STRATEGIES FOR PLANAR LASER-INDUCED FLUORESCENCE
THERMOMETRY IN SHOCK TUBE FLOWS
A DISSERTATION
SUBMITTED TO THE DEPARTMENT OF MECHANICAL ENGINEERING
AND THE COMMITTEE ON GRADUATE STUDIES
OF STANFORD UNIVERSITY
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
Jihyung Yoo March 2011
http://creativecommons.org/licenses/by-nc/3.0/us/
This dissertation is online at: http://purl.stanford.edu/sj041st9908
© 2011 by Ji Hyung Yoo. All Rights Reserved.
Re-distributed by Stanford University under license with the author.
This work is licensed under a Creative Commons Attribution-Noncommercial 3.0 United States License.
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I certify that I have read this dissertation and that, in my opinion, it is fully adequatein scope and quality as a dissertation for the degree of Doctor of Philosophy.
Ronald Hanson, Primary Adviser
I certify that I have read this dissertation and that, in my opinion, it is fully adequatein scope and quality as a dissertation for the degree of Doctor of Philosophy.
Mark Cappelli
I certify that I have read this dissertation and that, in my opinion, it is fully adequatein scope and quality as a dissertation for the degree of Doctor of Philosophy.
Mark Mungal
Approved for the Stanford University Committee on Graduate Studies.
Patricia J. Gumport, Vice Provost Graduate Education
This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file inUniversity Archives.
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Abstract
This thesis was motivated by the need to better understand the temperature
distribution in shock tube flows, especially in the near-wall flow regions. Two main ideas
in planar laser-induced fluorescence (PLIF) diagnostics are explored in this thesis.
The first topic is the development of a single-shot PLIF diagnostic technique
for quantitative temperature distribution measurement in shock tube flow fields. PLIF is a
non-intrusive, laser-based diagnostic technique capable of instantaneously imaging key
flow features, such as temperature, pressure, density, and species concentration, by
measuring fluorescence signal intensity from laser-excited tracer species. This study
performed a comprehensive comparison of florescence tracers and excitation
wavelengths to determine the optimal combination for PLIF imaging in shock tube flow
applications. Excitation of toluene at 248nm wavelength was determined to be the
optimal strategy due to the resulting high temperature sensitivity and fluorescence signal
level, compared to other ketone and aromatic tracers at other excitation wavelengths.
Sub-atmospheric toluene fluorescence yield data was measured to augment the existing
photophysical data necessary for this diagnostic technique. In addition, a new imaging
test section was built to allow PLIF imaging in all regions of the shock tube test section,
including immediately adjacent to the side and end walls. The signal-to-noise (SNR) and
spatial resolution of the PLIF images were optimized using statistical analysis.
Temperature field measurements were made with the PLIF diagnostic technique across
normal incident and reflected shocks in the shock tube core flow. The resulting images
show uniform spatial distribution, and good agreement with conditions calculated from
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the normal shock jump equations. Temperature measurement uncertainty is about 3.6% at
800K. The diagnostic was also applied to image flow over a wedge. The resulting images
capture all the flow features predicted by numerical simulations.
The second topic is the development of a quantitative near-wall diagnostic using
tracer-based PLIF imaging. Side wall thermal boundary layers and end wall thermal
layers are imaged to study the temperature distribution present under constant pressure
conditions. The diagnostic technique validated in the shock tube core flow region was
further optimized to improve near-wall image quality. The optimization process
considered various wall materials, laser sheet orientations, camera collection angles, and
optical components to find the configuration that provides the best images. The resulting
images have increased resolution (15μm) and are able to resolve very thin non-uniform
near-wall temperature layers (down to 60μm from the surface). The temperature field and
thickness measurements of near-wall shock tube flows under various shock conditions
and test gases showed good agreement with boundary layer theory.
To conclude this thesis, new applications and future improvements to the
developed PLIF diagnostic technique are discussed. These suggested refinements can
provide an even more robust and versatile PLIF imaging technique capable of measuring
a wider range of flow conditions near walls.
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Acknowledgements
My accomplishment would not have been possible without the generosity of all
those around me. I thank my advisor, Professor Ron Hanson, for his leadership and
guidance throughout my graduate studies at Stanford. I would also like to thank Dr.
David Davidson and Dr. Jay Jeffries for their motivation and inspiration. I thank all my
friends in the Hanson group for their invaluable advice and support and Daniel Mitchell
for his expertise in CFD. In particular, I thank Brian Cheung, a phenomenal lab mate and
a great friend.
I am sincerely grateful to my parents, for their constant encouragement and
support. None of this would be possible without them. Lastly, I am forever debted to my
wife, Suhwa, for unfailing love and sacrifice. My endeavor would not have been as
pleasant or meaningful without you.
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Table of Contents
Abstract .............................................................................................................................. v
Acknowledgements ......................................................................................................... vii
Table of Contents ............................................................................................................. ix
Chapter 1. Introduction ............................................................................................... 1
1.1 Background and Motivation ................................................................................ 1
1.2 PLIF diagnostic validation using shock waves .................................................... 3
1.3 Near-wall PLIF diagnostic in shock tubes ........................................................... 4
1.4 Thesis Overview .................................................................................................. 6
Chapter 2. Spectroscopy .............................................................................................. 7
2.1 Basic LIF theory .................................................................................................. 7
2.1.1 Quantum energy transfer processes in LIF diagnostics .............................. 7
2.1.2 LIF equation ................................................................................................ 9
2.2 PLIF tracer study ................................................................................................ 10
2.2.1 Tracer selection ......................................................................................... 10
2.2.2 Toluene absorption.................................................................................... 15
2.2.3 Toluene fluorescence quantum yield ........................................................ 16
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Chapter 3. Experimental setup ................................................................................. 25
3.1 Facility overview ............................................................................................... 25
3.1.1 Shock tube ................................................................................................. 26
3.1.2 PLIF test section ....................................................................................... 28
3.1.3 Laser system.............................................................................................. 31
3.1.4 Detection system ....................................................................................... 34
3.2 Data acquisition and processing ......................................................................... 36
3.2.1 Image processing and correction .............................................................. 37
3.3 Near-wall PLIF imaging facility optimization ................................................... 40
3.3.1 Wall selection ............................................................................................ 41
3.3.2 Optical configuration ................................................................................ 43
Polarization ......................................................................................... 44
Optical filter ........................................................................................ 45
Laser sheet orientation ........................................................................ 46
Laser sheet incident angle and collection angle .................................. 48
3.3.3 Metal wall diagnostics optimization ......................................................... 51
3.4 Conclusion ......................................................................................................... 52
Chapter 4. PLIF diagnostic validation using shock waves ..................................... 53
4.1 Theoretical background ..................................................................................... 53
4.1.1 Normal shock wave equations .................................................................. 54
4.1.2 Shock reflection (SMR) ............................................................................ 57
4.2 Experimental setup............................................................................................. 61
4.3 Core flow thermometry ...................................................................................... 64
4.3.1 Temperature measurement behind normal shocks .................................... 64
4.3.2 Signal-to-noise ratio analysis .................................................................... 66
4.3.3 Validation using analytical results ............................................................ 67
4.4 Flow over a wedge ............................................................................................. 68
4.4.1 PLIF measurement .................................................................................... 69
4.4.2 Numerical model ....................................................................................... 69
4.4.3 Comparison ............................................................................................... 70
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4.5 Conclusion ......................................................................................................... 72
Chapter 5. Near-wall PLIF diagnostic in shock tubes ............................................ 73
5.1 Theoretical background ..................................................................................... 74
5.1.1 Side wall boundary layer .......................................................................... 75
5.1.2 End-wall thermal layer .............................................................................. 80
5.2 Experimental setup............................................................................................. 81
5.3 Boundary layer temperature profile ................................................................... 84
5.3.1 Side wall boundary layer .......................................................................... 84
5.3.2 End wall thermal layer .............................................................................. 90
5.4 Boundary layer development ............................................................................. 92
5.4.1 Side wall.................................................................................................... 92
5.4.2 End-wall .................................................................................................... 96
5.5 Conclusion ......................................................................................................... 97
Chapter 6. Conclusion and future work .................................................................. 99
6.1 Summary of results .......................................................................................... 100
6.1.1 Study 1: PLIF diagnostic validation using shock waves ........................ 100
6.1.2 Study 2: Near-wall PLIF diagnostic in shock tubes................................ 101
6.2 Suggested future work ..................................................................................... 102
Appendix A. BSDF of transmitting samples ........................................................... 105
Appendix B. PLIF test section design ...................................................................... 107
Appendix C. DaVis codes .......................................................................................... 109
References ...................................................................................................................... 118
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List of Tables
Table 2.1: Comparison of candidate tracer. ................................................................................... 11
Table 2.2: Absolute FQY variation for three candidate tracers between 0.005 – 1bar pressure in N2 bath, 248nm excitation wavelength, and 296K [32]. ............................ 13
Table 2.3: Absolute FQY values of candidate tracers at different excitation wavelengths at 296K, 5-23mbar tracer partial pressure, 1bar total pressure, balanced with N2. ................................................................................................................................ 14
Table 2.4: Absorption cross-section measurement of candidate tracers at different excitation wavelength in units of 10-20cm2/molecule at room temperature, 1bar total pressure. ............................................................................................................... 14
Table 2.5: Coefficients for low-pressure toluene relative FQY correction. ................................... 20
Table 3.1: Specifications of the KrF excimer laser used in this study. .......................................... 33
Table 3.2: Specification of the ICCD camera used in this study. .................................................. 36
Table 4.1: Comparison of measured and synthesized PLIF signal values for various regions of the flow. Results from all but 1 region agree very well. ............................. 72
Table 5.1: List of core flow conditions behind incident shocks given in Figure 5.11. .................. 93
Table 5.2: Comparison of thermal boundary layer thickness, 1cm behind the incident shock. Flow conditions are listed in Table 5.1 ............................................................. 94
Table 5.3: List of core flow conditions behind the incident shocks given in Figure 5.12. ............ 95
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List of figures Figure 2.1: Plot of simulated fluorescence signal per unit mole fraction with respect to
temperature for three tracer candidates at 248nm excitation wavelength, 1bar pressure, and N2 bath gas. Plots of fluorescence near zero are magnified in the lower plot. These profiles are plotted using a best-fit numerical model to the photophysical parameter measurements. ........................................................ 12
Figure 2.2: Toluene absorption cross-section at the 248nm and 266nm excitation wavelengths. σ at 248nm is constant throughout the 300K - 900K temperature range while at 266nm σ increases due to the broadening of (0,0) band [32]. These profiles are plotted using a best fit to absorption cross-section measurements. .............................................................................................. 16
Figure 2.3: A simple photophysical diagram of the important decay processes for toluene LIF involving the ground and excited singlet state (S0 and S1, respectively) and the excited triplet state (T1). Internal conversion (IC) becomes important for some states at higher energies. Intersystem crossing (ISC) is the dominant non-collisional process at low vibrational energies. ................................. 17
Figure 2.4: Toluene relative fluorescence quantum yield at 248nm and 266nm excitation in 1bar total pressure balanced with N2. Both wavelengths show similar sensitivity to 300K – 900K temperature range. The plot is a best fit to data from [54]. .................................................................................................................. 18
Figure 2.5: Relative FQY for various partial pressures of toluene in N2 bath gas, 296K, and 248nm excitation wavelength. Solid lines are best fits to the data. The relative FQY values are normalized to the absolute FQY at 1bar total pressure for each of the corresponding toluene partial pressure. Extrapolation using the numerical fit is tested to be effective up to 2bar total pressure. .................................................................................................................... 20
Figure 3.1: Overall view of the Aerosol shock tube. Overall length is 16m. 3m driver section with 15cm internal diameter. 9.6m and 2.4m driven section with circular and square cross-section, respectively. ........................................................ 26
Figure 3.2: Schematic of operation. (A) The shock tube is filled with driven gas mixture and the driver section is rapidly filled until the diaphragm bursts. (B) The incident shock then compresses and heats the driven gas. (C) Upon reflection from the end wall, the reflected shock wave compresses and heats the driven gas for a second time. ............................................................................... 27
Figure 3.3: Photos of the PLIF test section. (LEFT) Side view, shown with the extension section and the aluminum base plate in place. The end wall is on the far right. Two of the four support rods are also shown. (RIGHT) End view, sensor array plate is visible on the bottom of the test section. .................................. 29
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Figure 3.4: Drawings of the PLIF test section. (LEFT) Side view, shown with the extension section and the aluminum base plate in place. The end wall is on the far right. (RIGHT) Exploded view, the four side window frames are modular. Support rods and base plate are not shown. ............................................... 29
Figure 3.5: Various types of excimer laser and their excitation wavelengths. ............................... 31
Figure 3.6: Potential energy state diagram of an excited dimer. The bound upper state undergoes spontaneous emission to a highly repulsive ground state. ....................... 32
Figure 3.7: Fluorescence signal with respect to laser fluence. Fluorescence signal begins to saturate at 130mJ/cm2. At this fluence level, fluorescence signal deviation from linearity is 4.7%. Test conditions are 5% toluene in nitrogen at room temperature and 0.1bar. ............................................................................................. 34
Figure 3.8: Cross-section of an ICCD camera optical element. ..................................................... 35
Figure 3.9: Correction process of PLIF image with reflected shock in frame. Image A: Raw image straight from the camera; Image B: Corrected for dark noise; Image C: Corrected for laser energy variation; Image D: Corrected for laser sheet and collection angle variation; Image E: Corrected for absorption and optical distortion. All images but image E are displayed using the same color scale. The image E color scale is altered to highlight the thermal layer near the end wall. ...................................................................................................... 39
Figure 3.10: Experimental setup for testing surface-laser interaction. Various metallic and non-metallic materials and surface finishes are tested. ............................................. 42
Figure 3.11: Laser light scatter comparison for different wall types and surface conditions. The schematic on the left depicts the location of sample material in the image, scatter, and laser sheet. Image A: Fused silica using 248nm notch filter; Image B: Aluminum #8 using 248nm notch filter; Image C: Fused silica (dirty surface) using 250 – 400nm bandpass filter; Image D: Fused silica (clean surface) using 250 – 400nm bandpass filter. .............................. 43
Figure 3.12: Comparison of surface scatter with respect to laser sheet polarization. Left: s-polarized light sheet; Right: p-polarized light sheet; each image is normalized for laser energy variation. ...................................................................... 44
Figure 3.13: Horizontal profile along the center of both images in Figure 3.12. The profiles are averaged across 5 pixels in width........................................................... 45
Figure 3.14: (TOP) Spectrally resolved KrF excimer laser wavelength and the subsequent toluene emission spectra. The broadband emission spectra range from 260nm to 400nm. (BOTTOM) Transmission curves of the two optical filters tested for this experiment. ............................................................................... 46
Figure 3.15: Schematic of the laser sheet orientation configuration with respect to the wall and near-wall flow phenomenon. 1: Bottom-up, 2: Top-down perpendicular orientation, 3: Parallel orientation. Shock tube end wall is located on the right. The incident shock in the schematic is traveling from left to right towards the end wall. The camera was placed perpendicular to the laser sheets, and the images were taken through the side wall window. ............. 47
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Figure 3.16: Laser sheet orientation direction comparison. Images of the side wall thermal boundary layer behind incident shock waves, immediately next to the side wall 7cm away from the end wall are measured using the perpendicular and parallel orientation. Image A: Acquired using the bottom-up perpendicular orientation. Image B: Acquired using the parallel orientation. Shock conditions are: T1=296K, P1=0.075bar, Vs=900m/s, and attn=4%/m. ................................................................................................................ 47
Figure 3.17: (LEFT) Schematic of an incidence angle and various collection angles with respect to the fused silica window in cylindrical coordinate. Only the limits of the collection angle are shown. (RIGHT) Images of surface scatter from fused silica at various collection in the XY-plane at normal incidence (θi=180°). The laser sheet is in the XZ-plane. The regular experimental setup collects the fluorescence signal at θr=90°. ................................................................ 48
Figure 3.18: Sample BRDF curve of silicon wafer at θi=0º and θi=45º for ϕ=0º. Incident and collection angles are defined using the schematic in Fig 3.17. In both cases (θi=0º, 45º), BRDF goes to zero at θr=-86º and -67º, respectively. .................. 49
Figure 3.19: Comparison of fused silica surface scatter measurements against silicon wafer BRDF under normal incidence. BRDF is in units of [sr-1], and the fused silica surface scatter measurements are normalized to the peak BRDF value at 0°. ................................................................................................................ 50
Figure 3.20: Comparison of surface scatter from mirrored metallic surface. (Left) Clean surface without surface treatment. (Right) Same surface treated with black felt tip pen. Small points of heavier scatter intensity may be attributed to bulk particulates. ....................................................................................................... 52
Figure 4.1: Schematic of a normal shock wave in shock-fixed coordinate system. The system is considered adiabatic and in steady-state. Flow conditions in region 1 and 2 are uniform. .................................................................................................. 55
Figure 4.2: Regular reflection in pseudo steady flow viewed from an inertial frame fixed in point P. .................................................................................................................. 57
Figure 4.3: Regular reflection in (θ,p)-space. The first and second locus is the incident and reflected shock, respectively. Note that the reflected shock locus intersects with θ = 0, allowing the flow behind the reflected shock to be parallel with the wedge. ............................................................................................ 58
Figure 4.4: Mach reflection in pseudo-steady flow viewed from an inertial frame fixed in triple point P. ............................................................................................................. 58
Figure 4.5: Mach reflection in (θ,P)-space. The second locus does not intersect with θ = 0 and the triple point is detached from the surface. A third locus, S, is needed to bring the flow back to θ = 0. ................................................................................. 59
Figure 4.6: Physical representation of Single Mach reflection (SMR) in pseudo-steady flow viewed from an inertial frame fixed in triple point P. ....................................... 60
Figure 4.7: Vortex sheet curling and streamlines near vortex sheet V behind the reflected shock in SMR. ........................................................................................................... 60
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Figure 4.8: Schematic of the shock tube and laser setup. In this configuration the horizontal laser sheet enters through the end wall, and is imaged through the top window. ............................................................................................................... 61
Figure 4.9: Diffraction due to grazing angle of laser sheet propagation. Arrows and angle values in the figure indicate grazing angle of incident laser sheet with respect to the shock wave front. Incident shock wave location and its propagating direction are also marked. The edge of the laser sheet (denoted by the dotted line in the bottom image) is visible just behind the incident shock wave in the bottom image with the same propagation direction as the diffraction effect. ....................................................................................................... 62
Figure 4.10: Top view of the test section. The test section was rotated 90° so that sensor array plate that the wedge is attached to is on the side. This allows the camera to see all three sides of the wedge through the top window. ........................ 63
Figure 4.11: Incident shock wave measurement. (LEFT) Corrected PLIF signal and (RIGHT) temperature image. Initial conditions: P1=0.067bar, Xtol=3.8%, T1=296K, VS=546m/s, incident shock attenuation = 1.3%/m. Downward-pointing arrow: direction of incident shock. ............................................................. 64
Figure 4.12: Reflected shock wave measurement. (LEFT) Corrected PLIF signal and (RIGHT) temperature image. Initial conditions: P1=0.031bar, Xtol=4.5%, T1=296K, VS = 723m/s, incident shock attenuation = 1.5%/m. Upward-pointing arrow: direction of reflected shock wave. ................................................... 65
Figure 4.13: Temperature and residual temperature (between measured and predicted) profiles in the core flow across the incident shock. Upper plots: vertical profile along the central column of pixels (averaged across 5 pixels width); Lower plots: horizontal profile along the row of pixels 0.5mm and 1cm behind incident shocks; a flat temperature distribution across the laser sheet is evident. .................................................................................................................. 65
Figure 4.14: Temperature and residual temperature (between measured and predicted) profiles in the core flow across the reflected shock. Upper plots: vertical profile along the central column of pixels (averaged across 5 pixels width); Lower plots: horizontal profile along the row of pixels 0.5mm and 1cm behind reflected shocks; a flat temperature distribution across the laser sheet is evident. .................................................................................................................. 66
Figure 4.15: SNR as a function of pixel resolution using hardware binning. Toluene mole fraction, Xtol, for both temperatures was fixed at 0.9%. ............................................ 67
Figure 4.16: Predicted versus measured temperature in the core flow. Single-shot images were taken at full resolution without hardware binning. ........................................... 68
Figure 4.17: PLIF image of an incident shock traveling over a wedge. Single Mach reflection is visible. ................................................................................................... 69
Figure 4.18: Temperature field simulated using Fluent 6.0. The incident shock is traveling from left to right. The reflected shock and the vortex sheet are also visible. ....................................................................................................................... 70
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Figure 4.19: (LEFT) Synthesized PLIF image created from the CFD results; (RIGHT) Experimental PLIF image measured in a shock tube. PLIF signal profile along the dotted line is shown in Figure 4.20. .......................................................... 71
Figure 4.20: PLIF signal profile along the dotted line in Figure 4.19. .......................................... 71
Figure 5.1: Schematic of laminar boundary layer velocity gradient. ............................................. 76
Figure 5.2: Two semi-infinite regions in perfect thermal contact. Temperature profile across the end wall window and the test section is also shown. ............................... 81
Figure 5.3: Schematic of the shock tube and laser setup. Mirror 2 deflects the laser sheet to enter the test section through its side or end wall window. It is removed when imaging through end wall window. ................................................................. 82
Figure 5.4: (TOP) Corrected image of the laser scatter level taken under vacuum in the absence of a shock wave. White pixels represent the side wall. A detailed view near the wall is also shown. (BOTTOM) A Plot of one-pixel wide laser scatter signal along the horizontal dashed line indicated on the image. ........... 84
Figure 5.5: (LEFT TOP) Experimental PLIF image of reflected shock bifurcation in toluene (4%) with nitrogen. (LEFT BOTTOM) Synthetic PLIF image calculated using CFD results. CFD modeling courtesy of Center for Turbulence Research at Stanford. A thin boundary layer is visible to the left of the shock wave bifurcation. Shock conditions are P1=0.04bar, T1= 293K, test gas: N2, with 4% toluene, Vs=710m/s, and incident shock attenuation = 0.5%/m. Conditions in the core flow are T2=498K, P2=0.25bar, and T5=696K, P5=1.05bar. (RIGHT) Schematic of the boundary layer and reflected shock interaction. ....................................................................................... 86
Figure 5.6: (LEFT) Side wall thermal boundary layer PLIF signal and (RIGHT) temperature image. Shock conditions are P1=0.08bar, T1= 293K, test gas: H2,
with 4% toluene, Vs=1030m/s, and incident shock attenuation = 0.7%/m. Conditions in the core flow are T2=346K, P2=0.144bar, and U∞=400m/s. The incident shock flow travels in the downward direction. .................................... 87
Figure 5.7: (TOP) Measured and predicted temperature profile 7.5cm away from the end wall in Figure 5.6. The measured profile is an average of a 5 pixel wide row horizontally across the temperature image at its center. A detailed view near the side wall is shown in the inset. (BOTTOM) Residual temperature (between predicted and measured temperatures) profile. The shock and flow conditions are listed under Figure 5.6. ...................................................................... 88
Figure 5.8: Predicted temperature distribution near the end wall for various thermal conductivity, k. .......................................................................................................... 89
Figure 5.9: Measured and predicted temperature profile about 30μs behind the incident shock. The measured profile is an average of a 5 pixel wide row. Temperature measurement in the side wall thermal boundary layer show good agreement with predicted values except for a thin region about 60μm from the surface. ....................................................................................................... 89
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Figure 5.10: (LEFT) End wall thermal layer PLIF signal and (RIGHT) temperature image. Shock conditions are P1=60torr, T1= 296K, bath gas: H2, with 3% toluene, Vs=1010m/s. Image was taken about 2.3ms after shock reflection. Core flow conditions behind reflected shock are T5=368K, P5=0.19bar. The reflected shock travels in an upward direction. ......................................................... 90
Figure 5.11: Measured and predicted temperature profile along the center of temperature image in Figure 5.9. Measured profile is an average of a 5 pixel wide column across the entire height of the image. A detailed view near the end wall is shown in the inset. (BOTTOM) Residual temperature (between predicted and measured temperatures) profile. The shock conditions are listed under Figure 5.9. Core flow conditions behind reflected shock are T5=368K, P5=0.19bar. Measured T5=364K. The discrepancy in core flow temperature measurement is within the measurement uncertainty. .......................... 91
Figure 5.12: Measured and predicted temperature profile close to the end wall at higher temperature. Flow conditions are: T5=934K and P5=0.45bar. Measured T5=910K. ................................................................................................................... 92
Figure 5.13: Continuous thermal boundary layer visualization. The image was constructed from 5 different PLIF signal images taken 10µs apart in succession. The image color scheme was adjusted to highlight boundary layer development with respect to distance behind incident shock wave front. Initial conditions are T1=293K, P1=0.02bar, H2, with 6% toluene. Core flow conditions are T2=345K, P2=0.04bar. ............................................................... 93
Figure 5.14: Side wall thermal boundary layer thickness behind incident shocks with respect to shock strength. Initial pressure was varied from P1=7 to 23torr to produce shocks in T1=293K and N2 bath gas. Solid lines are calculations from boundary layer theory. Flow conditions behind each shock are listed in Table 5.1................................................................................................................... 94
Figure 5.15: Side wall thermal boundary layer thickness behind incident shocks in N2, H2, and Ar bath gas. Initial conditions are P1=7torr and T1=293K. Lines are theoretical calculations from boundary layer theory. Toluene mole fraction in all three shocks was about 8.5%. Flow conditions behind each shock are listed in Table 5.3. ..................................................................................................... 95
Figure 5.16: End wall thermal layer thickness behind a reflected shock. Initial conditions are T1=293K and P1=0.14bar, bath gas: H2, with 1.5% toluene Vs=1100m/s. The solid line is calculated using the heat diffusion equation. Conditions in the core flow behind the incident shock are T5=340K and P5=0.24bar. ................... 97
Figure A.1: Geometry for defining BSDF. Subscript i and s refer to incident and scatter component. ............................................................................................................... 105
Figure B.1: Cross-section of the window frame assembly, shown here with two adjoining windows and window frames. ................................................................................. 107
Figure B.2: Cross-section of the end wall window assembly, shown here with side wall windows and frames. ............................................................................................... 108
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1
Chapter 1. Introduction
1.1 Background and Motivation
In 2008, nearly 85% of US energy consumption was derived from fossil fuels [1].
Despite increasing attention to renewable energy resources, combustion is still the
dominant process for energy conversion especially in the transportation sector [2,3].
