STRATEGIES FOR PLANAR LASER-INDUCED FLUORESCENCE THERMOMETRY IN SHOCK TUBE FLOWS

Transcription

1 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

2 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. This dissertation is online at: ii

3 I certify that I have read this dissertation and that, in my opinion, it is fully adequate in 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 adequate in 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 adequate in 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 in University Archives. iii

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5 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 v

6 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. vi

7 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. vii

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9 Table of Contents Abstract... v Acknowledgements... vii Table of Contents... ix Chapter 1. Introduction Background and Motivation PLIF diagnostic validation using shock waves Near-wall PLIF diagnostic in shock tubes Thesis Overview... 6 Chapter 2. Spectroscopy Basic LIF theory Quantum energy transfer processes in LIF diagnostics LIF equation PLIF tracer study Tracer selection Toluene absorption Toluene fluorescence quantum yield ix

10 Chapter 3. Experimental setup Facility overview Shock tube PLIF test section Laser system Detection system Data acquisition and processing Image processing and correction Near-wall PLIF imaging facility optimization Wall selection Optical configuration Polarization Optical filter Laser sheet orientation Laser sheet incident angle and collection angle Metal wall diagnostics optimization Conclusion Chapter 4. PLIF diagnostic validation using shock waves Theoretical background Normal shock wave equations Shock reflection (SMR) Experimental setup Core flow thermometry Temperature measurement behind normal shocks Signal-to-noise ratio analysis Validation using analytical results Flow over a wedge PLIF measurement Numerical model Comparison x

11 4.5 Conclusion Chapter 5. Near-wall PLIF diagnostic in shock tubes Theoretical background Side wall boundary layer End-wall thermal layer Experimental setup Boundary layer temperature profile Side wall boundary layer End wall thermal layer Boundary layer development Side wall End-wall Conclusion Chapter 6. Conclusion and future work Summary of results Study 1: PLIF diagnostic validation using shock waves Study 2: Near-wall PLIF diagnostic in shock tubes Suggested future work Appendix A. BSDF of transmitting samples Appendix B. PLIF test section design Appendix C. DaVis codes References xi

12 List of Tables Table 2.1: Comparison of candidate tracer Table 2.2: Absolute FQY variation for three candidate tracers between bar pressure in N 2 bath, 248nm excitation wavelength, and 296K [32] 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 N Table 2.4: Absorption cross-section measurement of candidate tracers at different excitation wavelength in units of cm 2 /molecule at room temperature, 1bar total pressure Table 2.5: Coefficients for low-pressure toluene relative FQY correction Table 3.1: Specifications of the KrF excimer laser used in this study Table 3.2: Specification of the ICCD camera used in this study 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 Table 5.1: List of core flow conditions behind incident shocks given in Figure Table 5.2: Comparison of thermal boundary layer thickness, 1cm behind the incident shock. Flow conditions are listed in Table Table 5.3: List of core flow conditions behind the incident shocks given in Figure xii

13 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 N 2 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 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 crosssection measurements Figure 2.3: A simple photophysical diagram of the important decay processes for toluene LIF involving the ground and excited singlet state (S 0 and S 1, respectively) and the excited triplet state (T 1 ). Internal conversion (IC) becomes important for some states at higher energies. Intersystem crossing (ISC) is the dominant non-collisional process at low vibrational energies Figure 2.4: Toluene relative fluorescence quantum yield at 248nm and 266nm excitation in 1bar total pressure balanced with N 2. Both wavelengths show similar sensitivity to 300K 900K temperature range. The plot is a best fit to data from [54] Figure 2.5: Relative FQY for various partial pressures of toluene in N 2 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 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 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 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 xiii

14 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 Figure 3.5: Various types of excimer laser and their excitation wavelengths Figure 3.6: Potential energy state diagram of an excited dimer. The bound upper state undergoes spontaneous emission to a highly repulsive ground state Figure 3.7: Fluorescence signal with respect to laser fluence. Fluorescence signal begins to saturate at 130mJ/cm 2. 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 Figure 3.8: Cross-section of an ICCD camera optical element 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 Figure 3.10: Experimental setup for testing surface-laser interaction. Various metallic and non-metallic materials and surface finishes are tested 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 nm bandpass filter; Image D: Fused silica (clean surface) using nm bandpass filter 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 Figure 3.13: Horizontal profile along the center of both images in Figure The profiles are averaged across 5 pixels in width 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 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 xiv

15 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 bottomup perpendicular orientation. Image B: Acquired using the parallel orientation. Shock conditions are: T 1 =296K, P 1 =0.075bar, V s =900m/s, and attn=4%/m 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 (θ i =180 ). The laser sheet is in the XZ-plane. The regular experimental setup collects the fluorescence signal at θ r = Figure 3.18: Sample BRDF curve of silicon wafer at θ i =0º and θ i =45º for ϕ=0º. Incident and collection angles are defined using the schematic in Fig In both cases (θ i =0º, 45º), BRDF goes to zero at θ r =-86º and -67º, respectively 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 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 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 Figure 4.2: Regular reflection in pseudo steady flow viewed from an inertial frame fixed in point P 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 Figure 4.4: Mach reflection in pseudo-steady flow viewed from an inertial frame fixed in triple point P 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 = Figure 4.6: Physical representation of Single Mach reflection (SMR) in pseudo-steady flow viewed from an inertial frame fixed in triple point P Figure 4.7: Vortex sheet curling and streamlines near vortex sheet V behind the reflected shock in SMR xv

16 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 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 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 Figure 4.11: Incident shock wave measurement. (LEFT) Corrected PLIF signal and (RIGHT) temperature image. Initial conditions: P 1 =0.067bar, X tol =3.8%, T 1 =296K, V S =546m/s, incident shock attenuation = 1.3%/m. Downwardpointing arrow: direction of incident shock Figure 4.12: Reflected shock wave measurement. (LEFT) Corrected PLIF signal and (RIGHT) temperature image. Initial conditions: P 1 =0.031bar, X tol =4.5%, T 1 =296K, V S = 723m/s, incident shock attenuation = 1.5%/m. Upwardpointing arrow: direction of reflected shock wave 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 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 Figure 4.15: SNR as a function of pixel resolution using hardware binning. Toluene mole fraction, X tol, for both temperatures was fixed at 0.9% Figure 4.16: Predicted versus measured temperature in the core flow. Single-shot images were taken at full resolution without hardware binning Figure 4.17: PLIF image of an incident shock traveling over a wedge. Single Mach reflection is visible 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 xvi

17 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 Figure 4.20: PLIF signal profile along the dotted line in Figure Figure 5.1: Schematic of laminar boundary layer velocity gradient 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 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 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 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 P 1 =0.04bar, T 1 = 293K, test gas: N 2, with 4% toluene, V s =710m/s, and incident shock attenuation = 0.5%/m. Conditions in the core flow are T 2 =498K, P 2 =0.25bar, and T 5 =696K, P 5 =1.05bar. (RIGHT) Schematic of the boundary layer and reflected shock interaction Figure 5.6: (LEFT) Side wall thermal boundary layer PLIF signal and (RIGHT) temperature image. Shock conditions are P 1 =0.08bar, T 1 = 293K, test gas: H 2, with 4% toluene, V s =1030m/s, and incident shock attenuation = 0.7%/m. Conditions in the core flow are T 2 =346K, P 2 =0.144bar, and U =400m/s. The incident shock flow travels in the downward direction 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 Figure 5.8: Predicted temperature distribution near the end wall for various thermal conductivity, k 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 xvii

