and
is rather well tabulated. Applying (3.7) to (3.8), the following is
obtained for the final solution for the temperature in the brass
layer:
oo
T2 (x,t) =
i erfc [x + 2.9[2.69i + 1]
T*(1-3)
2-4 i2t
i=O
(3.9)
From this, it is possible
differentiation, since in general:
qcond
25.
to
=
obtain
aT
- k ax
the
conduction
by
(3.10)
Since differentiation is a linear operator, the derivative may be
moved under the summation sign when applying (3.10) to (3.9).
As a final result:
0O
qcond
k2 T* (1
I)
r[
ie
i=0
=
q •2t
-(2i+1)2/197t
(3.11)
This
This expression was evaluated numerically by computer.
unsteady conduction, normalized by the steady conduction that
would occur if the brass support were at ambient temperature
(the previously mentioned steady model conduction), is plotted as
a function of time in Figures 3.1 and 3.2. Figure 3.1 represents a
plot with a linear time scale, and Figure 3.2 depicts the same plot
with the time axis on a logl 0 scale. Several features may be noted
This time axis
in these two figures (particularly Figure 3.2).
represents the time since the anemometers were turned on. Since
it is generally many thousands of seconds following this process
that the shock tube runs were made, the reduction of the
substrate conduction is seen to be striking. This gives much more
consistent results when attempting to predict the theoretical
voltage jump across a shock, due to the fact that the probe is now
much more sensitive to changes in the flow. The peak that occurs
after 10 ms in the conduction implies that a thermal wave is
propagating from the sensor through the substrate. It is only on
time scales of this order that the conduction would severely limit
the operation of the heater-passive or single-sensor gauge.
The effect of a finite thickness glue layer on the results
presented in Figures 3.1 and 3.2 was numerically investigated.
Assuming that the thermal properties of the glue are similar to
that of the kapton (a much more realistic assumption than
assuming equivalence with brass), this just increases the value of
8 in the previous calculation. In particular, a 5 gtm glue layer was
assumed and the results were recalculated.
Presented in Figures
3.3 and Figures 3.4 are the same plots as in Figures 3.1 and 3.2,
26.
except now the curve representing the scenario with a glue layer
are offered for comparison. As can be seen from the graphs, the
effect of the glue layer is to slightly move the peak of the
conduction graph to the right, towards increased time. This gives
slightly higher conduction values after the peak and slightly lower
values before the peak for the glue case, consistent with
predictions.
Since the glue layer thickness is somewhat beyond
the control of the experimentalist, it is important to demonstrate
that the effect of a glue layer is not a significant contribution to
the heat transfer process as modelled here.
3.2 PARALLEL VS. SERIES GAUGES
To completely determine the processes that take place in the
boundary layer on a flat plate or compressor blade, spatial
resolution of the candidate sensor is an important criterion.
In
particular, the single resistance bar (such as a DISA sensor) would
not allow for good spatial resolution in such an environment,
except with a large number of sensors placed in close proximity.
Therefore, a multiple-element gauge is desirable for spatial
resolution. However, this may adversely effect the signal to noise
ratio of the output voltage across the gauge.
Two types of
multiple-element geometries were investigated; in particular, a
parallel (or ladder) geometry and a series (or serpentine) gauge.
See Figure 3.5. The use of a series gauge as a hot-film probe has
been demonstrated [Epstein, Guenette, Norton, and Yuzhang]. It is
desired to compare the voltage across a ladder gauge with that of
a serpentine gauge with exactly the same properties. Figure 3.6
represents this relationship, graphing the ladder to serpentine
gauge output ratio as a function of the number of resistance
elements.
This basically scales as the inverse square of the
number of resistance elements.
Clearly, this dictates that a
serpentine pattern be used in the design of a mulitple-element
gauge.
3.3 VOLTAGE PREDICTIONS FOR A MULTI-ELEMENT GAUGE
Z1.
It is desired to know the expected voltage change as a shock
wave crosses one element of an n element gauge. This allows the
experimentalist to determine, by simply examining the voltage
trace from a thin-film heat flux sensor, the presence and the
motion of a shock. This is important for attempting to decipher
the flow structure on the surface of a transonic compressor blade.
Unfortunately, the absolute changes predicted by these models
are not physically relevant, since these models were derived using
the constant conduction into the substrate model, which has been
shown not to be a realistic assumption. However, the shape of the
plots will remain unchanged if the unsteady conduction model
derived previously is incorporated into the present model.
Figures 3.7-3.10 present the sensor voltage as a function of shock
position divided by gauge length. Therefore, the leftmost points
represent a shock just at one boundary of the gauge and the
rightmost points represent the shock after crossing the entire
length of the gauge. Two different sensor gauge overheat ratios
are presented for both laminar and turbulent flow. Although the
change in voltage as the shock propagates is larger in magnitude
than is shown here, the nearly linear profile of sensor voltage
with shock position over gauge length is expected to be seen, even
taking into account the unsteady heat transfer term derived last
chapter. Notice that in all cases that higher Mach numbers give
larger voltage changes as the shock propagates over the gauge,
consistent with intuition. Note also that the predicted value of the
absolute voltage level is an increasing function of the overheat
ratio, as is expected.
For the case where the heater and sensor are controlled to be at
the same temperature in a double-layer gauge (note the
distinction between multi-element and multi-layer),
the
conduction into the substrate can only equal zero if the heater and
sensor temperature are balanced exactly. Therefore, it is useful to
estimate the decrease in sensor voltage as the temperature
difference between the sensor and the heater is increased.
Figures 3.11-3.14 present the sensor output voltage change across
a shock (across all elements of the gauge) as a function of
temperature ratio, where the temperature ratio is defined to be
the temperature difference between the sensor and the heater
normalized by the ambient air temperature.
Again, results are
presented for both laminar and turbulent flows, with two
overheats and three Mach numbers investigated. As before, the
absolute voltage level presented here is not correct due to the fact
that this model incorporates a steady substrate conduction term.
However, the shape of the curve with temperature ratio is
consistent with the correct substrate conduction model.
In all
cases, there is a severe penalty for temperature mismatch
between the sensor and the heater. Many of the parameters that
determine the proximity of the heater and sensor temperatures
are beyond the control of the experimentalist. Good calibrations
for a are a necessity, as are carefully prepared control resistors or
carefully dialed resistance decade values, depending on the mode
of operation of the anemometer units.
3.4 MULTI-LAYER MULTI-ELEMENT GAUGE DESIGN TRADEOFFS
3.4.1
Element spacing
As mentioned above, the spatial resolution of a candidate heat
transfer gauge is an important criterion for gauge design.
The
physical shock oscillation on a transonic compressor blade has
been measured to have an amplitude of 0.5 mm. This, however,
does not represent the true supersonic interaction length, due to
shock wave/boundary layer interactions.
In particular, it is
desired to know whether the amplitude of shock oscillation is
larger or smaller than this supersonic interaction length. Figure
3.15 represents a schematic of this scenario. Correlations can be
found for scaling laws for the supersonic interaction domain. It is
found that many experimental data points collapse onto one
curve, described below:
29.
L* = 70 60* (Hi - 1)
(3.12)
where L* is the interaction length, 80* is the displacement
thickness of the boundary layer, and Hi is the incompressible
shape factor, which is a strong function of the Reynolds number
and a rather weak function of the shock Mach number (at least
until Ms becomes greater than 1.3, when separation may occur).
For this geometry, it is found that, for the Reynolds numbers
encountered on the compressor rotor blade, the supersonic
interaction length is roughly 2 mm, or about four times the shock
oscillation amplitude. Therefore, the boundaries of the oscillating
shock are smeared by the larger interaction region between the
oblique shock and the turbulent boundary layer. Hence, providing
a spatial resolution less than the shock oscillation amplitude is
futile. A design value of 1.00 mm, or 1000 gm was chosen as the
distance between adjacent gauge elements (denoted by e).
Therefore, the width of the gauge depends only on the the width
of the individual resistance elements (5) and the number of
resistance elements (n).
3.4.2
Power considerations in gauge sizing
It is an important design criterion that the power supplied by
the anemometer be equivalent to the power dissipated in the
thin-film gauge. This depends not only on the surface area of the
resistance elements, but on the surface area of the tags and leads
as well.
Tags are the electrical connections between resistance
elements (i.e., they are part of the serpentine pattern) and leads
are two electrical connections from one side of the heat-flux
gauge. In general, the leads for these thin-film gauges are goldplated to lower their resistance. There is usually no need to plate
the tags, as their total resistance is typically small in a serpentine
pattern. However, due to the fact that e is so large and that the
cold resistance of the gauge is being designed to have a value of
15 Q (to allow standard use on DISA or TSI anemometer units), as
well as the power limitations of the anemometer, the tags have a
30.
substantial resistance in the geometry employed here, so they will
need to be gold-plated as well. It was desired to have a gauge
that would work even with the failure of the gold-plating, but it
was demonstrated that such a gauge cannot be constructed.
Therefore, the successful operation of this multi-layer serpentine
For a
gauge hinges on the success of the plating process.
completely non-plated gauge, there is an optimum (i.e., lowest)
total tag and lead resistance for a given total resistance. This is
demonstrated in Appendix B.
It was decided to select the total tag resistance to be no more
than 20% of the total element resistance, since higher tag
resistances will reduce the sensitivity of the gauge to flow
changes. The effect of changing the parameter 8 is seen in Figures
3.16-3.18, which depict the dissipated electric power as a function
of the number of resistance elements. The three graphs represent
three different a values for the gauges, where a is the ohms per
square of the gauge. Due to power limitations of the anemometer,
a value of 8= 20 pm was selected. This is physically realizable
with vacuum sputtering technology.
Figure 3.19 presents the
correlation for dissipated heat flux as a function of overheat ratio
For a given overheat ratio and support
for various materials.
material for the bonded gauge, this fixes the allowed surface area
In particular, Figures 3.20 and 3.21 plot the
for the gauge.
dissipated to supplied power ratio as a function of gauge cold
resistance for different values of n. The horizontal line at one
represents the design point. Figure 3.20 shows the effect of the
number of resistance elements for a fixed tag to element
resistance ratio of 0.1. Figure 3.21 shows the effect of changing
the tag to element resistance ratio for a fixed ten-element gauge.
However, this is academic, as a value of 0.2 for the tag to element
resistance ratio may be too large to assure a sensitive thin-film
gauge.
3.4.3 Tag resistance tradeoffs:
and plating
effects of 2D electrical conduction
As mentioned before, the resistance of a material is a function
of the geometry of the material and a material property known as
the resistivity. In particular, for a rectangular conductor of width
W, length L, and thickness t [ t << W,L ], the resistance of the plate
along its length can be written as:
R=
(3.13)
where p is the resistivity of the material. However, this is only
true for the case where current is distributed evenly over each of
the sides of width W. The geometry for the thin-film resistance
tag is much different than this. Current is injected at one corner
of the rectangle and is lead off at an adjacent corner, the length of
the side between these two corners being L. Therefore, arbitrarily
increasing the width W of a tag element to lower the tag
resistance will not work according to (3.13), since the current lines
will thin out and therefore less resistance is offered to the total
flow of current than would be expected. The analytical solution of
the effective resistance of this 2D plate is extremely complex, and
numerous attempts at an analytical solution failed. A numerical
solution technique, though, can be readily applied. A computer
smoothing algorithm was used to solve Laplace's equation for this
geometry. Results were obtained for a case with four times fewer
grid points, with no noticeable change of the output.
This
demonstrates that the smoothing algorithm has converged.
Presented in Figure 3.22 is a plot of this true resistance,
normalized by the resistance expected using (3.13), as a function
of the width to length ratio of the tag.
This effect clearly
demonstrates that the current density rapidly decreases with
increasing W, so this is a substantial effect.
This model was
incorporated into the gauge design model with a noticeable shift
in the results. It is clear that this effect is more crucial for higher
values of the tag/element resistance ratio. It is also clear that the
solution to this problem is a strong function of the ratio of the
32.
width of the element to the width of the tag (i.e., how much of the
rectangle has current entering it and leaving it) This analysis was
performed for a tag to element width ratio of 52, but may be
performed for an arbitrary tag to element width ratio as well.
The effect of the thickness of the plating material, as well as the
choice of plating material, on the resistance of the plating material
for different values of n is presented in Figures 3.23-3.25. Figures
3.23 and 3.24 show that there is a severe (i.e., greater than linear)
penalty for choosing higher values of n. However, there is also a
sharp decrease in the plate resistance for thicker plates, which
may allow for a gauge to be designed with more elements. The
desired limit of (Rtag/Relement) < 0.1 may be difficult to obtain in
practice for gauges with more than a few elements. Figure 3.25
compares gold and copper as candidates for a plating material,
Although
with the plate and thin-film thicknesses set equal.
copper offers superior performance, the corrosion properties and
stability of gold make it a more attractive candidate for plating.
There is a practical limit on the thickness of plating that may be
allowed. Certainly, a plate thickness of 6000 A is reasonable, with
no significant boundary layer interaction phenomena.
A four-element and a ten-element gauge were designed
Table 3.1 presents the design
meeting all the above criteria.
specifications and the system parameters for both gauges,
allowing for either gold or copper plating. The symbols used are
defined as follows:
1.
2.
3.
4.
5.
6.
8 =
L =
e =
x =
1=
w =
7. tNi =
width of the individual gauge element
length of the individual gauge element
distance between adjacent gauge elements
width of individual tag
total length of gauge
total width of gauge
thickness of thin nickel film
8. tp= thickness of plate material
33.
9. (Pp/PNi) =
10. (RT)cold =
11. (Re)cold =
12. (Rt)cold =
13. (Rt/RT) =
ratio
total
total
total
ratio
of resistivities for plate and nickel
cold gauge resistance
cold resistance of n elements
cold resistance of (n-1) tags
of tag to total resistance
Figure 3.26 shows a scale drawing of the four-element gauge,
while Figure 3.27 depicts the ten-element gauge. The length of
the ten-element gauge is nearly one centimeter, so a spatial map
of the surface of a compressor rotor blade may be provided with a
minimum amount of difficult and complex instrumentation. These
gauges were designed with a stringent requirement that the cold
resistance be no more than 15 2 .
Very different gauge
geometries are possible if the cold resistance of the gauge is
allowed to be hundreds or thousands of ohms. This requirement
is largely one of familiarity, as this is a typical cold resistance
value for a hot wire probe. In addition, with this design, the
resistance decades control on the anemometer can be used
exclusively to set the overheat ratio, thus eliminating the need for
cumbersome homemade control resistors.
CHAPTER 4
DESCRIPTION OF EXPERIMENTAL APPARATUS
AND TEST GAUGES
4.1 EXPERIMENTAL APPARATUS FOR THE SHOCK TUBE
4.1.1
Introduction and principle of operation
The use of a shock tube offers the experimentalist a relatively
simple way to provide a step function in temperature or velocity.