Study of combustion and reactive flow phenomena is therefore extremely important. One
area of combustion research is chemical kinetics, the investigation of how different
experimental conditions can influence the speed of chemical reactions and products.
Shock tubes are commonly employed to provide test conditions necessary for chemical
kinetic research. However, like all experimental facilities, a good understanding of their
non-ideal behaviors is crucial. For example, boundary layer effects can strongly affect the
ideal nature of the experiment. Boundary layers are especially hard to characterize using
line-of-sight measurement techniques due to their proximity to shock tube wall surfaces,
and thickness. One solution is to use the planar laser-induced fluorescence (PLIF)
imaging. This technique can provide effectively instantaneous, spatially resolved 2-D
images of key flow parameters, such as temperature, and easily determine the extent of
the boundary layer and its effect on the core flow. Also, understanding of the temperature
distribution of a flow field is very important since temperature can affect chemical
reaction rates and mechanisms, thereby dictating chemical reaction pathways.
PLIF imaging is a diagnostic process dependent on the spectroscopic nature of the
target species. In this thesis, the target species utilized for the PLIF imaging technique is
2
a tracer molecule introduced into the system solely for the purpose of the diagnostic. In
the diagnostic process, the tracer molecules absorb a resonant photon from a light source,
and the resultant excited molecules subsequently spontaneously emit photons. The
emitted photons yield information regarding the tracer molecules and their immediate
surroundings, which can be collected using detectors, such as CCD cameras. The non-
intrusive nature of the diagnostic makes PLIF ideal for monitoring combustion and
reactive flows where conditions are extremely harsh and physical probes have the
potential to disturb flow structures and alter the flow parameters in question. The aim of
this thesis is to develop an innovative method of using the PLIF imaging technique that is
suited for instantaneous temperature field measurements in shock tube flows.
PLIF has made great contributions in the field of fundamental and practical
combustion research [4]. Improvements in laser and camera technologies have spurred an
explosion of development for PLIF, in a wide range of applications [5]. More and more
chemical species, such as OH [6], NO [7], CO2 [8], acetone [9], and 3-pentanone [10],
have been utilized as tracer species. Each chemical species is suited for different
applications and excitation strategies. No one tracer and excitation source is apparently
the best as an overarching diagnostic tool for all combustion and reactive flow
applications. In addition, many applications require PLIF signals to be averaged many
times over due to low signal yield and lack of proper excitation scheme. Therefore, much
of this thesis is focused on expanding applications on existing diagnostics and improving
single-shot signal quality.
In this thesis, an innovative diagnostic technique based on single-shot PLIF is
developed for monitoring high-speed flow phenomena in the core and the near-wall
sections of a shock tube through the use of optimized experimental setup and toluene
photophysical models. With some modifications, this technique can be used to study and
improve near-wall performance of many current and next generation energy conversion
devices.
Future research directions are also described in three main categories: diagnostic
system improvements, new flow field applications, and extension of photophysical
database.
3
1.2 PLIF diagnostic validation using shock waves
The use of quantitative single-shot PLIF diagnostics in shock tubes have been
discouraged by two key factors. First, lack of tracer-specific spectroscopic databases for
many tracer molecules limits PLIF diagnostics to qualitative analysis [11,12], such as
visualization of mixing [13,14] and flow instabilities [15,16]. Recent efforts have been
invested into determining photophysical parameters for a wide variety of small tracer
molecules. Complex spectroscopic models have been developed for simple molecules
such as NO [17]. For example, Lee et al. demonstrated temperature [18] and density [19]
field measurements in high-pressure conditions using NO and CO2, respectively in a
high-pressure flat flame. McMillin et al. demonstrated temperature measurement in a
transverse jet in a supersonic cross flow using two-line fluorescence of NO [14].
However large polyatomic molecules, such as acetone, 3-pentanone, and toluene
generally rely on incomplete empirical databases from which to extract photophysical
parameters. Second, PLIF signal intensities are weak due to the lack of optimized
excitation strategies. Previous measurements [18,19] circumvented this issue by
averaging repetitive measurement in relatively constant environments, to boost signal-to-
noise ratio (SNR). Averaged measurements limit diagnostics to steady-state applications,
but shock tubes are transient in nature. Therefore a single-shot imaging technique is
needed, requiring high levels of signal from the tracer.
This study is focused on developing a tracer-based PLIF diagnostic technique that
can provide high-quality single-shot temperature images. An optimal tracer and
excitation scheme was selected to allow the PLIF diagnostic technique for shock tube
imaging. A review of the photophysical parameters for the chosen tracer at the
temperature and pressure conditions of interest indicated that additional measurements of
fluorescence quantum yield (FQY) were needed. Additional measurements were thus
made to complete the photophysics database required to convert a PLIF signal image into
a quantitative temperature image. The resulting PLIF imaging technique is capable of
measuring the temperature field in regions of known pressure and tracer mole fraction.
Temperature images can be obtained with or without the presence of shock waves in the
flow field.
4
The PLIF diagnostic technique was validated in shock tubes against predicted
temperatures calculated with 1-D shock wave equations. Core flow images capture a step
rise in temperature across incident and reflected shock waves, as well as a uniform
temperature distribution in the shock-heated test gas behind the two shock waves. The
experimental results from the PLIF diagnostic technique agreed very well with theoretical
predictions. The PLIF diagnostic technique was then applied to a shock wave passing
over a wedge in which a well-defined single Mach reflection (SMR) was observed. The
PLIF image of the SMR was validated with a synthesized PLIF image calculated using
the results from a numerical analysis and was found to be in good agreement in almost all
flow regions. Temperature measurements away from the wedge that were unaffected by
the SMR agreed very well with numerical results. This study demonstrates the
diagnostic’s ability to accurately assess uniform temperature fields in any shock tube
flow conditions where the knowledge of pressure and tracer density distribution is
available.
1.3 Near-wall PLIF diagnostic in shock tubes
Near-wall flows in shock tubes are more difficult to image than core flows due to
their proximity to nearby surfaces and their narrow thickness. The rudimentary flow
visualization techniques developed for wide field applications at the beginning of last
century, such as smoke wires and dye injection, were not capable of discerning the
existence of thin layers near walls [20]. Some of the first experimental evidences of near-
wall boundary layers were provided in the 1940’s by Dryden et al., nearly 40 years after
the theory was introduced by Prandtl. Despite the continual development of new imaging
techniques, quantitative boundary layer analysis has largely been the subject only of
theoretical studies [21,22,23]. This is because developing an optical diagnostic near a
surface can be challenging. In PLIF diagnostics, for example, scattered and reflected light
from the surface can interfere with fluorescence signal.
This study aims to extend the PLIF diagnostic technique to regions of near-wall
flows in shock tubes. Various experiments were performed, in this thesis, to test different
5
types of wall materials, surface finishes, laser sheet polarization, optical filters, laser
sheet orientation, and incident and collection angle. These results were used to optimize
the experimental setup for near-wall imaging in shock tube flows. A minimal distance
from which a reliable quantitative measurement can be made was also determined.
Two near-wall shock tube flows were investigated using the optimized
experimental setup. The first near-wall flow of interest is the side wall boundary layer
(SWBL). This is a non-ideal flow due to the viscous forces generated in the fast moving
shock-heated gas behind the incident shock wave. In shock tubes, non-ideal effects from
the boundary layer may propagate into the core flow and lead to changes in flow
conditions. In general, the momentum and heat transfer across the boundary layer to the
free stream can induce flow separation, shock bifurcation, and other viscous phenomena
that are of great engineering interest. The Navier-Stokes equation can be used to solve for
boundary layers. A simplified 2-D Navier-Stokes equation was used to solve for
temperature distribution within the laminar boundary layer. No turbulent boundary layer
was detected in the current dataset. The experimental results of the SWBL temperature
distribution and thicknesses in various bath gases agreed well with theoretical
predictions.
The second near-wall flow of interest is the end wall thermal layer (EWTL). This
is a heat transfer phenomenon due to diffusion in the quiescent shock-heated gas behind
the reflected shock wave. A thermal layer should not be confused with a thermal
boundary layer, the latter of which is dominated by viscous effects. EWTLs are thicker
and continue to develop for longer period of time than SWBLs. Developing a diagnostic
technique to quantify this layer is of critical interest in shock tube chemical kinetics
research, as most measurements are made very close to the end wall where the EWTL
exists. A 1-D heat diffusion equation was used to solve for the temperature distribution
within the EWTL. The experimental results of EWTL temperature distribution and
thickness agreed well with theoretical predictions. This study demonstrates the
diagnostic’s ability to accurately assess the temperature distribution in non-uniform
regions, even in the presence of nearby walls.
6
1.4 Thesis Overview
This thesis is divided into six chapters. Chapter 2 reviews the basics of molecular
spectroscopy and PLIF diagnostics, with an emphasis on the toluene tracer. A literature
survey of previous studies on toluene spectroscopy is included which illustrates the need
for more photophysical measurements. The necessary data are presented in this chapter.
The first half of Chapter 3 details the design of the experimental setup, data acquisition,
and image processing procedures used throughout this thesis. The latter half elaborates on
the process of optimizing the experimental facility for near-wall imaging. The next main
topic, development of a quantitative temperature diagnostic using tracer-based PLIF, is
detailed in Chapter 4. Validation of the diagnostic technique for flow behind a normal
shock waves and flow over a wedge are presented. Subsequently, development of a
quantitative near-wall temperature measurement using tracer-based PLIF, is presented in
Chapter 5. Application of the optimized PLIF diagnostic technique for high-resolution
temperature measurements close to a wall surface is presented, along with measurements
of the boundary layer development. Chapter 6 concludes the research efforts covered in
this thesis, and discusses future directions and applications.
7
Chapter 2. Spectroscopy
2.1 Basic LIF theory
Laser-induced fluorescence (LIF) is a diagnostics tool widely used throughout
scientific and engineering disciplines. In the fields of reacting flow and combustion
research, LIF is used to measure key flow parameters using a tracer-specific laser light
source for quantitative imaging. The planar LIF (PLIF) diagnostic is a two-dimensional
variation of LIF, capable of visualizing planar distribution of flow parameters. Due to
continuing development of more sensitive optical equipment and faster diagnostic
techniques, PLIF imaging can be applied to fast-moving and transient flow phenomena
using single-shot measurements. The historic progression of PLIF diagnostics in the field
of reactive flows and combustion can be found in [24,25,26]. This chapter discusses the
basic LIF spectroscopy theory for interpreting and analyzing fluorescence signals
acquired experimentally. In addition, a survey of previous tracer-based LIF studies is
briefly presented followed by an in-depth discussion on UV-excited toluene
spectroscopy.
2.1.1 Quantum energy transfer processes in LIF diagnostics
A simplified LIF model is presented here, to introduce the concepts of LIF, and
the quantum energy transfer processes involved in LIF diagnostics. First, photons from a
light source, usually a laser, are selectively absorbed by a tracer species and excited to a
8
higher energy state. A properly-tuned laser provides the high-intensity resonant photons
required for LIF diagnostics. Excited tracer molecules in higher energy states
subsequently relax back down to their original state, the ground state, either through
radiative or non-radiative pathways. The radiative pathways include fluorescence in
which the excessive energy is released via photons. This process is of critical importance
in LIF diagnostics. Relaxation by any other means in either radiative or non-radiative
pathways competes with the fluorescence signal. Radiative relaxation pathways include
stimulated emission and spontaneous emission. Non-radiative relaxation pathways
include rovibrational energy transfer, collisional quenching, and dissociation. Each
energy transfer process is discussed briefly below.
Stimulated emission is solely due to the interaction between the resonant photon
and tracer molecule. Molecules in the excited upper state relax down to the ground state
by way of stimulated emission to counteract the changes in the ground and excited state
population distribution.
Spontaneous emission describes the rate of fluorescence as a result of photons
spontaneously relaxing from an upper excited state to a ground electronic state. The
emitted fluorescence signals are collected and interpreted using various LIF diagnostic
techniques. Spontaneous emission may relax the excited molecules into any number of
vibrational levels in the lower electronic state, not necessarily to the original ground state.
Rovibrational energy transfer is a non-radiative pathway due to molecular
collisions. It can shift the vibrational and rotational states of a molecule into nearby states
to counteract the disturbance to thermal equilibrium. Transfer rates will vary depending
on collision partners. Vibrational energy transfer plays a crucial role in low-pressure
toluene fluorescence. Detailed description of its effects on toluene can be found in section
2.2.3.
Collisional quenching is much like rovibrational energy transfer in that it also
involves molecular collisions. For collisional quenching, however, a molecule relaxes
down to its ground electronic energy state, completely eliminating the possibility of
fluorescence, unlike rovibrational energy transfer. It is one of the main competing
mechanisms to fluorescence and becomes more significant at higher pressures.
9
Dissociation is a chemical phenomenon as a result of collision, in which a
molecule separates into two or more smaller molecules. It competes with the fluorescence
process by reducing the tracer molecule number density. In the case of rovibrationally
excited toluene, a small portion dissociates into benzyl + H [27].
Dominant processes in LIF analysis are not limited to the energy transfer
mechanisms mentioned thus far. Excited molecules may relax via ionization, intersystem
crossing or other pathways. In some cases, the molecule may absorb more than one
resonant photon. Dominating energy transfer modes vary between molecules. Therefore a
comprehensive understanding of energy transfer processes is required to accurately
quantify LIF measurements. Further details on molecular energy states and spectroscopy
can be found in [28,29,30].
2.1.2 LIF equation
Tracer excitation in PLIF diagnostics is often achieved using short-pulsed lasers
(on the order of tens of nanoseconds). In addition, if the changes in the ground state
number density are not substantial, also known as the weak excitation regime, the time-
integrated fluorescence signal Sf (in units of photons) collected by the detector can be
described using a simple equation called the linear LIF equation.
Ω4
Equation 2.1
where E is the incident laser energy fluence [J/cm2], λ is the laser wavelength [nm], h is
the Planck’s constant [Js], c is the speed of light in vacuum [cm/s], A is the area of the
probed volume [cm2], L is the length of the probed volume [cm], n is the tracer number
density [cm-3], is the absorption cross-section [cm2], is the fluorescence quantum
yield (FQY), is the detector collection angle, and is the detector collection efficiency.
The absorption cross-section and the FQY describe the probability of a molecule
absorbing and emitting photons, respectively. The two parameters are collectively known
as photophysical parameters. Absorption cross-section and fluorescence quantum yield
10
are both functions of temperature, pressure, and excitation wavelength. Theoretical
evaluation of the absorption cross-section is simpler for diatomic molecules such as OH
and NO, as they have limited energy states in the rovibronic manifolds. For larger and
heavier molecules such as acetone, 3-pentanone, and toluene, overlaps amongst the
energy levels are such that individual energy transitions cannot be probed [31]. Rather, a
number of individual transitions are lumped together in the form of a broadband
excitation and evaluated experimentally. In most cases, larger molecules have higher
amounts of fluorescence due to broader absorption spectra [32].
2.2 PLIF tracer study
Proper tracer species and excitation strategy selection is very important in
developing LIF diagnostic techniques. Numerous tracer candidates such as, OH, NO,
CO2, acetone, 3-pentanone, toluene and etc., have unique characteristics that may be
advantageous in some applications but disadvantageous in others. A comprehensive list
of tracer candidates can be found in [9,33]. To further complicate the issue, each tracer
has its own set of optimized excitation strategies depending on the application at hand.
This section covers the selection process for the optimum tracer and excitation strategy
used throughout this thesis, followed by literature survey and detailed photophysical
description of the selected tracer.
2.2.1 Tracer selection
Certain PLIF diagnostic techniques rely on nascent molecules in the flow field as
tracer species. Examples include OH in flame front visualization [6,34] and NO in
premixed flat flames [35]. However in many cases, tracer molecules are seeded into the
flow field due to the lack of nascent fluorescent molecules. The ideal PLIF diagnostic
tracer should possess the following characteristics:
11
1. Strong non-resonant fluorescence spectrum in the near-UV
2. Accessible absorption spectrum using high-powered laser sources
3. High vapor pressure at room temperature and pressure (for easier seeding and
increased fluorescence signal)
4. Easy and safe handling procedures
Additional tracer requirements specific to this study are high temperature sensitivity and
adequate fluorescence signal at high temperature. Three tracers matching these criterions
are listed in Table 2.1.
Acetone 3-pentanone Toluene
Chemical formula (CH3)2CO (CH3CH2)2CO C6H5CH3
Accessible wavelength [nm] 248, 266, 308 248, 266, 308 248, 266
Sat. pressure (296K) [mmHg] 185 28 22
, (296K) [cm2] 1.6 x10-20 2 x10-20 3.1 x10-19
FQY, 0.84 x10-3 (308nm, 4-40torr)
0.45 x10-3 (308nm, 1-8torr)
0.056 (248nm, 23torr)
Table 2.1: Comparison of candidate tracer.
Acetone, a ketone compound, is a suitable tracer for near-room-temperature and
atmospheric-pressure conditions. It is used in a wide variety of applications, from
concentration measurements to flow visualizations [36,37,38,39,40,41]. 3-pentanone, a
heavier ketone counterpart, has also been used in similar applications. In particular for
fuel mixing studies in combustion systems [10,42,43,44] due to its similar evaporation
rate to iso-octane [45,46], a major component of gasoline surrogates.
Photophysical properties of toluene have been of interest to chemists for over a
century [47,48]. Toluene has been gaining popularity in the area of fuel-air mixing
visualization due to its strong quenching in the presence of oxygen [49]. Toluene is a
12
major aromatic component found in distillate fuels, such as gasoline and jet fuel, along
with other major components such as paraffins, alkenes, and napthenes [50]. It has strong
fluorescence features in the near-UV. These characteristics promote toluene as an ideal
candidate for a wide range of reactive flow and combustion applications such as fuel/air
ratio measurement in internal combustion engines [10], thermal stratification
measurement in an HCCI (Homogeneous Charge Compression Ignition) engine [51],
oxygen and residual gas concentration measurement [52]. The first application of
quantitative temperature field measurement using toluene-based PLIF was performed on
a heated turbulent free jet [53], using absorption cross-section and FQY data at elevated
temperatures reported by [54].
All three tracer candidates have proven their usefulness in other fields as
mentioned above, and show promise in shock tube flow application. For comparison
purposes, LIF signal level variations with respect to temperature are simulated using
tracer specific photophysical parameters and the LIF equation. Photophysical parameters
correspond to 248nm excitation wavelength, and can be found in [32,55]. Each tracer is
balanced with N2 gas to 1bar total pressure. The traces of three candidates are shown in
Figure 2.1.
0
200
400
600
800
1000
LIF
inte
nsity
[a.u
.]
3-Pentanone Acetone Toluene
300 400 500 600 700 800 900 10000
2
4
Temperature [K]
Figure 2.1: Plot of simulated fluorescence signal per unit mole fraction with respect to temperature for three tracer candidates at 248nm excitation wavelength, 1bar pressure, and N2 bath gas. Plots of fluorescence near zero are magnified in the lower plot. These profiles are plotted using a best-fit numerical model to the photophysical parameter measurements.
13
Most notably, toluene emits orders of magnitude more fluorescence signal near
room temperature compared to acetone and 3-pentanone. It is then rapidly decreased with
increasing temperature, until reaching similar amounts of fluorescence intensity with its
ketone counterparts around 1000K. The ketones share similar behavior and fluorescence
intensity, but their temperature sensitivity is much less than that of toluene. It is important
to note that LIF signal intensity also depends on pressure, excitation wavelength, tracer
seeding level, and bath gas. Consideration for the first two parameters and their effects on
LIF intensity is detailed below.
Pressure affects the LIF signal level through number density and FQY. The FQY
of candidate tracers are considered up to 1 bar in N2 bath gas, since conditions relevant to
this thesis are expected to be mostly sub-atmospheric and only occasionally exceed
atmospheric pressure. Empirically determined absolute FQY variations between 0.005 –
1bar at 248nm excitation wavelength and room temperature [32] are listed in Table 2.2.
FQY dependence on pressure for all three tracer candidates in sub-atmospheric
conditions pale in comparison with their respective temperature dependence, which
varies by one and three orders of magnitude for ketones and toluene, respectively. As a
result, the effect of pressure does little to change toluene’s overwhelming advantage over
its ketone competitions.
Tracer Absolute FQY variation
Acetone 0.00025 – 0.00034
3-Pentanone 0.00048 – 0.00083
Toluene 0.027 – 0.09
Table 2.2: Absolute FQY variation for three candidate tracers between 0.005 – 1bar pressure in N2 bath, 248nm excitation wavelength, and 296K [32].
Excitation wavelength affects both absorption cross-section and FQY. Three
commonly available pulsed laser excitation wavelength options for ketone candidates are
248nm, 266nm and 308nm. The two most convenient options for toluene are 248nm and
266nm. While other wavelengths are possible, the aforementioned wavelengths are the
14
most convenient choices. The number of candidate excitation wavelengths is limited by
the availability of the empirical photophysical database for a given tracer species.
Absolute FQY values of the three candidate species [54] at the aforementioned excitation
wavelength are listed in Table 2.3.
248nm 266nm 308nm Reference
Acetone 0.00034 0.00052 0.00082 [32]
3-Pentanone 0.00083 0.00101 0.00107 [32]
Toluene 0.056 0.19 N/A [56]
Table 2.3: Absolute FQY values of candidate tracers at different excitation wavelengths at 296K, 5-23mbar tracer partial pressure, 1bar total pressure, balanced with N2.
The corresponding absorption cross-section values are listed in Table 2.4 [32,57].
The dependence of LIF signal level due to excitation wavelength, much like pressure, is
smaller in comparison to that of temperature.
248nm 266nm 308nm Reference
Acetone 2 4.3 1.6 [57]
3-Pentanone 1.8 4.5 2 [32]
Toluene 31 19 N/A [32]
Table 2.4: Absorption cross-section measurement of candidate tracers at different excitation wavelength in units of 10-20cm2/molecule at room temperature, 1bar total pressure.
All in all, temperature dependence dominates pressure and excitation wavelength
dependence for all three tracer candidates. The comparison shows that, toluene has the
greatest amount of LIF signal variation within the range of pressure and excitation
wavelength conditions given above. The comparison indicates that between room
15
temperature and 1000K, toluene has the best temperature sensitivity among the three
candidate tracers due to greater absorption cross-section and FQY over ketone tracers.
Toluene is therefore chosen in this study as the tracer for all subsequent quantitative
study of temperature and flow phenomena in shock tube flows. Detailed discussion of
toluene photophysics and the choice of excitation scheme are provided in section 2.2.2
and 2.2.3.
2.2.2 Toluene absorption
The S0 - S1 (π,π*) absorption spectrum of toluene near room temperature has been
studied for over half a century [56] and is well documented [56,58]. The spectrum spans
from around 240nm to 270nm with distinct vibrational sequences, with the strongest
feature near 266nm for the (0,0) band. The peak absorption cross-section at this feature is
1.3x10-18cm2 [59]. Absorption features start to disappear with increasing temperature, and
by 600K, the entire spectrum becomes broadband (FWHM = 20nm) with a maximum
value of 5.6x10-19cm2 near 261nm. The absorption spectrum broadens and red shifts as
temperature increases, since hotter gas molecules tend to occupy higher vibrational states
in the ground electronic level. For temperatures greater than 1000K, the symmetry
allowed S0 - S2 transition (near 200nm) dramatically increases [60] and overlaps with the
S0 - S1 transition [61]. The absorption cross-section of toluene is roughly an order of
magnitude greater than that of the ketones (Table 2.4). This is due to stronger vibronic
coupling, despite a similar level of symmetry-allowed electronic transition strength.
High-power commercial UV lasers at 248nm and 266nm can access this spectrum.
Toluene absorption cross-section data at 248nm and 266nm are shown in Figure
2.2. The absorption cross-section for 248nm excitation wavelength is temperature
independent from room temperature up to around 1000K, at 3.1 ± 0.2x10-19cm2. For
temperatures above 1000K, the absorption cross-section increases due to the S0 - S2
transition overlap. The absorption cross-section for 266nm excitation wavelength
increases with respect to temperature in two stages. From room temperature to 600K,
absorption cross-section increases due to overlap of absorption features. For temperatures
16
greater than 600K, absorption cross-section increases due to broadening and red shift of
absorption spectra, but at a slower pace.
300 400 500 600 700 800 900
2
3
4
5
6
7
Abs
orpt
ion
cros
s-se
ctio
n [
10-1
9 cm2]
Temperature [K]
266nm 248nm
Figure 2.2: Toluene absorption cross-section at the 248nm and 266nm excitation wavelengths. σ at 248nm is constant throughout the 300K - 900K temperature range while at 266nm σ increases due to the broadening of (0,0) band [32]. These profiles are plotted using a best fit to absorption cross-section measurements.
A best fit to 266nm absorption cross-section data can be found in [32] and is shown in
Equation 2.2.
266 ,10
3.57 0.022 1.22 10 (T in units of K) Equation 2.2
2.2.3 Toluene fluorescence quantum yield
The fluorescence spectrum of toluene at room temperature due to 248nm
excitation wavelength spans from 260nm to 400nm with a maximum near 280nm. The
fluorescence spectrum rapidly decreases and slightly red shifts as temperature increases.
These characteristics are universal for all aromatic tracers [62,63]. For further discussion
on toluene FQY, consider the interactions between different electronic states in Figure
2.3.
tw
th
en
sh
fl
fo
b
d
th
fo
v
w
m
Figuretoluenrespecimportdomin
The re
wo electroni
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luorescence.
The st
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xample, som
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be due to r
17
ical diagram oround and eplet state (T1
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rate beyond
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ay experienc
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tant decay proglet state (S0
onversion (ICm crossing (Iies.
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leads to sm
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65,66]
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18
vibration mode of toluene exceeds a critical value [69,70] (νcrit≈2150cm-1 for toluene).
Vibrational levels of toluene in the S1 and S0 state have been reported in [71].
Measuring absolute FQY can be challenging due to the complexity of energy
levels, transitions and mechanisms. Luckily, in most LIF applications, knowledge of
absolute FQY is superfluous and relative FQY is used instead. Relative FQY is the
variation of FQY relative to its value at a reference condition for a given excitation
wavelength. For this study, the reference conditions are 296K and 1bar (balanced with
N2). Two cases, corresponding to the two available excitation wavelengths for toluene,
are plotted as a function of temperature in Figure 2.4 using an empirical model of the
toluene relative FQY given in [54] and expressed in Equation 2.3. Both cases show
excellent temperature sensitivity of toluene FQY.