18 Figure 5.10: (LEFT) End wall thermal layer PLIF signal and (RIGHT) temperature image. Shock conditions are P 1 =60torr, T 1 = 296K, bath gas: H 2, with 3% toluene, V s =1010m/s. Image was taken about 2.3ms after shock reflection. Core flow conditions behind reflected shock are T 5 =368K, P 5 =0.19bar. The reflected shock travels in an upward direction 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 T 5 =368K, P 5 =0.19bar. Measured T 5 =364K. The discrepancy in core flow temperature measurement is within the measurement uncertainty Figure 5.12: Measured and predicted temperature profile close to the end wall at higher temperature. Flow conditions are: T 5 =934K and P 5 =0.45bar. Measured T 5 =910K 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 T 1 =293K, P 1 =0.02bar, H 2, with 6% toluene. Core flow conditions are T 2 =345K, P 2 =0.04bar Figure 5.14: Side wall thermal boundary layer thickness behind incident shocks with respect to shock strength. Initial pressure was varied from P 1 =7 to 23torr to produce shocks in T 1 =293K and N 2 bath gas. Solid lines are calculations from boundary layer theory. Flow conditions behind each shock are listed in Table Figure 5.15: Side wall thermal boundary layer thickness behind incident shocks in N 2, H 2, and Ar bath gas. Initial conditions are P 1 =7torr and T 1 =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 Figure 5.16: End wall thermal layer thickness behind a reflected shock. Initial conditions are T 1 =293K and P 1 =0.14bar, bath gas: H 2, with 1.5% toluene V s =1100m/s. The solid line is calculated using the heat diffusion equation. Conditions in the core flow behind the incident shock are T 5 =340K and P 5 =0.24bar Figure A.1: Geometry for defining BSDF. Subscript i and s refer to incident and scatter component Figure B.1: Cross-section of the window frame assembly, shown here with two adjoining windows and window frames Figure B.2: Cross-section of the end wall window assembly, shown here with side wall windows and frames xviii

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21 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 1

22 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 nonintrusive 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], CO 2 [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. 2

23 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 CO 2, 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-tonoise 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. 3

24 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 nearwall 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 4

25 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. 5

26 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. 6

27 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 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 7

28 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 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. 8

29 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] 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 timeintegrated fluorescence signal S f (in units of photons) collected by the detector can be described using a simple equation called the linear LIF equation. Ω 4 Equation 2.1 where E is the incident laser energy fluence [J/cm 2 ], 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 [cm 2 ], L is the length of the probed volume [cm], n is the tracer number density [cm -3 ], is the absorption cross-section [cm 2 ], 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 9

30 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, CO 2, 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 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: 10

31 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 (CH 3 ) 2 CO (CH 3 CH 2 ) 2 CO C 6 H 5 CH 3 Accessible wavelength [nm] 248, 266, , 266, , 266 Sat. pressure (296K) [mmhg] , (296K) [cm 2 ] 1.6 x x x10-19 FQY, 0.84 x10-3 (308nm, 4-40torr) 0.45 x10-3 (308nm, 1-8torr) (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 11

32 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 N 2 gas to 1bar total pressure. The traces of three candidates are shown in Figure Pentanone Acetone Toluene LIF intensity [a.u.] 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 N 2 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

33 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 N 2 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 bar 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 Pentanone Toluene Table 2.2: Absolute FQY variation for three candidate tracers between bar pressure in N 2 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 13

34 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 nm 266nm 308nm Reference Acetone [32] 3-Pentanone [32] Toluene 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 N 2. 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 [57] 3-Pentanone [32] Toluene N/A [32] Table 2.4: Absorption cross-section measurement of candidate tracers at different excitation wavelength in units of cm 2 /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 14

35 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 and Toluene absorption The S 0 - S 1 (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 1.3x10-18 cm 2 [59]. Absorption features start to disappear with increasing temperature, and by 600K, the entire spectrum becomes broadband (FWHM = 20nm) with a maximum value of 5.6x10-19 cm 2 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 S 0 - S 2 transition (near 200nm) dramatically increases [60] and overlaps with the S 0 - S 1 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 ± 0.2x10-19 cm 2. For temperatures above 1000K, the absorption cross-section increases due to the S 0 - S 2 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 15

36 greater than 600K, absorption cross-section increases due to broadening and red shift of absorption spectra, but at a slower pace. Absorption cross-section [10-19 cm 2 ] nm 248nm Temperature [K] 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 , (T in units of K) Equation 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

37 Figure 2.3: A simple photophysical diagram of the important decay processes for toluene LIF involving the ground and excited singlet state (S 0 and S 1, respectively) and the excited triplet state (T 1 1). Internal conversion (IC) becomes important for some states at higher energies. Intersystem crossing (ISC) is the dominant non-collisional process at low vibrational energies. The red shift is presumably due to different vibrational energy spacing between two electronic states. The upper state has smaller vibrational level spacing compared to that of the lower level due to smaller electronicc bonding energy. This leads to smaller energy gaps or red-shifted transitions at higherr vibrationall levels. Higher temperature shifts the vibrational Boltzmann distribution upwards, leading to increased red-shifted fluorescence. The steep decrease in toluene FQY can also be seen in heavy aromatics [64,65,66] for high vibronic levels in the S 1 state. It was first reported by Parmenterr and Schuyler in benzene, above a certain excitation energy threshold [67]. This is accompanied by similar decrease in the triplet yield [56]. One theory suggests [68] that this phenomenon is due to the rapidly ncreasing non-radiative rate beyond a certain threshold. The threshold varies for different progressions depending on the relevant vibrational mode. At a given vibrational energy, for example, some levels may experience normal fluorescence yield while others are deactivated by the third channel mechanism. The third channel mechanism is thought to be due to rapidly increasing internal conversion rate when the 17

38 vibration mode of toluene exceeds a critical value [69,70] (ν crit 2150cm -1 for toluene). Vibrational levels of toluene in the S 1 and S 0 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 N 2 ). 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 Equation 2.3 Relative FQY (T)/ (296K) E-3 248nm 266nm Temperature [K] Figure 2.4: Toluene relative fluorescence quantum yield at 248nm and 266nm excitation in 1bar total pressure balanced with N 2. 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 18

39 248nm and 266nm excitation wavelengths at 296K and 27mbar of pure toluene are 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 S 0 state, and intermolecular and intramolecular vibrational energy transfer [71,76,77] in the S 1 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 S 1 state. If photons excite benzene molecules into high vibrational energy in the S 1 state at low pressures, benzene FQY thus decreases, owing to slower vibration relaxation to lower vibration levels where nonradiative 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/cm 2 within the static cell to avoid the effects of fluorescence signal saturation. For detailed discussion on fluorescence signal saturation, see section 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

40 Relative FQY [a.u.] Total pressure [mbar] Toluene partial P 5mbar 10mbar 20mbar 30mbar Figure 2.5: Relative FQY for various partial pressures of toluene in N 2 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. (P total in units of mbar) Equation 2.4 Equation 2.5 Toluene partial pressure [mbar] a b c Table 2.5: Coefficients for low-pressure toluene relative FQY correction. 20

41 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 preshock 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 k tot. 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 (k SV ), a ratio of oxygen quenching rate to the total intramolecular deexcitation 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