This is useful in measuring the unsteady frequency response of a
wide variety of flow probes, in this case for a thin-film heat
transfer probe.
Unsteady flow probe calibrations are also
provided via the shock tube. A schematic representation of the
GTL shock tube facility is presented in Figure 4.1. This device was
constructed with simplicity of operation as the most important
To this end, it was decided to use over-pressure to
criterion.
burst the diaphragm rather than a complex bursting device. This
has the disadvantage, of course, of not being able to select the
shock Mach number (which is a function of the break pressure)
for a given test.
Oil-free air is supplied from the GTL compressor and is
controlled via a supply valve. A pressure relief valve (50 psi) is
The region to the right of the
provided for safety purposes.
diaphragm (the "driver" side) in Figure 4.1 is pressurized
gradually, to allow for a quasi-equilibrium break of the
diaphragm. At this point, the gauge pressure in the driver side is
recorded. Upon bursting, a shock wave propagates to the left,
into the "driven" side of the shock tube. The action of the shock
wave on the pressure transducers will be described subsequently.
35.
At the moment of rupture, the pressure profile along the length
of the shock tube is a step function.
Figure 4.2 depicts this
configuration, with the moment of rupture arbitrarily called time
zero. This facility has the capacity to allow for an evacuation of
the driven side of the shock tube, to allow for greater pressure
ratios between the driver and driven sides.
This allows for
arbitrary increases in the shock Mach number, since the Mach
number is an increasing function of the break pressure ratio
(p4/Pl). However, for these sets of experiments, this vacuum
scenario was not employed.
Rather, a range of shock Mach
numbers were obtained through the use of different diaphragm
materials, as explained later.
The physical state of the shock tube somewhat after the burst
can best be described with the use of an x-t diagram (see Figure
4.3). All relevant features of the problem can be seen here. At
the far left, the shock wave is seen propagating to the left with
speed c s. To the immediate right of the shock is the contact
surface, which is moving to the left at speed u2 . Physically, the
contact surface represents the discontinuity between the two
fluids of different entropy. At the far left is an expansion wave,
which propagates to the right into the driver side of the shock
tube. The leading expansion wave moves at speed a4 , the speed of
sound in the driver gas at burst. The nomenclature for regions
(1)-(4) in Figure 4.3 is standard for the shock tube and shall be
used extensively here. At the instant in time cited in Figure 4.3,
the pressure and temperature profiles along the shock tube are
presented in Figure 4.4.
The relation between break pressure
ratio and Mach number is derived through standard nonstationary shock relations, with the requirement that the pressure
and the velocity are continuous between regions (2) and (3).
Notice the gradual change of flow properties through the
expansion wave, as compared with the (ideally) discontinuous
change between regions (1) and (2) and (2) and (3).
4.1.2
Data Acquisition and Triggering Mechanism
3G.
Since the data acquisition time is limited to less than 10
milliseconds for this shock tube (as explained presently), a highfrequency triggering device is clearly an important requirement.
High-frequency response static pressure transducers are an
Since the pressure
excellent choice for a triggering mechanism.
increases across a normal shock, as the shock in the shock tube
propagates to the left and reaches the rightmost pressure
transducer, a step increase in pressure is recorded. This step can
be used to trigger a digital oscilloscope to begin recording data
from the thin-film heat transfer probe (see Figure 4.1). The thinfilm heat transfer probe is located between the two pressure
tranducers. By adjusting the time scale on the oscilloscope, the
response of the heat transfer probe to a step in velocity and
temperature can be obtained.
Since the distance between the two pressure transducers is
known, an experimental value for the shock speed can be
obtained by measuring the time delay on the oscilloscope. This
experimental shock speed can then be compared to the shock
speed predicted by knowing the break pressure ratio, which is
also a measured quantity.
This gives an internal consistency
It was found that experimental and predicted shock
check.
speeds agreed very well (typically within 1-2 %), but only if the
break pressure was approached in a quasi-equilibrium fashion.
This is due to the fact that if the pressure is still increasing
significantly while the membrane breaks, a well-defined shock
front is not established by the time the shock has propagated to
the first pressure transducer.
From Figure 4.3, we can see that the data acquisition time is
limited by three different constraints. First, the shock wave may
reflect from the far left wall and pass over the heat transfer gauge
(again). This is called the driven reflection. Second, the contact
surface may pass over the heat transfer gauge as it moves left.
Finally, the expansion wave may reflect off of the far right wall
This is a driver
and may interact with the thin-film gauge.
The maximum data acquisition time for these three
reflection.
constraints is a function of the shock Mach number, and any one
of them may be the important constraint for a given Ms . Plotted
in Figure 2.5 is the maximum data acquisition time as a function
of Ms for the three different constraints mentioned above. It is
seen that the driven reflection is limiting for Ms<1.21, whereas the
contact surface is the constraint for Ms>1.21. This is significant,
because the Mach number range encountered in testing was
Ms=1.07-1.30.
4.1.3
Selection of diaphragm materials
As mentioned previously, to obtain a range of shock Mach
numbers, at least two options are available. The use of vacuum in
the driven side was not used due to the difficulty encountered in
sealing the driven side from small leaks, particularly at the heat
Therefore, another option
transfer probe attachment junction.
was needed to provide a reasonable Mach number range over
which to test the thin-film probes. For a shock tube activated by
over-pressure and not a manual bursting device, the only way to
obtain a variety of Mach numbers is to use different diaphragm
materials.
Many possible candidates for diaphragm materials
were tested.
In particular, four types of Flexel cellophane
products were tested, along with two thicknesses of common
aluminum foil.
Standard aluminum foil, although an attractive
diaphragm candidate due to its low burst pressure, was found not
to break cleanly enough to allow for a well-defined shock wave to
form.
This was determined by examining the shape of the
pressure pulse as it passed the first pressure transducer. A sharp
rise in pressure signals a well-defined shock wave, whereas a
gradual ramp in pressure indicates a shock wave that is getting
steeper and is still being formed.
Having eliminated standard aluminum foil, heavy duty
aluminum foil was tested.
It was found to be an excellent
39.
diaphragm material, with an intermediate average Mach number
(1.21) with very little variance. The four cellophanes tested were
"K"
Flexel products, with the following Flexel catalog numbers:
HB-20, MST, 123 "V" 58P, and 118 "V" 58F. A variety of trials
were made with all five of the candidate diaphragm materials.
Presented in Figure 4.6 is a plot of the mean break pressure for
each of the five diaphragm materials, with one standard deviation
shown. Notice that the most repeatable results are obtained with
heavy duty aluminum foil. This is a Stop 'n' Shop brand name
product, with a thickness of 1.5 mils. Figure 4.7 presents the
same data, except now the more physically relevant parameter of
shock Mach number is plotted rather than break pressure. It is
intended that Figure 4.7 aid future users of the shock tube by
offering a standard database for diaphragm material selection. In
particular, an experimentalist may choose the membrane that
provides the Mach number of interest or may use a variety of
materials to obtain a reasonable Mach number range.
The ultimate proof of concept test for the shock tube comes by
comparing the experimental and the theoretical shock speeds.
The theoretical shock speed is not truly analytical in an absolute
sense because it relies on the measurement of break pressure.
However, by comparing the speed implied by the pressure ratio at
burst with the speed measured between the two pressure
transducers, the degree of applicability of the standard onedimensional shock tube equations can be determined. Figure 4.8
presents the percentage error in theoretical and experimental
shock speeds as a function of Mach number for each shock tube
test run.
No distinction is made between the different heat
transfer gauge conditions utilized, since we are only verifying the
correct operation of the shock tube.
The excellent agreement
between theoretical and experimental shock speeds is clearly
seen.
4.2 EXPERIMENTAL APPARATUS FOR THE SUBSONIC WIND
TUNNEL
39.
The shock tube is an ideal diagnostic tool to obtain the unsteady
response (at least to a step function) of a thin-film heat transfer
gauge. However, it cannot be of assistance in determining the
steady response of one of these probes, nor in obtaining steady
calibrations. The ideal test situation would consist of a subsonic
wind tunnel, with provisions for changing the velocity and total
temperature of the air stream. Such a facility is readily available
and is sketched in Figure 4.9. The test section is split into two
separate sections. Both flow speed and total temperature of the
flow can be controlled, with a Mach number range for the tunnel
from 0.0-0.2 and temperature increase over ambient of up to 40 K
possible (for low speeds). Heating of the flow is accomplished
through resistive (ohmic) power dissipation far upstream of the
test section. The temperature of the airstream was not varied in
the experiments performed here.
Flow speed is readily obtained from the manometer board. The
static and total pressure at the test section are measured in inches
of oil. From Bernoulli's equation, the difference in these two
readings reflects the dynamic head of the system.
The flow
velocity is obtained as follows:
v=
2 po g h sine
Pa
(4.1)
where v is the speed of the flow, po is the density of the oil, h is
the height difference between the two relevant manometer
columns, g is the acceleration due to gravity, 0 is the angle of
inclination of the manometer board, and Pa is the density of the
airstream.
A compressible model is used to reduce the data,
however, as in the future these concepts may be tested on a
steady flow device capable of compressible flow speeds.
4.3 DESCRIPTION OF TEST GAUGES
40.
4.3.1
Probe supports for the thin film gauges
Several probe supports were constructed to allow the thin-film
gauges to be used in the shock tube. A flush-mounting system is
used with these gauges, to give minimum disturbance to the flow
Bonding is accomplished through standard
field of interest.
Both single-layer and doublestrain-gauge bonding techniques.
layer gauges were tested. A double-layer gauge consists of a top
thin-film resistor called the sensor, an insulating layer of kapton,
Figure 4.10
and a bottom thin-film resistor called the heater.
shows a schematic of the single-layer gauge used in shock tube
testing. The radius of curvature rc of the right end of the probe
support was machined to match the radius of the inner wall of the
shock tube (for flush-mounting). An external BNC plug was used
for ease of electrical connection with the anemometer units. The
probe support was constructed of brass for its desirable thermal
and electrical properties.
Additionally, a gauge support
constructed of anodized aluminum was used for the final set of
tests.
It was desired to have the same material supporting the
gauge, and hence the same thermal properties, as for the flat plate
probe support.
Figure 4.11 depicts the gauge support for the
double-layer gauge. Clearly, four leads are now necessary for the
circuitry. An aluminum minibox was used (far left) to facilitate
For both types of probe supports, the
two BNC connectors.
external groove was filled with epoxy to strain-relieve the leads
attached to the gauge itself.
The flat plate probe support sketched in the tunnel in Figure
4.9 is shown in detail in Figure 4.12, to scale. The thickness of
the anodized aluminum plate is 32 mils. The four square tags in
each corner of the flat plate each are equipped with a centered
0.25 inch diameter hole. This is for ease of mounting in the
subsonic tunnel as well as for providing a non-critical point of
attachment during the anodizing process. As for the shock tube,
standard strain-gauge bonding techniques are used to mount the
heat transfer gauge to the flat plate. The leads are strain-relieved
41.
via a connection to the underside of the plate to a kapton
soldering terminal. External connectors then connect the soldering
terminals to BNC cables. The location of the gauge on the flat plate
was dictated by boundary layer considerations. It was discovered
that there was a way to obtain both laminar and turbulent flow
depending on whether the flow came from the left or from the
right (as seen in Figure 4.12).
To assure a well-behaved boundary layer on the flat plate, the
leading edge was smoothed to give an approximately elliptic
profile, with the requirements that it be symmetric, blunt at the
leading edge, and have a major to minor axis ratio of the ellipse of
at least five. Shown in Figure 4.13 is a 3D sketch of the leading
edge approximately elliptical geometry.
Naturally, this profile
was produced on the other side of the flat plate (the side not
drawn, downstream in Figure 4.13) since it is meant to be
interchangeable.
The turbulent flow configuration is shown in
Figure 4.13.
If the flow direction were from the right, this
diagram would represent the laminar flow configuration. Without
this leading edge profile tailoring, the boundary layer will differ
substantially from a simplistic model, due to the discontinuity in
slope at the leading edge.
4.3.2 The calibration of a
Before a heat transfer probe may be tested in the shock tube,
the thermal coefficient of resistivity (a) of each thin film element
must be calibrated.
For sensors provided by a manufacturer (a
single sensor from DISA, in this case), the a is calibrated at the
company and its value is provided. Otherwise, a calibration must
be performed by the experimentalist. This would not be so except
for the fact that the thermal coefficient of resistivity of a material
is substantially different from the bulk value as the thickness of
the material decreases. In particular, for the sensors tested here,
the
value of a obtained from calibration is between two and
eight times smaller than the bulk value for pure nickel.
4'.
A facility is available for the calibration of a for these devices.
It consists of a well-insulated temperature bath accurate to 0.1 K,
with operator temperature control. The bath fluid is Fluorinert, a
non-reacting liquid with well-known thermal properties and
Initial attempts at calibration in distilled water were
stability.
unsuccessful, demonstrating that the distilled water sample was
more ionic than expected. The calibration procedure is simply to
measure the resistance of the thin-film gauge as a function of bath
temperature while the thin-film is completely immersed in the
fluid. The thin film must be tested after being mounted to the
probe support, as the bonding process might change the value of
a. From Equation (2.1), it is expected that the data from such a
Therefore, once the
calibration would fall on a straight line.
experimental points were obtained, a linear regression procedure
was used to determine the best fit line for resistance vs.
temperature.
Figure 4.14 presents such a calibration for a thin
nickel film with thickness 2600 A. This thin film was used as a
heater with a DISA single sensor, model number 55R47 providing
Figures 4.15-4.18 show
a homemade double-layer probe.
calibrations for ready-made double-layered probes, one mounted
on a brass support and the other mounted on an anodized
Notice that the heater and sensor must be
aluminum support.
calibrated separately, and in fact that the value of a is
substantially different between the heater and the sensor for each
case. This is not surprising, as the heater and sensor for a given
gauge are constructed separately by a vacuum sputtering
technique. In all cases, the data fits a straight line relatively well.
The approximately parabolic shape of the data points in Figure
4.17 represents a non-equilibrium heating process. This usually
may be avoided by carefully stabilizing the bath temperature
before taking a resistance measurement.
Unlike the shock tube, the only experiments performed in the
subsonic tunnel facility were experiments using _double-layer
gauges with the heater and sensor temperatures actively
43.