∅∅ 296
171 0.0175 0.337 0.0068
∅∅ 296
22.5 0.0105 Equation 2.3
300 400 500 600 700 800 900
1E-3
0.01
0.1
1
Rel
ativ
e F
QY
(T
)/(
296
K)
Temperature [K]
248nm 266nm
Figure 2.4: Toluene relative fluorescence quantum yield at 248nm and 266nm excitation in 1bar total pressure balanced with N2. Both wavelengths show similar sensitivity to 300K – 900K temperature range. The plot is a best fit to data from [54].
When the absolute FQY value is required, these empirical models can be used to
scale the absolute FQY at the reference value. Absolute FQY values of toluene for the
19
248nm and 266nm excitation wavelengths at 296K and 27mbar of pure toluene are 0.056
and 0.19, respectively [72].
Pressure also has a major influence on toluene FQY through its effect on
vibrational relaxation rates in the excited electronic state. Collision-induced vibrational
energy transfer in toluene has been studied previously [73,74]. Extensive study of
vibrational energy transfer [75] in the S0 state, and intermolecular and intramolecular
vibrational energy transfer [71,76,77] in the S1 state have also been reported. Notably, the
collision-induced non-radiative decay rate of benzene, a relative compound of toluene, is
known to increase with vibrational energy in the S1 state. If photons excite benzene
molecules into high vibrational energy in the S1 state at low pressures, benzene FQY thus
decreases, owing to slower vibration relaxation to lower vibration levels where non-
radiative decay is slower. A similar phenomenon is expected for toluene [78].
An experimental study was conducted, using a static cell, to assess the relative
FQY of toluene as a function of toluene partial pressure and total bath gas pressure in
sub-atmospheric conditions. The results are shown in Figure 2.5. Laser fluence was set to
40mJ/cm2 within the static cell to avoid the effects of fluorescence signal saturation. For
detailed discussion on fluorescence signal saturation, see section 3.1.3.
The relative FQY trace for each toluene partial pressure in Figure 2.5 is
normalized using the absolute FQY at 1bar total pressure and corresponding toluene
partial pressure as reference values. Note that the reference values are different for each
partial pressure. Toluene FQY increases with increasing total pressure and toluene partial
pressure. These sub-atmospheric variations must be considered when modeling toluene
fluorescence for partial pressures and total pressures below 50 mbar and 1bar
respectively. For pressure conditions above the aforementioned limits, the gas mixture
can be considered fully vibrationally relaxed and therefore, toluene FQY can be
considered as pressure independent up to about 2bar total pressure. Most, if not all, of the
experiments performed for this thesis are well below this limit.
Best numerical fits to the sub-atmospheric FQY data (shown in solid lines in
Figure 2.5) can be expressed using Equation 2.4 and Equation 2.5. The coefficients to
these equations are listed in Table 2.5.
20
0 200 400 600 800 10000.0
0.2
0.4
0.6
0.8
1.0
1.2
Rel
ativ
e F
QY
[a.
u.]
Total pressure [mbar]
Toluene partial P 5mbar 10mbar 20mbar 30mbar
Figure 2.5: Relative FQY for various partial pressures of toluene in N2 bath gas, 296K, and 248nm excitation wavelength. Solid lines are best fits to the data. The relative FQY values are normalized to the absolute FQY at 1bar total pressure for each of the corresponding toluene partial pressure. Extrapolation using the numerical fit is tested to be effective up to 2bar total pressure.
(Ptotal in units of mbar) Equation 2.4
Equation 2.5
Toluene partial
pressure [mbar] a b c
5 1.04172 0.76536 0.99717
10 1.03523 0.64187 0.99743
20 1.00064 0.45983 0.99638
30 1.00314 0.20920 0.98949
Table 2.5: Coefficients for low-pressure toluene relative FQY correction.
21
The relative FQY values ( ) are used to scale the normalized toluene FQY at the
248nm excitation wavelength presented in Equation 2.3 (typically applicable in the pre-
shock gas mixtures).
The presence of oxygen molecules affects toluene fluorescence significantly and
has been observed in other aromatic compounds and is well documented [79]. This is the
main reason why Lozano abandoned toluene as a viable tracer for his imaging work in air
[80]. For gases such as nitrogen, vibrational relaxation is the only relevant relaxation
mode affected by collision. For oxygen, however, a second mode called electronic
quenching exists. The de-excitation process is likely to occur by a charge-transfer
complex [81] in which a fraction of electronic charge is transferred between two or more
molecules. To account for oxygen quenching, toluene FQY is written as:
Equation 2.6
Since oxygen quenching dominates toluene fluorescence, intramolecular decay processes
are combined into a single term ktot. It is thought that oxygen affects toluene fluorescence
through Stern-Volmer processes, in which an intermolecular deactivation is accelerated
in the presence of another molecular species. Since individual quenching rates are
difficult to measure, oxygen quenching rates are generally measured using the Stern-
Volmer factor (kSV), a ratio of oxygen quenching rate to the total intramolecular de-
excitation rate as shown in Equation 2.7.
Equation 2.7
The Stern-Volmer factor can be calculated by dividing the fluorescence signal in the
absence of quenching molecules by the fluorescence signal in the presence of the
quenching molecules as shown in Equation 2.8.
22
1 Equation 2.8
Rearranging the above equation yields,
1 1 Equation 2.9
where is the FQY in the absence of quenching molecules. In the limiting case of
≫ 1, fluorescence signal is inversely proportional to oxygen number density.
∝ Equation 2.10
While no oxygen should be present in all subsequent experiments, oxygen may be
introduced by small vacuum leaks. Given that the pre-shock gas mixture in the shock
tube is normally well below atmospheric pressure, surrounding air can diffuse into the
test section, negatively affecting the test gas uniformity and dramatically reducing
toluene fluorescence. A detailed discussion about quantifying leaks and oxygen
contamination is found in section 3.1.2.
Of the two excitation wavelengths for toluene explored in this section, both offer
excellent temperature sensitivity and good fluorescence signal level up to 900K. The lack
of pressure-dependent data, difficult experimental timing procedures, and greater
uncertainty in absorption cross-section measurements diminishes the 266nm excitation’s
slight advantage in fluorescence signal temperature sensitivity. Therefore toluene
fluorescence excitation at a wavelength of 248nm was chosen as the strategy for
quantitative thermometry in shock tube flows.
This chapter introduced the basic concepts of LIF spectroscopy. The LIF equation
was presented to deduce quantitative flow parameters from a PLIF image. A
comprehensive study was conducted to select the best possible combination of PLIF
tracer and excitation wavelength for studying flow phenomena in shock tubes.
23
Temperature, pressure and excitation wavelength dependence on toluene fluorescence
were discussed in detail to accurately deduce temperature from a PLIF image. In
addition, sub-atmospheric toluene FQY pressure dependence was reported to expand the
existing toluene photophysical database. Based on the analysis, a 248nm laser was
selected to provide the necessary excitation energy in conjunction with experimental
facilities mentioned in Chapter 3. Detailed explanation of the temperature conversion
algorithm using the LIF equation will also be covered in Chapter 3.
24
25
Chapter 3. Experimental setup
This chapter covers two broad topics. The first topic is devoted to experimental
facilities and data processing procedures for planar thermometry using PLIF diagnostics
in shock tube flows. The second topic is devoted to engineering solutions and
experimental facilities optimization for near-wall imaging.
3.1 Facility overview
All experimental work performed for this thesis was done at the High
Temperature Gasdynamics Laboratory (HTGL) at Stanford University. The main body of
the Aerosol Shock Tube (AST), but without the aerosol generation apparatus, was used to
generate high temperatures and flow conditions required for the PLIF diagnostic. Two
laser systems are used, one for monitoring toluene loading levels and the other as the
primary light source for the PLIF diagnostic. The detection system consists of an
intensified camera, a laser energy monitor and a data collection computer. This study is
made possible due to the new shock tube test section designed and built for the express
purpose of PLIF imaging of shock tube flows.
3.1.1
A
condition
diagnosti
Further d
experime
seed and
section fo
corners.
overall o
measurem
need to p
of the sho
T
diameter
polycarb
section is
to square
cross-sec
test secti
stabilize
end of th
Fdrci
Shock tu
A shock tub
ns can be
ics can be pe
details of the
ents in the A
d vaporize ae
for their drive
The square
optical setu
ments are m
provide the l
ock tube, wo
The shock tub
and a 9.6
onate diaph
s followed b
e cross-secti
ctional area f
ion with stra
after the sud
he shock tube
igure 3.1: Ovriver section ircular and sq
be
be is a dev
readily gen
erformed on
e shock tube
AST was bas
erosol. All t
en section, w
cross-sectio
up. A round
made using li
large optical
ould protrud
be, shown in
6m driven s
hragm place
by a 2m long
ion of 10cm
fixed). At th
aight corner
dden change
e.
verall view owith 15cm in
quare cross-se
2
vice in whic
nerated for
n the heated t
design can
sed on its ph
the other sh
whereas the
on is prefer
d cross-sect
ne of sight o
accesses req
e into the flo
n Figure 3.1
section with
ed between
g recovery s
mx10cm with
he end of the
rs. This sect
e in cross-sec
f the Aerosonternal diame
ection, respect
26
ch uniform
short durat
test gas behi
be found in
hysical chara
ock tubes in
AST has a s
rred due to
tion may n
observation
quired for th
ow and disru
, has a 3m d
h 11cm int
the driven
section, that
h rounded c
recovery se
tion gives th
ctional area.
l shock tube.eter. 9.6m antively.
high temp
tion by sho
ind incident
[82,83]. Th
acteristics, no
n the HTGL
square cross-
simpler tes
ot be a pr
methods. H
his study, to
upt the shock
driver sectio
ternal diame
and driver
transitions
corners of R
ection is an 1
he shock wa
. The test se
. Overall lengnd 2.4m drive
erature and
ock heating
and reflecte
he decision to
ot due to its
L have a rou
-section with
st section de
roblem whe
However, the
access the f
k.
on with 15cm
eter, separa
section. Th
smoothly fr
R=1.8cm (ho
18cm transit
ave some di
ction is loca
gth is 16m. 3en section wi
d pressure
g. Optical
ed shocks.
o perform
ability to
und cross-
h rounded
esign and
en optical
windows
full height
m internal
ated by a
he driven
om round
olding the
tion to the
istance to
ated at the
3m ith
co
d
w
si
ar
8
re
lo
1
af
in
dr
tw
d
The im
onditions an
iscussion of
Incide
which isolate
imple operat
re typically
0mTorr. Th
esponse pres
ong section
200m/s, and
fter the arriv
ncident shoc
river section
wice-heated
enoted in Fi
Figuremixturincidenfrom tfor a s
maging end
nd is theref
f the new ima
ent shock w
es the low-p
tion schemat
evacuated
e incident s
ssure transdu
of the shoc
d the attenuat
val of the in
ck reflects a
n. The refle
region behin
gure 3.2.
e 3.2: Schemare and the drivnt shock thenhe end wall, econd time.
section is w
fore where
aging end se
waves are g
pressure dri
tic is shown
using mec
hock speed
ucer (PCB m
ck tube. The
tion rate is t
ncident shoc
at the end w
ected shock
nd the reflec
atic of operatver section isn compressesthe reflected
27
where the sh
all optical
ection can be
generated by
iven section
in Figure 3.
chanical pum
and shock a
model 132A
e incident sh
typically betw
ck is denote
wall and trav
heats the te
cted shock is
ion. (A) The rapidly filleds and heats tshock wave c
hock tube co
measureme
e found in th
y bursting a
n from the
.2. Both the
mps to an
attenuation
A32) evenly
hock speed
ween 0 to 5%
ed as region
vels back up
est gas mixt
s referred to
shock tube id until the diathe driven gacompresses a
onditions are
ents take p
he following
a polycarbo
high-pressur
driver and t
ultimate pr
are measure
spaced alon
is typically
%/m. The te
n 1 and 2, r
p the shock
ture for a s
o as region 5
is filled with aphragm burstas. (C) Uponand heats the
e closest to
lace. A det
section.
onate diaphr
re driver ga
the driven se
ressure of a
ed using six
ng the last 1
y between 60
est gas befor
respectively
tube towar
second time.
5. The region
driven gas ts. (B) The
n reflection driven gas
ideal
tailed
ragm,
as. A
ection
about
x fast-
1.5m-
00 to
re and
. The
rd the
. The
ns are
28
In the reference frame of the incident shock, the shock wave acts as the leading
edge with the shock heated test gas moving away from it. The boundary layer forms as
the flow over a flat plate with the free stream moving towards the diaphragm.
A uniform gas mixture is prepared in a separate stainless steel mixing tank before
being introduced into the shock tube driven section. The stainless steel mixing assembly
includes a multi-valve manifold and a magnetically driven stirring vane inside the tank.
Both the manifold and tank are heated and maintained at approximately 330K to allow
higher toluene loading levels. Mixtures are made manometrically using a capacitance
manometer (Baraton), and the pre-shock toluene concentrations in the shock tube (region
1) were confirmed using in situ 3.39μm HeNe laser absorption from the C-H stretch [84].
Industrial grade nitrogen (99.95%) is used along with spectroscopic grade toluene with
no further preparation. Any remaining dissolved volatiles and air in the mixing tank or
the lines in and out of the tank are purged before each mixture is prepared.
3.1.2 PLIF test section
A shock tube test section dedicated to PLIF diagnostics needs to satisfy several
requirements. First, it must allow, at minimum, optical access through two axes, one for
admitting the excitation laser sheet and the other for collecting the fluorescence signal.
Second, the dimensions of the PLIF image are limited by that of the optical access. In
other words, the windows need to be bigger than the imaging field of interest. Third, the
windows must not be opaque to the excitation laser sheet and the resulting fluorescence
signal.
The round-to-square transition section on the AST provides a square cross-section
for simpler experimental facility setup downstream. Unfortunately, rounded corners of
the AST do not match the straight edge window configurations of the test section. The
sudden jump at the four corners can disrupt nearby shock wave front and subsequent
flows, thereby disrupting the core flow. To circumvent this problem, an extension section
is placed between the end of the recovery section and the start of the test section to act as
a buffer zone. It has straight edges along the entire length of the section. The extension
se
nu
sa
th
in
ection length
ullify the dis
The te
ame size sen
he end wall.
n Appendix B
Figureextensright. array p
Figureextensright. Suppo
h is an order
sturbance cre
est section is
nsor array pl
Photos of th
B. An explo
e 3.3: Photos sion section anTwo of the fplate is visible
e 3.4: Drawingsion section an
(RIGHT) Exort rods and ba
r of magnitu
eated by the
s designed to
late on the o
he optical tes
ded view of
of the PLIFnd the aluminfour support re on the botto
gs of the PLInd the aluminxploded viewase plate are n
29
ude greater th
sudden chan
o hold 10x10
one remainin
st section alo
f the test sect
test section. num base platrods are also om of the test
F test sectionnum base platw, the four not shown.
than that of t
nge in geom
0x1.25cm3 w
ng side. A 1
ong with the
tion is also s
(LEFT) Sidete in place. Th
shown. (RIGsection.
n. (LEFT) Sidte in place. Thside window
the rounded
metry in the c
windows on
10x10x2.5cm
e extension s
shown.
e view, showhe end wall isGHT) End vie
de view, showhe end wall is
w frames are
corner radiu
corners.
three sides
m3 window f
section are sh
wn with the s on the far ew, sensor
wn with the s on the far e modular.
us, to
and a
forms
hown
30
The window material must be able to transmit near-UV light and have mechanical
properties that can withstand shock tube operating pressures. Three window materials
considered for the new test section are amorphous fused silica, Suprasil 2, and sapphire.
Stress analysis was performed to gauge their mechanical properties. In addition, cost
analysis is conducted since the required window dimensions are rather large and must be
custom made. Suprasil 2 and sapphire do have marginal advantage in terms of
mechanical properties, but amorphous fused silica was ultimately chosen due to higher
cost effectiveness over both Suprasil 2 and sapphire. Side wall fused silica windows of
1.25cm in thickness have been demonstrated to safely withstand 2bar of pressure. The
end wall fused silica window thickness is twice that of the side windows for additional
safety.
The test section is designed to be modular and provide vibrational and structural
support for the windows. The aluminum sensor array plate can hold up to two pressure
transducers or be used to mount a wedge or other impediment in the flow field. In most
cases, the sensor array plate is placed at the bottom to act as the floor of the test section.
The three windows then make up the two side walls and the top wall of the test section. A
complete description of the PLIF test section can be found in Appendix B. The completed
test section is capable of accepting a laser sheet input along multiple axes through either
one of the side, top or end wall windows. The test section is extensively tested for leaks,
with an ultimate leak rate of about 300mTorr/min for the entire shock tube. The shock
tube in the absence of the optical test section, leaks at a rate of 180mTorr/min. The
amount of leaked oxygen and its effect on toluene fluorescence is calculated by using a
semi-empirical model given in [32]. Oxygen partial pressure would be no more than
100mTorr given that it takes less than 3 minutes to fill the test section and run an
experiment. At this concentration level, fluorescence signal loss due the presence of
oxygen is about 3% at room temperature and drops below 1% at temperatures around
370K. This translates to a negligible 0.3% difference in temperature. Therefore, the
effects of oxygen contamination will be neglected for all subsequent analysis.
3
v
h
p
ca
v
th
d
v
h
(2
th
an
la
st
th
3.1.3 Las
Light
ital part in q
ighly directi
arameters su
an easily be
arious optica
A pul
han 100ns a
isturbance i
ariety of las
alf a century
248nm) is a
heir excitatio
Fig
An ex
nd halogen
aser have thr
tate involves
he UV regi
ser system
amplificatio
quantitative
ional and mo
uch as tempe
e altered by
al componen
sed laser, su
allowing nea
if the fluore
ser sources h
y ago. The e
accessible us
on waveleng
gure 3.5: Vario
xcimer laser
gas (krypto
ree notable
s different e
on. Second,
m
on by stimu
optical diag
onochromati
erature, pres
y changing
nts.
uch as the on
arly instanta
escence lifet
have becom
excitation wa
sing a KrF
gth are shown
ous types of e
(short for e
n and fluori
properties.
lectronic sta
, the groun
31
ulated emissi
gnostics. Co
ic [85] and a
sure, and sp
the spatial
ne used in thi
aneous visua
time is shor
me available
avelength re
excimer lase
n in Figure 3
excimer laser
excited dime
ine in the c
First, the tr
ates, and the
nd state pop
ion of radia
oherent phot
are used to s
ecies concen
distribution
is study, has
alization of
rt (hundreds
[86,87], sin
equired for t
er. Several
3.5.
and their exc
er laser) typi
ase of the K
ransition fro
e resulting la
pulation is e
ation (LASE
tons produce
selectively m
ntration. The
n of the lase
s a typical pu
the flow fie
s of nanose
nce the inven
the experime
different ex
citation wavel
ically uses a
KrF excimer
om the excit
aser wavelen
effectively z
ER) sources
ed by a lase
measure key
e probing vo
er beam thr
ulse width o
eld with no
econds). A
ntion of the
ents in this t
xcimer lasers
lengths.
a mixture of
r laser). Exc
ted to the gr
ngth is usua
zero due to
are a
er are
y flow
olume
rough
of less
flow
wide
laser
thesis
s and
f inert
cimer
round
lly in
o fast
dissociat
featurele
Nd:YAG
state [88]
A
molecule
be bound
form the
dimer un
ground s
atoms. T
emitted [
Fst
T
efficienc
from the
Without
since an
ion, and is
ss and relati
G laser) due
].
A potential e
e cannot be s
d in the excit
ese temporar
ndergoes stim
state, and qu
he stimulate
[89].
igure 3.6: Potate undergoe
The average
ies. Several
lasing medi
adequate co
excimer lase
modeled as
ively broad (
to the lack
energy diagr
stabilized in
ted state at it
ry complexe
mulated or sp
uickly (on t
ed emissions
tential energys spontaneou
excimer lase
factors lim
ium and elec
ooling the en
er can outpu
3
s a four-lev
(20-100cm-1
k of rovibrat
ram of an e
n the repulsiv
ts minimum
es that can
pontaneous e
he order of
s are amplifie
y state diagraus emission to
er efficiency
mit excimer l
ctric dischar
nergy deplet
ut several hu
32
vel system. T
, compared
tional transit
excited dim
ve ground st
energy leve
only exist i
emission, to
f picosecond
ed in a cavit
am of an excit a highly repu
y is 2-4%, du
laser power
ge reduces t
tion of the la
undred mJ pu
Third, the e
to 6cm-1 for
tions in the
mer is shown
tate. Howev
el. An electri
in the excite
a metastable
ds) dissociat
ty and a beam
ted dimer. Thulsive ground
ue to high p
output. Firs
the overall e
asing mediu
ulse at rates
emission sp
r a multi-mo
e unpopulate
n in Figure
ver, the mole
ic discharge
ed state. Th
e but highly
tes into two
m of near-U
he bound uppd state.
pumping and
st, the heat
efficiency of
um can occur
of up to sev
ectrum is
ode pulsed
ed ground
3.6. The
ecule may
is used to
he excited
repulsive
unbound
UV light is
per
d quantum
generated
f the laser.
r quickly,
veral kHz.
33
Second, the high absorption coefficient (k = 10-50cm-1) of the lasing medium in the
active state (KrF*, XeF*, etc.) limits the cavity size and thereby restricts the laser power.
A typical excimer laser cavity is limited to about a meter in length. Third, equipment
issues such as unstable discharge and inhomogeneous medium can further degrade laser
performance. The specifications of KrF excimer laser used in this study are listed in
Table 3.1.
Excimer Laser
Manufacturer Coherent
Model Compex Pro 102
Laser medium KrF excited dimer
Pumping source Gas discharge
Repetition rate 1 – 20Hz
Laser wavelength 248nm
Pulse energy 350mJ (5Hz, 30kV)
Pulse duration 20ns
Shot-to-shot energy variation
2.4%
M2 value Vertical: 990
Horizontal: 33
Table 3.1: Specifications of the KrF excimer laser used in this study.
The laser repetition rate is set to 1Hz, since measurements in the shock tube will
all be single-shot images. The M2 value is a dimensionless value indicating the quality
and the focus of the laser beam [90]. For example, a diffraction-limited beam would have
an M2 value of unity. A larger vertical M2 value indicates that this laser beam is more
likely to expand and focus poorly along its vertical axis.
34
Operation of the excimer laser below the saturation limit of toluene fluorescence
(i.e. weak excitation regime) is verified in situ for a typical shock tube test condition: 5%
toluene in nitrogen at room temperature and 0.1bar. Toluene PLIF signals were acquired
for laser fluence of 40 – 125 mJ/cm2. The results are shown in Figure 3.7. Fluorescence
response is found to be linear over the entire range of tested laser fluence (deviating less
than 5% at the highest fluence condition).
0 50 100 1500
2
4
6
8
10
Flu
ore
scen
ce s
igna
l [a
.u.]
Laser fluence [mJ/cm2]
Linear fit Data
Figure 3.7: Fluorescence signal with respect to laser fluence. Fluorescence signal begins to saturate at 130mJ/cm2. At this fluence level, fluorescence signal deviation from linearity is 4.7%. Test conditions are 5% toluene in nitrogen at room temperature and 0.1bar.
3.1.4 Detection system
The laser beam is shaped into a thin, loosely focused sheet (0.75mm thick) using
cylindrical lenses (f=1000mm) before entering the test section. Wavelength-specific high-
reflective mirrors precisely guide the laser sheet alignment. Fluorescence signals are
collected by an ICCD (Intensified Charge Coupled Device) at right angles to the laser
sheet. An ICCD camera combines an intensifier with a CCD detector for enhanced
sensitivity capable of detecting extremely low levels of photon events. An additional
benefit of using an ICCD camera is the very fast potential gate timing (on the order of
several-nanoseconds). An intensifier is made up of three parts: photo cathode, micro
ch
in
P
ph
ch
ac
ph
w
si
P
co
C
sp
f/
R
(L
hannel plate
n Figure 3.8.
When
hotoelectron
hosphorous.
hannels 10µ
cross the M
hotoelectron
walls. This pr
ide. The vo
hosphorous
onverts them
CCD chip and
The i
pecifications
/4.5 achroma
Rayleigh scat
LaVision CI
Figure
e (MCP) and
.
n fluorescenc
ns are draw
The MCP
µm in size.
MCP accelera
n has suffic
rocess is rep
oltage applie
(P43, Gd2O
m into photo
d read out us
intensified c
s are listed in
atic UV lens
ttering. The
O 16).
e 3.8: Cross-se
d phosphor. A
ce photons s
wn towards
is very thin
When the i
ating photoe
ient energy,
peated until
ed across th
O2S:Tb, 1.5m
ons at 545nm
sing a compu
camera used
n Table 3.2.
s (Nikkor-UV
laser sheet
ection of an I
35
A schematic
strike the ph
s the MCP
(typically a
intensifier is
electrons do
, a second
a cloud of p
he MCP de
ms decay to
m (yellow-gr
uter.
d in this stu
Images are
V). A filter
intensity is
CCD camera
c of an inten
hotocathode,
P by an el
about 1mm t
s turned on,
own one of
electron is
photoelectron
etermines th
o 10%) attr
reen). The ph
udy is a La
focused on t
is placed in
s monitored
a optical elem
nsifier cross-
, photoelectr
lectric field
thick) with h
, a high pot
its many ch
dislodged f
ns exit the M
he amount o
racts the ele
hotons are c
aVision Dyn
to the camer
n front of the
using a fast
ment.
-section is sh
rons are em
d (6kV) on
honeycomb
tential is ap
hannels. Wh
from the ch
MCP on the
of amplifica
ectron cloud
collected ont
namight, an
ra with a 105
e lens to sup
t energy mo
hown
mitted.
n the
glass
pplied
hen a
annel
other
ation.
d and
to the
nd its
5mm,
ppress
onitor
36
Typically, the achromatic UV lens is set to its lowest f-number to increase photon
yield. At this setting, optical aberrations are inevitable. Fortunately, the aberrations are
easily adjustable with a one-time calibration at a fixed camera location and setting. This
correction is especially important when imaging near-wall shock tube flows.
Intensified CCD camera
CCD type Marconi 47-10
Maximum rating 4kHz
Phosphorus P43
Minimum gating 5ns
Resolution 1024pixel x 1024pixel
Spectral response 180nm – 800nm
Sensitivity 2000 count/photoelectron
Cooling Peltier & water circulation
Table 3.2: Specification of the ICCD camera used in this study.