42 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 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. 22

43 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. 23

44 24

45 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. 25

46 3.1.1 Shock tube A shock tube is a device in which uniform high temperature and pressure conditions can be readily generated for short duration by shock heating. Optical diagnostics can be performed on the heated test gas behind incident and reflected shocks. Further details of the shock tube design can be found in [82,83]. The decision to perform experiments in the AST was based on its physical characteristics, not due to its ability to seed and vaporize aerosol. All the other shock tubes inn the HTGL have a round cross- section for their driven section, whereas the AST has a square cross-sectiosimpler test section design and with rounded corners. The square cross-section is preferred due to overall optical setup. A round cross-section may not be a problem when optical measurements are made using line of sight observation methods. However, the windows need to provide the large optical accesses required for this study, to access the full height of the shock tube, would protrude into the flow and disrupt the shock. The shock tube, shown in Figure 3.1, has a 3m driver section with 15cm internal diameter and a 9.6m driven section with 11cm internal diameter, separated by a polycarbonate diaphragm placed between the driven and driver section. The driven section is followed by a 2m long recovery section, that transitions smoothly from round to square cross-section of 10cmx10cm with rounded corners of R=1.8cm (holding the cross-sectional area fixed). At the end of the recovery section is an 18cm transition to the test section with straight corners. This section gives the shock wave some distance to stabilize after the sudden change in cross-sectional area.. The test section is located at the end of the shock tube. 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

47 The imaging end section is where the shock tube conditions are closest to ideal conditions and is therefore where all optical measurements take place. A detailed discussion of the new imaging end section can bee found in the following section. Incident shock waves are generated byy bursting a polycarbonate diaphragm, which isolates the low-pressure driven sectionn from the high-pressure driver gas. A simple operation schematic is shown in Figure Both the driver and the driven section are typically evacuated using mechanical pumps to an ultimate pressure of about 80mTorr. The incident shock speed and shock attenuation are measured using six fastresponse pressure transducer (PCB model 132A32) evenly spaced along the last 1.5mlong section of the shock tube. The incident shock speed is typicallyy between 600 to 1200m/s, and the attenuation rate is typically between 0 to 5% %/m. The test gas before and after the arrival of the incident shock is denoted as region 1 and 2, respectively. The incident shock reflects at the end wall and travels back up the shock tube toward the driver section. The reflected shock heats the test gas mixture for a second time. The twice-heated region behind the reflected shock iss referred to as region 5. The regions are denoted in Figure 3.2. Figure 3.2: Schematic of operation. (A) The shock tube is filled with driven gas mixture and the driver section is rapidly filledd until the diaphragm bursts. (B) The incident shock then compressess 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

48 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 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 28

49 section length is an orderr of magnitude greater than that of the rounded corner radius, to nullify the disturbance created by the sudden change in geometry in the corners. The test section is designed to hold 10x10x1.25cm 3 windows on three sides and a same size sensor array plate on the one remaining side. A 10x10x2.5cm 3 window forms the end wall. Photos of the optical test section along with the extension section are shown in Appendix B. An exploded view of the test section is also shown. 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. 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 windoww frames are modular. Support rods and base plate are not shown. 29

50 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. 30

51 3.1.3 Laser system Light amplification by stimulated emission of radiation (LASER) sources are a vital part in quantitative optical diagnostics. Coherent photons produced by a laser are highly directional and monochromatic [85] and are used to selectively measure key flow parameters such as temperature, pressure, and species concentration. The probing volume can easily be altered by changing the spatial distribution of the laser beam through various optical components. A pulsed laser, such as the one used in this study, hass a typical pulse width of less than 100ns allowing nearly instantaneous visualization of the flow field with no flow disturbance if the fluorescence lifetime is short (hundredss of nanoseconds). A wide variety of laser sources have become available [86,87], since the invention of the laser half a century ago. The excitation wavelength required for the experiments in this thesis (248nm) is accessible using a KrF excimer laser. Several different excimer laserss and their excitation wavelength are shown in Figure 3.5. Figure 3.5: Various types of excimer laser and their excitation wavelengths. An excimer laser (short for excited dimer laser) typically uses a mixture of inert and halogen gas (krypton and fluorine in the case of the KrF excimer laser). Excimer laser have three notable properties. First, the transition from the excited to the ground state involves different electronic states, and thee resulting laser wavelength is usually in the UV region. Second, the ground state population is effectively zero due to fast 31

52 dissociation, and is modeled as a four-level system. Third, the emission spectrum is featureless and relatively broad (20-100cm -1, compared to 6cm -1 forr a multi-mode pulsed Nd:YAG laser) due to the lack of rovibrational transitions in the unpopulated ground state [88]. A potential energy diagram of an excited dimer is shown in Figure 3.6. The moleculee cannot be stabilized in the repulsive ground state. However, the molecule may be bound in the excited state at its minimum energy level. An electric discharge is used to form these temporary complexes that can only exist in the excited state. The excited dimer undergoes stimulated or spontaneous emission, to a metastablee but highly repulsive ground state, and quickly (on the order of picoseconds) dissociates into two unbound atoms. The stimulated emissionss are amplified in a cavity and a beam of near-uv light is emitted [89]. Figure 3.6: Potential energy state diagram of an excited dimer. The bound upper state undergoes spontaneous emission to a highly repulsive ground state. The average excimer laser efficiency is 2-4%, due to high pumping and quantum efficiencies. Several factors limit excimer laser power output. First, the heat generated from the lasing medium and electric discharge reduces the overall efficiency of the laser. Without adequate cooling the energy depletion of the lasing medium can occur quickly, since an excimer laser can outpu several hundred mj pulse at rates of up to several khz. 32

53 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 Pumping source Repetition rate Laser wavelength Pulse energy Pulse duration Shot-to-shot energy variation M 2 value KrF excited dimer Gas discharge 1 20Hz 248nm 350mJ (5Hz, 30kV) 20ns 2.4% 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 M 2 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 M 2 value of unity. A larger vertical M 2 value indicates that this laser beam is more likely to expand and focus poorly along its vertical axis. 33

54 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 mj/cm 2. 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). Fluorescence signal [a.u.] Linear fit Data Laser fluence [mj/cm 2 ] Figure 3.7: Fluorescence signal with respect to laser fluence. Fluorescence signal begins to saturate at 130mJ/cm 2. 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 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 highreflective 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 34

55 channel plate (MCP) and phosphor. A schematicc of an intensifier cross-section is shown in Figure When fluorescence photons strike the photocathode,, photoelectrons are emitted. Photoelectrons are drawn towards the MCPP by an electric field (6kV) on the phosphorous. The MCP is very thin (typically about 1mm thick) with honeycomb glass channels 10µ µm in size. When the intensifier iss turned on,, a high potential is applied across the MCP accelerating photoelectrons down one of its many channels. When a photoelectron has sufficient energy, a second electron is dislodged from the channel walls. This process is repeated until a cloud of photoelectrons exit the MCP on the other side. The voltage applied across the MCP determines the amount of amplification. Phosphorous (P43, Gd 2 O 2 S:Tb, 1.5ms decay too 10%) attracts the electron cloud and converts them into photons at 545nm (yellow-green). The photons are collected onto the CCD chip and read out using a computer. The intensified camera used in this study is a LaVision Dynamight, and its specifications are listed in Table 3.2. Images are focused on to the camera with a 105mm, f/ /4.5 achromatic UV lens (Nikkor-UV). A filter is placed in front of the lens to suppress Rayleigh scattering. The laser sheet intensity iss monitored using a fast energy monitor (LaVision CIO 16). Figure 3.8: Cross-section of an ICCD cameraa optical element. 35