Ready-made, turbine heat transfer
controlled to be identical.
gauges were employed exclusively, due to their proven technology
and their availability. As for the shock tube, TSI anemometer
units were used to control the gauge sensor and heater at constant
temperature. The sensor and the heater were calibrated, after flat
plate mounting, in the Fluorinert temperature bath described
The calibrations for the first flat plate gauge are
previously.
presented in Figures 4.19 and 4.20, while those for the second flat
plate gauge are presented in Figures 4.21 and 4.22. In Figure 4.21
particularly, notice again the slight parabolic nature of the data
points, due to non-equilibrium heating of the gauge in the
temperature bath. As it will be demonstrated later, the largest
error source encountered in the subsonic wind tunnel experiments
is due to calibration errors for the coefficient of thermal
resistivity for the heater and the sensor. Tests would have been
performed exclusively on the the first flat plate gauge, but a
sensor failure lead to the construction of the replacement gauge.
4.3.3
Feasibility of balancing non-standard resistors
The anemometer units from TSI are typically used to balance
probes in a resistance range of 5-50 ohms. The so-called turbine
gauges typically have a cold resistance of between 500 and 1000
ohms for both the sensor and the heater.
When these gauges
were used in the MIT Blowdown Turbine Facility, homemade
bridge balance units specifically designed for these large gauge
resistances were employed.
According to the manufacturer, no
data exists on the ability of TSI anemometer units to balance
gauges in the centi-ohm to kilo-ohm range.
Figure 4.23
represents the data from a simple test to determine if these
anemometers can be used for this non-standard application. The
anemometer output voltage is plotted as a function of the sensor
cold resistance, holding the control (hot) resistance constant at
522.4 ohms. All three anemometer bridges (each one is a 5:1
bridge, with different current levels) were tested.
Since
saturation for these anemometers occurs at an output voltage of
44.
approximately 22.6 volts, the sensitivity to overheat ratio is seen
to be represented. However, due to the large values of the sensor
output voltage, a forced flow over a gauge with this resistance
may cause saturation (these tests were performed at zero flow).
No saturation occurred in any of the actual heat flux
Figure 4.24 represents a similar test,
measurements performed.
with now the cold resistance held constant and the overheat ratio
varied. Plotted is the output voltage vs. overheat ratio for a cold
resistance of 1510 ohms. There appears to be a tradeoff between
sensitivity and possible saturation for the different bridges.
Bridge #1, the standard bridge for most anemometry work, offers
the best sensitivity but may saturate at high flow velocities. This
bridge was used exclusively with no saturation occurring. Notice,
however, that the curve for bridge #1 is incomplete. At higher
overheat ratios, it became impossible to set the standby voltage of
the anemometer within the desired range of 2-5 volts for this
bridge.
One possible test of a double-layer gauge consists of running the
heater actively in a control loop and allowing the sensor to be
passive. In this case, it is expected that the temperature of the
sensor would rise until it approximately equalled the temperature
of the heater (in zero flow). Since resistance is a known function
of temperature for the sensor, if we measure the resistance of the
sensor in this configuration, we can calculate the implied
temperature of the sensor. Plotted in Figure 4.25 is the sensor
temperature vs. the heater temperature for such a test, with both
temperatures being non-dimensionalized by the ambient
Bridge #1
Again, all three bridges were tested.
temperature.
offers superior performance, as the expected curve is a line of
slope one through the origin and the curve for bridge #1 closely
approximates this. Bridge #3 is not acceptable, because with low
overheat ratios for the heater, the sensor temperature is too large.
Notice that beyond a heater to ambient temperature ratio of 1.11,
the sensor temperature remains roughly constant. It appears that
increasing the heater temperature beyond this point only
4•5.
increases the heat conduction into the probe support.
This
therefore may provide a limit on the overheat ratio that can be
employed. Figure 4.26 shows the voltage output for a doublelayer gauge operated so that Ts=Th versus the sensor overheat
ratio. To an overheat ratio of 1.08, the voltage value for this
heater-controlled gauge is sensitive to overheat ratio (again, for
zero flow). This does represent a much lower overheat than is
typically run for a hot-film probe (generally, ar=1. 4 -1.5 in air). At
higher overheat ratios, the voltage value for the double- layer
gauge will certainly saturate, at least for these high cold resistance
Therefore, overheat ratios were limited somewhat
gauges.
This may have affected the
severely in the tests performed.
results adversely, because over the overheat ratio range tested
here, higher overheat ratios generally provided better results
than lower ones.
G'1
CHAPTER 5
DATA REDUCTION AND ERROR ANALYSIS
5.1 DATA REDUCTION FOR THE SHOCK TUBE
A simplistic quasi-steady model for the heat transfer effects of
a propagating shock were examined in this study. It was assumed
in this scenario that an ideal, non-separating turbulent Blasius
boundary layer grew in thickness at the gauge location following
The Reynolds number for this
the passage of the shock.
configuration can be written as follows:
Re =
Rm (cst)
(5.1)
where 4 m is the mass flux in the shock tube, g is the viscosity of
the air, cs is the shock speed and t is the time since shock passage.
The quantity (ct) replaces the characteristic length in the
Reynolds number equation.
By examining the heat transfer
coefficient h, the effect of the propagating shock on the convective
heat transfer can be determined. In general:
Re0.8
Rex
h
x-0. 2
(5.2)
but, since x= cst:
h
1
t 1/5
(5.3)
Therefore, as the shock propagates away from the heat transfer
gauge, the value of h (and hence qconv and VO) decrease after an
initial infinite spike. In particular, since the output voltage scales
as the square root of the convected heat transfer, for a zero
conduction case:
1
Vo - tl/10
(5.4)
showing that the decay in voltage with time following shock
passage should be very slight.
The output voltage as a function of time shall be derived for the
case of no substrate heat conduction. The case of constant heat
conduction can be treated similarly.
The impedance of any
resistive element is a function of geometry and a material
property known as the resistivity. In particular, the resistivity of
a material divided by its thickness gives a quantity called the
ohms/square, denoted here by a. For a resistor of length L and
width W, the resistance can be expressed as follows:
R=
=aI
(5.5)
The measurement of the thickness or the resistivity of the thinfilm gauge is not a trivial process. As for the thermal coefficient
of resistivity, the resistivity of a thin-film material is a strong
function of the thickness of the material. However, this presents
no difficulty since the thickness and resistivity of the thin-film
material appear only in the form of a, and a is readily calculated
by dividing the measured resistance of the gauge by the length to
width ratio.
It can be shown [Blackwelder] that the voltage output from a
hot-wire or hot-film anemometer can be written as follows:
VO =
1+
s)
48.
Rscon
S
(5.6)
for a case with no heat conduction (again, this is just a power
balance). The parameter S is the area over which heat transfer
takes place. The bridge ratio (R1/R s ) is five in all cases tested.
Notice that Rs is the hot resistance of the gauge sensor. Combining
(5.5) with (5.6) and the definition of h, with the realization that S=
LW:
V0 = L I + R"
arsa h [T s - T]
(5.7)
Therefore, the voltage output per unit length of sensor is
independent of the surface geometry of the sensor, as is expected.
The heat transfer coefficient h can be expressed:
h = 0.0296 Pr1 / 3 kf LTf)08 (cst)-0. 2 (Ts - T)
(5.8)
where Tf is the film temperature as before and T is the fluid
temperature (before or after the shock, as the case may be).
Combining (5.7) and (5.8) gives the basic quasi-steady voltage
output relation:
Vo=L 1 + R
arsG[Ts - T]0.0296 Pr 1/ 3 kf
(Tf)
(ct)-02
(5.9)
This has the correct scaling, in agreement with (5.4). All shock
tube runs utilizing a zero conduction condition were analyzed with
(5.9), with an arbitrary time being chosen after the shock passage
to compare the change in the voltage output observed
This result is affected by
experimentally at that same time.
conduction into the substrate, which occurs when the heater is not
The unsteady
controlled to match the sensor temperature.
41.
modelling of this problem is presented later, with a companion
equation to (4.26) derived for these sets of shock tube runs.
5.2 DATA REDUCTION FOR THE SUBSONIC WIND TUNNEL
The problem that is needed to be solved in general is to
calculate the skin friction in a given flow when the velocity of the
stream (or mass flux, in compressible flow) and the total
temperature of the stream are unknown. This clearly represents
the situation of interest in a modern transonic compressor.
A
calculation procedure based on steady flow is proposed here.
Therefore, the validity of the analytical model can be ascertained
by examining the true skin friction in a nominally steady flow and
comparing it to the skin friction predicted by the model. Indeed,
that is what has been done in the steady testing performed. The
analytical model for predicting the skin friction is derived in this
section. For all heat transfer modelling presented here, steady,
quasi-steady, or unsteady, the heat transfer process of radiation
was ignored because the emissivity of pure nickel is extremely
low (eNi= 0.03). In addition, the fourth power dependance of the
radiative heat transfer on temperature allows the radiation to be
ignored, since low overheat ratios were used throughout testing.
The Nusselt number is a non-dimensional heat transfer
coefficient useful for demonstrating heat transfer correlations.
It
can be shown [Incropera and DeWitt] that the Nusselt number, for
a flat plate in parallel flow with an unheated starting length, can
be correlated as follows:
Nu x =
(5.10)
where Nux is the Nusselt number at a given streamwise location,
Nug is the Nusselt number at the leading edge of the flat plate, x'
is the distance from the leading edge to the heated location (the
50.
thin-film gauge, in this case), x is the streamwise coordinate, and
m and m2 are, respectively, 3/4 and 1/3 for laminar flow and
9/10 and 1/9 for turbulent flow. To obtain the average Nusselt
numbers over the region of interest, these expressions would have
to be numerically integrated, for
(5.11)
I x m (a + bxn)p dx
is only solvable when p is an integer, (m+l)/n is an integer, or p +
(m+l)/ n is an integer. However, for the situation of interest here,
a good approximation to the integral can be obtained by
expanding the integrand in a Taylor series and retaining the first
few terms only. This is possible because the width of the gauge
(Ax) is small compared to the length from the flat plate leading
edge to the gauge (x'). By performing the above mentioned Taylor
series expansion, the following expressions are obtained for the
average Nusselt numbers across the gauge width:
Nul =
Nu
t
Nu-=
3al
1/3
x'
)
1/ 3
x
9a9 ('101/9 (x'
(5.12)
(5.12)
1/ 9
A
8
(5.13)
where equations (5.13) and (5.14) represent the laminar and
turbulent subcases, respectively, and the coefficients al and at are
defined as follows:
a, = 0.332 Pr1/3 Rex,1/2
at = 0.0296 Pr1/3 Rex,4/5
(5.14)
(5.15)
with Pr representing the Prandtl number for air (0.72) and Rex,
denoting the Reynolds number based on the unheated starting
length.
51.
To obtain the skin friction, the modified form of Reynold's
analogy is employed:
Cf = 2 St Pr 2/ 3
(5.16)
where Cf is the skin friction and St is the Stanton number, another
non-dimensional heat transfer coefficient defined as follows:
St
Nu
PrRe
Pr-Re
(5.17)
To relate the heat transfer coefficients to the sensor voltage, a
power balance must be performed. In general, the heat lost to
convection and conduction is balanced by the power input to the
sensor, or equivalently:
=
V
k (Ts - Th) + qconv
(5.18)
where the first term on the right is the conduction and the term
In this
on the left is the power dissipated in the sensor.
expression, ks is the thermal conductivity of the substrate, 8s is
the thickness of the substrate, Ts is the controlled temperature of
the sensor, Th is the controlled temperature of the heater, VO is
the output voltage of the sensor, and Rs is the controlled (hot)
resistance of the sensor. In general, the convection cannot be
explicitly calculated from this expression, due to the fact that
temperature at the substrate/support bonding site is unknown.
For a heater passive case, it may be calculated by measuring the
resistance of the heater. If the sensor and heater are controlled to
be at an identical temperature, however, the steady conduction
term goes to zero and the convection can be calculated since the
voltage output and hot resistance of the sensor are known. The
convection can be related to heat transfer coefficients as follows:
52..
qconv = h [Ts - Pr 1/ 3 Tt]
(5.19)
where Tt is the unknown total temperature of the airstream and h
is the heat transfer coefficient, which may be calculated as
follows:
hx =
Nu, kf
f
x
(5.20)
The only
where kf is the thermal conductivity of the fluid.
fundamental unknowns in equations (5.10) and (5.12) to (5.20)
are the total temperature of the airstream Tt and the mass flux of
the airstream p v, which appears in the expression for the
Reynolds number as follows:
pv x'
Rex' =(Tf)
(5.21)
where pg(Tf) is the viscosity calculated at the film temperature Tf,
defined as the average of Ts and Tt.
The procedure used to predict the skin friction is as follows:
1.
Select an overheat ratio and calculate the sensor
temperature from eq. (2.1).
2.
Balance the anemometer so that no heat ideally is
conducted through the kapton substrate (i.e., set Ts= Th using the
In actuality, this alignment process is
control resistors).
approximate only.
Measure the output voltage in a given total
3.
temperature and mass flux.
4. Calculate the convected heat transfer from eq. (5.19).
5. Combine equations (5.19), (5.20), (5.21), (5.10), (5.12)
or (5.13), and (5.14) or (5.15) to obtain one equation for the two
unknowns Tt and pv, utilizing (5.12) and (5.14) for laminar flow
and (5.13) and (5.15) for turbulent flow.
53.
6. At the same flow conditions, choose another overheat
ratio and repeat steps (2)- (5).
This will give two equations in the two unknowns Tt and pv,
which may be solved numerically. It is imperative that different
overheat ratios be run for the two trials, or the same equation will
be produced from steps (2) to (5). Once the total temperature and
the mass flux of the stream are known, the skin friction can be
calculated as follows:
Cf =
2 Pr 2 / 3 h
(5.22)
pv CP
where Cp is the specific heat of the flow in question. Assuming
the boundary layer is well-behaved, the theoretical skin friction
can be calculated from the same formula, with the true total
temperature and mass flux replacing the calculated Tt and p v. In
particular, it may be shown that the experimental to actual skin
friction ratio may be calculated as follows:
(Cf)e
(pv)
~
(Cf)a L(pv)aJ
+ (Tt)a 3(m-1)/2
Ts + (Tt)eJ
Ts+ T' +(Tt)e m
T + T' + (Tt)aJ
(5.23)
where the subscript e denotes experimental, the subscript a
denotes actual, T' is a constant (221.2 K), and m is 0.8 or 0.5,
depending on whether or not the flow is turbulent or laminar,
respectively. It is through the use of equation (4.14) that the
graphs of subsequent chapters were prepared.
5.3 ERROR ANALYSIS
Many possible sources of error exist that will cause a
discrepancy between the theoretical and experimental values of
skin friction.
A standard error analysis was performed to
investigate the relative importance of the error terms to the
54.
calculation of the skin friction ratio. For a typical test case, the
most important error-producing sources are the thermal
coefficients of resistivity of the sensor and the heater (as and ah,
This is not due to the inherent error encountered
respectively).
when attempting to calibrate the value of a, but is due rather to
the very large coefficient multiplying a that occurs in the error
analysis. The next most important source of error comes from the
drift of the sensor or heater cold resistance or the error
encountered when setting the overheat ratio. The output voltage
measurements represent the next most important source of error.