3.2 Data acquisition and processing
Data acquisition involves synchronizing laser pulse, intensifier, and camera
timing with the incident shock, and monitoring laser energy through a custom acquisition
routine given in Appendix C.1. The routine is programmed on DaVis, an image
acquisition and processing platform developed by LaVision. It can control a family of
products including camera, intensifier, energy meter, and the timing sequence through a
TTL I/O card. The trigger mechanism consists of a pressure transducer about 10cm
upstream of the test section (in the extension section) connected to a delay generator.
When the delay generator is triggered, it sends out a TTL-high signal after a
predetermined time delay (roughly 200µs and 400µs for incident and reflected shock,
respectively). This delay may vary significantly depending on shock strengths, initial
37
conditions, and flow region of interest. Proper delay settings are based on previous
measurements of similar shock strength and initial conditions. When the time delay
lapses, the excimer laser is fired, and the resulting fluorescence signal is collected by the
camera (raw PLIF image). The intensifier is gated for just 150ns to minimize unwanted
signals from nearby noise sources. The fluorescence image and the time-dependent laser
energy profile from the camera and the energy meter, respectively, are read into DaVis
simultaneously, and stored for image processing.
3.2.1 Image processing and correction
Image processing is done asynchronously using a separate routine (Appendix C.2)
on the DaVis software platform. Two raw PLIF images, preferably from the same
experiment, are required to construct a normalized PLIF image. Normalized PLIF signals
can then be converted to relevant flow parameters using the relationship given in
Equation 3.1. The first raw PLIF image, the reference image (S296K), is averaged from 10
single-shot images taken in region 1 of the test section, where temperature and pressure
conditions are well-known and constant. Averaging the images improves the signal-to-
noise ratio (SNR) of the normalized image (Snorm), compared to single-shot images. The
second raw PLIF image, the shock image (ST), is a single-shot image taken where
temperatures are unknown (region 2 or 5).
Ω4
Ω4
Equation 3.1
The above equation can be simplified by cancelling common terms, and assuming a
constant tracer mole fraction in the test section, and ideal gas behavior.
Equation 3.2
38
By doing so, normalized PLIF signal becomes a simple function of temperature and
pressure. To fully solve for TT, pre-shock temperature and pressure measurements (T296K
and P296K) and post-shock pressure prediction (PT) are substituted into Equation 3.2. Post-
shock pressure (PT) is calculated using the normal shock jump equation using initial
conditions and shock speed measurement as inputs. Equation 3.2 then reduces to an
implicit function of only post-shock temperature (TT). This equation is solved iteratively
for every pixel and the entire process takes about 10 minutes to complete.
Prior to image processing, both raw PLIF images must be corrected for various
factors to ensure proper quantitative analysis. The first step is to correct for dark noise. It
is one of two major sources of noise in this PLIF diagnostic setup, the other being shot
noise. Dark noise is due to thermally excited electrons that randomly crosses the CCD
band gap in the absence of a photon. It is a temperature-dependent process that can be
controlled by regulating the CCD temperature using a water-cooled Peltier junction. The
background noise then becomes predictable and can be easily quantified by imaging a
background image in the absence of tracer species, preferably under vacuum conditions.
The background image is averaged from 10 single-shot images just like the reference
image, and taken right before each experiment. It is used to subtract the effects of
thermally generated charge in each pixel for both the reference and shock image. Figure
3.9 (A and B) shows raw PLIF images before and after background subtraction.
The second step is to correct for shot-to-shot laser energy variation. The excimer
laser in use exhibits pulse-to-pulse laser energy variation, which is found with nearly all
lasers. To correct for these inherent fluctuations, an energy meter is employed to measure
the energy of each laser pulse during an experiment. Energy measurements associated
with the raw PLIF images are used to normalize the said image. This is possible because
in the weak excitation limit of PLIF diagnostics, LIF signal is proportional to the laser
energy. Figure 3.9 (C) shows the raw PLIF image after laser energy correction. Careful
study is conducted to insure saturation does not occur under the laser energy conditions
relevant to this study.
The third step is to correct for laser sheet and collection angle variations. Ideally,
laser sheets would have uniform spatial distribution but in practice this is not always the
case. Spatial variations of the laser sheet intensity can be quite substantial across its
w
sp
d
d
st
T
sa
op
w
re
m
co
C
im
co
width. To cor
patial distrib
ictated by
istribution o
tudying the r
FigureImage noise; laser sopticalscale. end wa
The measured
ame day, as
perational. A
walls, is coll
educes the a
most of the r
ollect as mu
C). However
maging field
orrections is
rrect for this
bution are al
the size of
of the laser
resulting PL
e 3.9: CorrecA: Raw imImage C: C
sheet and colll distortion. AThe image Eall.
d intensity d
s spatial var
Another spat
lection angl
amount of LI
raw PLIF im
uch LIF sign
, this pheno
d and determ
s shown in F
phenomeno
llowed to en
f the imag
sheet that
IF image un
ction processage straight
Corrected for lection angle All images b
E color scale
distribution i
riation tends
tial correctio
e variation.
IF signal rea
mages for th
nal as possib
omenon can
mining the sca
igure 3.9 (D
39
on, portions
nter the test
ing field a
enters the t
nder uniform
of PLIF imfrom the camlaser energyvariation; Im
but image E is altered to
is used to co
s to remain
on that must
The restric
aching the C
his thesis w
le, and its e
be corrected
aling factor a
D).
of the laser
section. The
and optical
test section
m toluene con
mage with refmera; Image
y variation; Immage E: Corre
are displayedhighlight the
orrect raw P
relatively u
t be made, e
cted collecti
CCD. This is
were taken u
ffect is evid
d by scannin
at each pixe
sheet with r
e amount of
component
is tested fo
ncentration c
flected shock B: Corrected
mage D: Corected for absod using the se thermal laye
PLIF images
unchanged w
especially wh
ion angle ne
s exacerbate
using the low
dent in Figur
ng the laser
l location. T
elatively uni
f cutoff is us
s. The inte
or uniformit
conditions
k in frame. d for dark rrected for
orption and same color er near the
taken durin
while the las
hen imaging
ear the end
d by the fac
west f-numb
re 3.9 (A thr
r sheet acros
The result of
iform
sually
ensity
ty by
ng the
ser is
g near
wall
ct that
ber to
rough
ss the
these
40
The fourth step is to correct for optical distortion due to the collection lens. The
collection lens used for this thesis shows signs of mild radial distortion which can be
corrected using the Brown’s distortion model [91]. The camera control software includes
such a distortion correction algorithm. The algorithm determines the necessary correction
factors by imaging a predetermined target. All subsequent raw PLIF images can be
corrected using the same correction factor as long as the optical configurations are
unchanged. The result of distortion correction is shown in Figure 3.9 (E).
The final step is to correct for LIF signal loss due to laser sheet absorption.
Toluene has a large absorption cross-section, and more absorption leads to greater LIF
signal while at the same time reducing the laser sheet energy as it progresses into the test
section. The correction factors are therefore a function of distance and toluene partial
pressure. It can be expressed using the Beer-Lambert relations as shown in Equation 3.3.
Equation 3.3
I0 and I are the initial and transmitted laser sheet intensity across distance l, respectively.
σ is the toluene absorption cross-section (See section 2.2.2 for details). Knowledge of
temperature and pressure is also required for proper absorption correction. The reference
image is corrected using measured values in region 1, and the shock image is corrected
using estimated values in region 2 or 5. The correction factors are adjusted to reflect the
actual temperature at each pixel during image processing.
3.3 Near-wall PLIF imaging facility optimization
PLIF imaging near a wall presents significant engineering challenge. This is
because PLIF signals are several orders of magnitude less intense than the laser source,
and as such detectors are sensitized to extreme low amounts of photons. If a small
fraction of the excitation laser sheet was to scatter into the detector it would be enough to
prohibit quantitative analysis, and even destroy the sensitive equipment. When
41
performing PLIF diagnostics near a wall, however, scattered light at the wall surface is
unavoidable.
Surface scatter is defined as diffuse reflection due to the light-matter interactions
at a surface. A fraction of the scattered laser sheet can easily end up on the detector
mixed with the fluorescence signal. Experiments are performed to find the best
combination of wall material and optical configuration for minimizing laser sheet
reflection and scatter thereby maximizing image quality near walls. This section
discusses the results of optimizing each component in detail, and identifies the best
combination of optical components and configuration for imaging near shock tube walls
using PLIF diagnostics. In addition, techniques to reduce surface scatter from metallic
surfaces are explored.
3.3.1 Wall selection
Wall materials considered in this analysis includes two metals, aluminum and
steel, and one non-metal, amorphous fused silica. Surface finishes considered for
aluminum and steel are #2B mill, #3, #4 satin, and #8 mirror. Fused silica surfaces treated
with and without anti-reflective coating were examined. Surface scatter is tested by
aiming the laser sheet perpendicularly into a sample with the camera placed at a right
angle to the beam path. Sample surfaces were cleaned and inspected thoroughly before
each test to prevent scatter from bulk particulate or surface contamination. The
experimental setup used for near-wall imaging optimization is shown in Figure 3.10.
Tests were performed in atmospheric air at room temperature. Different optical filters and
laser sheet polarizations were tested simultaneously, but for the sake of continuity, those
results will be discussed in the following section. Experimental results showed significant
differences in scatter intensities between materials. While metallic samples showed
similar amounts of scattered intensity at the surface, fused silica samples showed
significantly less. This is because fused silica transmits most of the incident laser light
while its metallic counterpart does not. Examples of fused silica and aluminum surface
scatter are shown in Figure 3.11 (A and B, respectively).
N
surfaces,
tested. T
despite d
Similar r
much sm
fabricate
Fm
F
Repeated
surfaces
tube surf
Example
3.11 (C a
localized
performe
baseline
surface.
Next, the effe
little to no
They all regi
different surf
results were
maller than m
d with 20/40
igure 3.10: Emetallic and no
inally, the
d exposure t
that are diff
face was sim
s of surface
and D, respe
d to several
ed on metalli
of surface s
fects of surfa
o difference
stered high
face finish ty
found amon
metallic samp
0 surface rou
Experimentalon-metallic m
effects of s
to laser shee
fficult to rem
mulated by e
e scatter of d
ectively). A
spots (pres
ic surfaces a
scatter make
4
ace finish on
was found
amounts of
ypes, the sur
ngst the two
ples. Both A
ughness spec
l setup for tematerials and s
surface clea
et and toluen
move and ca
exposing sam
dirty and cle
s expected,
sumably, wh
as well, and s
es it hard to
42
n scatter inte
amongst th
f scatter at th
rface roughn
different fu
R and non-A
cifications.
esting surfacsurface finish
anliness on
ne vapor lea
ause excessiv
mples to tolu
ean fused sil
dirty surfac
here bulk p
similar resul
pick out the
ensity are ob
he four diffe
he surface. T
ness may be
used silica su
AR coated fu
e-laser interahes are tested.
scatter inte
ads to carbo
ve surface s
uene vapor,
lica samples
es show gre
particulates
lts are found
e location o
bserved. Fo
erent surface
This may be
of similar m
urface finish
used silica s
action. Vario.
ensity are e
on buildup a
scatter. A di
dust, and la
s are shown
eater scatter
are). Same
d. However, t
f contamina
r metallic
e finishes
e because
magnitude.
hes, albeit
ample are
ous
examined.
at window
irty shock
aser sheet.
in Figure
intensity,
tests are
the strong
ants at the
sc
si
p
op
3
op
an
re
co
sh
an
P
Overa
catter, and w
ilica has add
lastic deform
peration.
Figureconditthe imfilter; (dirty surface
3.3.2 Opt
The a
ptical arrang
nd their con
eaching the
ontamination
heet polariza
ngles were t
LIF imaging
all, fused sili
was therefore
ditional bene
mation there
e 3.11: Laser ions. The sch
mage, scatter, Image B: Alsurface) usine) using 250 –
tical conf
amount of s
gement. Car
nfiguration c
e camera.
n, bulk inde
ations, optic
tested to find
g.
ica without a
e selected as
efits in that i
eby preventi
light scatter hematic on th
and laser shluminum #8 ung 250 – 400n– 400nm band
figuration
cattered ligh
reful conside
can significa
Surface sca
ex fluctuatio
al filters, las
d the optima
43
an AR coati
the wall ma
it is stiffer th
ing the wall
comparison he left depictsheet. Image Ausing 248nmnm bandpass dpass filter.
n
ht observed
eration and
antly reduce
atter is cau
on, and bulk
ser sheet orie
al optical co
ing produced
aterial for ne
han its meta
l from flexin
for different s the locationA: Fused sili
m notch filter;filter; Image
at a surfac
proper sele
e or even el
used by su
k particulate
entations, in
onfiguration
d the least a
ear-wall PLIF
allic counterp
ng as a resu
wall types an of sample mica using 248 Image C: Fu
e D: Fused si
ce is greatly
ection of opt
liminate surf
urface topo
es [92]. In th
ncident angle
for the purp
amount of su
F imaging. F
parts, minim
ult of shock
and surface material in 8nm notch used silica ilica (clean
y affected by
tical compo
face scatter
ography, su
his section,
es, and colle
pose of near
urface
Fused
mizing
k tube
y the
onents
from
urface
laser
ection
r-wall
Polariza
W
sample sh
wave d
electrom
compone
of the E
polarized
A
sheet pol
magnesiu
The pola
ordinary
angle for
and trans
to comp
experime
shown in
Fpoim
ation
When light is
hape, materi
description,
agnetic wav
ent vector (E
E-vector for
d laser sheet,
An experimen
larization on
um fluoride
arizer separa
beam devia
r 248nm is a
smits about 8
ly with the
ent. Scatter i
n Figure 3.12
igure 3.12: olarization. Lmage is norma
s scattered a
ial, and incid
the electr
ve and mate
E-vector) is u
s-polarized
, the E-vecto
ntal setup si
n scatter inte
is placed be
ates the ext
ation is less t
bout 1.05º. T
80% of the i
polarizer d
intensities at
2.
ComparisonLeft: s-polarizalized for lase
4
at a surface,
dent beam p
ric compon
erial interact
used to defin
d laser shee
or direction i
imilar to Fig
ensity at the
etween the f
traordinary r
than 6 arc m
The clear ap
incident beam
damage thre
t the surface
n of surfacezed light sheer energy vari
44
its polarizat
olarization.
nent is re
tion. Therefo
ne the direct
ets is norma
is in plane of
gure 3.10 wa
surface. A
fused silica s
ray from th
minute and th
perture of the
m. The laser
eshold. No
as a result o
e scatter wieet; Right: p-iation.
tion is chang
In the transv
esponsible
fore the dire
tion of polar
al to illumi
f the illumin
as used to te
Rochon pris
sample and
he undeviate
he extraordi
e polarizer is
r fluence is
optical filte
of s-polarize
th respect t-polarized lig
ged dependi
verse electro
for most
ection of thi
rization. The
ination shee
nation sheet.
est the effect
sm polarizer
beam shapin
ed ordinary
nary beam s
s 14.5mm in
adjusted to 2
er was used
ed and p-pol
to laser sheght sheet; ea
ing on the
omagnetic
observed
is electric
e direction
et. For p-
ts of laser
r made of
ng optics.
ray. The
separation
n diameter
20mJ/cm2
d for this
arized are
eet ach
B
ce
sc
in
op
O
ex
se
op
p
u
sc
(~
h
qu
Both images
enter of the
catter was ob
n the directio
ptical filters
FigureThe pr
Opticalfilte
Optica
xcitation las
eparated, as
ptical filters
ass filter (25
sing these fi
catter are sti
~0.7nm) is s
and, the ba
uantitative a
are normal
e two image
bserved for
on of its E-v
.
e 3.13: Horizorofiles are ave
er
al filters can
ser wavelen
shown in F
s tested for t
50nm - 400n
ilters are sho
ill visible thr
smaller than
and-pass fil
analysis clos
lized for las
es are plotte
s-polarized l
vector. Howe
ontal profile eraged across
n selectively
ngth and su
Figure 3.14
this experim
nm). Reduct
own in Figu
rough the no
n the linewid
ter does aw
er to the sur
45
ser energy v
ed in Figure
laser sheet, b
ever, the red
along the ce 5 pixels in w
y reject surfa
ubsequent to
. Also show
ment: A notch
tions of scat
ure 3.11 (ima
otch filter. T
dth of the K
way with s
face.
variations. H
e 3.13. Sign
because pho
duction wasn
enter of both width.
ace scattered
oluene emis
wn are trans
h filter (cen
tter intensity
age A and D
This is becau
KrF excimer
surface scatt
Horizontal p
nificant redu
otons are les
n’t enough to
images in Fi
d light. This
ssion spectr
smission cu
ntered at 248
y at the surfa
D). Small am
use the notch
r laser (~1nm
ter allowing
profiles alon
uction in su
s likely to sc
o forgo the u
igure 3.12.
is possible w
ra are spec
urves for the
8nm) and a b
face as a resu
mounts of su
h filter bandw
m). On the
g more acc
g the
urface
catter
use of
when
ctrally
e two
band-
ult of
urface
width
other
curate
46
0.0
0.2
0.4
0.6
0.8
1.0
Nor
ma
lize
d F
luor
esce
nce
[a.u
.]
KrF Excimer laser Toluene fluorescence
240 280 320 360 4000
20
40
60
80
100
Tra
nsm
issi
on
[%
]
Wavelength [nm]
Notch filter Band-pass filter
Figure 3.14: (TOP) Spectrally resolved KrF excimer laser wavelength and the subsequent toluene emission spectra. The broadband emission spectra range from 260nm to 400nm. (BOTTOM) Transmission curves of the two optical filters tested for this experiment.
Spectral transmission efficiency of the bandpass filter is mostly constant between the
broadband fluorescence signal ranges from 260nm to 400nm [32] and thus has negligible
effect on toluene fluorescence, other than absorption.
Lasersheetorientation
The unique design of the test section permits laser sheet orientations in three
configurations: Two perpendicular and one parallel orientation. The two perpendicular
configurations are called the bottom-up orientation and the top-down orientation
depending on the laser sheet routing configuration with respect to the surface of interest
as shown in Figure 3.15. Bottom-up and top-down perpendicular orientations are denoted
as 1 and 2, respectively and the parallel orientation is denoted as 3 with respect to the
surface of interest.
It is possible to completely eliminate surface scatter using carefully aligned
parallel orientation. However toluene absorption reduces the laser sheet incident flux (as
much as 15% under certain conditions) before reaching the imaging field. Also, minute
diaphragm pieces and large dust particles prevent uniform laser sheet illumination,
especially at longer test times. Perpendicular orientations, despite the unavoidable surface
scatter, provide more robust illumination in the imaging field. Images of the side wall
th
7
or
hermal boun
cm away f
rientation an
Figurethe wperpenon thetowardand th
Figurewall ththe sidand paorientaare: T1
ndary layer b
from the en
nd compared
e 3.15: Schemwall and neandicular oriene right. The inds the end wae images wer
e 3.16: Laserhermal boundde wall 7cm aarallel orientaation. Image 1=296K, P1=0
behind incid
nd wall are
d side-by-sid
matic of the lasar-wall flow
ntation, 3: Parncident shockall. The camere taken throu
r sheet orientdary layer beaway from thation. Image B: Acquired
0.075bar, Vs=
47
dent shock w
e measured
de in Figure 3
ser sheet oriew phenomenorallel orientatk in the scheera was place
ugh the side w
tation directiohind incident
he end wall arA: Acquiredusing the pa
=900m/s, and
waves, imme
using the
3.16.
entation configon. 1: Botttion. Shock tu
ematic is traved perpendicu
wall window.
on comparisot shock wavere measured u
d using the boarallel orientaattn=4%/m.
ediately next
perpendicu
guration withtom-up, 2: ube end wall
veling from leular to the la
on. Images oes, immediateusing the perottom-up peration. Shock
t to the side
ular and pa
h respect to Top-down
l is located eft to right aser sheets,
of the side ely next to rpendicular rpendicular conditions
e wall
arallel
T
laser she
perpendi
orientatio
the imag
wall of i
surface s
silica) to
direction
field. Spe
be signif
higher te
Lasersh
T
the amou
collection
laser she
incident a
Fanlimfu
The image ta
eet incident
cular config
on in two ke
ing field sim
interest. Sec
since the las
o that of low
n wherein the
ecular reflec
ficant enoug
mperatures.
heetincide
The final step
unt surface
n angle. A s
eet incidence
angle and va
igure 3.17: (ngles with resmits of the coused silica at
aken with pa
flux. Both i
gurations, t
ey areas. Fir
mply due to
ond, the bot
ser is travel
wer optical d
e incident w
ctions from
gh to affect
ntanglean
p in near-wa
scatter by a
schematic de
e is shown
arious collec
(LEFT) Schespect to the fuollection anglvarious colle
4
arallel illumi
images are t
the bottom-
rst, the form
the fact that
ttom-up orie
ling from a
density (test
wall reflects t
a fused silic
the tempera
ndcollectio
all imaging f
adjusting the
escribing the
in Figure 3
ction angle ar
ematic of an used silica wile are shown.ection in the X
48
ination (B) i
taken using
-up orientat
mer delivers
t the imagin
entation elim
material wi
gas). The o
the specular
ca (n ~ 1.5)
ature measur
onangle
facility optim
e laser shee
e collection
.17. Surface
re also show
incidence anindow in cyli(RIGHT) Im
XY-plane at
is slightly n
the band-pa
tion outperf
more laser
ng field is att
minates spec
ith higher o
opposite is t
r reflection b
sample are
rement unce
mization was
et incident a
angle with
e scatter ima
wn.
ngle and varindrical coord
mages of surfanormal incid
noisier due to
ass filter. O
forms the
sheet incide
tached to the
cular reflecti
optical densi
true for the
back into the
about 4%, w
ertainty, esp
s focused on
angle and th
respect to th
ages taken a
rious collectidinate. Only tace scatter froence (θi=180
o reduced
Of the two
top-down
ent flux in
e incident
ion at the
ity (fused
top-down
e imaging
which can
pecially at
n reducing
he camera
he normal
at normal
on the om °).
49
The laser sheet is in the XZ-plane. The regular experimental setup collects the fluorescence signal at θr=90°. The amount of surface scatter with respect to the incident and scattered angle is
given by the bi-directional transmittance distribution function (BTDF). It quantifies the
amount of scatter for a given incident angle, wavelength, and power, as well as sample
parameters. For further information about BTDF, please refer to Appendix A.
Unfortunately BTDF of fused silica is unavailable in literature. Instead, the bi-directional
reflectance distribution function (BRDF) of a silicon wafer sample [93], that shares
similar surface properties, is used to make qualitative comparison with the surface scatter
measurements.
Two types of experiments are performed for this study. First, the camera was
fixed in place at θr=90º, while the incident laser sheet was tilted in grazing angles (<±5°)
about the normal incident angle (θi=180º). Incident (θi) and collection (θr) angles are
defined in Figure 3.17. Results from this experiment showed negligible variation in the
amount of scatter intensity with respect to small changes in the incident angle. A similar
behavior is found in silicon wafer BRDF at (θi=0º) as shown in Figure 3.18. BRDF is 0
near the θ=90º collection angle.
It is interesting to note that once the collection angle reaches a critical value with
respect to the incident angle, BRDF becomes zero as evident from Figure 3.18. Critical
values for θi=0º and 45º are θr,crit=-86º and -67º, respectively.
-90 -60 -30 0 30 60 900.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
BR
DF
[sr-1
]
Scatter angle [degree]
i=0
i=45
Figure 3.18: Sample BRDF curve of silicon wafer at θi=0º and θi=45º for ϕ=0º. Incident and collection angles are defined using the schematic in Fig 3.17. In both cases (θi=0º, 45º), BRDF goes to zero at θr=-86º and -67º, respectively.
50
Second, the camera is tilted from θ=13º to 90º while the incident laser sheet was
held in place at normal incidence. The results are shown in Figure 3.19. For material with
an isotropic surface, as was the case for fused silica, BRDF should peak at the incident
angle and decrease as the collection angle moves away from the incident angle as is
shown for the silicon wafer BRDF at normal incidence. Fused silica surface scatter
measurement follows the silicon wafer BRDF relatively well. The least amount of surface
scatter at normal incidence is observed near θ= 90°. Please note that silicon wafer BRDF
only serves to show that fused silica surface scatter measurements are purely due to
surface topography. No quantitative comparison between the surface scatter
measurements and silicon wafer BRDF should be made.
The PLIF diagnostic technique is optimized in accordance with the results of
these analyses. Studies of boundary layer flow phenomena using the optimized diagnostic
technique are discussed in Chapter 5.
90 60 30 00.0
0.1
0.2
0.3
0.4
Predicted BRDF
BR
DF
[sr
-1]
scatter
[degree]
0.0
0.2
0.4
0.6
0.8
1.0
1.2N
orm
aliz
ed s
catte
r in
tens
ity [
a.u.
] Measured surface scatter
Figure 3.19: Comparison of fused silica surface scatter measurements against silicon wafer BRDF under normal incidence. BRDF is in units of [sr-1], and the fused silica surface scatter measurements are normalized to the peak BRDF value at 0°.
51
3.3.3 Metal wall diagnostics optimization
Optimization efforts mentioned in the previous section are also applicable to
metallic surfaces with one exception. The perpendicular bottom-up orientation is no
longer feasible due to material constraints and the top-down orientation is used instead.
Otherwise, the same incident and collection angle strategy can be used, the main
difference being the scatter intensity at the surface. Since metals do not transmit light, the
scattered intensity is much stronger than fused silica. So much so, that even the band-pass
optical filter is unable to completely eliminate it.
To mitigate surface scatter, three different surface coatings with everyday items are tested
on a mirrored aluminum surface. They are black permanent marker (Sharpie), black felt-
tip pen (Paper Mate), and black matte spray paint. All three options show significant
reduction in scatter intensity at the surface. Spray paint, despite having the most even
coating, is quickly ablated after one or two laser pulses. The ablated spray paint
fluoresces and renders the PLIF image useless. Permanent marker and felt-tip pen stayed
on much longer than spray paint, but the latter can be coated more evenly reducing scatter
from bulk particulates. Result of the surface treated with black felt-tip pen is shown in
Figure 3.20. Surface scatter from a clean metal surface is also shown for comparison.
Both images were taken using the band-pass optical filter. Roughly 96% reduction in
surface scatter was observed. The combination of optical filter and a good coat of black
felt-tip pen can significantly improve imaging capabilities near metallic surfaces.
FCfepa
3.4 C
T
well as t
chapter a
PLIF ima
optical c
achieved
camera c
similar ap
surface tr
igure 3.20: CClean surface elt tip pen. Sarticulates.