56 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 Maximum rating Phosphorus Minimum gating Resolution Spectral response Sensitivity Cooling 4kHz P43 5ns 1024pixel x 1024pixel 180nm 800nm 2000 count/photoelectron 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 36

57 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 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 (S 296K ), 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-tonoise ratio (SNR) of the normalized image (S norm ), compared to single-shot images. The second raw PLIF image, the shock image (S T ), is a single-shot image taken where temperatures are unknown (region 2 or 5). Ω 4 Ω 4 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

58 By doing so, normalized PLIF signal becomes a simple function of temperature and pressure. To fully solve for T T, pre-shock temperature and pressure measurements (T 296K and P 296K ) and post-shock pressure prediction (P T ) are substituted into Equation 3.2. Postshock pressure (P T ) 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 (T T ). 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 38

59 width. To correct for this phenomenon, portions of the laser sheet with relatively uniform spatial distribution are allowed to enter the test section. The amount of cutoff is usually dictated by the size of the imaging field and optical components. The intensity distribution of the laser sheet that enters the test section is tested for uniformity by studying the resulting PLIF image under uniform toluene concentration conditions 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 energyy 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 displayedd using the same color scale. The image E color scale is altered to highlight the thermal layer near the end wall. The measured intensity distribution is used to correct raw PLIF images taken during the same day, as spatial variation tends to remain relatively unchanged while the laser is operational. Another spatial correction that mustt be made, especially when imagingg near walls, is collection angle variation. The restricted collection angle near the end wall reduces the amount of LIF signal reaching the CCD. This iss exacerbated by the fact that most of the raw PLIF images for this thesis were taken using the lowest f-number to collect as much LIF signal as possible, and its effect is evident in Figure 3.9 (A through C). However, this phenomenon can be correctedd by scanning the laser sheet across the imaging field and determining the scaling factor at each pixel location. The result of these corrections is shown in Figure 3.9 (D). 39

60 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 I 0 and I are the initial and transmitted laser sheet intensity across distance l, respectively. σ is the toluene absorption cross-section (See section 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 40

61 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 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 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). 41

62 Next, the effects of surface finish on scatter intensity are observed. For metallic surfaces, little to no difference was found amongst the four different surface finishes tested. They all registered high amounts of scatter at the surface. This may be because despite different surface finish types, the surface roughness may be of similar magnitude. Similar results were found amongst the two different fused silica surface finishes, albeit much smaller than metallic samples. Both AR and non-ar coated fused silica sample are fabricated with 20/400 surface roughness specifications. Figure 3.10: Experimental setup for testing surface-laser interaction. Various metallic and non-metallic materials and surface finishes are tested.. Finally, the effects of surface cleanliness on scatter intensity are examined. Repeated exposure to laser sheet and toluene vapor leads to carbon buildup at window surfaces that are difficult to remove and cause excessive surface scatter. A dirty shock tube surface was simulated by exposing samples to toluene vapor, dust, and laser sheet. Examples of surface scatter of dirty and clean fused silica sampless are shown in Figure 3.11 (C and D, respectively). As expected, dirty surfaces show greater scatter intensity, localized to several spots (presumably, where bulk particulates are). Same tests are performed on metallic surfaces as well, and similar results are found. However, the strong baseline of surface scatter makes it hard to pick out thee location of contaminants at the surface. 42

63 Overall, fused silica without an AR coating producedd the least amount of surface scatter, and was thereforee selected as the wall material for near-wall PLIF imaging. Fused silica has additional benefits in that it is stiffer than its metallic counterparts, minimizing plastic deformation thereby preventing the walll from flexing as a result of shock tube operation. Figure 3.11: Laser light scatter comparison for different wall types and surface conditions. The schematic on the left depictss 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 nm bandpass filter; Image D: Fused silica (clean surface) using nm bandpass filter Optical configuration The amount of scattered light observed at a surface is greatly affected by the optical arrangement. Careful consideration and proper selection of optical components and their configuration can significantly reducee or even eliminate surface scatter from reaching the camera. Surface scatter is caused by surface topography, surface contamination, bulk index fluctuation, and bulkk particulates [92]. In this section, laser sheet polarizations, optical filters, laser sheet orientations, incident angles, and collection angles were tested to find the optimal optical configuration for the purpose of near-wall PLIF imaging. 43

64 Polarization When light is scattered at a surface, its polarization is changed depending on the sample shape, material, and incident beam polarization. In the transverse electromagnetic wave description, the electric component is responsible for most observed electromagnetic wave and material interaction. Therefore the direction of this electric component vector (E-vector) is used to define the direction of polarization. The direction of the E-vector for s-polarized laser sheets is normal to illumination sheet. For p- polarized laser sheet, the E-vector direction is in plane off the illumination sheet. An experimental setup similar to Figure 3.10 was used to test the effects of laser sheet polarization on scatter intensity at the surface. A Rochon prism polarizerr made of magnesium fluoride is placed between the fused silica sample and beam shaping optics. The polarizer separates the extraordinary ray from the undeviated ordinary ray. The ordinary beam deviation is less than 6 arc minute and the extraordinary beam separation angle for 248nm is about 1.05º. The clear aperture of thee polarizer iss 14.5mm in diameter and transmits about 80% of the incident beam. The laserr fluence is adjusted to 20mJ/cm 2 to comply with the polarizer damage threshold. No optical filter was used for this experiment. Scatter intensities at the surface as a result of s-polarized and p-polarized are shown in Figure 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

65 Both images are normalized for laser energy variations. Horizontal profiles along the center of the two images are plotted in Figuree Significant reduction in surface scatter was observed for s-polarized laser sheet, because photons are less likely to scatter in the direction of its E-vector. However, the reduction wasn t enough to forgo the use of optical filters. Figure 3.13: Horizontal profile along the center of both The profiles are averaged across 5 pixels in width. images in Figure Optical filter Optical filters can selectively reject surface scattered light. This is possible when excitation laser wavelength and subsequent toluene emission spectra are spectrally separated, as shown in Figure Also shown are transmission curves for the two optical filters tested for this experiment: A notchh filter (centered at 248nm) and a band- of pass filter (250nm - 400nm). Reductions of scatter intensity at the surface as a result using these filters are shown in Figure 3.11 (image A and D). Small amounts of surface scatter are still visible through the notch filter. This is because the notch filter bandwidth (~ ~0.7nm) is smaller than the linewidth of the KrF excimerr laser (~1nm). On the other hand, the band-pass filter does away with surface scatter allowing more accurate quantitative analysis closer to the surface. 45

66 Normalized Fluorescence [a.u.] Transmission [%] KrF Excimer laser Toluene fluorescence Notch filter Band-pass filter Wavelength [nm] 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. Laser sheet orientation 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 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 46

67 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 and compared side-by-side in Figure 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 walll 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. Figure 3.16: Laser sheet orientation direction comparison. Images of the side wall thermal boundary layer behind incidentt shock waves, immediately next to the side wall 7cm away from the end wall are measured using the perpendicular and parallel orientation. Image A: Acquiredd using the bottom-up perpendicular orientation. Image B: Acquired using the parallel orientation. Shock conditions are: T1=296K, 1 P 1 =0.075bar, V s =900m/s, and attn=4%/m. 47