All other errors, including those due to Prandtl number (Pr),
distance from leading edge of flat plate to the gauge location (x),
angle of inclination of the manometer board (0), width of gauge
(Ax), ambient pressure (PO), total pressure (Pt), and ambient
temperature (TO) are negligible. This is depicted graphically in
Figure 5.1, for a typical case of turbulent flow, arsl= 1.04, and
ars -2=1.08. This has important ramifications for the thin-film heat
transfer gauge designer. The calculation of a is seen to be one of
the most critical steps in the entire skin friction measurement
process. Since the coefficient of the a error term cannot be
altered significantly, the only way to lower this error source is to
reduce the error in a itself during the calibration procedure.
The error analysis proceeds as follows: for a given measured
quantity
which is a function of the n variables al, a2 , a3 , ..., a.
such that ai is independent of aj when i,j= 1 to n and i and j are
not equal, the error in 0 can be calculated from the chain rule to
be as follows:
*,
Ilr-
Amd
i=l ýaai
55.
w
ai
(5.24)
This is a classic Gaussian distribution on the possible error sources
For this case, equation (5.23) was used to
in the problem.
function, with the ratio of experimental to actual
describe the
skin friction being *. The error terms evaluated were a s and ah,
V 1 and V2, Rcs 1, Rcs2, Rch1, and Rch2, Pr, 0, Ax, x', T t , Pt, and P0 . By
far the most influential of the error terms evaluated above are the
This may be explained by
coefficients of thermal resistivity.
looking at the how the coefficient of the a error term scales in this
with respect to
error analysis. It was found that the variation in
a is directly proportional to the variation in Tg with respect to a:
*
*
(5.25)
Sa1
However, the variation of Tg with respect to a can be readily
calculated:
TT
=
-da ra]
1
+ T
TrO = -
I1
aaar"
2
(5.26)
Even for low overheats, this quantity is large due to the fact that
the value of a is small and a appears to the negative two power.
This mandates a very careful calibration for the value of a, for the
only way to reduce the error due to a in (5.24) is to reduce the
variation in a divided by a term. The accuracy in calculating a, i.e.
-- , is assumed to be 5%.
the order of 30-35%.
The total error term for as or ah is on
The reason that the gas temperature or the wall to gas
temperature ratio is not included in the error analysis is because
it is not independent of the fifteen variables selected above.
Indeed, it is desired to know the error associated with the drift of
A
the tunnel temperature, which could be as much as 5 K.
standard error analysis shows that the effect may indeed be
found to 5.5% and 22 % for
substantial, with the error in
*
56.
turbulent and laminar flows, respectively, for a low overheat ratio
of around 1.04. It is also seen that the error increases as the wall
to gas temperature ratio approaches one , as is expected.
Experiments need to be performed with various gas temperatures
and wall temperatures to discover how the experimental error
scales with the wall to gas temperature ratio. In these sets of
tests, only the wall temperature was varied, and the experimental
errors observed were indeed more substantial for lower wall to
gas temperature ratios (lower overheats).
5q .
CHAPTER 6
EXPERIMENTAL DATA AND COMPARISON OF DATA
WITH THEORY
6.1 SHOCK TUBE EXPERIMENTAL RESULTS
Ten separate shock tube runs were performed.
that characterized these runs are listed below:
The parameters
Run #1:
Shock tube familiarity testing; no heat transfer data
recorded; heavy duty aluminum foil diaphragms only; brass
support
Run #2: Shock tube familiarity testing; no heat transfer data
recorded; heavy duty aluminum foil diaphragms only; brass
support
Run #3:
Range of diaphragm materials testing:
standard
aluminum foil, heavy duty aluminum foil, and 118 "V" 58F
cellophane; no heat transfer data recorded; brass support
Run #4: Single DISA sensor testing; heat transfer data recorded;
brass support; ars= 1.23
Run #5: Double-layer gauge testing; DISA sensor; DISA heater;
heater passive; heat transfer data recorded; brass support; ars=
1.20
Run #6: Double-layer gauge testing; DISA sensor; 2600 A nickel
thin-film heater; heater passive; heat transfer data recorded;
brass support; ars= 1.20
58.
Run #7: Double-layer gauge testing; DISA sensor; 2600 A nickel
thin-film heater; heater active; Ts=Th; heat transfer data recorded;
brass support; ars= 1.20
Double-layer gauge testing; turbine gauges; heater
Run #8:
heat transfer data recorded; anodized aluminum
active; Ts=Th;
support; ars= 1.06
Double-layer gauge testing; turbine gauges; heater
Run #9:
active; Ts=Th; heat transfer data recorded; anodized aluminum
support; ars= 1.08
Double-layer gauge testing; turbine gauges; heater
Run #10:
active; Ts=Th; heat transfer data recorded; anodized aluminum
support; ars= 1.11
Tables C.1 through C.10 represent these ten shock tube runs,
Each of these tables provide
presented in Appendix C.
supplementary information to the heat transfer plots that shall
The turbine gauges mentioned above are
appear presently.
readily available, double-layer heat flux gauges that are so
labelled for their extensive application in the MIT Blowdown
Turbine Facility.
Figures 6.1-6.6 and Figures D.1-D.15 represent the unsteady
voltage trace from the gauge sensor as a function of time for runs
#4-#10 above. The point of zero time represents the interaction
As mentioned
of the shock with the first pressure transducer.
previously, the sensor voltage is expected to rise as the shock
passes the heat transfer gauge, since heat is now being
Indeed, this is
transferred downstream by forced convection.
observed in nearly every voltage trace.
Figures 6.1-6.3 represent the six data points taken during Run
#4. The voltage (and hence heat transfer) closely approximates a
5"0.
step.
After shock passage, the voltage level remains roughly
constant, in contrast with later runs. The voltage jump across the
shock increases with shock Mach number, as expected..
Figures 6.4-6.6 are the voltage traces for Run #5. Again, the
The
voltage traces generally reflect the classic step response.
highest Mach number traces, in Figure 3.14, exhibit a gradual rise
in voltage after the passage of the shock. All traces exhibit a
greater voltage discontinuity for higher Mach numbers, as before.
The second trace in Figure 6.5 unfortunately has been shifted on
the time axis, so time zero no longer corresponds to the passage of
the shock by the first pressure transducer.
Comparing traces in
Run #5 vs. Run # 4 demonstrates that, for a given Mach number,
the voltage jump is less for the lower overheat ratio case. Again ,
this is predicted by theory. Appendix D contains the remaining
voltage traces and their description, representing Runs #6-10.
6.2 SUBSONIC WIND TUNNEL PROOF OF CONCEPT TESTING AND
EXPERIMENTAL RESULTS:
The use of the subsonic wind tunnel facility has been
demonstrated in various experiments since its completion.
A
well-defined steady flow is assumed to be provided, with
reasonable flow calibrations having been performed for previous
experiments to verify the operation of the infra-red camera and
the manometer board for measuring flow temperature and
velocity, respectively.
No independent sensing devices were
employed in these experiments to verify the accuracy of the
pressure probes in the test section and the manometer board.
The ambient temperature during subsonic tunnel testing
maintained a constant value of 300 K, with less than 1 K variation.
However, the temperature of the tunnel was not recorded during
testing. To verify the sensitivity of the gauge to velocity (or mass
flux), a calibration curve is needed. Figures 6.7-6.10 represent
the voltage across the sensor and the heater for laminar and
40.
turbulent flow as a function of the mass flux for the overheat
ratios ars= 1.02, 1.04, 1.06, and 1.08. Due to the scale of these
plots, they do not truly represent a calibration curve. On a much
more expanded voltage scale, these would resemble classic hotfilm calibration curves. Notice the increase in voltage level as a
function of the overheat ratio, as is predicted by theory. These
plots basically confirm that the anemometer is operating
favorably under these atypical large gauge resistance conditions.
The sensor curves are more sensitive to mass flux at lower mass
flux values, as is expected from the approximately one-quarter
power relation between voltage and mass flux.
6.3 SHOCK TUBE COMPARISON OF THEORY AND EXPERIMENT
Figure 6.11 shows a comparison of the theoretical and
experimental voltage output for a single sensor at an overheat
This
ratio of 1.23 as a function of Mach number [Run #4].
represents a test for the analytical model employed. It is seen
that the analytical model predicts the output voltage very well,
including the trend with Mach number. As the two widely spaced
data points at Ms= 1.21 indicate, the error on the output voltage
may well encompass the theoretical curve comfortably. To define
a voltage after the shock in each trace, an arbitrary time is agreed
upon after the shock passage to take the data. In this case, that
time difference is 0.2 ms.
For Run #5, which is a double-layer gauge with the heater not
controlled (passive), Figure 6.12 shows the output voltage versus
Mach number for the experimental data and the analytical model.
In this case, the analytical model does a reasonably good job of
predicting the level of the voltage change, except that the trend
with Mach number is reversed. As before, the time delay is 0.2
ms for the measurement of the voltage change. For Run #6, the
equivalent plot is presented in Figure 6.13. The analytical model
in this scenario represents an unsteady heat conduction model.
61.
The fact that the experimental points remain roughly constant
with Mach number suggests that a thermal equilibrium is being
set up, with unmodelled heat transfer processes driving the
phenomenon. With a steady, no conduction model, the theoretical
curve in Figure 6.13 would appear roughly constant, but at a level
over twice the experimental values.
If all unsteady heat
processes could be properly modelled, a theoretical curve would
predict the experimental data points to a much higher degree of
accuracy. However, the decrease in sensor voltage change with
Mach number would still not be expected, even in that scenario.
As before, the voltage after the shock was recorded at 0.2 ms.
For Run #7, which is identical to Run #6 except for the fact that
the heater is now controlled so that there is no steady-state
conduction into the substrate, Figure 6.14 offers the comparison
between theory and experiment for the voltage output as a
function of Ms . Although the trend with Mach number is again
reversed, the voltage levels between the theoretical and
experimental curves are reasonably similar. Hence, in this case,
the use of an actively controlled heater has allowed for a better
prediction of the experimental voltage output.
This is
demonstrated more strikingly in Figure 6.15, which gives the
percentage error in voltage change across the shock (theoretical
vs. experimental) as a function of Mach number for both the
heater passive and heater active cases [Run #6 and Run #7,
respectively].
The heater active case predicts the experimental
voltage output far better than the heater passive case. Data is
recorded after the shock passage at a time difference of 0.2 ms.
Figures 6.16-6.18 represent the runs #8-#10, respectively, with
the time after shock passage when voltage data was recorded
being 0.8 ms.
Figures 6.19-6.21 represent the runs #8-#10,
respectively, with the time after shock passage when voltage was
recorded being 1.27 ms. The extreme disagreement between the
theoretical and the experimental values as compared with
42.
previous runs can be observed. Clearly, the large voltage dips
present account for some of the discrepancy, but not nearly
enough to explain the much larger theoretical prediction for the
voltage output. Notice that the results are improved somewhat
for the 1.27 ms case. It is postulated that the reason for the large
discrepancy in both cases may be due to a non-standard operation
of the anemometer unit.
As mentioned previously, there may exist two possible drivers
for the large voltage dips seen following shock passage; namely,
separation of the boundary layer or an unmodelled heat transfer
process. By examining a greatly expanded trace of the pressure
pulse recorded by the first pressure transducer after a shock
passage, it may be possible to estimate whether or not the
boundary layer has separated. Figure 6.22 shows such a pressure
pulse. If the boundary layer were not separated, a smooth rise in
pressure would be seen, even at this time scale magnification.
However, the existence of an inflection point (even a small
horizontal region) around a time of 0.03 ms suggests the
possibility that the boundary layer is indeed separating. More
extensive tests would need to be performed to see what the true
state of the boundary layer is at the heat transfer gauge location.
The severity of the voltage dip is an increasing function of the
shock Mach number and a decreasing function of the overheat
ratio (or physically the temperature of the sensor). The increase
in the voltage dip with increasing shock Mach number is perfectly
consistent with a separation model. The decrease of the size of
the voltage dip with increasing sensor temperature cannot be
explained with a simple separation model, so some unmodelled
heat transfer effect must be dominate in this instance.
6.4 SUBSONIC WIND TUNNEL COMPARISON OF THEORY AND
EXPERIMENT
Presented in Figures 6.23 and 6.24 are the experimental to
theoretical skin friction values as a function of the measured mass
,3.
flux. Ideally, all curves should fall on a horizontal line of value
one. For each mass flux, four overheat ratios were run, for both
laminar and turbulent flow. By using any two overheat ratios and
the measured sensor output voltages, the experimental skin
friction can be obtained. The trends seen in Figure 6.23 and 6.24
are clear:
(1) results are better for higher overheat ratio
combinations; (2) results are better for two overheat ratios that
are not adjacent (i.e, 1.02 and 1.04, 1.04 and 1.06, and 1.06 and
1.08); (3) theoretical skin friction tends to overpredict the
experimental value at low mass flux values and underpredict the
value at higher mass fluxes; and (4) turbulent results are better
than laminar, consistent with error analysis predictions.
Figures
6.25 and 6.26 graph the actual values of the theoretical and
experimental skin friction as a function of the test section Mach
number, a more useful parameter for scaling. Similar to the shock
tube, it may be said that the theoretical curve is overpredicting
the change due to Mach number.
Figures 6.27-6.32 show the theoretical to experimental skin
friction ratio as a function of mass flux, with calculated error bars
on each data point. Basically, Figures 6.23 and 6.24 represent a
composite of all of the curves in Figures 6.27-6.32, albeit without
the error bars. A composite curve was not utilized here for the
sake of clarity.
The laminar error bars consistently extend
beyond the boundaries of the graph, comfortably enclosing the
expected output curve. It should be mentioned, though, that the
largest error bars occur for the case of laminar flow, ars l= 1.04,
and ars2 = 1. 0 6 , which represents the largest experimental
deviation as well (see Figure 6.30).
Turbulent error bars are
much smaller, and typically do encompass the predicted line
except at the lowest overheat ratios. The laminar error bars are
much larger than the turbulent ones due to the fact that the
exponent in heat transfer/boundary layer correlations for.. laminar
flow is 0.5, while it is 0.8 for turbulent flow. It is seen that the
use of the double-layer heat transfer gauge with Ts=T h does a
(0+.
reasonable job of predicting the experimental skin friction values
in a steady flow of unknown mass flux and total temperature.
Whether or not the agreement will hold in an unsteady flow
situation remains to be seen.
(5.
CHAPTER 7
CONCLUSIONS AND RECOMMENDATIONS FOR
FURTHER STUDY
An experimental feasibility study for a new mode of operation
In
for a double-layer heat transfer gauge has been performed.
particular, three operating modes were tested:
a single-sensor
mode, a heater-passive mode, and a heater-active mode.
