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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ix

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

x

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

hat of the lo

nergy gaps

hifts the vib

luorescence.

The st

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ecrease in th

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e 2.3: A simple LIF invol

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teep decreas

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due to small

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eld [56]. One

n-radiative r

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be due to r

17

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gher energiess at low vibra

due to differ

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ns at higher

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e. It was firs

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e theory sugg

rate beyond

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e “third cha

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of the importexcited sing

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rent vibratio

er vibrationa

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hold [67]. Th

gests [68] th

a certain thr

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ay experienc

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easing intern

tant decay proglet state (S0

onversion (ICm crossing (Iies.

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al level spac

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leads to sm

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e threshold v

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65,66]

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imilar

due to

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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

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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

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The result of

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ensity

ty by

ng the

ser is

g near

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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

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105

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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

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IF test

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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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