68 The image taken with parallel illumination (B) is slightly noisier due to reduced laser sheet incident flux. Both images are taken using the band-pass filter. Of the two perpendicular configurations, the bottom-up the former delivers more laser sheet incident flux in orientation outperforms the top-down orientation in two key areas. First, the imaging field simply due to the fact thatt the imaging field is attached to the incident wall of interest. Second, the bottom-up orientation eliminates specular reflection at the surface since the laser is traveling from a material with higher optical density (fused silica) to that of lower optical density (test gas). The opposite is true for the top-down direction wherein the incident wall reflects the specularr reflection back into the imaging field. Specular reflections from a fused silica (n ~ 1.5) sample are about 4%, which can be significant enough to affect the temperature measurement uncertainty, especially at higher temperatures. Laser sheet incident angle and collection angle The final step in near-wall imaging facility optimization wass focused on reducing the amount surface scatter by adjusting the laser sheet incident angle and the camera collection angle. A schematic describing the collection angle with respect to the normal laser sheet incidencee is shown in Figure Surfacee scatter images taken at normal incident angle and various collection angle are also shown. 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 (θ i =180 ). 48

69 The laser sheet is in the XZ-plane. The regular experimental setup collects the fluorescence signal at θ r =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 θ r =90º, while the incident laser sheet was tilted in grazing angles (<±5 ) about the normal incident angle (θ i =180º). Incident (θ i ) and collection (θ r ) angles are defined in Figure 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 (θ i =0º) as shown in Figure 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 Critical values for θ i =0º and 45º are θ r,crit =-86º and -67º, respectively i =0 i = BRDF [sr -1 ] Scatter angle [degree] Figure 3.18: Sample BRDF curve of silicon wafer at θ i =0º and θ i =45º for ϕ=0º. Incident and collection angles are defined using the schematic in Fig In both cases (θ i =0º, 45º), BRDF goes to zero at θ r =-86º and -67º, respectively. 49

70 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 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. BRDF [sr -1 ] Measured surface scatter Predicted BRDF scatter [degree] Normalized scatter intensity [a.u.] 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

71 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 felttip 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 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. 51

72 Surface scatter [a.u.] W/O surface treatment With surface treatment Horizontal spatial coordinate [cm] 0.2 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 intensityy may be attributed to bulk particulates. 3.4 Conclusi on This chapter introduced the experimental facilities used throughout this thesis as well as the image correction and processing procedures. DaVis codes mentioned in this chapter are available in Appendix C. Thesee facilities are then optimized for near-wall PLIF imaging. Several factors are tested to find the best combinationn of wall material and optical configuration n. It is shown that the least amount of surface scattered light is achieved by normal laser sheet incidence through a fused silica wall and having the camera collect the resulting fluorescence perpendicula ar to the incident laser sheet. A similar approach may be used for metallic surfaces withh the addition of black felt-tip pen surface treatment. 52

73 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. 53

74 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 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 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 Equation 4.1 Equation 4.2 Equation

75 For simplification purposes, the system is assumed to be adiabatic and at steady- is state. Also, assume uniform flow conditions in region 1 and 2. The reference frame fixed on the shock wave. Viscous effects and heat transfer phenomena are small and can be neglected for a Newtonian fluid. Under these assumptions, Equation 4.1 through Equation 4.3 can be integrated to Equation 4.44 through Equation 4.6, using notations given in Figure 4.1: 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. Equation 4.4 Equation 4.5 Equation 4.6 For further analysis, assume ideal gas behaviorr with constant specific heat at constant pressure (c p ). Rankine-Hugoniot and Prandtl relations are shown in Equation 4.7 and Equation 4.8 respectively, Equation

76 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: Equation 4.9 where. Apply Equation 4.9 to the Rankine-Hugoniot relation to express the pressure ratio as: Equation 4.10 Ultimately, the temperature ratio can be derived from the ideal gas law 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. 56

77 4.1.2 Shock reflection Consider a shock wave interacting with a wedge in a pseudo-steady inviscid flow as shown in Figure 4.2. The normal incident shock wave (I) is traveling from left to right and the reflected shock wave (R) is generated ass a result of the interaction. q 1 is the flow velocity in region 1 in the initial shock wave reference frame. Figure 4.2: Regular reflection frame fixed in point P. in pseudo steady flow viewed from an inertial When the angle between the incident shock and the wedge, α, is small, the incident shock wave deflects the flow by an angle of θ 2. The positive deflection of the flow must be reverted back to zero for the steady assumption to hold [95]. A reflected shock wave is formed so that θ 3 = 0, and the flow behind the reflected wave becomes parallel with the wedge. This phenomenon n is called regular reflection. The regular reflection can also be plotted as shock polar in the (θ,p)-space as shown in Figure 4.3, where θ is the flow deflection angle and p is the pressure ratio. Shock polar is the locus of all possible states after an oblique shock. From Figure 4.3, region 2 is located on the incident shock locus I, below M 2 = 1 point. 57

78 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. A second locus, the reflected shock, is plotted for M = M 2 from (θ 2, p 2 ) to return the flow deflection back to θ = 0. Point P moves up the wedge at a constant rate of q 1 and thereforee distance d increases linearly with time. As α is increases it reaches a threshold α = α d (M1,γ), 1 after which, the locus of the reflected shock cannot intersect with θ = 0. Deflection is still positive (θ > 0), indicating that the flow is still directed towards the surface. A buffer zone is required to transition from θ > 0 to θ = 0. A physical representation of such flow is shown in Figure 4.4. Figure 4.4: Mach reflection in pseudo-steady flow viewed from an inertial frame fixed in triple point P. 58

79 A third shock S, lifts the triple point P away from the surface and a vortex sheet V is formed to separate the gases goingg through S,, and throughh I and R. This phenomenon is known as Mach reflection and can be expressedd as Figure 4.5 in (θ,p)-space. 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 neededd to bring the flow back to θ = 0. Pressure and streamline deflection are continuouss across V. However other physical properties such as density, velocity, andd entropy are not. If conditions within the vortex sheet are assumed uniform, V is straight in the reference frame of point P forming an angle θ 3 with the triple point trajectory. Velocity differences across V in region 3 and 4 (q 3 q 4 ) leads to several different shock reflection phenomena depending on the value of (q 3 - q 4 ). It also dictates whether flow in regionn 3 move away from or into the wedge. When q 3 is greater than q 4, and (q 3 - q 4 ) iss smaller than the local speed of sound in region 3, Single Mach reflection (SMR) is observed. This is the only type of Mach reflection observed during this study and is the simplest form of Mach reflection. A schematic of SMR is shown in Figure 4.6. The reflected shock is straight until point D because region 3 is supersonic with respect to thee triple pointt but is subsonic with respect to point B [96]. Another interesting phenomenon n is the curling of the vortex sheet V. In the case of SMR, flow is deflected near point B. The locall pressure continues to build until B becomes a stagnation point, at which timee the flow is directed out in all directions, 59