Experiments were performed to verify predicted models of gauge
output in these modes for both unsteady and steady flow.
Unsteady flow results were generally in good agreement with
the analytical model, except that the model tended to overpredict
the change in output due to Mach number. In addition, unsteady
flow results for the anodized aluminum support were
substantially different than those predicted by theory. The model
correctly predicted the observed increase in voltage jump for an
increase in the overheat ratio. Voltage dips following the passage
of the shock in the shock tube were observed, and may be
explained by a local separation of the boundary layer coupled
with unmodelled heat transfer effects.
An expanded view of a
typical pressure profile during shock passage demonstrates that
separation is probably present.
The magnitude of the dip in
voltage increased with increasing shock Mach number and
decreased with increasing sensor temperature.
It is found that
the agreement between theory and experiment for all modes
tested is better for higher overheat ratios than for lower ones. For
a fixed overheat ratio and Mach number, the heater-active
experimental output of the double-layer sensor was found to be
better predicted than the heater-passive experimental output,
showing some justification for the concept of a controlled heater.
It was found that the calibration of a, the coefficient of thermal
6G.
resistivity, and the accuracy of setting the operating resistance of
a gauge are important to realize the heater-active mode, for small
differences in the heater and sensor temperature can adversely
effect the sensitivity of the gauge. In addition, the use of TSI
anemometers on non-standard centi-ohm and kilo-ohm probes
has been demonstrated via anemometer testing.
Steady-state experimental results attest to the ability of the
heater-controlled multi-layer heat flux gauge to be used as a skin
friction measurement device in a flow of unknown mass flux and
In particular, for the varieties of overheat
total temperature.
ratios, mass fluxes, and flow types (laminar, attached and
turbulent, attached) tested here, the experimental and theoretical
skin friction values were in agreement within the accuracy of the
Again, the
measurement, except at the lowest overheat ratios.
analytical model overpredicted the effect of the Mach number.
The theoretical value of the skin friction is obtained via a
simplified assumption about the velocity boundary layer over the
gauge and the thermal boundary layer incident at the gauge,
increasing downstream of the gauge. It was noted that the largest
errors occurred during the flow situation which allowed for the
largest error bars. Turbulent results were generally better than
laminar ones, consistent also with the error analysis. Larger gaps
between the two overheat ratios used to experimentally calculate
the skin friction offered better results, as did higher overheat
ratios in general.
Again, this is in agreement with the error
analysis. The calibration of the thermal coefficients of resistivity
of the heater and sensor is the major source of error in the steady
experiments, due to the large coefficient on the error term
corresponding to a (it is not due to the inherent error in
calculating a itself).
A simplistic steady model of the
substrate by assuming that the gauge
conductor is not adequate. For a case
it is run passively, an unsteady model
'1.
heat conduction into the
support is a good thermal
where there is no heater or
was developed to estimate
the conduction into the substrate as a function of time. This
model predicts the sensor output voltage far more accurately than
a simplified steady model.
A new gauge was designed to meet the criteria previously
mentioned, specifically suited for use on a transonic compressor
rotor blade. It was found that a serpentine gauge is preferable to
a ladder gauge for sensitivity. The shock wave/boundary layer
"smear" was calculated to be roughly four times the expected
shock oscillation amplitude, dictating the choice for the element
spacing. The 2D electrical conduction in the tags of the thin-film
gauge was found to be significantly different than a simplistic
model of the conduction through that region.
This was
incorporated into the gauge design. It was shown that optimally
the total tag resistance and the total lead resistance should be the
same, and also that the thin-film nickel resistor is thermally
transparent for a steady heat conduction calculation. Both a fourelement and a ten-element gauge were designed after a
parameter trade-off study.
It is recommended that the double-layer heat transfer gauge
designed here, or one similar, be tested in a transonic compressor
facility to understand the time-resolved boundary layer, shock
wave, and separation point structure in that environment. Also,
an unsteady heat transfer problem accounting for the dynamics of
the anemometer feedback loop and the heat generated within the
thin-film must be solved, with periodic as well as step boundary
conditions on convection. Additionally, it is recommended that an
error analysis be performed for the thermal coefficient of
resistivity as it is presently calibrated. In this way, methods of
reducing the inherent error in calculating cc may be discovered,
which will greatly reduce the experimental error encountered in
steady testing, due to the dominance of this source of error.
GJ8.
BIBLIOGRAPHY
1. Berry, Robert W., Hall, Peter M., Harris, Murry T., "Thin Film
Technology,", Van Nostrand, Princeton, N. J., 1968.
2. Blackwelder, Ron F., "Hot-Wire and Hot-Film Anemometers,"
Academic Press, Inc., New York - London, 1981.
3. Carslaw, H. S. and Jaeger, J. C., "Conduction of Heat in Solids,"
Clarendon Press, Oxford [Eng.], 1947.
4. Eckert, Ernst R. G. and Drake, Robert M., Jr., "Analysis of Heat
and Mass Transfer," McGraw-Hill, New York, 1972.
5. Epstein, A. H., Gertz, J. B., Owen, P. R. and Giles, M. B., "Vortex
Shedding in High-Speed Compressor Blade Wakes," Journal of
Propulsion and Power, Vol. 4, No. 3, pp. 236-244, May-June 1988.
6. Epstein, A. H., Guenette, G. R., Norton, R. J. G. and Yuzhang, Cao,
"High-frequency res1ponse heat-flux gauge," Review of Scientific
Instruments, Vol. 57, No. 4, pp. 639-649, April 1986.
7. Hayashi, Masanori, Sakurai, Akira and Aso, Shigeru, "A Study of
a Multi-Layered Thin Film Heat Transfer Gauge and a New Method
of Measuring Heat Transfer Rate with It," Transactions of the
Japan Society for Aeronautical and Space Sciences, Vol. 30, No. 88,
pp. 91-101, 1987.
8.
Hayashi, Masanori, Sakurai, Akira and Aso, Shigeru,
"Measurements of Heat-Transfer Coefficients in the Interaction
Regions between Oblique Shock Waves and Turbulent Boundary
Layers with a Multi-Layered Thin Film Heat Transfer Gauge,"
Transactions of the Japan Society for Aeronautical and Space
Sciences, Vol. 30, No. 88, pp. 102-110, 1987.
69.
9. Hildebrand, Francis B., "Advanced Calculus for Applications,"
Prentice-Hall, Englewood Cliffs, N. J., 1976.
10. Incropera, Frank P. and DeWitt, David P., "Fundamentals
Heat Transfer," Wiley, New York, 1981.
of
11.. Leipmann, H. W. and Roshko, A., "Elements of Gasdynamics,"
Wiley, New York, 1957.
12. Rohsenow, Warren M. and Choi, Harry Y., "Heat. Mass. and
Momentum Transfer," Prentice-Hall, Englewood Cliffs, N. J., 1961.
13. Sabjen, M., Morris, M., Bogar, T. and Kroutil, J., "Confined
Normal-Shock Turbulent Boundary-Layer Interaction followed by
an Adverse Pressure Gradient," American Institute of Aeronautics
and Astronautics, No. AIAA-89-0354, 1989.
14. Shapiro, Ascher H., "The Dynamics and Thermodynamics of
Compressible Fluid Flow: Vol. I," Ronald Press Co., New York,
1953-4.
15. Schlicting, Hermann S., "Boundary-Layer
Hill, New York, 1979.
Theory," McGraw-
16. Strang, Gilbert , "Introduction to Applied Mathematics, "
Wellesley, Mass., Wellesley-Cambridge Press, 1986.
17. White, Frank M., "Viscous Fluid Flow," McGraw-Hill, New York,
1974.
10.
LL
L2-=
FI GURE, 2..1-:
Co•s-rAtJT
-TEPErhTUOE
APEMOME-ETERP
FEFbt
ACV
LOOP
P0SSIBLE SEc6ND
ATICLET
FIGURE _,2 :
'THIM-FILM iEAT -ItRANMFER
GAUGE C•ADf-5ECcTIdN
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s
SUKAPTON
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FIGURE Z.3:
Douk\e-- i&lr G6leý
Reicr Pjfi'je
CoMPARISON
Headcr
OF GAUGE5 AND OPErATING
Adrve
MoDE-
I--
Time dependence of the substrate heat conduction
Z
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Od
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<D
o
o
100.
200.
_
·
·
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300.
400.
500.
600.
700.
800.
TIME [SEC]
FIGURE 3.1:
NORMAL1ZE)
UMSTEADYn SVUSTRATE coNI)UCTION
VS, -TIMe
0
7I-¢q
Time dependence of the substrate heat conduction
z
0
o
o
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W
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-3.
-2.
FIGURE3.3: NoRMALl[ED
-1.
0.
LOG TIME
1.
2.
3.
UNSlEADIY 5u6ITRATE CONDOCTWdlO VS.
4.
L06.jo [TIME]
u
1-D model; effect of the glue layer
z
0
to
C4
o
0
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o
q
0
5~~ Jlu~ I~ltr
100.
200.
300.
400.
0o0.
6oo.
700.
800.
TIME [SEC]
FIGURE 3.3-
NOPJALIZED OUNSTEADY
SUBSTRATE CoNDucTnoa
VS. TIME
o
1-D model; effect of the glue layer
z
o
o
!5
Pq
1,,-
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LOG1 OTIME
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NOIRMALI-E)
ONSTEADY SU6ST.ATE' CONDUCT(oN
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PAALLEL- ELE~MIT
5 EiLEIN3JT (
GAU
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FIGURE 3.5
Co•rAPIs•E
OF PAMeLLEL AND SEIES 6ALUE GEorWETPIE5
Comparison of ladder and serpentline gauges
0
I-
Ill
ElT
-I__________________________El_______
_1~1~ ·
1.
2.
NIUMBEri
FICGUR
OF RESISTANICE ELEMENTS
I
I
SERI ES/PAMALLEL GAUGE VOLTAGE rIATO
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N
Overheat ratio- 1.2; flow type- laminar
o
0
•
O
I11
M, (.4
0.8
1.0
1.2
SHOCK POSITION / GAUGE LENGTH [
FIGUR, 3.1:
SENSoa
VoLtFPAGE
VS.
1.4
\l0MAL1WED SftCK PoSIT\oNJ
Overheat ratio- 1.4; flow type- laminar
0.2
FIGURE 3.8
0.4
0.6
1.0
1.2
0.8
SHOCK POSITION / GAUGE LENGTH [ I
SENSoR VoL~AG E VS_.
1.4
NOKMALIED) SHoCK POSI~TIo
o
Overheat ratio- 1.2; flow type- turbulent
a
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MS1L3
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SHOCK POSITION / GAUGE LENGTH f
FIGVRE 3.1
•
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to
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0.2
0.4
0.8
0.6
1.6
SHOCK POSITION / GAUGE LENGTH ( ]
FIGUE 3.10:
SENSoI
VOLTAGE
VS.
NoAMALIaED
-51oclK PoSITIONJ
Overheat ratio- 1.2; flow type- laminar
E
0
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FIGORE 3.1:
SENSOR
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v
r..u
TEMPERATURE RATIO
VOLTAGE
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u-
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u
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VS-. "TEMPERATURE RKATIO
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E
O
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u.uu
u.ou
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FIGURE 3.12_: SENSoR0
1.50
VOL-TrE
2.00
2.50
TEMPERATURE RATIO [
CHANGE
3.00
3.50
4.00
VS. 'TEMtpERATOE RVAT)I
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E
0
1.3
1.3
0
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3.13:
x10**-2
2.50
TEMPERATURE RATIO
_NSok, Vo L'TA4 E
3.00
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I
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TEMPERATURE RATIO ( ]
FIGKRE 3.14; SENS•Ot VOLTMhE CfI+AJ6E
3.00
3.50
4.00
VS. -TEMPEJTO-RE RATI
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oO
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FIGURE 315:
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GAUGE
GADGE •
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A
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20.
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NUMBER OF RESISTANCE ELEMENTS I ]
VS.
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35.
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d - Ni gauge
m
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FIG6RE 3.1 :
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ELECTI7R
15.
POWER
20.
25.
30.
NUMBER OF RESISTANCE ELEMENTS I
35.
ST
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c,
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FAGURE 3.18:
5.
10.
15.
30.
25.
20.
NUMBER OF RESISTANCE ELEMENTS I
ELECTR\(C POER DI>\SItM-TEb
VS.
idrABRE
20y
35.
40.
I
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Effect of test material
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1.4
RESISTIVE OVERIIEAT RATIO
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1.7
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OVERA.EAT
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GAUGE RESISTANCE IAL
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0
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GAUGE RESISTANCE
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ceffE
2D
e
lect
a
r
U
n
c
cI
cJl
d
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
W/L I I
F(GOCRE 3.27.:
ACtUAL (21 /EMAECTEbD
ib-]
RESISTANCE£ (RATIO V;.
W/ L.
Effect of ohms/square of plate material; material- copper
IUJ
da
LU
C
-9-2
'Ist.
G:=
if = 03a
%
it ; C
0.5•,
0.181 lrt.
it ;
0dO
oO
c2
3.
FIG()E 3.23:
4.
5.
---
# OF ELEMENTS
PLATE /ELEMENT
·
u.
lo
I I
RZE7SISTANNCE IA-TIO
Vs. NUMBER- OF ELLFPE1T-
Effect of ohms/square of plate material; material- gold
u'CAr
C-
1c
tV
k/st.
).2AL2
90
6.
# OF ELEMENTS
FIGOE 3oz24: PLATE/ ELEMENTT RES-TA•IuLE
7.
8.
9.
I )
-RA*1o V5. NUMBER OF
10.
ELEMENT5
Effect of material choice for a given plate thickness
Ltr ts]
Il
fIit
0
uq
0t
Cu p0"t
0
(3
o-
2.5
3.0
3.5
4.0
# OF ELEMENTS
FIGURE 3.25:
PL&TE /ELEMENT
4.0
b.0
U.0
I I
RE-jS5P1&JCE RK11b
VS. NUMthEl of ELEOfEP-
3. L-
-TABLE
E
CAOG
L Lt-
()E5 Ju:
5'sTh\
{
9
tAAnot
J
Io
EkJ T
C'
+
Au
GUG C
ILco y-
45.4
114
= looo /.,,.
=
+
4-3.0
100o
654+y"
=
+A~
Au
..0
2.o
=
A~
[zoo
-30g
30 •o0,
[q50
w=
t•34 ?,,
1500
-=
PJli
(500
6wo
A
0ooo
=
,o =
..• ., .u
7-
=
S 0.2.44
7..
O5.0
IS.o .q
14.4. _10.51 .P
I
0. 32.1
15".
?.oo5
O14
zp
i
0.37Z7
\4.07
0.19
i
Z.7I
I.'7
M1.