Conclusi
This chapter
he image co
are available
aging. Sever
configuration
d by normal
collect the r
pproach may
reatment.
Comparison ofwithout surfamall points o
on
introduced t
orrection and
e in Append
ral factors ar
n. It is show
laser sheet
resulting flu
y be used fo
5
1
1
Sur
face
sca
tter
[a.u
.]
f surface scattace treatment.of heavier sca
the experim
d processing
dix C. These
re tested to fi
wn that the
t incidence
uorescence p
or metallic su
52
-0.2 -00
20
40
60
80
100
120
Horizo
ter from mirr. (Right) Samatter intensity
ental faciliti
g procedures
e facilities a
find the best
e least amou
through a f
perpendicula
urfaces with
0.1 0.0
ontal spatial co
W/OWit
rored metallicme surface trey may be att
ies used thro
s. DaVis cod
are then opt
combination
unt of surfa
fused silica
ar to the inc
h the addition
0.1
oordinate [cm]
O surface treatmth surface treatm
c surface. (Leated with bla
tributed to bu
oughout this
des mention
timized for
n of wall ma
ace scattered
wall and h
cident laser
n of black fe
0.2
mentment
eft) ack ulk
s thesis as
ned in this
near-wall
aterial and
d light is
having the
sheet. A
elt-tip pen
53
Chapter 4. PLIF diagnostic validation using shock waves
A new PLIF diagnostic technique is developed for high-speed flow applications
and is validated behind various shock waves in this chapter. Temperature measurement
behind normal incident and reflected shocks in the absence of non-ideal effects are
validated against analytical results. The same detection strategy is then applied to
measuring PLIF signal distribution of supersonic flow and shock reflection over a wedge.
These results are validated using numerical simulation.
4.1 Theoretical background
A shock wave is a sudden disturbance that changes the medium properties it is
traveling in, be it gas, liquid, or solid [94]. It can even propagate in the absence of a
medium, as is the case for an electromagnetic shock wave. Shock waves are supersonic,
and are accompanied by a rise in temperature, pressure, and density across the shock
wave. Although the total energy is conserved across a shock wave, exergy is reduced, and
simultaneously, entropy is increased. Shock waves are of great interest, especially in the
field of aeronautics, due to their connection to vehicle performance and efficiency. In
airplanes, for example, shock waves can lead to additional drag and ultimately reduce the
overall fuel efficiency. Substantial research is currently invested into reducing the
likelihood of shock formation on airplanes.
54
In a shock tube, normal shocks are generated with the bursting of a diaphragm. It
is a controlled process for achieving the required temperature and pressure conditions
behind incident and reflected shock waves for kinetic studies. In the AST, this is done by
altering the plastic diaphragm thickness and/or adjusting the cutter distance from the
diaphragm. Diaphragms used in this study range from 0.002″ - 0.06″. In some shock
tubes, a scored metal diaphragm is used to generate even higher temperature and pressure
conditions. When the diaphragm bursts, pressure waves are formed in series, with each
wave increasing the speed of the following waves. These pressure waves all coalesce and
compress into a shock and propagate into the stationary (in the laboratory frame) driven
gas with a normal wave front in the direction of propagation. The shock wave produces
hot and compressed gas that travels towards the shock at speeds slower than the shock.
At the same time, a rarefaction wave is created and travels in the opposite
direction, into the driver gas. The boundary between the driver and the driven gas is
known as the contact surface. It travels down towards the shock-heated driven gas and
eventually meets up with the reflected shock.
4.1.1 Normal shock wave equations
The normal shock wave theory is well established and the results agree well with
shock tube experiments. In this section, normal shock wave equations are derived for
predicting temperature and pressure behind incident and reflected shock.
Consider the control volume analysis of a 1-D flow shown in Figure 4.1. The
conservation equations of mass, momentum, and energy are expressed as Equation 4.1
through Equation 4.3, where ρ is the density, P is the pressure, U is the bulk velocity, and
2⁄ is the total enthalpy.
0 Equation 4.1
0 Equation 4.2
0 Equation 4.3
st
fi
b
E
g
F
pr
E
For s
tate. Also, a
ixed on the s
e neglected
Equation 4.3
iven in Figu
FigureThe sy1 and 2
or further a
ressure (cp).
Equation 4.8
implification
assume unifo
shock wave.
for a New
can be inte
ure 4.1:
e 4.1: Schemaystem is consi2 are uniform
analysis, assu
. Rankine-H
respectively
n purposes,
orm flow co
. Viscous eff
wtonian fluid
egrated to E
atic of a normidered adiaba
m.
ume ideal g
Hugoniot and
y,
1111
55
the system i
onditions in
ffects and he
d. Under th
Equation 4.4
mal shock wavatic and in ste
gas behavior
d Prandtl re
1
is assumed t
region 1 an
eat transfer p
hese assump
4 through E
ve in shock-fieady-state. Flo
r with const
elations are
to be adiabat
nd 2. The re
phenomena a
ptions, Equa
Equation 4.6
fixed coordinaow condition
E
E
E
tant specific
shown in E
E
tic and at ste
eference fram
are small and
ation 4.1 thr
, using nota
ate system. s in region
Equation 4.4
Equation 4.5
Equation 4.6
heat at con
Equation 4.7
Equation 4.7
eady-
me is
d can
rough
ations
nstant
7 and
56
Equation 4.8
Where γ is the heat capacity ratio and a is the local speed of sound. Using the Prandtl
relations and the energy equation (Equation 4.6), the density ratio is expressed as:
1 121
2
Equation 4.9
where ⁄ . Apply Equation 4.9 to the Rankine-Hugoniot relation to express
the pressure ratio as:
21 1
11
Equation 4.10
Ultimately, the temperature ratio can be derived from the ideal gas law.
12 1
11
1 Equation 4.11
These equations, also known as the normal shock jump equations, are used to
calculate the temperature and pressure values in region 2 and 5 as shown in Figure 3.2.
For this study, an in-house program called FROSH is used to solve these equations and
generate temperature and pressure values in region 2 and 5. Input parameters for FROSH
are the temperature, pressure and tracer concentration in region 1 along with the
measured incident shock speed.
4
as
an
v
W
w
re
fo
w
sh
S
re
4.1.2 Sho
Consi
s shown in F
nd the reflec
elocity in re
Figureframe
When the ang
wave deflects
everted back
ormed so tha
wedge. This p
The r
hown in Fig
hock polar
egion 2 is loc
ock reflec
ider a shock
Figure 4.2. T
cted shock w
gion 1 in the
e 4.2: Regulafixed in point
gle between
s the flow b
k to zero for
at θ3 = 0, an
phenomenon
regular refle
gure 4.3, wh
is the locus
cated on the
ction
wave intera
The normal i
wave (R) is g
e initial shoc
ar reflection t P.
the incident
by an angle
r the steady
nd the flow b
n is called re
ection can a
here θ is the
of all possi
incident sho
57
acting with a
incident shoc
generated as
ck wave refe
in pseudo st
t shock and t
of θ2. The
assumption
behind the r
egular reflect
also be plott
e flow defle
ible states a
ock locus I, b
a wedge in a
ck wave (I)
s a result of t
erence frame
teady flow v
the wedge, α
positive def
to hold [95
reflected wav
tion.
ted as shock
ection angle
after an obliq
below M2 =
a pseudo-stea
is traveling
the interactio
e.
iewed from
α, is small, th
flection of t
5]. A reflecte
ve becomes
k polar in th
and p is th
que shock. F
1 point.
ady inviscid
from left to
on. q1 is the
an inertial
he incident s
the flow mu
ed shock wa
parallel wit
he (θ,p)-spa
he pressure
From Figure
d flow
right
e flow
shock
ust be
ave is
th the
ace as
ratio.
e 4.3,
Fininw
A
the flow
therefore
= αd (M1
Deflectio
surface.
represent
Ffi
igure 4.3: Rencident and rntersects with
with the wedge
A second loc
deflection b
e distance d i
1,γ), after w
on is still po
A buffer z
tation of suc
igure 4.4: Maixed in triple p
egular reflectreflected shoch θ = 0, allowe.
us, the refle
back to θ = 0
increases lin
which, the lo
ositive (θ >
one is requ
h flow is sho
ach reflectionpoint P.
5
tion in (θ,p)-sck, respective
wing the flow
ected shock,
0. Point P mo
nearly with ti
ocus of the r
0), indicatin
uired to tran
own in Figur
n in pseudo-st
58
space. The fiely. Note thabehind the re
is plotted fo
oves up the w
ime. As α is
reflected sho
ng that the f
nsition from
re 4.4.
teady flow vi
irst and seconat the reflecteeflected shoc
or M = M2 f
wedge at a c
increases it
ock cannot
flow is still
m θ > 0 to
iewed from an
nd locus is ted shock loc
ck to be paral
from (θ2, p2)
constant rate
reaches a th
intersect wi
directed tow
o θ = 0. A
n inertial fram
the cus lel
) to return
of q1 and
hreshold α
ith θ = 0.
wards the
A physical
me
is
is
ph
v
an
4
o
re
re
sc
b
to
th
un
A thir
s formed to
s known as M
Figurewith θneeded
Pressu
hysical prop
ortex sheet a
n angle θ3 w
(q3 ≠ q4) le
f (q3 - q4). It
When
egion 3, Sin
eflection ob
chematic of
ecause regio
o point B [9
he case of S
ntil B becom
rd shock S, l
separate the
Mach reflect
e 4.5: Mach rθ = 0 and thed to bring the
ure and stre
perties such a
are assumed
with the tripl
ads to sever
t also dictate
n q3 is greate
ngle Mach r
served durin
SMR is sho
on 3 is super
6]. Another
SMR, flow i
mes a stagnat
ifts the triple
gases going
ion and can
reflection in ( triple point iflow back to
eamline def
as density, v
d uniform, V
e point traje
ral different
es whether fl
er than q4, an
reflection (S
ng this stud
own in Figu
rsonic with r
interesting p
s deflected
tion point, at
59
e point P aw
g through S,
be expressed
(θ,P)-space. Tis detached fr θ = 0.
flection are
velocity, and
is straight i
ectory. Veloc
shock reflec
ow in region
nd (q3 - q4) is
SMR) is ob
dy and is th
ure 4.6. The
respect to the
phenomenon
near point B
t which time
way from the
, and through
d as Figure 4
The second lfrom the surfa
continuous
d entropy are
in the referen
city differen
ction phenom
n 3 move aw
s smaller tha
bserved. Thi
he simplest
reflected sh
e triple point
n is the curl
B. The local
e the flow is
surface and
h I and R. T
4.5 in (θ,P)-
locus does noace. A third l
s across V.
e not. If cond
nce frame of
nces across V
mena depend
way from or i
an the local s
is is the onl
form of Ma
hock is strai
t but is subs
ling of the v
l pressure co
directed out
d a vortex sh
This phenom
space.
ot intersect locus, S, is
However
ditions withi
f point P for
V in region 3
ding on the v
into the wed
speed of sou
ly type of M
ach reflectio
ght until po
sonic with re
vortex sheet
ontinues to
t in all direct
heet V
menon
other
in the
rming
3 and
value
dge.
und in
Mach
on. A
int D
espect
V. In
build
tions,
even into
streamlin
schemati
Fst
N
numerica
(CFD) s
experime
Fre
o the vortex
ne to meet th
c of the vort
igure 4.6: Phteady flow vie
No straightfo
al model is r
software pac
ents.
igure 4.7: Voeflected shock
sheet. This
he surface a
tex sheet cur
hysical represewed from an
orward theor
required to s
ckage Fluen
ortex sheet cuk in SMR.
6
causes the v
at right angle
rling and nea
entation of Sn inertial fram
ry yet exists
solve it. For
nt 6.0 is u
urling and str
60
vortex sheet
es due to th
arby streaml
ingle Mach rme fixed in trip
s for solving
this study, t
used to mo
reamlines nea
t to deflect i
e absence o
lines are show
reflection (SMple point P.
g flow condi
the computa
odel the SM
ar vortex shee
inwards, allo
of vorticity [
wn in Figure
MR) in pseud
itions in SM
ational fluid
MR observe
et V behind t
owing the
97,98]. A
e 4.7.
do-
MR, and a
dynamics
ed in the
the
4
4
T
th
an
in
se
en
co
p
se
re
4.2 Exp
The e
.8. For mor
The beam fro
hick laser sh
n iris just b
ntensity at ei
ection was ro
The la
nd wall win
ollect the flu
ath. The im
eparated from
esolution wa
Figurehorizowindo
perimenta
experimental
re detailed d
om the KrF
eet using sh
efore enterin
ither edges o
oughly 3cm.
aser sheet w
ndow to avoi
uorescence s
maging regio
m the end w
as about 0.06
e 4.8: Schemaontal laser shew.
al setup
l setup of th
description o
excimer lase
eet-forming
ng the test s
of the laser
.
was configure
id any possi
signal throu
on, shown i
wall by 3cm
6mm/pixel.
atic of the shoeet enters thro
61
he PLIF diag
of individua
er was loose
optics. Edge
section. Thi
sheet. The a
ed to enter t
ible non-ide
gh the top w
in Figure 4.
to avoid the
ock tube and ough the end
gnostic for th
al equipment
ely focused
es of the lase
is was done
actual width
the test secti
eal effects. T
window, per
.8, was abo
e non-uniform
laser setup. Iwall, and is i
his study is
t, please ref
into a 5cm w
er sheet wer
to remove
h of the laser
ion through
The ICCD c
rpendicular t
out 3cm wid
m thermal la
In this configuimaged throu
shown in F
fer to Chapt
wide and 0.7
re truncated u
regions of l
r sheet in th
the center o
amera was s
to the laser
de and 6cm
ayer. The ca
uration the ugh the top
Figure
ter 3.
75cm
using
lower
e test
of the
set to
sheet
m tall,
amera
S
shock c
Tempera
from a s
shock wa
In
side win
appeared
showed t
to the sh
effect tha
±10° dep
shock wa
normal sh
Fanrediinim
W
through t
efforts, m
ingle-shot i
onditions b
ature in regio
mall area (5
aves, respect
nitially, the
dow. Howev
d adjacent to
that the angl
ock wave fr
at occurs wh
pending on s
ave and dis
hock front.
igure 4.9: Dind angle valuespect to the sirection are an the bottom image with the
While careful
the end wal
maintaining
mages of in
by varying
ons 2 and 5 w
5pixels by 5
tively. Samp
laser sheet
ver, it was
o the norma
les coincided
ront as show
hen a collima
shock streng
appears whe
iffraction dueues in the figushock wave frlso marked. Timage) is visie same propag
l alignment
ll to circumv
alignment w
6
ncident and
the diaphr
were sample
5 pixels) abo
pled tempera
was configu
quickly disc
al shock wa
d with the la
wn in Figure
ated beam of
gth [99]. Th
en the laser
e to grazing aure indicate g
front. IncidentThe edge of thible just behingation directio
is always an
vent the issu
with pinpoin
62
reflected sh
ragm thickn
ed by averag
out 0.5mm b
ature range is
ured to illum
covered that
aves at grazi
aser sheet pr
4.9. This ph
f light strike
his streak ca
r sheet is ali
angle of lasergrazing angle t shock wavehe laser sheetnd the incidenon as the diffr
n option, the
ue altogethe
nt accuracy
hocks were
ness and i
ging per-pix
behind the i
s 296K – 800
minate the t
t a faint stre
ing angles.
ropagation d
henomenon i
s the shock a
an appear in
igned perfec
r sheet propa of incident llocation andt (denoted bynt shock wav
fraction effect
e laser sheet
er. This was
was extrem
taken unde
nitial press
xel temperatu
incident and
0K.
est section t
eak of weak
Further inv
direction wit
is due to a d
at grazing an
n front of or
ctly parallel
agation. Arrowlaser sheet wiits propagati
y the dotted live in the bottot.
t was instead
because de
mely challeng
er various
sure (P1).
ure values
d reflected
through a
ker signal
vestigation
th respect
diffraction
ngle up to
r behind a
l with the
ws ith ng ine om
d rerouted
espite best
ging. The
re
w
m
th
g
sh
se
al
th
sh
an
fr
m
erouted laser
while simulta
measurement
Howe
hrough the e
enerate SMR
hown in Fig
ection was r
llows the ca
he sensor ar
haped to imp
nd 7.5cm in
rom the end
minimize surf
Figuresensorcamera
r sheet was
aneously rem
t uncertainty
ever when an
end wall, sid
R is such an
gure 4.10. Th
rotated a qu
amera to see
rray plate u
prove flow t
length with
d wall. The
face scatter.
e 4.10: Top vir array plate ta to see all th
less sensitiv
moving the
y near shock
n obstacle i
de wall illum
n example. T
he laser shee
uarter turn s
all three sid
sing two co
through the
an angle of
hypotenuse
iew of the testhat the wedgree sides of th
63
ve to minute
diffraction e
waves.
s placed in
mination is i
The location
et is illumin
o that the s
des of the w
olumns (2.5c
underside of
30 degrees.
is coated w
st section. Thege is attachedhe wedge thro
e fluctuations
effect. This
the test sec
inevitable. A
n of the wed
nated in a to
sensor array
wedge. The w
cm in heigh
f the wedge
The leg of t
with a thin l
e test section d to is on though the top w
s in its prop
helps to red
ction prohibi
An aluminum
dge within t
op-down orie
plate was o
wedge is sec
ht). The col
. The wedge
the wedge is
ayer of blac
was rotated 9he side. This window.
pagating dire
duce temper
iting illumin
m wedge us
the test secti
entation. Th
on the side.
curely attach
lumns are w
e is 5cm in w
s about 1cm
ck felt tip p
90° so that allows the
ection
rature
nation
sed to
ion is
e test
This
hed to
wedge
width
away
pen to
4.3 C
4.3.1
A
temperatu
Figure 4.
FanTar
Note that
shock ex
of Figure
Vertical
columns
temperatu
reflected
Core flow
Tempera
An example
ure distribut
.12.
Figure 4.11: Ind (RIGHT)
T1=296K, VS=rrow: directio
t the two ca
xperiment. H
e 4.11 and F
profiles are
of the tem
ure values a
shock.
w thermo
ature meas
of the sing
tion of an in
Incident shocktemperature
=546m/s, incidon of incident
ases presente
Horizontal an
Figure 4.12
constructed
mperature im
across 5 row
6
ometry
surement
gle-shot, ful
ncident and a
k wave meas image. Initdent shock attshock.
ed in Figure
nd vertical te
are shown i
d by averagi
mage. Horiz
ws approxim
64
t behind n
l-frame PLI
a reflected sh
surement. (LEial conditiontenuation = 1
4.11 and Fi
emperature a
in Figure 4.1
ing tempera
zontal profi
mately 0.5mm
normal sh
IF signal an
hock is show
EFT) Correctns: P1=0.067b.3%/m. Dow
igure 4.12 a
and residual
13 and Figu
ature values
iles are pro
m behind ei
hocks
nd the corre
wn in Figure
ted PLIF signbar, Xtol=3.8%
wnward-pointi
are not from
l temperatur
ure 4.14, resp
across 5 ce
oduced by
ither an inci
esponding
e 4.11 and
nal %, ng
the same
re profiles
pectively.
enter-most
averaging
ident or a
Figureand (RT1=29arrow:
Figurepredicverticawidth)behindeviden
e 4.12: ReflecRIGHT) tem6K, VS = 723: direction of
e 4.13: Tempted) profiles al profile alo); Lower plotd incident shont.
350
400
450
Tem
p [K
]
-10
0
10
Re
sidu
al T
[K]
Dist
300
400
Te
mp
[K]
-10
0
10
Re
sidu
al T
[K]
cted shock wamperature ima
3m/s, incidenreflected sho
perature andin the core
ong the centrts: horizontal ocks; a flat t
-1 0
tance from the center ofDistance
3 4D
0.5mm
65
ave measuremage. Initial cnt shock attenck wave.
d residual tem flow acrossral column oprofile along
temperature d
350
400
450
Te
mp
[K]
-1-10
0
10
Res
idua
l T [K
]
Distance1
f shock tube [cm]e from the center of t
MeasurePredicte
5 6
Distance from end w
1
ment. (LEFT)conditions: Pnuation = 1.5
mperature (bs the incidenof pixels (aveg the row of distribution a
0
e from the center of shocthe shock tube [cm]
ed profiled profile
7wall [cm]
1cm
) Corrected P1=0.031bar, X
5%/m. Upwar
between meant shock. Uperaged acrospixels 0.5mm
across the las
1ck tube [cm]
8
PLIF signal Xtol=4.5%, rd-pointing
asured and pper plots: s 5 pixels
m and 1cm er sheet is
66
Figure 4.14: Temperature and residual temperature (between measured and predicted) profiles in the core flow across the reflected shock. Upper plots: vertical profile along the central column of pixels (averaged across 5 pixels width); Lower plots: horizontal profile along the row of pixels 0.5mm and 1cm behind reflected shocks; a flat temperature distribution across the laser sheet is evident.
Note that temperature measurement uncertainty of the higher temperature region behind a
reflected shock is worse compared to that behind an incident shock (i.e. larger residual
temperature profile in Figure 4.14 than Figure 4.13) due to lower PLIF signal levels.
Despite this shortcoming, temperature profile measurements exhibit relatively uniform
distribution throughout all regions and the measured temperature values agree well with
theoretical predictions.
4.3.2 Signal-to-noise ratio analysis
The study of PLIF image signal-to-noise ratio (SNR) with respect to the ICCD
camera hardware binning level is presented in Figure 4.15. The two major sources of
noise that affects the ICCD camera, and therefore all PLIF images, used for this thesis are
dark and shot noise. The causes and ways to circumvent dark noise are thoroughly
discussed in the previous chapter. Unfortunately, the effects of shot noise cannot be
easily removed because it is due to the inherent uncertainty of photons and has greater
significance for low-photon events, for example in PLIF diagnostics. In the case of shot-
500
600
700
Te
mp
[K]
-1 0 1-20
0
20
Res
idua
l T [K
]
Distance from the center of shock tube [cm]
500
600
700
Te
mp
[K]
-1 0 1-20
0
20
Res
idua
l T [K
]
Distance from the center of shock tube [cm]
400
500
600
Te
mp
[K]
Measured profile Predicted profile
3 4 5 6 7 8-25
0
25
Re
sid
ua
l T [K
]Distance from end wall [cm]
Distance from the center of the shock tube [cm]
0.5mm 1cm
67
noise-limited behavior, such as our setup, SNR increases with higher binning level at the
cost of image resolution. Measurements showed that at 440K, SNR increased from 66 to
195 with increasing binning level from 1×1 to 16×16. At 620K, SNR increased from 16
to 51 with increasing binning level from 1×1 to 16×16. Conversely, image resolution
drops from 60µm/pixel (no hardware binning) to about 1mm/pixel (maximum binning:
16×16 pixels). Results show SNR at 800K without hardware binning was about 10,
which was good enough for the purpose of this study. However, for higher temperature
application where even lower PLIF signals are expected or when imaging small-scale
flow features such as boundary layer and turbulent mixing, an optimum balance of SNR
and image resolution is required.
0 200 400 600 800 10000
50
100
150
20016x168x84x42x2
Sig
nal-t
o-N
oise
rat
io
Pixel resolution [m/superpixel]
620K (Region 5) 440K (Region 2)
1x1Hardware binning [pixels]
Figure 4.15: SNR as a function of pixel resolution using hardware binning. Toluene mole fraction, Xtol, for both temperatures was fixed at 0.9%.
4.3.3 Validation using analytical results
Approximately 50 single-shot images of incident and reflected shock
measurements in the shock tube core flow are used to assess the variation of
measurement accuracy with respect to temperature using the PLIF diagnostic technique.
A plot of the predicted versus measured temperature is shown in Figure 4.16.
68
300 400 500 600 700 800
300
400
500
600
700
800
Me
asu
red
tem
pera
ture
[K
]
Predicted temperature [K]
Incident shock Region 1 Region 2
Reflected shock Region 2 Region 5
Figure 4.16: Predicted versus measured temperature in the core flow. Single-shot images were taken at full resolution without hardware binning.
Images are taken without hardware binning to maximize pixel resolution. For these
measurements, effects of shock attenuation are neglected due to their small effect on
temperature in these experiments. Near room-temperature, mean measurement error is
within 0.4%. However, as temperature increases, mean error increases to about 1.6% and
3.6% for measurements behind incident and reflected shocks, respectively. This is
attributed to the decrease in PLIF signal at higher temperatures as well as absorption
cross-section and relative FQY model uncertainties (6% and 10%, respectively).
4.4 Flow over a wedge
Having successfully demonstrated the accuracy of the PLIF diagnostic technique
in shock tube core flow region clear of any impediments, the same technique was applied
to a more complex flow field: an incident shock wave propagating over a wedge.
Conditions inside the test section were such that Single Mach reflection (SMR) is
observed following the incident shock wave. Instead of a direct comparison of
temperature measurement with that of prediction, as was the case for normal shock
waves, PLIF images were validated against a synthesized PLIF image. It was calculated
using the temperature, pressure, and tracer density results provided by the CFD
ca
st
kn
co
4
te
st
d
ex
d
4
pr
sh
alculation a
traightforwa
nowledge o
onvert PLIF
4.4.1 PLI
An in
echnique, an
tem, the vo
istinguishab
xperimental
etailed in se
FigureMach
4.4.2 Num
While
redictable us
hock and the
and the LIF
ard analytica
f the pressu
signal level
IF measu
ncident shock
nd shown in
ortex sheet
le and matc
facilities an
ction 3.3.
e 4.17: PLIF reflection is v
merical m
e the pressur
sing simple
e vortex she
F equation.
l solution of
ure field, the
l to temperat
urement
k traveling o
Figure 4.17
and the st
ch those sho
nd optical co
image of anvisible.
model
re fields in t
theory, the s
et. Therefor
69
This is be
f the pressur
e PLIF diagn
ture.
over a wedg
. Character
traight and
own in Figu
onfigurations
n incident sho
the region i
same cannot
re, a numeric
ecause in ce
re distributio
nostic techn
ge was image
ristic feature
curved ref
ure 4.6. This
s optimized
ock traveling
immediately
t be said for
cal solver (F
ertain parts
on does not e
nique is una
ed using the
es of SMR, s
flected shoc
s image was
for near-me
g over a wed
y after the in
r regions beh
FLUENT 6.0
of the flo
exist. Withou
able to accur
e PLIF diagn
such as the M
ck, were cl
s taken usin
etal-wall ima
dge. Single
ncident shoc
hind the refl
0) is employ
ow, a
ut the
rately
nostic
Mach
learly
ng the
aging,
ck are
lected
yed to
calculate
coupled d
The rati
polynom
model [1
used for
field of S
left to rig
shock an
known p
close agr
Ftrvi
4.4.3
A
temperatu
paramete
Figure 4.
shown (R
the pressur
density solv
o of specif
mials, and vi
00]. 3rd ord
discretizatio
SMR over a
ght, and all
nd vortex sh
ressure (far
reement with
igure 4.18: Traveling fromisible.