80 even into the vortex sheet. This causes the vortex sheett to deflect inwards, allowing the streamline to meet the surface at right angles due to the absence of vorticity [ 97,98]. A schematic of the vortex sheet curling and nearby streamlines are shown in Figure 4.7. Figure 4.6: Physical representation of Single Mach reflection (SMR) in pseudo- steady flow viewed from an inertial frame fixed in triple point P. No straightforward theory yet existss for solvingg flow conditions in SMR, and a numerical model is required to solve it. For this study, the computational fluid dynamics (CFD) software package Fluent 6.0 is used to model the SMR observed in the experiments. Figure 4.7: Vortex sheet curling and streamlines near vortex sheet V behind the reflected shock in SMR. 60

81 4.2 Experimental setup The experimental setup of the PLIF diagnostic for this study is shown in Figure 4.8. For more detailed description of individual equipment, please refer to Chapter 3. The beam from the KrF excimer laser was loosely focused into a 5cm wide and 0.75cm thick laser sheet using sheet-forming optics. Edges of the laser sheet were truncated using an iris just before entering the test section. This was done to remove regions of lower intensity at either edges of the laser sheet. The actual width of the laser sheet in the test section was roughly 3cm. The laser sheet was configured to enter the test section through the center of the end wall window to avoid any possible non-ideal effects. The ICCD camera was set to collect the fluorescence signal through the top window, perpendicular to the laser sheet path. The imaging region, shown in Figure 4..8, was about 3cm wide and 6cm tall, separated from the end wall by 3cm to avoid thee non-uniform thermal layer. The camera resolution was about 0.06mm/pixel. 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

82 Single-shot images of incident and reflected shocks were taken under various shock conditions by varying the diaphragm thickness and initial pressure (P 1 ). Temperature in regions 2 and 5 were sampled by averaging per-pixel temperature values from a small area (5pixels by 5 pixels) about 0.5mm behind the incident and reflected shock waves, respectively. Sampled temperature range iss 296K 800K. Initially, the laser sheet was configured to illuminate the test section through a side window. However, it was quickly discovered thatt a faint streak of weaker signal appeared adjacent to the normal shock waves at grazing angles. Further investigation showed that the angles coincidedd with the laser sheet propagation direction with respect to the shock wave front as shown in Figure 4.9. This phenomenon is due to a diffraction effect that occurs when a collimated beam of light strikes the shock at grazing angle up to ±10 depending on shock strength [99]. This streak can appear in front of or behind a shock wave and disappears when the laser sheet is aligned perfectly parallell with the normal shock front. Figure 4.9: Diffraction due to grazing angle of laserr 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 sheett (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. While careful alignment is always an option, thee laser sheett was instead rerouted through the end wall to circumvent the issue altogether. This was because despite best efforts, maintaining alignment with pinpoint accuracy was extremely challenging. The 62

83 rerouted laser sheet was less sensitive to minutee fluctuationss in its propagating direction while simultaneously removing the diffraction effect. This helps to reduce temperature measurement uncertainty near shock waves. However when an obstacle is placed in the test section prohibiting illumination through the end wall, side wall illumination is inevitable. An aluminumm wedge used to generate SMR is such an example. The locationn of the wedge within the test section is shown in Figure The laser sheet is illuminated in a top-down orientation. The test section was rotated a quarter turn so that the sensor array plate was on the side. This allows the camera to see all three sides of the wedge. The wedge is securely attached to the sensor array plate using two columns (2.5cm in height). The columns are wedge shaped to improve flow through the underside off the wedge. The wedgee is 5cm in width and 7.5cm in length with an angle of 30 degrees. The leg of the wedge is about 1cm away from the end wall. The hypotenuse is coated with a thin layer of black felt tip pen to minimize surface scatter. Figure 4.10: Top view of the test section. Thee test section was rotated 90 so that sensor array plate that the wedge is attachedd to is on the side. This allows the cameraa to see all three sides of the wedge through the top window. 63

84 4.3 Core flow thermometry Temperature measurement behind normal shocks An example of the single-shot, full-frame PLIF signal and the corresponding temperature distribution of an incident and a reflected shock is shown in Figure 4.11 and Figure Figure 4.11: Incident shock wave measurement. (LEFT) Corrected PLIF signal and (RIGHT) temperature image. Initial conditions: P 1 =0.067bar, X tol =3.8% %, T 1 =296K, V S =546m/s, incident shock attenuation = 1.3%/m. Downward-pointing arrow: direction of incident shock. Note thatt the two cases presented in Figure 4.11 and Figure 4.12 are not from the same shock experiment. Horizontal and vertical temperature and residuall temperature profiles of Figure 4.11 and Figure 4.12 are shown in Figure 4.13 and Figure 4.14, respectively. Vertical profiles are constructed by averaging temperature values across 5 center-most columns of the temperature image. Horizontal profiles are produced by averaging temperature values across 5 rows approximately 0.5mmm behind either an incident or a reflected shock. 64

85 Figure 4.12: Reflected shock wave measurement. (LEFT)) Corrected PLIF signal and (RIGHT) temperature image. Initial conditions: P1=0.031bar, X tol =4.5%, T 1 =296K, V S = 723m/s, incident shock attenuation = 1.5%/m. Upward-pointing arrow: direction of reflected shock wave. Temp [K] Measured profile Predicted profile Residual T [K] Temp [K] Residual T [K] Distance from end wall [cm] mm 1cm Distance from the Distance center of f shock from tube the center [cm] Distance of the from shock the center tube of [cm] shock tube [cm] Temp [K] Residual T [K] Figure 4.13: Temperature and residual temperature (between measured and predicted) profiles in the core flow acrosss the incident shock. Upper plots: vertical profile along the central column of pixels (averaged across 5 pixels width) ); Lower plots: horizontal profile alongg the row of pixels 0.5mmm and 1cm behind incident shocks; a flat temperature distribution across the laser sheet is evident. 65

86 Temp [K] Residual T [K] Temp [K] Residual T [K] Temp [K] Residual T [K] Distance from the Distance center of shock from tube the center [cm] Distance of the from shock the center tube of [cm] shock tube [cm] 0 Measured profile Predicted profile Distance from end wall [cm] 0.5mm 1cm 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 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 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- 66

87 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 At 620K, SNR increased from 16 to 51 with increasing binning level from 1 1 to Conversely, image resolution drops from 60µm/pixel (no hardware binning) to about 1mm/pixel (maximum binning: 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. Signal-to-Noise ratio x1 2x2 Hardware binning [pixels] 4x4 8x8 620K (Region 5) 440K (Region 2) 16x Pixel resolution [ m/superpixel] Figure 4.15: SNR as a function of pixel resolution using hardware binning. Toluene mole fraction, X tol, for both temperatures was fixed at 0.9% 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

88 Measured temperature [K] Incident shock Region 1 Region 2 Reflected shock Region 2 Region Predicted temperature [K] 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 68

89 calculation and the LIF equation. This is because in certain parts of the flow, a straightforward analytical solution of the pressure distribution does not exist. Without the knowledge of the pressure field, the PLIF diagnostic technique is unable to accurately convert PLIF signal levell to temperature PLIF measurement An incident shock traveling over a wedge was imaged using the PLIF diagnostic technique, and shown in Figure Characteristic features of SMR, such as the Mach stem, the vortex sheet and the straight and curved reflected shock, were clearly distinguishable and match those shown in Figure 4.6. Thiss image was taken using the experimental facilities and optical configurationss optimized for near-metal-wall imaging, detailed in section 3.3. Figure 4.17: PLIF image of an incident shock traveling over a wedge. Single Mach reflection is visible Numerical model While the pressure fields in the region immediately after the incident shock are predictable using simple theory, the same cannott be said forr regions behind the reflected shock and the vortex sheet. Therefore, a numerical solver (FLUENT 6.0) is employed to 69