143
T 12Ir
m
S
FIGUCRE
3.2--
CA LEi
-ou- ELEM ENT
DE!S\GN
• i1ip
491.
4
o
loooýA
1Z/M
IOOO~~mf7#
IA2I 15.•/-/
t
-.
~W7f
I
v
p
-1
Stoopm
SCALE
F(G6RE
3.2'7:
=
-TEN- ELEME • T GAOGE
PESIGr\)
OIL-FRKCE""TRAI45 UCEi
s~-A AT ON
OiSTA NfCE
SUPPLY
VALVE
lx
b
J---
SHOCI
TUBE
PKESSURPE /
MATIEMAL / j
DIA&PHiAGM
BRIDGE BALAI4Ci E AN D
AMPLI FIE UNIT
DIGITAL
TRANSIT TIiE
OSC.ILLASCOE"
(Cr)
FI6ORE 4.1_
SFhOCK -FU3E
EX PFEI ME N'TAL
t
iF
'ALVE
10
&,*I'st5yraveo
I
Pa= P
FIGURE 4.L:
SIo(CK TO-E OFFIGUAnT(OoJ
•BEFORE
R)&ST
x-t
d;,, j,.,,
(d'
\ rl
I
:?$1
L
t:
I
'
CONT(CT
CosmerIL
SHoc K
WAVE'
(z)
(1)
((3)
T\
I
•~·
•
//
/
/
)
,,
(3)
,,
-EXPrANSio7
1
F:O NT
f•/
1
JJ
FIGUýE 4.3: SRHOc TOE
+/t
~
OF\iGU ATIoNC
-- r
_LS)Jfl9 Y3IAV'o :I-)N-
O'D IA(00
-:'%V3~n91d
3aLL- )MO 5
`L3
3il
I
11-
-4
31~
(·tT)
~b
e-
Vz)
r
'
I m41 f(TO
-;n
?JA
d
( Jns-aJ
11
.I.
d
5D
S-(T
MI
III
CO•'Af
Sr
.uAFACE
C-.
oZ
4:
o•
o
a
ý
FLEC•TJM
DR•VEA
LIMIT
x
4:
1.00
1.05
1.10
1.15
1.20
1.25
SHOCK MACH NUIMBER
F\GU1E 4.5 -AXIMUM
1.30
1.35
1.40
I
DATA ACaU\SM\noN TIME
vs. MACIA
WIMUMF
Database for material selection
C
jfEPAE5ENTS
±
AVEJAGE
1. STAIIDARD
PEVIAIION
U. C4
uiid
d
I-
ad
1.
FIG6RE 4.
2.
3.
MEANJ AD tEVjTA-iOJ
4.
5.
o0 DIAM••W
P
BREM•
PRKESOVF OR
MATERIALS
Database for material selection :
dard deviaAIon on
I-&A reprtserts (Acan :t A st1.
I----0---
--e-------
i
I--s--I
pos
5 mON
M1ATEIAL
aIt
, 140- 2- 0
I--O--
J1-
23
119I
"VII6
5•-~f
iit
'"
'Hi~v
-ciTy
A\.
-o~
lvave' 58P
_L
1.15
1.17
1.19
1.21
i!/.*
(sA
gL
p
p
I
I
1.23
1.25
1.27
1.29
1.31
MACH NUMBER I
FIGURE 4.q: MEAN ANb) DEVT\AnToN MACR NMBEF-L FOR DO\At~AAGM HMATEUAL•
I
I
k').
ofal
jo'1
I
I
I
ze)
LCac
LO
%
I
Lu
P
1
LO·
C) bg
T13rJ
FLAT
MoulJToJ
TEST
sj
ý',C
110
IIkWEPI
FIGoKE 4. SIUBsorl C WIND TOWNEL
EXP)(?EglErTiM
AL APPQAIATU
tiEAT T•A- fWE
THIZEADED 14OLe
Fok IWC PLUG
5IGNAL -TEMtihAL
INTErJWAL ELECTRicfAL
CoNNeCtoJ
PASIA6E"
GROOUN TERAMNAL
=AltNINAL 15NLu
PWG
FIGo E410:
SINGLE-LAYEKR SENSol
r-
#"
"'f
.
&'
LEAD
C4.oVE
rc = JIfyL
1ocK TuBE
P1ROE
SUPfdgT
150$
ifi-~--SEt
PLU4
BINJ
rTjMJSFFER
- SeJoA, GdOUND
TEPMIMAL
INTEPWAL ELECTI.(AL
C4J)ECTIOIJ
P&AA66
SEN50JoLS1GIL TEAMPJAL
--
~IL-
~I~Z~P~-H~-l-L-Y
1: 0.q5 '°
rc = 1 3
"lsnsl r-
[tIEATE
FIGOKE 4.1.:
00d
oruvsw
I
I In
%-^
L-
I3NtC PLUG
E
LAYEFR SENSof. St+o -TufE
ePRoE 5uProRT
^ ,,11
^i rl r
11
0.25
3.50
F\GURE 4.12:-.
r1#TE PIOBE SUffoRT
SU6SOMC WND TouPELL FLAT
ANoDRIs
GRIP TA
IGE
J
FLOWJ
D\WECT 10 N
iEN-TE-R LEAD
SENSOR
ECLENCTIC J\GWLY
K LEAP
ELLIPTLC PRoFILE
k(Arrku~lnlrlr
FI16KE 413:
lI
LEADS
- ILt I r'L-hl
YROBb
SUPPORT
FLAT PLATE LADING EDGE P?'oFILE GEoMETfK Y
The determination of
i
Z00
A
N f-film
0
<N
CJ
o
<N
CF)
014
N
oIj
Oi
0)
35.0
FIGORE .14:
37.5
40.0
1TES
FIATERIAL
42.5
45.0
47.5
TEST MATERIAL TEMPERATURE
FESTAsCwc
50.0
['K I
52.5
VS. TET- MNHTERIAL
55.0
EMPEATUKE
The determination of os
30.
F160fW 4+
15 SENIoSO
i
40.
brass s5uport
50.
70.
60.
SENSOR TEMPERATURE ('K
ESTISThN CC
vs.
80.
90.
100.
I
-Etm PErPATU-R
The determination of o>
28.0
FIGURE +,1-6:
35.5
I brass sUeport
43.0
50.5
65.5
58.0
HEATER TEMPERATURE [' K I
HEATE - RE~ICPSTN CEF
vs C
73.0
HET9E-
80.5
88.0
-rMPEi-A-TURE
The determination of cgs
30.
FIGOcE 4.1.1
40.
:SESOR
i a•tlidJ Al suport
50.
70.
60.
SENSOR TEMPERATURE ['K
R.EISTA-NCE
80.
90.
100.
I
oSENSOR
-T-O PeFZlATURE
The determination of
30.
FIG7RE0
4.1-9 :
<,i ;
40.
HEA-TEKR
aMwieA Al sveprd
50.
70.
60.
1 EATER TEMPERATURE I'K I
EI STA-nýCE
VS.
80.
90.
100.
1EETER EM PEPfATURE
The determination of P(s ; nro'lOtd
30.
PCGURE 44t( SUfSSog
40.
At.
50.
C TUcJEL S)JSoP
rupp,,• -
70.
60.
SENSOR TEMPERATURE
R
5
80.
90.
100.
'KI
VS.S.elSTmE
SWJOR TEPERATVPTE
The determination of p
Al luFPdt
,A
E
h
o
1i
I-I
13
U)
z,
C2
0,
C
30.
FIG OUE 426:
40.
50.
60.
70.
HEATER TEMPERATURE I'K
_SV5ONIC -TuLOJEL OEATE& RE•STAlMCE
80.
90.
100.
]
V;.
EATER -'I-MPE ATI)RE
d
r-
The determination of o.s i ano;•d
Al suppart
E
-C
o
c(
U)
z I-
0z tr
(/)
30.
FIGogM
40.
50.
60.
70.
SENSOR TEMPERATURE [ K I
42I: 5u650Nlc -TONNEL gEtSoK 9 \SANCE
80.
90.
100.
S'JSofz -MPa~ATLKE
The determination of o~A
30.
FIGokE
4.7jj
Z
40.
a"iute Al -upport
50.
60.
70.
HEATER TEMPERATURE ('K
SvU65ONI C.1rNEL EATTR ?-.ESISThMCE
80.
90.
100.
I
V5.
HATEKR -EMERATUvE
Feasibility of balancing
CCq
o
centiohm resistors IR1- 522.4 .1]
n~~hrr
II~
J
-.
#3
>0
-c\J
'U
(L
0-j
0
d
c\j
4
L0
G3)
r
O0
11--
1
~
3410.
360.
380.
1
400.
~__
420.
440.
SENSOR COLD RESISTANCE
FG(UE 4.23:
ANEIMoMETER OUTPUT VOLTAGE
460.
480.
500.
[ohmsl
SESOI.Ko
COL( (UE.S\TMrJ)C
Feasibility of balancing kilo-ohm resistors (R.- 1510
]Li
c
-
>d
Lii
a
BRUIE
&u
DBKG 0 3
1.
(it
FCq
>0
0o
0
0
1.00
FIGUOF. 4Z...
1.05
1.10
ANEMoMETEAT
1.15
1.20
1.25
RESISTIVE OVERHEAT RATIO
OUTPUT VoLTh
i1
VS.
1.30
1.35
1.40
[ ]
_WS.o
OlELHRENFT
L
R,.•O
Sensor passive; effect of bridge choice
N
r-
[ T.o 300 K]
0
O
I-
0
Wo
0
to
0
(I)
V9
1.00
4.Z5
I
r
I
1.02
1.04
1.06
a
BRItE i IL
o
13.DGE
&
BIDGE 4 3
-2.
-----
T
1.08
1.10
HEATER/AMBIENT TEMP. RATIO
45-JSo. /AMBIEW~T -TEpERTVUE
'\S.
1.12
1.14
1-
1.16
(
HEhTEP /ANMB\ET
-EMPRATIgE
Sensor, heater temp. balanced; zero flow
SENSoI OUTIPUT VOLTAGE
IIEATER Ou•lTf
VoLTAGE
to
05e
4:
-J
et-~------~Mi
---
c~c~-Mi
~c~-Mi
1.01
FIcuaE 4.24:
1.02
1.03
1.04
1.05
1.06
SENSOR OVERI IEAT RATIO
BALANCED- GAUGE \OLTAGE6
VS.
1.07
1.08
1.09
(
SENo(L OVEIAEAT FATIO
Relative importance of error terms
+rbutnf
C
aSs. Z1,0+ 1as, 1.081
ERRaoR- PRoRoucWG
NUMBER
1.
C'
os
2a
W-
Sovo5Iu
3
RCeA
4I11
V,
Vi
'ii
5
AK
0
19AL4
T.
Pt.t
sEcoINOY
c<
c
-" •TIAKY
NECLIGI.BLE
A
6
S--
1.,
I-
2.
-
3~
4.
ERROR-PRODUCING SOURCE
FIGoUE 5.J:
PERCENT,,E
Ebt
Fok, ElPRt-
jtoDuCl G
So WcEJS IN Ou65N\% TEL
"
3-14-90
NO
S=lI.Z3
iEATEA :
P= Z.1.7yI
71
i I i
(
ao
o'
I--
I
0fl
C
Tii I
II
_J
I
I
i
I I i i i I
ýI ---TI -III II I I I 1
Co
S0.00
0.80
0.40
1.60
1.20
2.40
2.00
TI ME (MS)
3-14-90
NO AEATER
aKs 1..3
=
20.3..
1.v0
I
'
_____
cO
(I- J 0
-..
4-
LT
Vjt
________________________
1 i
IT
"ii~s?·~'4-
u
~c'
I
•>
I
w
MF
RTR
'0O.00
1~T~ ~!flr i
q'IF~r~Ffl
~flMF
NOT
0VFamn
0.40
n
I
I
I
0.80
I
1.20
I
I
1.60
2.40
2.00
TI ME (MS)
FkwQ ý,t:
UNSTEAMD
VOLTAGE
a1l.
IWE
VS.
TIME
3-14-90
1
qxz I.Z3
"4EA,
:
NO
M
Kr
2 NAWU" t'vv L"Uý
pI~
_______
\2.-.L
122
I
I
L il11~
_.
co
Co.
AMF
I
'0.00
ATP NIT
'VF
--
0.80
0.40
1.20
1'.60
TIME (MS)
3-14-90
N4o E•ATE.
doA 1.27.3
a 7-.1
,'1i s 1.2.1
TIt
2. 40
2.00
itr
I
19
i,
In.,MU
(J.
.-
c
1
-r
co RflMF
I
'0.00
j -- 1
:F1TT NITTVF
0.40
~F1T;Fn
0.80
1
Ii
1.20
TIME (MS)
1
i
1 .60
i
Ii
2.00
i
I
2.40
FIGKE ..L: U(STEADM VOLTM E 1TALES VS. TIME
130.
3-14-90
NO 4TM
4': L.,3
:
Cf
I IMt.lM~)
3-14-90
NO
REA17-0
'
*1.23
Uc
C-
TIMELM ~jM
FIGURE (og UNVSTEAbY VOLTAGE TACE5 VS. "TIME
131.
4 -24-90
atrs
PA\SWE
HEATEri
(.'ZO
: I..03
.0
Mr =
I. 2.
1
j
|
rr
'I i
7-, cn
11
I
.,
cz
L
i
;mF
0.00
rpTp
P,_
_
_7
-J
7
~I
ý
1
y
b
1ss'
-'F
NA0.40 VE
I
0.80
I
i
1.20
'
1.60
2.40
2.00
TI ME (MS)
4-24-90
HEATEM fiv
40V=
Lo
Ms; [g*'~;
-r
I
.Jn
v,
~!i
~~r
-:
II
i
I~L"rC~,~P--IR-
cS
I
~o~~n
QVFýpf-Fn
,
1jCMF r-PTq -ljfjT
)
IIU.0
U
0. 40
F
I
MF
T(F
OOTA
Aff
FlUKJE ýA4: ONVSTEIO
0.80
1.20
TI ME (MS)
I
1.60
40IAUE 11ThlEs
132.
2.00
vs.
2.40
1T ME1
4-24-90
4A;,
HEATEik PPAIMV :
.2.
_i
Mft
=.22
I
I
1
i
i
i
I
w,I
__
Mi
co
)m
UJ
K
y
dU-·
tI I·
I
d
flMF
·- · kp .··
IraRg
0.40o
0'.00
0.80
S1.60
1.20
2.40
2.00
T I ME (MS)
'4-24-90
i.ZA
tAr2
EA.TEa. PASIVE:
I
i _111
C
1Y1~
Il
cn
k A[
h
L,
?6a
Ms
1
I
s
1.2.2.
-ri~
J ~_Li ~I
I-4
3
Z7-.
I
I
I
I
CO
or•
_J
\. .
U
.....