Compari
A synthesize
ure, pressur
ers are factor
.19 (LEFT).
RIGHT). Bo
re, temperatu
er was used
fic heats fo
iscosity was
der AUSM (A
on [101], and
wedge is sh
the SMR fe
heet show i
away from
h those of Fig
Temperature fm left to right
son
d PLIF ima
re, and tol
red into the
An experim
oth images a
7
ure, and tolu
to solve the
or toluene
s treated via
Advection U
d an explicit
hown in Figu
eatures are c
inhomogene
the wedge),
gure 4.18.
field simulatedt. The reflect
age can be c
luene densi
LIF equatio
mental PLIF i
are displaye
70
uene species
e continuity
and nitroge
a the Mente
Upstream Sp
t solver was
ure 4.18. The
clearly visib
eous tempera
, converted t
d using Fluented shock an
constructed
ity distribut
on pixel-by-p
image with m
ed in the sam
s density dis
equation in
en are expr
er Shear Str
litting Meth
used. The c
e incident sh
ble. Regions
ature distrib
temperature
nt 6.0. The innd the vortex
from the nu
tion. The a
pixel and the
matching ini
me false co
stribution of
control volu
ressed as th
ress Transpo
hod) flux spli
alculated tem
hock is trave
s behind the
bution. In r
measureme
ncident shockx sheet are al
umerically c
aforemention
e results are
itial conditio
olor scale fo
f SMR. A
ume form.
hird-order
ort (SST)
itting was
mperature
eling from
e reflected
egions of
ents are in
k is lso
calculated
ned flow
shown in
ons is also
or a direct
co
in
4
ex
pr
omparison. P
n Table 4.1.
.20. Distanc
Figure(RIGHprofile
Figure
PLIF
xcept within
ressure and t
PLIF signal
PLIF signal
e along the d
e 4.19: (LEFHT) Experime along the do
2
4
6
8
10
Flu
ore
scen
ce s
igna
l [a.
u.]
e 4.20: PLIF s
signal from
n the vortex
temperature
values from
l profile alon
dotted line is
T) Synthesizental PLIF i
otted line is sh
30
200
400
600
800
000
Dis
MeasSimu
signal profile
m both image
sheet. Gene
conditions c
71
m both image
ng the dotte
s measured s
zed PLIF imaimage measuhown in Figur
2
stance along the
suredulated
along the dot
es agree wel
erally, a 5%
corresponds
es at various
ed line in Fig
starting from
age created ured in a shre 4.20.
1
e line [cm]
tted line in Fi
ll (within 4%
discrepancy
to only 0.5%
regions of th
gure 4.19 is
m the right ha
from the CFock tube. PL
0
igure 4.19.
%) in all reg
y in the PLI
% variation i
he flow are
shown in F
and side.
FD results; LIF signal
gions of the
IF signal at
in temperatu
listed
Figure
flow
these
ure.
72
Regions Measured PLIF signal level
Synthesized PLIF signal level
Difference [%]
Bow shock at leading edge 260 250 4.0
Behind reflected shock 280 275 1.81
Behind incident shock 375 365 2.74
Within vortex sheet 310 135 130
Table 4.1: Comparison of measured and synthesized PLIF signal values for various regions of the flow. Results from all but 1 region agree very well.
One reason for the discrepancy within the vortex sheet is is the difference in flow
geometry. The angle between the wedge and the triple point (P in Figure 4.4), χ, for the
synthesized and the measured PLIF images are 11° and 6°, respectively. It should also be
noted that this is the only region in which viscous terms are significant, so it may be that
the model is unable to capture the necessary non-ideal flow physics in this region.
4.5 Conclusion
A quantitative temperature field measurement technique based on toluene PLIF
diagnostic is for shock tube flows. Toluene is extremely sensitive to temperature and is
an ideal tracer for such application. SNR analysis is performed to find the optimum
balance between measurement uncertainty and image resolution. The diagnostic
technique was validated by imaging normal incident and reflected shock waves in the
core flow and single Mach reflection in the flow over a wedge. Temperature
measurements in the uniform flow conditions behind normal incident and reflected
shocks agreed well with theoretical predictions. Near room-temperature, mean
measurement error is only 0.4%. The error slightly increases with temperature to about
3.6% near 800K. PLIF signal measurements of SMR agreed well with CFD results in all
regions (about 4% discrepancy) but one. Overall, the newly developed PLIF diagnostic
technique can accurately determine temperature distribution up to 800K in shock tube
flows with high spatial resolution.
73
Chapter 5. Near-wall PLIF diagnostic in shock tubes
With the successful validation of the PLIF diagnostic technique under relatively
uniform flow fields, such as behind normal shock waves and SMR in the previous
chapter, the next step is to apply the PLIF diagnostic technique to non-uniform flow
fields. This chapter studies the temperature distributions of the side wall boundary layer
(SWBL) and the end wall thermal layer (EWTL). These flow regions provide steep
temperature gradients at constant pressure equal to that of the core flow region, making
them ideal candidates for the PLIF diagnostic technique. The aforementioned near-wall
flow fields are of interest because non-ideal effects from these layers may propagate into
the core flow and affect its conditions. A quantitative near-wall imaging technique can
improve shock tube characterization and lead to more accurate experiments by providing
spatially resolved temperature distribution data that are not available with line-of-sight
optical diagnostic techniques. However, these flow regions only occur in close proximity
to shock tube walls where laser sheet scatter and reflection at the wall surface can
interfere with nearby fluorescence signal in the PLIF image. To compound the issue even
further, these flow regions require higher spatial resolution than what was used in the
previous study to adequately resolve the minute details within.
The optimized experimental setup detailed in Chapter 3 is implemented to
improve near-wall image quality. Temperature profile measurements in both the SWBL
and EWTL are validated against theoretical profiles. Also, measurements of the SWBL
74
and EWTL development under various shock strengths and test gases are performed to
study the extent of near-wall flows.
5.1 Theoretical background
The boundary layer concept was introduced by Prandtl in 1904 [102]. Although
the idea of viscosity and equations of motion (Navier-Stokes equation) had been well
established by then, solutions to these equations were unavailable due to complex
mathematics and the lack of computational resources near the end of the 19th century.
Prandtl, based on both theoretical and experimental data, separated the flow over
a body into two regions. A very thin layer close to the surface where viscous effects
cannot be neglected (boundary layer) and the rest of the flow where viscous effects can
be neglected (free stream). His theory not only provided a connection between viscous
forces and drag, but reduced the mathematical complexity substantially, enabling
explosions of development in modern fluid mechanics during the past century. Detailed
formulation of laminar boundary layer theory is given in the following section.
The dominant form of heat transfer in the static gas behind the reflected shock
with the end wall is conduction. An EWTL is formed as a result and tends to grow thicker
than a SWBL. The theoretical consideration of heat diffusion started much earlier than
that of boundary layer theory. Fourier first laid out the foundation and instigated the
development of modern heat transfer and mathematical physics in 1878 [103]. Heat
diffusion on a microscopic level is a complex physical transport phenomena that includes
molecular collision of gases [104]. Macroscopic effects as a result of microscopic
phenomena can be formulated using statistical mechanics [105,106]. However, this
bottom-up approach quickly runs into practical limitations, and equations derived from
empirical data are used instead. Further consideration of the end wall heat transfer
phenomenon is covered in section 5.1.2.
In the span of 60 years since the experimental evidence of boundary layers was
reported by Dryden et al. [107], near-wall imaging techniques have made steady
progress. Various attempts to image near surfaces using traditional line-of-sight
visualization technique, such as shadowgraph, schlieren, or interferometry, have been met
75
with difficulties. This is because these techniques are required to restrict optical access to
avoid specular and diffusive (scattering) reflection from the nearby surface as well as
unable to resolve complex 3-D flow features [108]. Optical diagnostics that utilize
fluorescence or Raman spectroscopy can circumvent these issues. This is because in
many cases, the excitation laser wavelength used to perform these diagnostics is
spectrally separated from the resulting fluorescence, resulting in lower noise levels in the
images. 3-D features can also be resolved by scanning the laser sheet within the volume
of interest. Near-wall flow measurements using PLIF [109,110,111,112] and Raman
spectroscopy [113] have been previously demonstrated. Smith et al. [109] and Fajardo et
al. [110] reported spatial resolution on the order of 0.3mm and 59μm, respectively but did
not mention how close they were able to make quantitative measurements from the wall
surface. Schrewe et al. [111] and Hultqvist et al. [112] made measurements 0.75mm and
0.2mm from the wall, respectively.
The current study details the development of a technique to image boundary layer
temperature distributions and measure boundary layer development near the side and end
walls of a shock tube, with a goal of determining diagnostic accuracy and capability near
walls.
5.1.1 Side wall boundary layer
According to Prandtl, flows with high Reynolds number can be separated into the
free stream and boundary layer. Reynolds number (Re) is a dimensionless number that is
a ratio of inertial forces to viscous forces. The boundary layer can be further divided into
laminar and turbulent boundary layers. The boundary layer over a flat plat is laminar at
inception (immediately behind the incident shock wave). As the shock wave moves
downstream, the boundary layer and the Reynolds number grows until the latter reaches a
critical value (Recrit ≈ 5×105). This point is known as the transition point and all
subsequent flow becomes turbulent. The transition point is important because heat
transfer and fluid resistance (drag) strongly depend on its location.
For the purposes of this study, turbulent boundary layer cases will not be
considered, since the boundary layers imaged for this study are all laminar. Discussions
of the tur
laminar
boundary
incompre
where u
respectiv
temperatu
rbulent boun
boundary la
y layer can b
essible Navie
and v are
vely, ρ is the
ure, and µ is
Figure
ndary layer t
ayer shown
be solved us
er-Stokes eq
1
the velocity
density, cp i
s the viscosit
5.1: Schemat
7
theory can be
in Figure
sing the Bla
quations (Equ
0
1
1
y componen
is the heat ca
ty. Buoyancy
tic of laminar
76
e found in [2
5.1. A 2-D
asius solution
uation 5.1 th
2
nts in the x
apacity, k is
y forces are
boundary lay
20]. Conside
D steady inc
n which is d
hrough Equa
2
x and y dire
the thermal
neglected fo
yer velocity g
er a cross-se
compressible
derived from
ation 5.4).
Equation
Equation
Equation
ection of Fi
conductivity
or simplicity
gradient.
ection of a
e laminar
m the 2-D
n 5.1
n 5.2
n 5.3
Equation 5.4
igure 5.1,
y, T is the
y.
77
To simplify the 2-D Navier-Stokes equation, assumptions of steady-state, constant free
stream velocity, and a very thin laminar boundary layer (Re » 1) are made. The 2-D
incompressible Navier-Stokes equations then reduce to:
0 Equation 5.5
Equation 5.6
Equation 5.7
These equations can be reduced even further by defining the stream function Ψ ,
where Ψ⁄ , and Ψ⁄ . If so, Equation 5.5 and Equation 5.6 are
simplified to Equation 5.8 and Equation 5.9, respectively.
Ψ Ψ0 Equation 5.8
Ψ Ψ Ψ Ψ Ψ Equation 5.9
The boundary conditions are as follows:
Ψ x, 0 0; , 0 0; , ∞ → Equation 5.10
From experimental observation, velocity profiles at various locations along the x axis
collapse into one profile in the √⁄ coordinate. This indicates that the laminar boundary
layer velocity profile is self-similar. The complex partial differential equation given in
Equation 5.9 can be simplified to an ordinary differential equation in η, the similarity
variable, where:
78
η y Equation 5.11
The dimensionless function f(η) is such that:
Ψ Equation 5.12
The velocity component u and v can be expressed in terms of the newly defined
dimensionless variable and function:
⋅ ′ Equation 5.13
12
Equation 5.14
where ⁄ . Likewise, the momentum equation (Equation 5.9) and the boundary
condition (Equation 5.10) can be simplified as follows:
12
0 Equation 5.15
0 0 0; ′ → ∞ → 1 Equation 5.16
Equation 5.15 is famously known as the Blasius equation. It can describe the entire
laminar momentum boundary layer using a single variable, η.
To determine the temperature distribution within a boundary layer requires
solving the laminar boundary layer energy equation (Equation 5.7) in addition to the
Blasius equation. To simplify the laminar boundary layer energy equation, assume
constant cp, k, and μ. This is a good first order approximation for the range of temperature
79
relevant to this study. Under these assumptions, the energy equation becomes a linear
function and the temperature distribution can be expressed as a superposition of two
components: wall plate cooling and viscous dissipation in the velocity boundary layer.
The first and second term on the right hand side of Equation 5.17 correspond to wall plate
cooling and viscous dissipation, respectively.
Equation 5.17
where is the thermal diffusivity. The boundary conditions for Equation 5.17 are:
0 ; → ∞ Equation 5.18
As is the case for the momentum equation, the energy equation (Equation 5.17)
can also be reduced using the similarity variable η and the dimensionless function f(η) as:
2′′ Equation 5.19
where the right hand side is the forcing function due to the viscous dissipation. Prandtl
number, Pr, is a dimensionless number that is a ratio of momentum and thermal
diffusivity. The boundary condition to the energy equation then becomes:
0 ; → ∞ Equation 5.20
Equation 5.19 is a linear function with respect to T, and a solution can be written as:
2 Equation 5.21
80
where Tw and 0 are the temperature and the adiabatic temperature at
the wall, respectively. θ2(0) can be approximated as Pr1/2 for Pr<50 [114]. θ1 is the
solution without viscous dissipation, and θ2 is the solution due to viscous dissipation:
′′
′′ Equation 5.22
2 ′′ ′′ Equation 5.23
The combined system of equations can only be solved numerically unless Pr = 1 [115].
5.1.2 End-wall thermal layer
After shock reflection, the gas behind the reflected shock ideally comes to rest, creating
uniform temperature and pressure conditions ideal for wide varieties of scientific and
engineering application. Consider a test section end wall as shown in Figure 5.2. The gas
is ideally at rest and is cooled by heat transfer through the end wall window, assuming no
chemical reaction. Since there are no bulk motions of the gas, the heat transfer in the test
section is dominated by diffusion. Temperature distribution of the gas can be modeled
using the 1-D heat diffusion equation, shown in Equation 5.24.
Equation 5.24
where Tg is the gas temperature, kg is the thermal conductivity, ρ is the density, cp is the
heat capacity of the gas. This partial derivative equation can be solved numerically with
variable thermal properties (α, ν, and cp) of the gas. α is the thermal diffusivity and
defined as ⁄ . Thermal properties in the end wall window are assumed to be
co
fe
w
th
w
5
5
la
u
onstant sinc
ew degrees).
where T5 is th
he end wall s
wall at room
Figureprofile
5.2 Exp
The e
.3 (for more
aser beam w
sed in the pr
e the tempe
. The initial a
, 0
0
he test gas t
surface, T∞ i
temperature
e 5.2: Two see across the en
perimenta
experimental
e detailed de
was loosely f
revious study
erature withi
and boundar
∞,
,
temperature
is the room t
, and L is the
emi-infinite rnd wall windo
al setup
l setup of th
scriptions of
focused and
y, as to main
81
in the end w
ry conditions
behind the r
temperature,
e thickness o
regions in peow and the te
he PLIF diag
f each indivi
shaped into
ntain the fluo
wall will var
s are:
0
reflected sho
kw is the the
of the end w
erfect thermaest section is a
gnostic for th
idual facility
o a laser she
orescence sig
ry slightly (o
E
E
E
ock, Tw is th
ermal condu
wall.
al contact. Tealso shown.
his study is
y, please see
eet with the
gnal linearit
on the order
Equation 5.25
Equation 5.26
Equation 5.27
he temperatu
uctivity of th
emperature
shown in F
e Chapter 3)
same dimen
ty. Test imag
r of a
5
6
7
ure of
he end
Figure
). The
nsion
ges of
the side
using the
temperatu
collection
imaging
resolution
section t
width, on
actual wi
Flare
S
7cm awa
between
EWTL a
Figure 5.
of the ex
weaker s
arrival of
wall bound
e camera se
ure distribut
n lens were
area down t
n (15µm/pix
to cutoff reg
nly the porti
idth of the la
igure 5.3: Scaser sheet to emoved when
WBL were
ay from the e
the arrival
are imaged r
.3. Thermal
xpansion or
hocks, unifo
f the expans
dary layer sh
etup used in
tion within th
e reconfigur
to about 1cm
xel). The la
gions of low
ion of the la
aser sheet in
chematic of tenter the tes
n imaging thro
imaged righ
end wall as
of the incid
right up aga
layer image
compression
orm conditio
sion or comp
8
howed that t
the previou
he boundary
red to boost
m by 1cm. T
ser sheet ed
wer intensity
aser sheet wi
the test sect
he shock tubst section throough end wal
ht up agains
shown in Fi
dent shock w
ainst the sho
s were taken
n wave refle
ons behind re
pression wa
82
the thickest
us study. Th
y layer. As a
t spatial res
This amount
dges were tr
y. Given tha
ith the most
tion was roug
be and laser sough its sidel window.
st one of the
igure 5.3. Bo
wave and th
ock tube end
n between th
ected from th
eflected shoc
ave reflected
SWBL wa
his was inad
a result, the I
solution, ult
ted to a 4-fo
runcated bef
at the imagi
uniform int
ghly 2cm.
setup. Mirrore or end wall
e shock tub
oundary lay
he return of
d wall at its
he shock refl
he contact s
cks begin to
d from the c
s only 5 pix
dequate for
ICCD camer
imately redu
old increase
fore entering
ing field is
tensity was u
r 2 deflects tl window. It
e side walls
yer images w
f the reflecte
s center, as
lection and t
surface. How
deteriorate b
contact surfa
xels wide
resolving
ra and the
ucing the
in spatial
g the test
1.5cm in
used. The
the is
s, roughly
were taken
ed shock.
shown in
the arrival
wever, for
before the
ace due to
83
the encroachment of vorticity from the interaction between the SWBL and the reflected
shock. Temporally resolved images for the SWBL and the EWTL were measured by
varying the time delay after the incident shock wave and shock reflection, respectively.
Due to a smaller imaging region, predicting the arrival of the incident shock wave
and shock reflection within a reasonable tolerance became very important. Average speed
of an initial shock wave was about 0.7 – 1mm/µs, opening up a 15µs window of
opportunity to image the passing shock wave or a particular region of the flow. This,
compared to about 60µs in the previous study, was a significant reduction. The time
delay uncertainty inherent to the detection system is about ±3µs, which was fine for the
previous study, but can substantially reduce the PLIF measurement yield for the current
study. The uncertainty in timing is due in part by the initial shock wave speed and
attenuation measurement uncertainties and the diaphragm busting process. Both factors
were somewhat mitigated by tighter diaphragm and initial condition tolerances to reduce
the shock-to-shock variation in shock speed.
Optical components used to increase ICCD camera spatial resolution in turn,
decreased the depth of field considerably to a point where even brushing against the
camera lens would defocus the image. Hence, the camera was suspended from an
independent railing above the AST relatively free from disturbances. The intensifier was
gated for 150ns, long enough to collect most of the fluorescence from the toluene tracer
and short enough to relatively freeze the shock wave or flow of interest in motion and
prevent motion blurring. Extreme care was taken to gate the intensifier so that it
coincides with the toluene tracer fluorescence. The collection lens f-stop was adjusted to
its highest setting to collect as much fluorescence as possible and thereby increase the
image SNR. As a result, the optical performance was compromised in the form of image
distortion. It was corrected using the image correction routine detailed in Chapter 3.
In addition, the near-wall imaging optimization detailed in section 3.3 was
implemented to ensure high quality images, particularly near the wall. An image of the
corrected laser scatter level, taken without toluene tracer in the test section, is shown in
Figure 5.4 along with a detailed view near the wall. A plot of one-pixel wide laser scatter
signal with respect to the distance from the side wall in Figure 5.4 reveals small amounts
of scatter signal near the wall, despite the optimized experimental setup. Statistical study
shows th
about 60
Finvisc
5.3 B
5.3.1
W
towards t
four side
stream. T
grows in
boundary
hat reliable P
μm) away fr
igure 5.4: (TOn the absenceiew near the catter signal a
Boundary
Side wall
When a diaph
the end wall
e walls devel
The leading e
n thickness
y layer is de
PLIF signal i
rom a wall.
00.0
0.5
1.0
Sca
tter
leve
l [a.
u.]
OP) Correcte of a shock wwall is also
along the hori
y layer t
l boundar
hragm burst,
l in the gas b
lop moment
edge of the b
as a functi
efined as th
8
nterpretation
2 4Distance from
d image of thwave. White p
shown. (BOizontal dashed
temperat
ry layer
, a normal in
behind it. As
tum and ther
boundary lay
on of time
he distance f
84
n can be mad
6
m side wall [pixe
he laser scattepixels represe
OTTOM) A Pd line indicate
ture prof
ncident shoc
s a result, ga
rmal bounda
yer is attache
or distance
from the sid
de up to a di
8 10
el]
er level takenent the side wPlot of one-ped on the ima
file
ck wave heat
ases in very c
ary layers in
ed to the inc
e. The thick
de wall at w
istance of 4
n under vacuuwall. A detailpixel wide lasage.
ts and induc
close proxim
n the fast mo
cident shock
kness of the
which the no
pixels (or
um led ser
es motion
mity to the
oving free
wave and
e thermal
ormalized
85
temperature θ (=T-Tw/T∞-Tw) is 99% of the core flow temperature, where Tw and T∞
represent wall and core flow temperature, respectively.
For laminar boundary layers, empirical relations between a momentum and
thermal boundary layer is expressed as a function of the Prandtl number in the following
equation:
⁄ Equation 5.28
where δ and δT are the momentum and thermal boundary layer thickness, respectively.
Prandtl number is a dimensionless number comparing the relative importance of the
kinematic and thermal viscosity. It is expressed as:
Equation 5.29
For fluids with Prandtl number less than unity, such as N2 (Pr = 0.69), the thermal
boundary layer tends to be thicker than the momentum boundary layer. The opposite is
true for fluids with Prandtl number greater than unity, such as liquid water (Pr ≈ 7). The
transition between laminar and turbulent boundary layer occurs around Recrit = 5×105.
The characteristics length used to calculated the Reynolds number is the x-wise distance
behind the leading edge. For conditions presented in this study, Remax (≈ 2×105) is below
the critical value of Recrit = 5×105 by the arrival of the reflected shock. At which point, a
complex shock wave-boundary layer interaction, such as bifurcation or flow separation
occur. The test time (time between passing of the incident shock and arrival of the
reflected shock) varied depending on the shock strength and initial conditions, extending
up to about 400µs. Depending on test gases, the thermal boundary layer thickness was up
to 2mm thick by the end of the test time.
Analytical comparisons of several different gases were performed to select
appropriate test gases for this study and to find optimum test conditions for selected
species. Among many different combinations of driven and driver gases, N2, H2, and Ar
are chosen as driven gases, while N2 is chosen as the driver gas.
N
therefore
Also, nit
SWBL te
capacity
behind th
viscosity
FincaRw4%thS
H
tested dr
magnitud
1200m/s)
incident
pressure
shock wa
Nitrogen (N2)
e longer test
trogen bifurc
est time as
(cp) and the
he incident a
y of nitrogen
igure 5.5: (LEn toluene (4alculated usin
Research at Stwave bifurcati
% toluene, Vhe core flow chematic of t
Hydrogen (H
river gas. T
de higher th
) shock wav
shock wave
behind the i
aves studied
) was chosen
time (up to 4
cates well w
shown in F
erefore is ca
and reflected
leads to thin
EFT TOP) Ex4%) with ning CFD resultanford. A thion. Shock co
Vs=710m/s, anare T2=498K
he boundary
H2) produces
This is beca
han that of
ve speed. H
e Mach num
incident sho
only reach u
8
n for its slow
400µs after t
with the refle
Figure 5.5. I
apable of re
d shock wav
nner SWBL.
xperimental Ptrogen. (LEFlts. CFD modhin boundary onditions are nd incident shK, P2=0.25balayer and refl
s the thicke
ause kinem
f nitrogen o
However, hy
mber which le
ck wave. Te
up to 350K a
86
wer incident
the incident
ected shock,
In addition,
eaching temp
es, respectiv
PLIF image oFT BOTTOMdeling courtes
layer is visiP1=0.04bar, T
hock attenuatiar, and T5=6lected shock i
st thermal b
atic viscosi
or argon de
drogen has
eads to sma
emperatures
and 450K, re
shock speed
shock passe
, clearly sig
nitrogen ha
mperatures up
vely. As a tr
f reflected shM) Syntheticsy of Center ible to the leT1= 293K, teion = 0.5%/m96K, P5=1.0interaction.
boundary la
ity of hydro
espite havin
very high c
aller increase
behind the i
espectively.
d (600 - 850
es the imagin
gnaling the e
as relatively
p to 500K a
radeoff, relat
hock bifurcatic PLIF imafor Turbulenft of the sho
est gas: N2, wim. Conditions
5bar. (RIGH
ayer among
ogen is an
g the faste
cp and relat
es in temper
incident and
0m/s), and
ng frame).
end of the
low heat
and 800K
tively low
on age nce ock ith in
HT)
the three
order of
st (850 -
ively low
rature and
d reflected
u
re
un
g
m
h
re
w
th
T
sh
b
F
(7
F
Argon
sed as a bu
equire very
nderstanding
as, facility-
measurement
igher shock
eflected shoc
A sam
with the conv
he incident s
T=346K, P=0
hock wave e
alanced with
igure 5.6. A
7.5cm away
igure 5.7.