90 calculate the pressure, temperature, and toluene speciess density distribution of SMR. A coupled density solver was used to solve the continuity equation in control volume form. The ratio of specific heats for toluene and nitrogen are expressed as third-order polynomials, and viscosity was treated via the Menter Shear Stress Transport (SST) model [100]. 3rd order AUSM (Advection Upstream Splitting Method) flux splitting was used for discretization [101], and an explicit solver was used. The calculated temperature field of SMR over a wedge is shown in Figure Thee incident shock is traveling from left to right, and all the SMR features are clearly visible. Regionss behind the reflected shock and vortex sheet show inhomogene eous temperature distribution. In regions of known pressure (far away from the wedge), converted temperature measurements are in close agreement with those of Figure 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 Comparison A synthesized PLIF image can be constructed from the numerically calculated temperature, pressure, and toluene density distribution. The aforementioned flow parameters are factored into the LIF equation pixel-by-pixel and the results are shown in Figure (LEFT). An experimental PLIF image with matching initial conditions is also shown (RIGHT). Both images are displayed in the same false color scale for a direct 70

91 comparison. PLIF signal values from both images at various regions of the flow are listed in Table 4.1. PLIF signal profile along the dotted line in Figure 4.19 is shown in Figure Distance along the dotted line is measured starting from the right hand side. 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 Fluorescence signal [a.u.] Measured Simulated Distance along thee line [cm] 0 Figure 4.20: PLIF signal profile along the dotted line in Figure PLIF signal from both images agree well (within 4% %) in all regions of the flow except within the vortex sheet. Generally, a 5% discrepancy in the PLIF signal at these pressure and temperature conditions corresponds to only 0.5% variation in temperature. 71

92 Regions Measured PLIF signal level Synthesized PLIF signal level Difference [%] Bow shock at leading edge Behind reflected shock Behind incident shock Within vortex sheet 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. 72

93 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 73

94 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 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 74

95 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 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 (Re crit ). 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 75

96 of the turbulent boundary layer theory can be found in [20]. Consider a cross-section of a laminar boundary layer shown in Figure 5.1. A 2-D steady incompressiblee laminar boundary layer can be solved using the Blasius solutionn which is derived from the 2-D incompressible Navier-Stokes equations (Equation 5.1 through Equation 5.4). 0 Equation Equation Equation Equation 5.4 where u and v are the velocity components in the x and y direction of Figure 5.1, respectively, ρ is the density, c p is the heat capacity, k is the thermal conductivity, T is the temperature, and µ is the viscosity. Buoyancyy forces are neglected for simplicity. Figure 5.1: Schematic of laminar boundary layer velocity gradient. 76

97 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 Ψ 0 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: 77

98 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 Equation 5.14 where. Likewise, the momentum equation (Equation 5.9) and the boundary condition (Equation 5.10) can be simplified as follows: Equation ; 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 c p, k, and μ. This is a good first order approximation for the range of temperature 78

99 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

100 where T w and 0 are the temperature and the adiabatic temperature at the wall, respectively. θ 2 (0) can be approximated as Pr 1/2 for Pr<50 [114]. θ 1 is the solution without viscous dissipation, and θ 2 is the solution due to viscous dissipation: Equation Equation 5.23 The combined system of equations can only be solved numerically unless Pr = 1 [115] 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 Equation 5.24 where T g is the gas temperature, k g is the thermal conductivity, ρ is the density, c p is the heat capacity of the gas. This partial derivative equation can be solved numerically with variable thermal properties (α, ν, and c p ) of the gas. α is the thermal diffusivity and defined as. Thermal properties in the end wall window are assumed to be 80

101 constant since the temperature within the end wall will vary slightly (on the orderr of a few degrees). The initial and boundary conditionss are:, 0 0 Equation 5.255, Equation , Equation 5.27 where T 5 is the test gas temperature behind the reflected shock, T w is the temperature of the end wall surface, T is the room temperature, k w is the thermal conductivity of the end wall at room temperature, and L is the thickness of the end wall. 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. 5.2 Experimental setup The experimental setup of the PLIF diagnostic for this study is shown in Figure 5.3 (for more detailed descriptions of each individual facility, please seee Chapter 3) ). The laser beam was loosely focused and shaped intoo a laser sheet with the same dimension used in the previous study, as to maintain the fluorescence signal linearity. Test images of 81

102 the side wall boundary layer showed that the thickest SWBL was only 5 pixels wide using the camera setup used in the previous study. This was inadequate for resolving temperature distribution within the boundary layer. As a result, the ICCD camera and the collection lens weree reconfigured to boost spatial resolution, ultimately reducing the imaging area down to about 1cm by 1cm. This amounted to a 4-fold increase in spatial resolution (15µm/pixel). The laser sheet edges were truncated before entering the test section to cutoff regions of lower intensity. Given that the imaging field is 1.5cm in width, only the portion of the laser sheet with the most uniform intensity was used. The actual width of the laser sheet in the test section was roughly 2cm. Figure 5.3: Schematic of the shock tube and laser setup. Mirrorr 2 deflects the laser sheet to enter the test section through its sidee or end walll window. It is removed when imaging through end wall window. SWBL were imaged right up against one of thee shock tube side walls, roughly 7cm away from the end wall as shown in Figure 5.3. Boundary layer images were taken between the arrival of the incident shock wave and the return off the reflected shock. EWTL are imaged right up against the shock tube endd wall at itss center, as shown in Figure Thermal layer images were taken between the shock reflection and the arrival of the expansion or compression wave reflected from the contact surface. However, for weaker shocks, uniform conditions behind reflected shocks begin to deteriorate before the arrival of the expansion or compression wave reflectedd from the contact surface due to 82

103 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 83

104 shows that reliable PLIF signal interpretationn can be made up to a distance of 4 pixels (or about 60μm) away from a wall. Scatter level [a.u.] Distance from side wall [pixel] 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 dashedd line indicated on the image. 5.3 Boundary layer temperat ture profile Side walll boundary layer When a diaphragm burst, a normal incident shock wave heats and induces motion towards the end walll in the gas behind it. As a result, gases in very close proximity to the four side walls develop momentum and thermal boundary layers in the fast moving free stream. The leading edge of the boundary layer is attached to the incident shock wave and grows in thickness as a function of time or distance. The thickness of the thermal boundary layer is defined as the distance from the side wall at which the normalized 84

105 temperature θ (= T-Tw / T -Tw ) is 99% of the core flow temperature, where T w 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 δ T 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 N 2 (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 Re crit = The characteristics length used to calculated the Reynolds number is the x-wise distance behind the leading edge. For conditions presented in this study, Re max ( ) is below the critical value of Re crit = 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, N 2, H 2, and Ar are chosen as driven gases, while N 2 is chosen as the driver gas. 85