S h(lHt
0.00
IIWIU.
.
-. ....
..
.Ynl
. . UV~qFll;ill
0.40
I
I
0.80
I
I
1.20
1
I
1.60
I
I
2.00
2.40
V5.
TiMt
TIME (MS)
FIGrkE 6.5 U%5ITEAW VoLT6E TM1LE
133.
4-24-90
alk i
1rATEA PASSEV6:
Y
*
?6- 31.5 ps,?
I
I
I1
LA
f I-Wi7
I
___
I
cn2
.n
C
~NrL.h4'N1N
1
i
I
RfMFOIJ
,
0.00
h
iii
0.40
I
/
0.80
I
1.20
1.60
I
2.40
2.00
TIME (MS)
4-24-90
hEATER
G
PASS•NE:
I.o•
.. o
j
Iw
A q
I
I
U
Pi= 35.1 s:
M- = f.3o
i
I
i
a
I
Ify
67&s41
U-)
I
•nMF
Iut,
ArMT
TA
•IFJT;A
|
'0.00
I
j
/
I I 1.20
/ i
UL
0.80
TI ME (MS)
FI6LRE C.6:
II
i
0.40
UNSTENAY
1.60
2.00
i
I
2.40
VoLTME T1-P-E( '4V.TIME
134.
Turbulent flow calibration curves
a aIs 1.02ap
12
& "A,
t
O
-0
0,=
=
1.0+
:;LOG
1.08
(w2
c
Il
c/I r-
-I
l
16.
21.
26.
31.
MASS FLUX
FIGuRE
36.
41.
46.
(kg/m/m/sl
SENSOR \IOLTAhGE
vs.
AMI
FLUX
Laminar flow calibration curves
o qAS7 1.02.
o 0•s = 1.04
q
cjg
I.O(
it-
nr
~----a
0
ul
U)
MASS FLUX
FG6Ug% 6.8:
5EWJfO(.
VoLT6FE
ikg/m/m/ls
OlAs
FLUx
Turbulent flow calibration curves
t
0
0
0
IO0L
r
02
ao CaS. 1.02.
o aAr=
..
.-.
. I-
-
(.91:
,As-.0LO
+
4& - 1.08
-
-
21.
FvGOke
1.0V
A
26.
SEaTER.
31.
MASS FLUX
-- !--
....- I..
(kg/m/ml/s
VO LTA E
V\.
MtAs
FLU X,
Laminar flow calibration curves
I
·
·
__C_
I
< o
0-4
O
I
r
0
aGR, 1.02.
o
1.04-
pel
---
T~
-7
r
MASS FLUX
FIG16KE
.-i
IREATEt
r~---
~7-
VOLTT6aC
-I~~------~-~
[kghn/m/m/s
VS.
jANs PLUX
d
Experimental vs. theoretical comparison:
as,
i.13
i
s',Iat sensor ;i bra. Suft#r
E
UO
I--
cor
0
5
--
1.20
I7-
1
1.21
I
FlI9E 6.iI:
--
1.22
SER~KO
1.23
1.24
1.25
SHOCK TUBE MACH NUMBER
VOLTMe
vs.
1.26
1.27
$
1.28
( I
MACH
UMB13ER
Experimental vs. theoretical comparison:
d
(0
al,= l, zo;
e
Igrt°
kukic rdlyt ý,eLr
d
E
oi<
o
0- (1)
00
0
ORETICAL POINTS
EtIERIMENTAL
a]
POIlMT
d
•r--
Nq
1.18
--
~-~
..r
FIGURE C.I_
---
-
1.28
SHOCK TUBE MACH NUMBER
SEMSo(L \oLTiG.DE
.30
1.32
1.34
I
M\cI4
NutJMi3ER
dci
Experimental vs. Ilheoretical point comlparison,
0
I--
ar = i.20 ; he5dc1r
F&
" I IV
'1bA
rof
I-
d
o
(D
E
uo
Sdi
0
o
RE II(AL
I)
ItIErI IAL
I011, [5
po1lr)i
d0
0
N
---------r
o
________________
1
1.24
--
1.22
1.24
I.I
C
1.28
-
r-
i.18
1.16
1.14
F16UkE
1.16
.13:
1.20
1.30
SIHOCK TUBE MACII IJUMBEI1
SENSo
\JoLTAGE
\f•.
M'. j
Num 6II
Experimenlal vs. liheorelical point comparison a
ap' . j.2-0 i ýer arclvc ; brgaLi ivfr
-CL
C
~
---
TIIEORETI-AL
poo'Tf
EYpERIyflEiITAL PollPTI
.
I. 180
I
..
1.195
FIBGUE 4.t4
1.210
SENOR~
-
I
1.225
I-
1.255
1.240
SIIOCK UIRE MACII IfAJMBER
VoLTIk4E
1.270
1.285
1.300
I
Vs.
r1AcK WKJUMOFE
.
Comparisoll of heater active and healer passive
O
1.•
.LO
.
I
0
III
an
O
IL
.4
TIlv
0II
TIVC
Iii
6
\'I
!l`
1.16
1.18
1.20
1.22
1.24
SIHOCK TUBE MACII WIMBER
1.28
30
I
FLk*UE (.I5- PERLEVW DIOFFR•EVLE OF THEDRE"T"hL WAD EER\NE NTA L
VOL11GE ,&l0S5 1RE SEJorL
Experimental vs. theoretical point comparison i ars-
·
1.o
io a)vc
j su,(en
i td= 0.89
s
lo -~
---
<o
0
0E
o
00
U)l
ij
w---1.16 6
--- r----1.176
FIGUI -E .1u:
-~--II--1
1.186
1
1.196
SENSoR.
1.206
1.216
SHOCK TUBE MACH NUMBER
VOLTMGE
1.226
1.236
1.246
I
Vs.
MIALC
NVUM6 Ek
O
Experimental vs. theoretical point comparison i
a
r = 1.08
0
i
'e)
-C=
ruf,
0..
(t
O
V
j
1.16
0....
i0
0
1.175
....... 1
1. 175
FIG60KE .il:
1.190
.190-
1.190
$ENýSOR
1.205
1.205
1.220
I 2
1.220
1.235
1.235
1.235
SHOCK TUBE MACH NUMBER
VOLTPr4E
Vs.
1.250
1.250
I
f
1.250
1.265
1.26
1.265
1.280
MACH WvrMER
0
Experimental vs. theoretical point comparison
0
1,1
ai,
1.11L
_
I~RtcJ
dI
ut
;1
L';
0.8mr
I
5'
E
O0
0o
Ul
0n
U)
-I~
-----
1.17
1.18
1.19
133
s~fS~a
L9--e
~~~1~-.
~
1.20
1.21
1.21
1.23
1.22
SHOCK TUBE MACH NUMBER
FIGURE .~ : SEISOR( VOLTAGE
I
1.23
I
1.22
VS.
-
~
1.24
1.24
[
Mi-CH
JUiMER
1.25
0
Experimental vs. theoretical point comparison
i
ars
.0.a o•
ic•)
iu(prt
i
t'= I.2'ns
r
1
-
-----------
- - - - - - - - - -.
1.168
FIGU
1.178
G.1t-
1.188
1.198
1.208
1.218
SHOCK TUBE MACGI NUMBER
SEW5foR VoLTAx6
Is.
1.228
1.238
1.248
I
IALVi
NUM6ER
O
0l
Experimental vs. theoretical point comparison
ai ,
I-
1_S
j.01
a'
Ale) su',tr,
i
•
' I. Zh
I
--------------------------------
-----
1.160
-
1.175
-I
-1
1.190
--
1.205
-T--
I
1.220
1.235
SHOCK TUBE MACH NUMBER
F\GUAE .ZD"0 SEN.SOP \oL-LTMcE
\VS-
-
-
1.250
-
--1.265
1.265
1.280
[
~)uM
IMQh
rE
0
0
03
Experimental vs. theoretical point comparison
a[
i.lL
I
anoLacA
'
u~oart( i
1.25
V_
______~.-----------4
0
r
..-
9-
----
-
i
I
1.17
1.18
F\GN RE .z.£-I
1.19I
1.19
SEnso0(
I
1.20
I
---- I---~--r--
1.21
1.22
SHOCK TUBE MACH NUMBER
VOLTA-EC
vs
1.23
I1 .-
1.24
. . ..
. . . .
1.25
I[
M LIA t)VM EA
C
C
c
co
JI
1l
TIME (MS)
F1GL0
6.2 .:
5RXVIc
TUBE PREFSLt/E
euusiE:
EXeP~NDEb TINE
SALe
Flow type- turbulent
0
I-
U)
0
r:
-0
i
I11
co
d
aa
0
l7.L.07
AL rý1o0
Arg1.0(
4
AAj ILO-
LO
,
41kj
d
1.04 ap-- 1A
hZ
cz
o
i°
16_
21.
r.04+
aQ
o
i akl-s
1O0
108
Ak.Lg LOS
36.
31.
ACTUAL MASS FLUX [kg/mlm/sl
lN
FIGUE 6.13: EXfLPEplvETl/UEfETrAL Sl\) EICTIO
V/S.
ALTUAL MASI
FLUA
I
r-• I,I
Flow type- laminar
Z
0
CI-
LLc
zn¢0
ci,i4 a
U)
[02.1.02
W(1- 1.0c
'P
0
t,._1
<7
A-I =
:
aLl• =
0i
(.04I04.
I,06 ;
'*
= 1.08
Ana)~
"&t.i
1.08
(.08
(.08
0
0
2.
lU
15.
20.
25.
30.
35.
40.
ACTUAL MASS FLUX [kg/m/m/s]
F60KE .Z4: ExRE&IMETAL/7TEROETI(AL
I
SlAlIJ
FRKCTIOIJ
45.
VS.
50.
ACThL IAffJ FLux
Flow type= turbulent
,
-"lfl
D CQTif AI
/II 0I\I
o
O0
o
z
0
z
U)
--
"----------
0
N.
0.08
0.
0.10
0.12
0.14
TEST SECTION MACH NUMBER
F=Iu.E .z5:
S1KI FR\C1\ot
e
CoEFF\ECIEJT
,
0.16
0.18
0.18
I I
V\S
MANI
NUMB3EK
Flow type- laminar
0
u
I
a
TIlC[ORfKAL
i
I~irn
.
EXOMEJTAL
i
CURVES
.•,
COOM
Al•: (l08
al 1t
L
1.04
1.01
o
0
z
z
___--
0.02
F\GO6
Z E.:
0.04
SK(1
0.06
ftRZ CT\j6
0.08
u. IZ
.10
TEST SECTION MACHI NUMBER
·
0
I
I
r
Fr~---
0.16
u. 14
i
COEFFICIEWT\ VS.
_~
0.18
I
MNk
WUMBEk
r
OHR #1=
1.02; OHR #2-
1.04
z
O
z
U)
0
0
0
ACTUAL MASS FLUX
FI6v 6..:
.E
EXPEJIMEN1TAL /-I
Ikg/m/m/s]
JETYAL SUP IrLiCT\oN Vf AiCTUAL MINs5
FLUX
OHR #1
102: OUIR #2-
1.06
0
z
0
-,-
t)
0
(u
0
TOBOULEN
o
LAMIAIAK
I
.J
--I
16.
21.
26.
EXPERjMETwfhl/-TEbIFnET
41.
36.
31.
ACTUAL MASS FLUX (kg/m/m/si
L StcN
,FRK(TIn
46.
VS. AcIUAL MINf FLUX
03
OHR #1- 1.02; OHR #2- 1.08
z
O
C)
z
u}
U)
TURBULENT
,,o
r-
,tmNAmm
I
I.
jF--....
r---1-
I
|
___________
_ ,
|
__________
ACTUAL MASS FLUX
FIGURE
TI
,6_L EXPERIMNTAL/I"HEDREICAL -.
ikg/m/m/si
,lC7IIONVS. ACTvAL MWI FLUX,
uo
O|
O iR # 1- 1.04; OHR #2-
1.06
z
0
00
z
U)
O
O
a-
t0
0
I r-
flr
11.
16.
21.
26.
31.
36.
41.
ACTUAL MASS FLUX (kg/m/m/s]
FROm
E 6,30. EXPERINENThL /il•EDbtT L S•6, F9•cLno1J
46.
51.
vs. Actr•UL FIASf fLU\
M
OHR #1- 1.04; OHR #2= 1.08
O
0
u-
z
U)
-J
O
a
TURULENT
0
LmINAR-
14:
0
o
16.
11.
F'6v~E 43t-:
M
21.
LPfrEN./1tEtIc7I
26.
41.
36.
31.
ACTUAL MASS FLUX [kg/m/m/sl
WIN FPIcTlol10
46.
V5. NCTUAL HfNIf FLUX
OHR #1- 1.06; OHR #2= 1.08
z
O
I--
u(I
-J
C0)
ar
xlU
16.
FIG6UE .32.:
21.
EfEuy.M•/,L/IEO
26.
36.
41.
31.
ACTUAL MASS FLUX [kg/m/ml/s
r'FI(.AL SON•
MWIl
VS.
/RIcTIOl
46.
FLUR
APPENDIX A
THERMAL TRANSPARENCY OF THE THIN FILM
It may be shown in a straight-forward manner that the thinfilm's non-uniform temperature profile may be ignored.
Therefore, models may be employed that neglect the actual heat
conduction within and through the thin-film, treating the surface
at the thin-film location as a constant-temperature boundary
condition. Consider a region composed of a thin-film resistor with
thickness t (region 1) and an insulating substrate of thickness B - t
(region 2). Therefore, the problem to be solved is:
D2T
1
2
= -A ;
0
x
t
(A.1)
a2T
2
2
ax
-0
;
tSx<B
(A.2)
subject to the following boundary conditions:
aT
-Tx1 (0) = 0
(A.3)
T 2 (B) = 0
(A.4)
T l (t) = T2 (t)
(A.5)
aTxT1
kl T 1 (t)= k2 -x
IWI.
(t)
(A.6)
where A is the steady heat conducted within the thin-film gauge
and can be written as follows:
i2 R
A=WLtk
WL t k,
(A.7)
where i is the current through the sensor, R is the operating
resistance of the sensor, W and L are the width and length,
respectively, of the thin-film gauge, k 1 is the thermal conductivity
of the thin-film, and t is the thickness of the thin-film.