Figuretemper4% tol
n was chosen
uffer gas in
uniform te
g the extent
-related erro
ts. Argon ha
k wave spee
ck waves.
mple PLIF i
verted tempe
shock passed
0.15atm, an
equations giv
h H2. A wel
A horizontal
y from end w
e 5.6: (LEFT)rature image.luene, Vs=10
n due to the
high purity
mperature d
of non-unifo
ors can be
as similar bo
ed and there
mage of the
erature in Fig
d through the
d U∞=400m
ven in Chap
ll-defined si
temperature
wall) with r
) Side wall th Shock condi
030m/s, and in
87
interest in s
y chemical k
distributions
orm regions
reduced th
oundary laye
efore higher
e side wall
gure 5.6. Th
e imaging fi
m/s. These v
pter 2. Prem
de wall ther
e profile acr
respect to d
hermal bounditions are P1=0ncident shock
shock tube p
kinetic expe
s for high p
(for exampl
hereby impr
er thickness
r temperatur
thermal bou
hese images w
eld. Flow co
values were
mixed test ga
rmal bounda
ross the cent
distance from
dary layer PL0.08bar, T1= k attenuation
performance
eriments. Th
precision m
le boundary
roving the
s as nitrogen
res behind
undary layer
were taken a
onditions in
calculated u
as compositio
ary layer is
ter of the te
m the side w
LIF signal and293K, test ga
n = 0.7%/m. C
es. Argon is
hese experim
measurements
layers) in th
chemical ki
n, but with m
the incident
r is shown a
about 200µs
the core flow
using the no
on is 4% to
clearly visib
emperature im
wall is show
d (RIGHT) as: H2, with Conditions
often
ments
s. By
he test
inetic
much
t and
along
s after
w are
ormal
luene
ble in
mage
wn in
88
in the core flow are T2=346K, P2=0.144bar, and U∞=400m/s. The incident shock flow travels in the downward direction.
275
300
325
350
375
Tem
pera
ture
[K
] Measured profile Predicted profile
0 1 2 3-5
0
5
Res
idua
l T [
K]
Distance from side wall [mm]
Figure 5.7: (TOP) Measured and predicted temperature profile 7.5cm away from the end wall in Figure 5.6. The measured profile is an average of a 5 pixel wide row horizontally across the temperature image at its center. A detailed view near the side wall is shown in the inset. (BOTTOM) Residual temperature (between predicted and measured temperatures) profile. The shock and flow conditions are listed under Figure 5.6.
The predicted temperature profile in Figure 5.7 was calculated using the laminar
boundary layer theory. The measured profile is averaged from a 5 pixel wide row across
the temperature image. The residual temperature between the two profiles is also shown.
The experimental results agree well with analytical predictions, with a mean
measurement uncertainty of about 1%. The small residual temperature fluctuation within
the boundary layer may be attributed to the constant thermodynamic property
assumptions in the model. The same calculation was repeated with various values of k,
and the results are shown in Figure 5.8. Predicted temperature profile using k(296K)
agreed well with measurements near the side wall while predicted temperature profile
using k(348K) agreed will with measurements about 1mm away from the side wall.
The wall surface temperature was held constant at 296K in the model due to the
short time scale (about 200µs after shock heating) and the fused silica window thickness.
Beyond the time scale of these experiments, the surface temperature increase slightly (up
0.0 0.4 0.8
300
320
340
Te
mp
era
ture
[K]
Distance from side wall [mm]
89
to 5K). By then however, conditions inside the shock tube would be no longer uniform
and predictable, due to the convolution of shock wave, expansion waves, and other non-
ideal effects inside the shock tube. The thermal boundary layer thicknesses from the
measured and predicted temperature profiles are 1.16mm and 1.21mm, respectively (a
difference of 4.7%).
0.0 0.1 0.2
300
320
340
T
empe
ratu
re [K
]
Distance from side wall [mm]
Measurement Predicted w/ k(320K) Predicted w/ k(296K) Predicted w/ k(348K)
Figure 5.8: Predicted temperature distribution near the end wall from Figure 5.6 calculated using various thermal conductivity, k.
A side wall thermal boundary layer temperature profile at about 30μs behind the
incident shock is plotted in Figure 5.9. Good measurement agreement was found with the
predicted profile except for a thin region about 60μm from the surface.
0 1 2 3250
300
350
400
450
Tem
pera
ture
[K]
Distance from side wall [mm]
Measured profile Predicted profile
Figure 5.9: Measured and predicted temperature profile about 30μs behind the incident shock. Temperature measurement in the side wall thermal boundary
la60HCT
5.3.2
A
temperatu
reflection
P=0.19at
in Chapte
defined E
respect t
predicted
between
about 1%
falls with
Fte
ayer show go0μm from the
H2, with 2% Calculated flowT2=418K.
End wall
A sample P
ure image in
n at the en
tm. These va
er 2. The pre
EWTL is cle
o the distan
d temperatur
the two pro
% (363K and
hin the tempe
igure 5.10: emperature im
od agreemente surface. Shotoluene, Vs=w conditions
l thermal
PLIF image
n Figure 5.1
nd wall. Co
alues were c
emixed test g
early visible
nce from the
re profile is
ofiles is also
d 367K for t
erature meas
(LEFT) Endmage. Shock c
9
t with predictock condition
=910m/s, and are T2=414K
layer
of the EW
0. These im
onditions in
calculated us
gas composi
in Figure 5
e end wall a
shown in F
o shown. Th
the measure
surement un
d wall thermconditions are
90
ted values exns are are P1=
incident shoK, P2=0.05bar,
WTL is sho
mages were ta
the core f
sing the nor
ition is 3% t
.10. Also, a
across the te
Figure 5.11.
he difference
d and predic
certainty giv
mal layer Pe P1=60torr, T
xcept for a th0.09bar, T1= ock attenuati, and U∞=380
own along
aken about 2
flow of reg
rmal shock w
toluene balan
vertical tem
emperature i
The residua
e in the core
cted profile,
ven in [116].
PLIF signal T1= 296K, bat
in region abo293K, test gaion = 0.5%/m0m/s. Measur
with the
2.3ms after
gion 5 are
wave equatio
nced with H
mperature pr
image along
al temperatu
e flow temp
, respectivel
.
and (RIGHth gas: H2, wi
out as: m.
red
converted
the shock
T=368K,
ons given
H2. A well-
rofile with
g with the
ure profile
perature is
ly), which
HT) ith
91
3% toluene, Vs=1010m/s. Image was taken about 2.3ms after shock reflection. Core flow conditions behind reflected shock are T5=368K, P5=0.19bar. The reflected shock travels in an upward direction.
275
300
325
350
375
Tem
pera
ture
[K
]
Measured profile Predicted profile
0.0 0.2 0.4 0.6 0.8 1.0-5
0
5
Res
idua
l T [
K]
Distance from end wall [cm]
Figure 5.11: Measured and predicted temperature profile along the center of temperature image in Figure 5.9. Measured profile is an average of a 5 pixel wide column across the entire height of the image. A detailed view near the end wall is shown in the inset. (BOTTOM) Residual temperature (between predicted and measured temperatures) profile. The shock conditions are listed under Figure 5.9. Core flow conditions behind reflected shock are T5=368K, P5=0.19bar. Measured T5=364K. The discrepancy in core flow temperature measurement is within the measurement uncertainty.
The temperature profile was calculated by solving the heat diffusion equation
with the corresponding boundary conditions given in section 5.1.2 using MATLAB. As a
result of EWTL, the temperature at the window surface can be up to 5K higher than the
room temperature. While most of region 5 is quiescent, the relatively dense and colder
gas near the surface induces a slight displacement velocity towards the end wall.
However, these effects are negligible when calculating the reflected shock strength [117].
Also, due to the lack of large velocities, viscous effects can be neglected thereby
simplifying the boundary layer equations [117].
The thermal layer thicknesses from the measured and predicted temperature
profiles are 2.9mm and 3.01mm, respectively (a difference of 3.8%). The experimental
result agrees well with the predicted value calculated using the heat conduction equation.
0.0 0.2 0.4 0.6 0.8290
300
310
320
330
Tem
per
atur
e [K
]
Distance from end wall [mm]
92
The EWTL thickness is defined as the distance from the end wall at which the
normalized temperature θ (=T-Tw/T∞-Tw) is 99% of the core flow temperature, where Tw
and T∞ represent wall and core flow temperature, respectively.
Weaker signal at higher temperatures affect the EWTL temperature distribution
less than the core flow as shown in Figure 5.12 due to higher PLIF signal level in the
EWTL. This concludes the discussion on temperature profile measurement within the
side and end wall boundary layers. The following section focuses on the SWBL and
EWTL development under various shock strengths and test gases.
0.0 0.1 0.2 0.3 0.4 0.50
200
400
600
800
1000
Tem
pera
ture
[K]
Distance from end wall [cm]
Measured profile Predicted profile
Figure 5.12: Measured and predicted temperature profile close to the end wall at higher temperature. Flow conditions are: T5=934K and P5=0.45bar. Measured T5=910K. The temperature measurement was made about 50μs after shock reflection.
5.4 Boundary layer development
5.4.1 Side wall
Development of the SWBL can be visualized using the PLIF diagnostic
technique. This is done by taking series of images at different times behind the incident
shock with a fixed camera. A sample image constructed from five separate images taken
at 10µs intervals is shown in Figure 5.13. Note that these images were not taken
sequentially in a single experiment. Rather, from five separate images under the same
flow conditions. The core flow temperature and pressure variations are less than 1% and
3%, respectively for all five images.
S
1
sc
d
to
v
at
3
b
an
FigureconstruThe imwith reT1=29P2=0.0
ince the sho
0µs delay in
cheme in F
evelopment
o seamlessly
isible at the
t a rate of a
75K and 0
oundary laye
The si
nd toluene te
To
Fre
Table 5
e 5.13: Continucted from 5
mage color scespect to dist3K, P1=0.02b
04bar.
ock wave sp
n time direct
Figure 5.13
with respect
y stitch the fi
far right end
about 610m/
.15atm, resp
er is seen gr
ide wall ther
est gas is sho
Pressure
Temperatu
oluene mole f
ee stream ve
5.1: List of co
nuous thermadifferent PL
cheme was adtance behind bar, H2, with
peed is relati
tly correspo
is scaled
t to the dista
five separate
d of the imag
/s. The temp
pectively. T
owing imme
rmal bounda
own with co
[atm]
ure [K]
fraction [%]
elocity [m/s]
re flow condi
93
al boundary LIF signal imadjusted to higincident shoc6% toluene.
ively consta
nds to abou
to easily
ance from le
images toge
ge. The shoc
perature and
The incident
ediately behi
ary layer thic
rresponding
Shock
0.09
400
8.5
735
itions behind
layer visualizages taken 10ghlight boundck wave fronCore flow co
ant for each
ut 1cm delay
visualize th
eading edge.
ether. The in
ck heated ga
d pressure be
t shock spe
ind the incid
ckness for va
g theoretical
1 Shock
0.14
580
4.5
608
incident shoc
zation. The i0µs apart in sdary layer dent. Initial cononditions are
of the five
y in distance
he boundar
Figure 5.13
ncident shoc
as is flowing
ehind the in
eed is arou
dent shock.
arious shock
results in Fi
k 2 Shoc
4 0.1
0 55
2.
8 49
cks given in F
image was succession. evelopment ditions are T2=345K,
separate im
e. The false
ry layer an
3 has been tr
ck and region
from left to
ncident shoc
und 850m/s.
k conditions
gure 5.14.
ck 3
16
50
6
92
Figure 5.11.
mages,
color
nd its
reated
n 1 is
right
ck are
The
in N2
94
0.0 0.5 1.0 1.5 2.00.0
0.1
0.2
0.3
0.4
0.5
Shock 1 Shock 2 Shock 3
The
rmal
bou
ndar
y la
yer
thic
knes
s [m
m]
Distance behind incident shock [cm]
Figure 5.14: Side wall thermal boundary layer thickness behind incident shocks with respect to shock strength. Initial pressure was varied from P1=7 to 23torr to produce shocks in T1=293K and N2 bath gas. Solid lines are calculations from boundary layer theory. Flow conditions behind each shock are listed in Table 5.1.
The thermal boundary layers develop proportionally to the square root of distance
behind the incident shock, coinciding with conclusions drawn from the laminar boundary
layer theory. The large error bars are due to the limited spatial resolution of the PLIF
image; in the present experiments, thermal boundary layers only account for about 50
pixels in width (2% of an image) at maximum thickness. The list of core flow conditions
behind incident shocks in Figure 5.14 are listed in Table 5.1. The thermal boundary layer
thickness measurement 1cm behind each incident shocks is listed in Table 5.2 along with
corresponding theoretical results.
Shock 1 Shock 2 Shock 3
Measured [µm] 283 308 325
Calculated [µm] 278 312 320
Error [%] 1.8 1.28 1.56
Table 5.2: Comparison of thermal boundary layer thickness, 1cm behind the incident shock. Flow conditions are listed in Table 5.1
95
Development of the thermal boundary layer in different bath gases (N2, H2, and
Ar) was also studied. Flow conditions behind the incident shocks for the three tested
gases are listed in Table 5.3 and the results are shown in Figure 5.15. Solid lines in Figure
5.15 correspond to theoretical results, calculated using the laminar boundary layer theory.
The thermal boundary layer for all three gases develops proportionally to the square root
of distance behind the incident shock wave.
0.0 0.5 1.0 1.5 2.00
200
400
600
800
1000
Th
erm
al b
ound
ary
laye
r th
ickn
ess
[m
]
Distance behind incident shock [cm]
N2
H2
Ar
Figure 5.15: Side wall thermal boundary layer thickness behind incident shocks in N2, H2, and Ar bath gas. Initial conditions are P1=7torr and T1=293K. Lines are theoretical calculations from boundary layer theory. Toluene mole fraction in all three shocks was about 8.5%. Flow conditions behind each shock are listed in Table 5.3.
N2 H2 Ar
Pressure [atm] 0.09 0.025 0.11
Temperature [K] 400 375 860
Free stream velocity [m/s] 735 440 700
Table 5.3: List of core flow conditions behind the incident shocks given in Figure 5.12.
96
5.4.2 End-wall
Quantifying the EWTL development is important as all optical measurements
used to record species time-history in chemical kinetics research are normally made very
close to the end wall (1-2cm away from the end wall). This is to achieve the closest
agreement to the predicted flow conditions as possible, while staying out of the EWTL.
Identifying the extent of the EWTL is critical for judging the shock tube performance. A
test condition for producing the maximum EWTL thickness was selected and its
thickness was measured at various delay time after shock reflection. A plot of EWTL
thickness with respect to time is shown in Figure 5.16.
An EWTL is considerably thicker than a side wall thermal boundary layer mainly
due to significantly longer test times (by about an order of magnitude). The EWTL
thickness is expected to grow with respect to the square root of time, for times much
greater than ⁄ ≪ 1. Where VR is the reflected shock velocity, and α is the thermal
diffusivity of gas behind a reflected shock, and ⁄ . Pe (Péclet number) is a
dimensionless number that is defined as the ratio of advection to the rate of diffusion of
the test gas.
The solid line in Figure 5.16 represents the predicted thermal layer thickness
using the heat diffusion equation. This particular EWTL continues to grow with respect
to the square root of time until about 12ms after the shock reflection, and levels off until
about 22ms. At that time, the arrival of the expansion or compression wave reflected
from the contact surface disrupts the thermal layer uniformity. A typical EWTL lasts up
to tens of milliseconds.
97
0 2 4 6 8 100.0
0.2
0.4
0.6
0.8
Measured thickness Best theoretical fit
The
rmal
laye
r th
ickn
ess
[cm
]
Time after shock reflection [ms]
Figure 5.16: End wall thermal layer thickness behind a reflected shock. Initial conditions are T1=293K and P1=0.14bar, bath gas: H2, with 1.5% toluene Vs=1100m/s. The solid line is calculated using the heat diffusion equation. Conditions in the core flow behind the incident shock are T5=340K and P5=0.24bar.
5.5 Conclusion
A quantitative study of near-wall thermometry in shock tube flows was performed
based on the PLIF diagnostic technique. High-resolution 2-D images of near-wall shock
tube flow were made possible by experimental facility optimization. The diagnostic was
used to measure temperature distribution in two near-wall flows in a shock tube, namely
the SWBL and EWTL. Temperature profile measurements in the SWBL and EWTL
agreed with theoretical predictions very well. Temperature measurement accuracies in the
SWBL and EWTL are about ±5K. Also, measurements of the SWBL development under
various shock strengths and test gases agreed very well with theoretical predictions. The
side wall thermal boundary layer thickness measurement accuracy is within 5% for all
tested conditions. The findings showed that measurements must be made at least 1cm
away from the end wall to avoid the EWTL. The PLIF diagnostic technique is determined
to be capable of making accurate temperature measurement down to about 60μm from the
shock tube wall. This is roughly a fourfold improvement from previous measurements
found in literature.
98
The near-wall flow fields are of interest because non-ideal effects from these
layers may propagate into the core flow and affect its conditions. A quantitative near-wall
imaging technique was used to characterize these flow fields and provided spatially
resolved temperature measurements that were not available with line-of-sight optical
diagnostic techniques. In the future, this diagnostic technique could be used to identify
pockets of local temperature variation in shock tube experiments with chemical reactions
behind the incident or reflected shock wave. This diagnostic technique also could be
extended to monitor pressure and tracer number density through the use of multiple
excitation wavelengths or detectors.
99
Chapter 6. Conclusion and future work
This chapter provides an overall view of the current toluene-based PLIF
diagnostic technique development and discusses a number of possible future research
directions using the technique. This diagnostic technique was developed to satisfy the
need to verify temperature uniformity in shock tube flows, and also to visualize
temperature distributions across a various types of shock tube flows. PLIF was chosen for
the visualization technique for its instantaneous, species-specific quantitative probing
capability without disturbing the flow. Toluene was chosen as the tracer to be seeded into
the flow to serve as the fluorescence agent in low enough levels to minimize flow
disturbance caused by its introduction. The excitation at 248nm was utilized to take
advantage of high temperature sensitivity and florescence signal level within the
temperature range of interest.
The focus was then shifted to generating quality images that can be used in
quantitative analysis. Test images were taken using a pre-existing shock tube test section
optimized for line-of-sight measurement using small diameter laser beams. The proof of
concept PLIF images of incident and reflected shock waves showed promise and
indicated the need for a PLIF-optimized test section and sub-atmospheric pressure
dependence data of toluene FQY. The necessary photophysical data on pressure
dependence was quantified in a static cell while the new PLIF test section was being
built.
With all the fixes in place, the shock tube core flow temperature distribution and
flow over a wedge were studied to validate the diagnostic technique. Next, the
100
investigation was focused on near-wall regions of shock tube flows, mainly the SWBL
and EWTL. To overcome the challenges associated with near-wall imaging, a number of
modifications to the detection strategy were made. These modifications were preceded by
analyses of various experimental factors that could reduce surface scatter and reflection
such as choice of wall materials, surface finishes, optical components and configuration.
The modification process mostly pertained to the experimental setup, and the image
processing routine remained unchanged. The near-wall temperature distribution was then
measured using the modified diagnostic technique. Refer to the following sections for a
more detailed conclusion of the two studies.
6.1 Summary of results
The objective of this thesis was to perform accurate temperature measurement in
shock tube flows of known pressure distribution. Two studies are discussed. The former
served to validate the PLIF diagnostic technique in the well-defined core flow. The latter
quantified temperature distribution near shock tube walls and expanded the diagnostic
technique applicability.
6.1.1 Study 1: PLIF diagnostic validation using shock waves
Toluene-based PLIF diagnostic technique developed for the purpose of
quantitative temperature measurement in a shock tube was validated. The core flow
region, away from any non-ideal effects, can replicate ideal flow conditions in a carefully
controlled shock tube experiment. Prior to this study, SNR of the experimental facility
was studied by varying the hardware binning level and image resolution.
First, images of the incident and reflected shock waves were taken and checked
for signal uniformity with respect to spatial coordinates. Once signal uniformity was
confirmed, the PLIF diagnostic technique was validated by measuring temperature in the
shock tube core flow where flow conditions are very well defined. Near room-
temperature, mean measurement error is only 0.4%. The error slightly increased to about
101
1.6% and 3.6% behind the incident and reflected shock, respectively. The diagnostic
technique was capable of accurate temperature measurement up to 800K.
Next, the PLIF diagnostic technique was validated by measuring PLIF signal level
in flow over a wedge. Pseudo-steady single Mach reflection was observed as predicted by
theory. Due to the lack of analytical solutions in some regions of the flow, the measured
PLIF image was validated with a synthesized PLIF image. This image was constructed
from the temperature, pressure, and toluene number density results from the CFD
calculations. The PLIF signals from both images agreed to within 4% in all regions of the
flow but one.
In both cases, the normal shock and SMR, the diagnostic technique was found to
have good agreement to theoretical predictions. This study showed that under uniform
conditions, the diagnostic technique is capable of performing accurate temperature field
measurement up to 800K.
6.1.2 Study 2: Near-wall PLIF diagnostic in shock tubes
Engineering challenges associated with near-wall PLIF imaging were
investigated. In particular, efforts to reduce laser sheet scatter and reflection at shock tube
walls were heavily studied. The optimized experimental facility showed dramatic
reduction in laser sheet scatter and reflection. Also, image resolution was substantially
improved (about 15μm/pixel) to resolve the thin near-wall flow features in shock tubes.
Core flow temperature measurement capabilities did not diminish as a result of this effort.
Measurements of SWBL and EWTL temperature profile and thickness were performed to
determine the measurement capabilities of the PLIF diagnostic technique. Temperature
measurement accuracies in the SWBL and EWTL were determined to be about ±5K. The
side wall thermal boundary layer and EWTL thickness measurements uncertainty was
below 5%. It was shown that the PLIF diagnostic technique can accurately measure
temperature down to about 60μm from a surface.
In conclusion, the newly developed toluene-based PLIF diagnostic technique is
well-suited for quantitative temperature measurement in regions of shock tube flows with
102
known pressure and toluene mole fraction regardless of temperature uniformity and
vicinity to walls.
6.2 Suggested future work
With the successful development of toluene-based PLIF diagnostic technique in
shock tube flows of known pressure and uniform tracer number density, a number of
interesting future research opportunities using this technique can be proposed. They are
divided into three main categories: Possible diagnostic system improvements, new flow
field applications, and extension of photophysical database.
The first area of interest is diagnostic system improvements. So far, this
diagnostic technique has been limited to regions of flow field with known pressure and
number density. While these restrictions are fine for simple flows, the same cannot be
said for complex flows such as shock reflection, bifurcation, and flow separation where
regions of the flow field lacks uniform and predictable pressure field. Additional
modifications are required to accurately probe temperature distribution without the
knowledge of the local pressure field. This can be done in two ways. First, using two
pulsed lasers at different excitation wavelength and recording fluorescence signal with a
camera asynchronously. Second, spectrally filtering fluorescence signals from a single
pulsed laser and recording them synchronously with two cameras. These methods could
provide calibration-free PLIF thermometry technique that may be applicable in non-
uniform flow fields. This could be effective in mixing and turbulence applications.
The second area of interest is new flow field applications. The side wall boundary
layer created by the normal incident shock provides an interesting shock wave boundary
layer interaction known as bifurcation. Suppose a boundary layer is assigned an overall
Mach number Mbl, for simplicity. Due to its vicinity to walls and their temperature (T1,
room temperature), Mbl is considered to be a function of M1 (Mach speed prior to the
arrival of incident shocks) and as such, the stagnation pressure of the boundary layer
(Pbl,stag) also becomes a function of M1 and γ. For a given M1 and γ, two phenomena can
take place when boundary layer and reflected shock (P5) interact. First, if P5<Pbl,stag, the
boundary layer is expected to pass continuously under the foot of the shock wave and
103
into region 5. The boundary layer continues to grow in thickness. More interestingly, if
P5>Pbl,stag (for γ = 1.4, 1.33 < M1 < 6.45), the boundary layer flow cannot overcome P5
even at the stagnation pressure and cannot enter region 5. The boundary layer builds up in
a region adjacent to the foot of the shock wave and the buildup grows with time.
The study of reflected shock bifurcation is a natural extension of side wall
boundary layer imaging. Work on the reflected shock bifurcation is currently underway.
Furthermore, this work may be applied to temperature field measurement around flow
separation thereby providing valuable data to improve numerical modeling capabilities.
The third area of interest is extending the photophysical database. Observations
made in this thesis prove the effectiveness of toluene as a tracer species up to 800K, at
which point the lack of measureable fluorescence signal dramatically increases the
temperatures measurement uncertainty. At temperatures above 1200K, toluene starts to
breakdown and can no longer function as a viable tracer species. For quantitative
measurement in combustion events or high temperature reactive flows, a new tracer that
is optimized for high temperature conditions is required. Unfortunately, the three tracers
discussed in Chapter 2 are all inadequate at these conditions. Tracers such as NO would
be a better suited choice due to its chemical stability and easy seeding capability. It would
push the upper temperature limit of the current PLIF diagnostics by a significant margin.
While new tracer requires new excitation strategy, the benefit of discrete spectral
absorption and fluorescence lines of NO can help improve measurement accuracy and
build a robust PLIF thermometry technique for higher temperature conditions.
104
A
ce
in
tr
h
co
ac
U
Appen
Surfac
entered abou
ncident angl
ransmittance
omogeneity,
ommonly us
ccording to N
Figurescatter
Using the not
ndix A.
ce scatter is
ut the sample
le, wavelen
e, reflectanc
, contaminat
sed to descri
Nicodemus
e A.1: Geomer component.
tation given
. BSDsam
a complica
e. The distrib
ngth, and po
ce, absorpta
tion, etc.). B
ibe scattered
[118] is show
etry for defini
in Figure A.
105
DF of mples
ated phenom
bution of lig
ower, as w
ance, surfa
Bidirectional
d light about
wn in Figure
ing BSDF. Su
.1, BSDF is
transm
menon that c
ght within th
well as samp
ace finish,
l scatter dist
t a surface. G
e A.1.
ubscript i and
expressed as
mitting
an fill the e
he hemispher
ple paramet
index of
tribution fun
Geometry fo
d s refer to in
s:
g
entire hemisp
re is a functi
ters (orienta
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nction (BSD
or defining B
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ation,
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DF) is
BSDF
106
Ω⁄ Equation A.1
The distribution is bidirectional in that it depends both on the incident (θi,ϕi) and
scattered (θs,ϕs) directions. Often, the cosine term is dropped from the definition and the
remaining equation is called cosine corrected BSDF. It can be measured using a
gonioreflectometer, or in the case of optical surfaces, be approximated using the
Rayleigh-Rice vector perturbation theory. This technique was first proposed by Rayleigh
in 1895. Rice later showed that it was possible to express the mean square value of the
scattered plane-wave coefficients as a function of the surface power spectral density
(PSD) function. While the theoretical derivation is beyond the scope of this thesis, its
result is shown below:
Ω⁄ ΩP
16, Ω Equation A.2
The left hand side of Equation A.2 is the power scattered in the s direction
through dΩs per unit incident power. Also, it is the product of cosine corrected BSDF and
differential solid angle dΩs, which is added to both side of the equation to facilitate a later
integration. Q is the dimensionless polarization factor that describes the dependence of
scatter from smooth, clean, and reflective surfaces. It can be evaluated exactly in terms of
the complex dielectric constant for four incident and scattered combination – ss, sp, ps,
and pp. Scattering from rough surfaces can be characterized in terms of polarization wave
vectors that are acted upon by sample-dependent matrices. The matrix elements are not
derived from field theory, but are generally found empirically and have no well-defined
relationship to material constants. This is known as the Stokes-Mueller approach for
scatter characterization. S(fx,fy) is the two-sided, two-dimensional surface PSD function in
terms of the sample spatial frequencies fx and fy.