In
addition, the hot resistance of the gauge can be written:
L
R= Wt
R 1 + a (Tg - To)]
(A.8)
Finally, it seen that the the average temperature over the gauge
must be equal to the temperature Tg, or:
t
I
Tg = t
f
T (x) dx
(A.9)
0
Since the value of A is nominally constant, (A.1) and (A.2) can be
integrated favorably:
Tl(x) =
1
-2Ax
T2 (x) = cx + d
+ ax + b
(A.10)
(A.11)
where the parameters a, b, c, and d are arbitrary constants of
integration. Applying (A.3) to (A.10), (A.4) to (A.11), (A.6) to
(A.10) and (A.11), and (A.5) to (A.10) and (A.11), the values for a,
b, c, and d can be shown to be:
a= 0
(A.12)
16z..
b = At
+ 28 k
(A.13)
c = -Atk
k2
(A.14)
d = ABt
(A.15)
The ambient temperature T o is now added back into the solutions
obtained for T 1 and T 2 , since TO was originally subtracted from
the original problem. With this in mind, (A.12)-(A.15) may be
combined with (A.10) and (A.11) to obtain the temperature
profiles with x for the thin-film region and the substrate region:
TI(x) = T +
t(t + 28
) -
(A.16)
x2
T 2 (x) = TO + At k2 [B - x]
(A.17)
Note the parabolic temperature profile within the thin-film gauge,
as expected. Now the gauge temperature can be solved for in
terms of the heat produced in the thin-film, by combining (A.16)
with (A.9):
t
Tg = t
To +
t(t + 28 kt) - x2
dx
0
(A.18)
Tg = To +
At t + 38 k8
Recalling the definition of the resistive overheat ratio:
143.
(A.19)
ar
=
Rhot
Rcol d - 1 + a(Tg - To)
(A.20)
the equations (A.20) and (A.19) can be combined to give:
A=
k2 (ar - 1)
k1 a 5 t
(A.21)
The values of the heat conduction to the substrate for this model
and a simplistic model can now be compared. The heat flux to the
substrate can be written in general:
(A.22)
qcond = -k2 ax (t)
Applying (A.22) to (A.17) and utilizing (A.21), the following may
be obtained for the conduction:
(qcond)thin-film modelled
(A.23)
=
For a simplistic model, the conduction is easily shown to be:
(qcond)thin-film ignored
k2 (a - 1)
k2 (ar - 1)
(A.24)
Therefore, the relative effect of the thin-film can be seen by
forming the ratio of (A.23) to (A.24). Calling this ratio Q:
1
Q=
1 k2 t
(A.25)
3 k1 8
Therefore, more conduction is seen than is actually modelled with
a simplistic assumption. However, the value is very slight due to
the fact that k2 << kl, since kapton is an insulator and nickel is a
164.
reasonable conductor, and that t << 8, which is just a manifestation
of the design used in thin-films. In particular, reasonable values
for the parameters can be taken as follows:
kl1 = 5
W
mK
k2 = 0.202
mK
t = ooo000 A
8= 25 Pm
With these values, the value for Q is 0.999946, effectively equal to
one for the accuracy given here. Hence, for a steady calculation,
the non-uniform temperature profile within the thin-film may be
ignored.
145.
APPENDIX B
OPTIMIZATION OF ELEMENT RESISTANCE FOR A
GIVEN TOTAL GAUGE RESISTANCE
For the use of thin-film gauges, in order to assure the maximum
sensitivity of the gauge, the sum of the lead and tag resistances
should be kept to a minimum. One way to do this, previously
mentioned, is to plate the leads and tags with a low resistance
material, such as copper or gold. However, it is desirable to design
the gauge so that the sensor resistance to total resistance ratio is
In reality, this
maximized in case of a plate material failure.
analysis was performed before the plate process was discovered
to be applicable. For a gauge with total resistance of 15 0, the
element resistance can be written as follows:
(R)(RT)
(Re)0 =
(B.1)
1 + X + co(B.1)
where (Re) 0 is the cold resistance of the elements, (RT)O is the cold
resistance of the sensor (15 0), . is the tag resistance divided by
the element resistance (cold or hot), and co is the lead resistance
Therefore, it is desired to
divided by the element resistance.
maximize (B.1) with the choice of X and co. From a power balance
of the sensor, it can be demonstrated that co can be found as a
function of X. In particular, for a case with ar= 1.5, a thin-film
thickness of 1500 A, a= 0.3 %/K, 8= 20 .m, e= 508, imax = 0.35 amp,
8s= 25 pm, and ks= 0.202 W/mK, the power balance equation gives
the following expression for oo:
c(,) =C0•-
C4 [(C - 2)
- 2] -(1 +)
(B.2)
166.
where C is defined as follows, for a given number of gauge
elements n:
91.5
n1
C
(B.3)
From (B.1), it is seen that to maximize (Re) 0 is the same as
minimizing (1 + X + o). However, from (B.2), the expression (1 + X
+ co) can be written as a function of X only:
l+X+o
= f(X)= CO-
4
CX [(C - 2)k - 2]
(B.4)
af
To find the optimum X, the quantity a must be calculated and set
equal to zero. The X then obtained by solving the equation
The
represents the optimum choice for greatest sensitivity.
presence of an optimum is expected, for the power limitation
imposes that the total surface area of the elements, tags, and leads
be a constant. This allows for a gauge design with too high of
resistance for the tags and too low a resistance for the leads, or
vice versa, depending on the length to width ratios of the tags and
leads. There should be an intermediate geometry that minimizes
the sum of the tag and lead resistances, which is the same as
In fact, the
maximizing the element resistance from (B.1).
optimum X for this scenario is readily calculated from (B.4):
af
0 =
0=
C[(C - 2)X - 2] + C(C -2))
C -
24 C[(C - 2)k -2]
=0
(B.5)
Manipulating (B.5):
'61.
C4 [(C - 2))- - 2] = X(C-2) - 1
(B.6)
Squaring each side and cancelling terms:
(C- 2) X 2 - 2 X -
1
=
0
(B.7)
This is readily solved via the quadratic equation to give the
optimum value of tag to element resistance:
1+ 40.5 C
t
o°P
C - 2
(B.8)
Combining (B.8) with (B.3), the optimum tag to element resistance
ratio can be determined as a function of the number of gauge
elements:
oPt ( n )
=
(n - 1) + 6.764 4 n - 1
93.5 - 2n
(B.9)
It is an increasing
This expression is presented in Figure B.1.
By
function of the number of gauge elements, as expected.
combining (B.9) and (B.2), the optimum lead to element resistance
ratio (m) can be obtained as a function of n. This is not presented
here due to algebraic complexity. However, it can be noted that,
for a given n, the value of o is, within rounding errors, equal to
the value of M! Although at first glance this is a startling result, it
makes perfect sense when the mathematics of the problem are
Having obtained the
focused on rather than the physics.
expression for the optimum o (wopt = Xopt), the optimum element
resistance can be plotted as a function of the number of gauge
elements. This presented in Figure B.2. Notice the severe penalty
for increasing the value of n, although it is not as severe as an
inverse square law. The values of the resistance of the tags and
j4%.
leads are changed by changing the length to width ratio,
consistent with the constraint that the total surface area remain
constant. This optimization procedure may be used to design the
most sensitive non-plated gauge possible for a given fixed total
resistance.
(09.
0
u' o
ul
(3 r
--
I-
0
.........
0.
4.
6.
NUMBER OF RESISTANCE ELEMENTS
8.
R()
b
B.1
I1
· n
--
-2.
OfTIMUM TAG/ELEME"
2Bý\STWMN
10.
I
MWTo
2.
I I
V5.
I
4.
N\M6E
OF ELE}METf
cxi
Total resistance- 15.0 ohm
ed
r
p:
r
r\l
r-
d
r
e6
·-
0.
2.
4.
6.
8.
10.
12.
NUMBER OF RESISTANCE ELEMENTS I )
OfTIMlUM ELEMENT I%-•\E~AN CE
vs.
of ELEMENVTS
APPENDIX C
TABLES OF FLOW PARAMETERS FOR THE TEN
SHOCK TUBE RUNS
Presented below are the material, break pressure P4 [psig],
break pressure ratio P4 /P 1 [ ], shock pressure ratio P2 /P 1 [],
shock Mach number M 1 [ ], predicted shock speed (cs)pred [m/s],
distance of shock travel Ax [m], shock transit time r [ms],
measured shock speed (cs)meas [m/s], and the percentage error in
the shock speeds [ ] for each trial of the ten shock tube data runs
performed.
Tables C.1-C.10 correspond to Runs #1-#10,
respectively.
Ilz,
COMPAKISON
OF pl(DICTED AND
G6.rv If 11
WD-
P•.20( +)5i )
AAFDAl
:3
1
+3"+
tv (4)
'r ( s)c,
1.7
1.2-
22O
0.7
0.1971
2.S5
O.rlzir
i.2_o
2.5 ,
Al Fc;d
'1-
(MIS)
'7~,error
4oC -Oi387a
2.21
1.51
418 N3Y.1l-~r
1.14-
1. 9+
3... 2_
#O.L4 Zi,-
0.12r
..
5L
+13
MAl Fo,
5S
Tu3E-
a
3
[A.,vt Duty
Shock +vbe -fl y
/.3
2lUe.,y D&/
SHocK SPEEDS FOR TIIC 5lIcr0
1M1,
I•Aa.Irw\
Al F'ol
MEASU&RED
5_-%
O~727
0o.2rz
At
0.7l7
--
iL
OF
COMPAKISONI
PIEDICTED AND
MEASURED
azs Shock
IDi Gre.,r
Pie
("ri~l
P~.
u•Ae famo.•,i
LAY'. Inl
r
/
'-pJ
£Her
mis
-
,-- e•rror
1.1U&
I
+0A8l
A412V
I
,,
IewyU Dty
Al Foil
I '/Yc·. 5
?71
L.C
I
I I
7
1.158
LZA-.
3
lAenvy Puty
Z.%
.. L.
HeAvy o0t4
1. 63
ZZA4
+O.rqa7
1
4 2.5'lr
413 +o.72%
0.J'1
L-51
Al Fo't
5
kC
I
2
A-ehvyI ut,
Ali Iol
(.'WiI
4j-4
Al Foil
Al Foil
I- (
~--
ZA.4
Z4.ct
TuE
FORK -I-E StI-kCF.I
-l-esting
A
mIl
--
fhlecy Du0•
S1OC(K SrEEDS
03.77
4-111
411
2.52_ i.5(
4·1~1
+o.€8•
+648 7w.
1.1521
G
---
I
----
I
I
I
I-
-
-
I
COM1PAKISOIA
Of
113
D[J- Gre.v
:
M•\
..
1h. A•1.48
FolI
G3
•,•o
Do
3._.
Siloc((
FO• TH-E St511K TuI3E
SPEEDS
Plate +f Wiarpyi
1j
I~xi4eri-
M&At
MEASURED
PIEDICTED AND
Maeriats
(P)
is
Oq
373
V.727
(Irts)
CS(r4)
7trecror
1.13L
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Hervy Duty 2.50
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47
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Al Fo:I
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3.31
118"58F
1.8
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CeflopIne
1.G
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14686
COMIPAKISON
OF PREIICTED
AND
MEASURED
SIIocK SPEEDS
DA Gr.r fb + ts S;'I3le 5••au ; tad "trakrfer
roKR -IIlE 511•cK Tu6EaLrec-ded
c
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(MS)
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(,,,s)
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2-"K"
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20.
1.1-8
I
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20.3
1'
2.38
1.52-
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3
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leavy Dull
At Foil
5
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Cellopane
32.1-.7
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4-17
1.G16
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COMPAKISOIN
OF
PREDICTED
IDX
AND
Govr It5 :
I
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9ST
2AST
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410
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At Foil
He4vy DLAy
Al Fodi
11.563
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1.1r60
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414. +0.1IL
1.144
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11.21
5
18'V" 8F
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SIIOCIK SfEEDS
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lJ Grof 11 CG
P4../
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Dou
le-
lyer pup S
1p,
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FOR THE 511cCKir TuE-
SllOCIK SPEEDS
2.50
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3.18
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Of
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(I'-e)
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AND
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(ms),
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FOR -I-IlE
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APPENDIX D
VOLTAGE TRACES FOR SHOCK TUBE RUNS #6-#10
Presented below are the voltage traces for shock tube Runs #6#10 in Figures D.1-D.15. Figures D.1-D.3 represent the data points
for Run #6. This case is nominally the same as Run #5. As before,
the highest Mach number traces (Figure D.3) display a gradual rise
The voltage dip
in voltage after the passage of the shock.
precisely at the moment of shock passage increases with
increasing Mach number as well, diminishing the trend of
increasing voltage jump across the shock with increasing Ms. The
reason for this voltage dip may be a local separation of the
An
boundary layer or an unmodelled heat transfer process.
argument shall be presented for the former explanation
subsequently.
Comparing the voltage jump for a given Mach
number between Run #5 and Run #6, it is seen that the voltage
changes are comparable.
Figures D.4-D.6 represent the voltage traces for Run #7, which is
identical to Run #6 except that now the heater is being actively
controlled to be at the same temperature as the sensor.
The
reason for this operating condition is explained later during the
theoretical modelling of the problem.
Compared with Run #6,
these voltage dips seem slightly less pronounced. The sensitivity
to Mach number seems to have been reduced, as compared with
the heater passive runs. Large noise spikes (due to laboratory
background electromagnetic radiation) muddle the heat transfer
signal throughout all six of the traces in this run.
Since all
electronic components in the experimental setup were already
shielded from background noise, no further action could be taken
to minimize stray electromagnetic signals.
183.
Figures D.7-D.9
represent the voltage traces for Run #8.
Particularly at this low overheat value, there is a quite large
voltage dip at the shock passage point. This voltage dip is more
pronounced as the Mach number increases. All plots display a
rise in output voltage following the shock passage, contrary to
theoretical predictions.
Due to the pronounced voltage dip, the
voltage change across the shock decreases with increasing Mach
number, also in contradiction with theory. In general, it is seen
that lower overheat values give less satisfactory predictions for
the voltage change across a shock than higher overheat ratios.
Figures D.10-D.12 display the six data trials for Run #9, identical
to Run #8 except that the overheat ratio of the sensor is 1.08, not
1.06. Again , we see that voltage dips are present and are more
prevalent at larger Mach numbers, but they are much smaller
than for Run #8. As before, the trend of voltage change across the
shock with Mach number is reversed from what is expected. The
voltage increases, for each of the six traces, after the passage of
the shock (again, as before).
Compared with Run #8, a
corresponding Mach number for Run #9 gives a larger voltage
jump across the shock, consistent with theory since the overheat
ratio is greater.
Finally, Figures D.13-D.16 represent the six voltage traces for
Run #10, which is similar to Run #9 and Run #8 except that the
overheat ratio is now 1.11. All trends cited above hold here as
well: (1) voltage dips are present, much smaller than in Run #8 or
#9, and get larger with increasing Ms; (2) voltage increases for
each trace after the passage of the shock; (3) voltage change
across shock is much higher for a given Ms than for the lower
overheat ratio cases; and (4) voltage jump increases with Mach
number are not seen, inconsistent with theory. Although in some
respects incorrect, the runs #8-#10 seem to form a consistent data
group within themselves.
184.
*581
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