In many case, a more specific BRDF or BTDF is used to describe the surface
scatter about reflected or transmitted specular reflection, respectively. The two
distribution functions are similar and can be used interchangeably for isotropic surfaces.
A
se
gu
se
R
ea
fr
v
w
p
v
Appen
The a
ealed with a
uided into p
eal between
RTV159). Gr
asily penetra
rames are req
Each
ibration iso
windows are
lace with RT
ibrations tha
Figureadjoin
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luminum ba
an o-ring (Pa
place with tw
the base pl
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ate the seam
quired to ho
window fra
lation for th
shown in F
TV adhesive
at may occur
e B.1: Cross-sing windows
. PLI
ase plate con
arker 2-259)
wo positionin
ate is a com
tched into th
ms and provi
ld the three
ame is desig
he window.
igure B.3. T
e, and not wi
r during shoc
section of theand window
107
IF test
nnects to the
). Each win
ng rods and
mbination of
he window f
de air tight
side window
gned so tha
. A close u
The window
ith a mechan
ck tube oper
e window fraframes.
sectio
extension s
ndow frame
attached wi
f o-rings and
frames so th
seals. A tota
ws and a sens
at it provide
up of the si
w float on top
nical fastener
ration.
ame assembly
on desi
section via fo
sits on the b
th three scre
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hat excess R
al of four al
sor array pla
es normal lo
ide window
p of the fram
r, to isolate
y, shown here
ign
our screws a
base plate a
ews. The vac
sive (Mome
RTV adhesiv
luminum win
ate.
oads support
w frame and
me and is he
the window
e with two
and is
and is
cuum
entive
ve can
ndow
t and
d side
eld in
from
T
edge-to-e
interface
brittle an
treated. I
the wind
the fused
end wall
shares th
end wall
Fsi
A
seal betw
affixed to
window
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additiona
The windows
edge visuali
s. Great atte
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In order to av
dow-to-windo
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window is
he similar tra
section.
igure B.2: Cide wall wind
An o-ring en
ween the edg
o the end wa
frames via
n section. Th
al stress to th
s are design
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ention went i
hic failure m
void failure,
ow interface
Teflon to imp
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apezoidal cro
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16 screws.
his is done t
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10
ed in the sh
provide air-
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may occur w
a thin strip
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prove vacuu
igure B.4. T
oss sectional
of the end wmes.
the end wal
de windows
sing RTV ad
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08
hape of isosc
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w design and
when silica-s
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thinner strip
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to the side
wall to the
nd prevent
109
Appendix C. DaVis codes
C.1 Imagecaptureroutine
void ShockGrab () int id; if(GetDialogStatus("ShockGrab")) id = GetDialogId("ShockGrab"); UpdateDialog(id); ShowDialog(id); else DialogShockGrab(); void DialogShockGrab() string month = Time('b'); string day = Time('d'); date = month+day; DialogAttributes = 0; int id = Dialog("ShockGrab3",100,100,200,540,"ShockGrab"); //button //x-origin, y-origin, x-length, y-length AddItem(id, 1, 5, 10, 5,170, 20, "ShockGrab 3.00", "S,12,N,6,-1" ); AddItem(id, 2, 5, 10, 25,170, 20, "with T Correction", "S,12,N,6,-1" ); AddItem(id, 3,16, 10, 47,170, 0, "6,1,0,0", "" ); AddItem(id,11, 5, 10, 55, 50, 20, "Date:", "S,12,N,6,-1" ); AddItem(id,12, 8, 60, 55, 50, 20, "", "date" ); AddItem(id,13, 2,120, 55, 60, 20, "Update", "DateChange(date)" ); AddItem(id,14, 5, 10, 85, 50, 20, "Run:", "S,12,N,6,-1" ); AddItem(id,15, 8, 60, 85, 50, 20, "", "run" ); AddItem(id,16, 2,120, 85, 30, 20, "<", "RunChange(-1)" ); AddItem(id,17, 2,150, 85, 30, 20, ">", "RunChange(1)" ); AddItem(id,41, 5, 10,115, 50, 20, "Delay:", "S,12,N,6,-1" ); AddItem(id,42, 8, 60,115, 50, 20, "", "delay" ); AddItem(id,43, 5,120,115, 30, 20, "us", "S,10,N,6,-1" ); AddItem(id,44, 2,150,115, 30, 20, "Go", "DelayChange(delay)" ); AddItem(id,46,16, 10,140,170, 0, "6,1,0,0", "" ); AddItem(id,21, 2, 10,145,170, 50, "Take Background", "TakeBG()"); //x-origin, y-origin, x-length, y-length AddItem(id,22, 2, 10,200,170, 50, "Take Test Image", "TakeIMG()"); //x-origin, y-origin, x-length, y-length AddItem(id,23, 2, 10,255,170, 50, "Take Ambient", "TakeAMB()"); //x-origin, y-origin, x-length, y-length AddItem(id,24, 2, 10,310,170, 50, "Capture Shock", "TakeShock()"); //x-origin, y-origin, x-length, y-length AddItem(id,25, 2, 10,365,170, 50, "Calculate", "Calculate()"); //x-origin, y-origin, x-length, y-length AddItem(id,26, 2, 10,420,170, 50, "Convert", "master()"); //x-origin, y-origin, x-length, y-length AddItem(id,99, 1, 10,475,170, 50, "Close", "ShockGrabEnd()"); ShowDialog(id); void ShockGrabEnd()
110
int id; id = GetDialogId("ShockGrab"); ApplyDialog(id); void EnergyGrab(int w) int id; if(GetDialogStatus("EnergyGrab")) id = GetDialogId("EnergyGrab"); UpdateDialog(id); ShowDialog(id); else DialogEnergyGrab(w); void DialogEnergyGrab(int w) DialogAttributes = 0; int id = Dialog("EnergyGrab3",300,100,265,60,"EnergyGrab"); //button //x-origin, y-origin, x-length, y-length if(w==2) AddItem(id, 1, 5, 10, 5, 80, 20, "Ambient Image", "S,12,N,6,-1" ); if(w==3) AddItem(id, 1, 5, 10, 5, 80, 20, "Shock Image", "S,12,N,6,-1" ); AddItem(id,11, 5, 10, 25,100, 20, "Enter energy:", "S,12,N,6,-1" ); AddItem(id,12, 8,115, 25, 50, 20, "", "energy" ); AddItem(id,13, 5,170, 25, 20, 20, "mV", "S,12,N,6,-1" ); if(w==2) AddItem(id,21, 1,200, 25, 50, 20, "Save", "ProcessEnergy(2)"); if(w==3) AddItem(id,21, 1,200, 25, 50, 20, "Save", "ProcessEnergy(3)"); ShowDialog(id); void TakeBG() LoadAcqFile("C:\\DaVis62\\ACQ\\yoo062209.acq"); InfoText("Taking Background..."); TakeBackground(); InfoText("Background saved"); void TakeIMG() LoadAcqFile("C:\\DaVis62\\ACQ\\yoo062209.acq"); InfoText("Taking test image"); TakeImage(1); Show(1); void TakeAMB() int i; LoadAcqFile("C:\\DaVis62\\ACQ\\yoo062209.acq"); if(!FileExists(dir+date)) MkDir(dir+date); if(FileExists(dir+date+"\\Ambient"+run+".imx")) if(Message("This file already exists:\nDo you want to overwrite?",-1) == 1) return; else InfoText("Taking image"); TakeImage(2); b[2]=0; for(i=0;i<repeat;i++) TakeImage(1); b2=b2+b1/repeat; StoreBuffer(dir+date+"\\Ambient"+run+".imx",2); EnergyGrab3(2); else InfoText("Taking image"); TakeImage(2); b[2]=0; for(i=0;i<repeat;i++) TakeImage(1); b2=b2+b1/repeat; StoreBuffer(dir+date+"\\Ambient"+run+".imx",2); EnergyGrab3(2); InfoText("Taking image"); Show(2);
111
void TakeShock() int trigger; LoadAcqFile("C:\\DaVis62\\ACQ\\yoo062309.acq"); trigger=SetAcqPar(1,2,1,delay/1000,""); if(~FileExists(dir+date)) MkDir(dir+date); if(FileExists(dir+date+"\\Shock"+run+".IMX")) if(Message("This file already exists:\nDo you want to overwrite?",-1) == 1) return; else InfoText("Waiting for shock..."); TakeImage(3); StoreBuffer(dir+date+"\\Shock"+run+".IMX",3); EnergyGrab(3); else InfoText("Waiting for shock..."); TakeImage(3); StoreBuffer(dir+date+"\\Shock"+run+".IMX",3); EnergyGrab(3); Show(3); InfoText("Shock image saved"); void Calculate() int i,xb,yb,fb; LoadBuffer(dir+date+"\\Ambient"+run+".imx",2); LoadBuffer(dir+date+"\\Shock"+run+".IMX",3); b4=b3/(b2/1000); StoreBuffer(dir+date+"\\Signal"+run+".IMX",4); Show(4); InfoText("Normalized image saved"); void ProcessEnergy(int w) int id; Pix[w,0,0]=energy; if(w==2)StoreBuffer(dir+date+"\\Ambient"+run+".imx",2); if(w==3)StoreBuffer(dir+date+"\\Shock"+run+".IMX",3); id = GetDialogId("EnergyGrab2"); ApplyDialog(id); void RunChange (int delta) int id; if(delta>0) run +=1; else run -=1; if(GetDialogStatus("ShockGrab3")) id = GetDialogId("ShockGrab3"); UpdateDialog(id); ShowDialog(id); void DateChange (string date) int id; id = GetDialogId("ShockGrab3"); ApplyDialog(id); void DelayChange (float delay) int id; id = GetDialogId("ShockGrab3"); ApplyDialog(id);
112
C.2 Imageprocessingroutine
static string dir = "E:\\OfficeBackup\\Jon\\P_AerosolST\\Data\\"; static string date = "Jan22"; static float pres[6] = 0, 0.00921053, 0.119, 0.0158418, 0.3975, 0.676 ; static float temp[6] = 0, 292, 817, 304.507, 1069.5, 1322 ; static float n[6] = 0, 5.41018e+018, 6.98996e+019, 9.30536e+018, 2.33488e+020, 3.97077e+020 ; static float ab[6] = 0, -0.00462224, -0.0597194, -0.00795013, -0.199483, -0.339246 ; static float Pt = 0.000736842; static float kb = 1.38e-023; static float sigma = 3.1e-019; static float leng = 0.002756; static float mf = 0.08; static int region = 13; //1,2,5, 3=caught incident shock, 4=caught reflected shock static int ys = 507; static int ystart = 15; static int yend = 520; static int xstart = 58; static int xend = 150; static float x1 = 140; static float x2 = 145; static int run = 9; static int y[8] = 68, 76, 488, 497, 517, 327, 329, 140 ; static int x[2] = 93, 144 ; static int ba = 6; //power correction static int bb = 7; //pressure correction static int bc = 8; //absorption correction_region1 static int bd = 9; //absorption correction_simple static int be = 10; //temperature field_iterative mode:3 static int bf = 11; static int bg = 12; static int bh = 13; static int bi = 14; ///////////////USER INPUT///////////////// static string date1 = "Jan22"; static int run1 = 9; void master() int fp; string smpl; fp=Open(dir+"shock_data_Jan.txt","r"); ReadLine(fp,smpl); //Discard top row if(date1 =="" && !run1) InfoText("----------------------------------"); InfoText("Processing everything"+"> "+Time('X')); while(date1==""&&!(EndOfFile(fp))) ReadLine(fp,smpl); DoSomething(smpl); if(date1!="" && !run1) InfoText("----------------------------------"); InfoText("Processing "+date1+"> "+Time('X')); while (date1!=GetTokenN(smpl,"\t",1) && !(EndOfFile(fp))) ReadLine(fp,smpl); do DoSomething(smpl); ReadLine(fp,smpl); while (date1==GetTokenN(smpl,"\t",1));
113
if(date1!="" && run1) InfoText("----------------------------------"); InfoText("Processing "+date1+", Run: "+run1+"> "+Time('X')); ReadLine(fp,smpl); while (date1!=GetTokenN(smpl,"\t",1) && !(EndOfFile(fp))) ReadLine(fp,smpl); while (date1==GetTokenN(smpl,"\t",1) && run1!= (int)GetTokenN(smpl,"\t",2)) ReadLine(fp,smpl); DoSomething(smpl); void DoSomething(string smpl) mf =(float)GetTokenN(smpl,"\t",3); pres[1]=(float)GetTokenN(smpl,"\t",4); pres[2]=(float)GetTokenN(smpl,"\t",5); pres[5]=(float)GetTokenN(smpl,"\t",6); temp[1]=(float)GetTokenN(smpl,"\t",7); temp[2]=(float)GetTokenN(smpl,"\t",8); temp[5]=(float)GetTokenN(smpl,"\t",9); region =(float)GetTokenN(smpl,"\t",10); ys =(float)GetTokenN(smpl,"\t",11); yend =(float)GetTokenN(smpl,"\t",12); xstart =(float)GetTokenN(smpl,"\t",13); xend =(float)GetTokenN(smpl,"\t",14); x1 =(float)GetTokenN(smpl,"\t",15); x2 =(float)GetTokenN(smpl,"\t",16); leng =(float)GetTokenN(smpl,"\t",17); date=GetTokenN(smpl,"\t",1); run=(float)GetTokenN(smpl,"\t",2); mf=mf*0.01; if(pres[1]>1)pres[1]=pres[1]/760; InfoText(GetTokenN(smpl,"\t",1)+","+GetTokenN(smpl,"\t",2)+"> P:("+mf+" "+pres[1]+","+pres[2]+","+pres[5]+", T:"+temp[1]+","+temp[2]+","+temp[5]+", region: "+region+", ys: "+ys+", x: "+xstart+","+xend+" leng: "+leng); if(!FileExists(dir+date+"\\Signal"+run+".IMX")) AbortMacro(); else LoadImages(); void AbortMacro() InfoText("Necessary file does not exist"); RotateBuffer(40,41,260,263,0.9) void LoadImages() //variable declaration\\ int i,xb,yb,fb; float m,g,beta; //Load images\\ LoadBuffer(dir+date+"\\Ambient"+run+".imx",2); LoadBuffer(dir+date+"\\Shock"+run+".IMX",3); LoadBuffer(dir+date+"\\Signal"+run+".IMX",4); if(FileExists(dir+date+"\\SigCorr"+run+".IMX")) LoadBuffer(dir+date+"\\SigCorr"+run+".IMX",4); if(FileExists(dir+date+"\\SigCorrEdge"+run+".IMX")) LoadBuffer(dir+date+"\\SigCorrEdge"+run+".IMX",4); GetBufferSize(4,xb,yb,fb); b5=b4; for(i=0;i<xstart;i++) c[5,i]=0; for(i=xend;i<xb;i++) c[5,i]=0; for(i=0;i<ystart;i++) r[5,i]=0; for(i=yend+1;i<yb;i++) r[5,i]=0; //Declare constants\\ Pt = mf*pres[1]; //Calculate absorbance\\ for(i=1;i<sizeof(pres);i++) n[i]=mf*pres[i]*101325/kb/1e6; //n[i]=mf*pres[i]*1e5/kb/temp[i]/1e6; ab[i]=-n[i]*sigma*leng; void main(int check)
114
//variable declaration\\ int i,j,xb,yb,fb,l1,l2,l3,l4; float asc,pv,test,test1,test2,test3,test4,test5,test6,test7,test8, abs_corr,p_corr,e_corr; GetBufferSize(5,xb,yb,fb); SetSpaces(5,check); SetRect(2,x1,y[0],x2,y[1]); //Rectangle @ end window : zone 1 SetRect(3,x1,y[2],x2,y[3]); //Rectangle @ near shock : zone 1 SetRect(4,x1,y[4],x2,y[5]); //Rectangle @ near shock : zone 2 SetRect(5,x1,y[6],x2,y[7]); //Rectangle @ end image : zone 2 SetRect(6,x1,y[5],x2,y[6]); //Rectangle @ end image : zone 2 //power correction b[ba]=(float)b[5]; e_corr = 0.66*1; b[ba]=b[ba]/e_corr; test=AvgRect(ba,6); if(check)InfoText("Energy correction: "+e_corr+" TEST: "+test);Show(ba); //pressure correction b[bb]=b[ba]; if(region<9) switch (region) case 1:p_corr=1; break; case 2:p_corr=pres[1]/pres[2]*TolFit(mf,pres[1])/TolFit(mf,pres[2]); break; case 3:p_corr=1; break; case 4:p_corr=pres[1]/pres[5]*TolFit(mf,pres[1])/TolFit(mf,pres[5]); break; case 5:p_corr=pres[1]/pres[5]*TolFit(mf,pres[1])/TolFit(mf,pres[5]); break; case 9:p_corr=pres[1]/pres[5]*TolFit(mf,pres[1])/TolFit(mf,pres[5]); break; for(j=ys;j<=yend;j++) r[bb,j]=r[bb,j]*p_corr; if(check)InfoText("Pressure correction @ bottom: "+p_corr); switch (region) case 1:p_corr=1; break; case 2:p_corr=pres[1]/pres[2]*TolFit(mf,pres[1])/TolFit(mf,pres[2]); break; case 3:p_corr=pres[1]/pres[2]*TolFit(mf,pres[1])/TolFit(mf,pres[2]); break; case 4:p_corr=pres[1]/pres[2]*TolFit(mf,pres[1])/TolFit(mf,pres[2]); break; case 5:p_corr=pres[1]/pres[5]*TolFit(mf,pres[1])/TolFit(mf,pres[5]); break; case 9:p_corr=pres[1]/pres[2]*TolFit(mf,pres[1])/TolFit(mf,pres[2]); break; for(j=ystart;j<ys;j++)r[bb,j]=r[bb,j]*p_corr; if(check)InfoText("Pressure correction @ top: "+p_corr); //absorption correction b[bc]=b[bb]; if(region<9) for(j=yend;j>=ystart;j--) r[bc,j]=r[bc,j]*exp(ab[1]*(yend-j)/temp[1]); test1=exp(ab[1]*(yend-j)/temp[1]); test=AvgRect(bc,2); if(check)InfoText("ab1: "+ab[1]+" yend: "+yend+" yb: "+yb+" TESTbc: "+test);Show(bc); //Temperature conversion if(!FileExists(dir+date+"\\Temp"+run+".imx")) LoadBuffer(dir+date+"\\Temp"+run+".imx",bf); StoreBuffer(dir+date+"\\Temp_backup"+run+".imx",bf); if(!FileExists(dir+date+"\\TempC"+run+".imx")) LoadBuffer(dir+date+"\\TempC"+run+".imx",bf); DisplayTemp(); return; else b[bf]=b[bc]; b[bh]=b[bc]; b[bi]=b[bc]; if(region<9) for(j=yend;j>ys;j--) for(i=xstart;i<xend;i++) CheckZero(bf,i,j,1); switch (region) case 1:pix[bf,i,j]=TempFit3(i,j,295,300,bf,2); break; case 2:pix[bf,i,j]=TempFit3(i,j,350,450,bf,2); break; case 3:pix[bf,i,j]=TempFit3(i,j,295,300,bf,2); break; case 4:pix[bf,i,j]=TempFit3(i,j,400,600,bf,2); break;
115
case 5:pix[bf,i,j]=TempFit3(i,j,400,600,bf,2); break; BusyProgress((yend-j)*100/(yend-ystart)); for(j=ys;j>=ystart;j--) for(i=xstart;i<xend;i++) CheckZero(bf,i,j,1); switch (region) case 1:pix[bf,i,j]=TempFit3(i,j,295,300,bf,2); break; case 2:pix[bf,i,j]=TempFit3(i,j,350,450,bf,2); break; case 3:pix[bf,i,j]=TempFit3(i,j,350,450,bf,2); break; case 4:pix[bf,i,j]=TempFit3(i,j,350,450,bf,2); break; case 5:pix[bf,i,j]=TempFit3(i,j,400,600,bf,2); break; BusyProgress((yend-j)*100/(yend-ystart)); BusyDone(); b[bi]=b[bf]; test1=AvgRect(bi,2); test2=AvgRect(bi,3); test3=AvgRect(bi,4); test4=AvgRect(bi,5); test5=(AvgRect(bi,3)+AvgRect(bi,2))*2; test6=(AvgRect(bi,5)+AvgRect(bi,4))*2; switch (region) case 1:test8=temp[1];test7=temp[1]; break; case 2:test8=temp[2];test7=temp[2]; break; case 3:test8=temp[1];test7=temp[2]; break; case 4:test8=temp[5];test7=temp[2]; break; case 5:test8=temp[5];test7=temp[5]; break; float minimizer(line theLine) int i; float minLine=10000; for(i=0;i<sizeof(theLine);i++) if(theLine[i]!=0) minLine=fmin(minLine,theLine[i]); else return minLine; float minLocal(line theLine,float tip) int i=0; while((tip!=theLine[i])) i++; return i; float TolFit(float mf, float pres) //Calculates correction for toluene FQY pressure dependence using linear interpolation float Pt,P_conv,corr,hi_y,lo_y,hi_x,lo_x,q,w; int i; Pt=mf*pres*1013.25; P_conv=pres*1013.25; float y[4]; y[0]=1.04172-0.76536*power(0.99717,P_conv); //5mbar y[1]=1.03523-0.64187*power(0.99743,P_conv); //10mbar y[2]=1.00064-0.45983*power(0.99638,P_conv); //20mbar y[3]=1.00314-0.20920*power(0.98949,P_conv); //30mbar if(Pt<5) hi_y=y[1];lo_y=y[0]; hi_x=10;lo_x=5; corr=lo_y+ (Pt-lo_x)/(hi_x-lo_x)*(hi_y-lo_y);
116
if(Pt>=5&&Pt<10) hi_y=y[1];lo_y=y[0]; hi_x=10;lo_x=5; corr=lo_y+ (Pt-lo_x)/(hi_x-lo_x)*(hi_y-lo_y); if(Pt>=10&&Pt<20) hi_y=y[2];lo_y=y[1]; hi_x=20;lo_x=10; corr=lo_y+ (Pt-lo_x)/(hi_x-lo_x)*(hi_y-lo_y); if(Pt>=20&&Pt<30) hi_y=y[3];lo_y=y[2]; hi_x=30;lo_x=20; corr=lo_y+ (Pt-lo_x)/(hi_x-lo_x)*(hi_y-lo_y); if(Pt>30) corr=1; corr=lo_y+ (Pt-lo_x)/(hi_x-lo_x)*(hi_y-lo_y); InfoText(" Pres: "+pres+" Pconv: "+P_conv+" mf: "+mf+" Pt: "+Pt+" y1: "+lo_y+" y2: "+hi_y+" x1: "+lo_x+" x2 "+hi_x+" corr: "+corr); return corr; float TempFit3(int i,int j,int cold, int hot,int buf,int tick) //Secant method float xo,xn,fo,fn,d,asc,abd; int k=0; xo=cold;xn=hot; if(tick==1) asc=GetAsc(i,j,1,buf); if(Pix[bg,i,j]<100) abd=ab[3];xo=450;xn=700; if((Pix[bg,i,j]>100)&&(Pix[bg,i,j]<200)) abd=ab[5];xo=500;xn=900; if((Pix[bg,i,j]>200)&&(Pix[bg,i,j]<220)) abd=ab[2];xo=400;xn=600; if(Pix[bg,i,j]>220) abd=ab[1];xo=290;xn=300; if(tick==2) asc=GetAsc(i,j,2,buf); do fo=(xo/temp[1])*asc/((171*exp(-0.0175*xo)+0.337*exp(-0.0068*xo))); fn=(xn/temp[1])*asc/((171*exp(-0.0175*xn)+0.337*exp(-0.0068*xn))); fo=1-pix[buf,i,j]*leako*fo/1000; fn=1-pix[buf,i,j]*leakn*fn/1000; d=(xn-xo)/(fn-fo)*fn; xo=xn; xn=xn-d; k+=1; while (abs(d)>0.01 && k<30); return(xn); float GetAsc(int i,int j, int setting, int buf) int xb,yb,fb; float asc=1,abd; if(setting==1) if(Pix[bg,i,j]<100) abd=ab[3]; if((Pix[bg,i,j]>100)&&(Pix[bg,i,j]<200)) abd=ab[5]; if((Pix[bg,i,j]>200)&&(Pix[bg,i,j]<220)) abd=ab[2]; if(Pix[bg,i,j]>220) abd=ab[1]; if(setting==2) if(j<ys) if(region==1) abd=ab[1]; if(region==5) abd=ab[5]; if(region==2||region==3||region==4) abd=ab[2]; else if(region==2) abd=ab[2]; if(region==5||region==4) abd=ab[5]; if(region==1||region==3) abd=ab[1]; if(region<9) if(j==yend) asc=1;
117
// asc=1/exp(-nd*sigma*leng/pix[bf,i,j]); pix[bh,i,j]=asc; pix[bi,i,j]=1/asc; else asc=pix[bh,i,j+1]/exp(abd/pix[buf,i,j+1]); pix[bh,i,j]=asc; pix[bi,i,j]=1/asc; return(asc); void SetSpaces(int buf, int check) int xb,yb,fb,yt; GetBufferSize(buf,xb,yb,fb); if(region<9) if((ys-ystart)<0.08*yb) y[0]=ystart+10; y[1]=(ystart+ys)/2-1; y[2]=(ystart+ys)/2+1; y[3]=ys-10; else y[0]=ystart+10; y[1]=ystart+0.035*yb; y[2]=ys-0.035*yb; y[3]=ys-10; if((yend-ys)<0.08*yb) y[4]=ys+10; y[5]=(ys+yend)/2-1; y[6]=(ys+yend)/2+1; y[7]=yend-10; else y[4]=ys+10; y[5]=ys+0.035*yb; y[6]=yend-0.035*yb; y[7]=yend-10;
118
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