106 Nitrogen (N 2 ) was chosen for its slower incident shock speed ( m/s), and thereforee longer test time (up to 400µs after the incident shock passes the imaging frame). Also, nitrogen bifurcates well with the reflected shock,, clearly signaling the end of the SWBL test time as shown in Figure 5.5. In addition, nitrogen has relatively low heat capacity (c p ) and therefore is capable of reaching temperatures up to 500K and 800K behind the incident and reflected shock waves, respectively. As a tradeoff, relatively low viscosity of nitrogen leads to thinner SWBL. 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 P 1 =0.04bar, T 1 = 293K, test gas: N 2, with 4% toluene, V s =710m/s, and incident shock attenuation = 0.5%/m. Conditions in the core flow are T 2 =498K, P 2 =0.25bar, and T 5 =696K, P 5 =1.05bar. (RIGHT) Schematic of the boundary layer and reflected shock interaction. Hydrogen (H 2 ) produces the thickest thermal boundary layer among the three tested driver gas. This is because kinematic viscosity of hydrogen is an order of magnitude higher than that of nitrogen or argon despite having the fastest ( m/s) shock wave speed. However, hydrogen has very high c p and relatively low incident shock wave Mach number which leads to smaller increases in temperature and pressure behind the incident shock wave. Temperatures behind the incident and reflected shock waves studied only reach up to 350K and 450K, respectively. 86

107 Argon was chosen due to the interest in shock tube performances. Argon is often used as a buffer gas in high purity chemical kinetic experiments. These experiments require very uniform temperature distributions s for high precision measurements. By understanding the extent of non-uniform regions (for example boundary layers) in the test gas, facility-relatemeasurement ts. Argon has similar boundary layer thicknesss as nitrogen, but with much errors can be reduced thereby improving the chemical kinetic higher shock wave speed and therefore higherr temperatures behind the incident and reflected shock waves. A sample PLIF image of the side wall thermal boundary layer is shown along with the converted temperature in Figure 5.6. These images were taken about 200µs after the incident shock passed through the imaging field. Flow conditions in the core flow are T=346K, P=0.15atm, and U =400m/s. These values were calculated using the normal shock wave equations given in Chapter 2. Premixed test gas composition is 4% toluene balanced with H 2. A well-defined side wall thermal boundary layer is clearly visible in Figure 5.6. A horizontal temperaturee profile across the center of the temperature image (7.5cm away from end wall) with respect to distance from the side wall is shown in Figure 5.7. Figure 5.6: (LEFT) Side wall thermal boundary layer PLIF signal and (RIGHT) temperature image. Shock conditions are P 1 =0.08bar, T 1 = 293K, test gas: H 2, with 4% toluene, V s =1030m/s, and incident shockk attenuationn = 0.7%/m. Conditions 87

108 in the core flow are T 2 =346K, P 2 =0.144bar, and U =400m/s. The incident shock flow travels in the downward direction. Temperature [K] Residual T [K] Measured profile Predicted profile Temperature [K] Distance from side wall [mm] 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 88

109 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 nonideal 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%). 340 Temperature [K] Measurement Predicted w/ k(320k) Predicted w/ k(296k) Predicted w/ k(348k) Distance from side wall [mm] 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. 450 Temperature [K] Measured profile Predicted profile Distance from side wall [mm] Figure 5.9: Measured and predicted temperature profile about 30μs behind the incident shock. Temperature measurement in the side wall thermal boundary 89

110 layer show good agreement with predicted values except for a thin region about 60μm from the surface. Shock conditions are are P 1 = 0.09bar, T 1 = 293K, test gas: H 2, with 2% toluene, V s =910m/s, and incident shock attenuation = 0.5%/m. Calculated flow conditions are T 2 =414K, P 2 =0.05bar,, and U =380m/s. Measured T 2 =418K End walll thermal layer A sample PLIF image of the EWTL is shown along with the converted temperature image in Figure These images were taken about 2.3ms after the shock reflection at the end wall. Conditions in the core flow of region 5 are T=368K, P=0.19atm. These values were calculated using the normal shock wave equations given in Chapter 2. The premixed test gas composition is 3% toluene balanced with H 2. A well- with defined EWTL is clearly visible in Figure Also, a vertical temperature profile respect to the distance from the end wall across the temperature image along with the predictedd temperature profile is shown in Figure The residual temperature profile between the two profiles is also shown. The differencee in the core flow temperature is about 1% (363K and 367K for the measured and predicted profile,, respectively), which falls within the temperature measurement uncertainty given in [116].. Figure 5.10: (LEFT) End wall thermal layer PLIF signal and (RIGHT) temperature image. Shock conditions are P 1 =60torr, T 1 = 296K, bath gas: H 2, with 90

111 3% toluene, V s =1010m/s. Image was taken about 2.3ms after shock reflection. Core flow conditions behind reflected shock are T 5 =368K, P 5 =0.19bar. The reflected shock travels in an upward direction. 375 Temperature [K] Residual T [K] Measured profile Predicted profile Temperature [K] Distance from end wall [cm] Distance from end wall [mm] 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 T 5 =368K, P 5 =0.19bar. Measured T 5 =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 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. 91

112 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 T w 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. Temperature [K] Measured profile 200 Predicted profile Distance from end wall [cm] Figure 5.12: Measured and predicted temperature profile close to the end wall at higher temperature. Flow conditions are: T 5 =934K and P 5 =0.45bar. Measured T 5 =910K. The temperature measurement was made about 50μs after shock reflection. 5.4 Boundary layer development 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 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. 92

113 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 T 1 =293K, P 1 =0.02bar, H 2, with 6% toluene. Core flow conditions are T 2 =345K, P 2 =0.04bar. Since the shock wave speed is relatively constant for each of the five separate images, 10µs delay in time directly corresponds to about 1cm delay in distance. The false color scheme in Figure 5.13 is scaled to easily visualize the boundary layer and its development with respect to the distance from leading edge. Figure 5.13 has been treated to seamlessly stitch the five separate images together. The incident shock and region 1 is visible at the far right end of the image. The shock heated gas is flowing from left to right at a rate of about 610m/ /s. The temperature andd pressure behind the incident shock are 375K and 0.15atm, respectively. The incidentt shock speed is around 850m/s. The boundary layer is seen growing immediately behind the incident shock. The side wall thermal boundary layer thickness for various shock conditions in N 2 and toluene test gas is shown with correspondingg theoretical results in Figure Shock 1 Shock 2 Shock 3 Pressure [atm] Temperature [K] Toluene mole fraction [%] Free stream velocity [m/s] Table 5.1: List of core flow conditions behind incident shocks given in Figure

114 0.5 Thermal boundary layer thickness [mm] Shock 1 Shock 2 Shock 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 P 1 =7 to 23torr to produce shocks in T 1 =293K and N 2 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] Calculated [µm] Error [%] Table 5.2: Comparison of thermal boundary layer thickness, 1cm behind the incident shock. Flow conditions are listed in Table

115 Development of the thermal boundary layer in different bath gases (N 2, H 2, 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 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 Thermal boundary layer thickness [ m] N 2 H 2 Ar Distance behind incident shock [cm] Figure 5.15: Side wall thermal boundary layer thickness behind incident shocks in N 2, H 2, and Ar bath gas. Initial conditions are P 1 =7torr and T 1 =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. N 2 H 2 Ar Pressure [atm] Temperature [K] Free stream velocity [m/s] Table 5.3: List of core flow conditions behind the incident shocks given in Figure

116 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 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 V R 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. 96

117 0.8 Thermal layer thickness [cm] Measured thickness Best theoretical fit Time after shock reflection [ms] Figure 5.16: End wall thermal layer thickness behind a reflected shock. Initial conditions are T 1 =293K and P 1 =0.14bar, bath gas: H 2, with 1.5% toluene V s =1100m/s. The solid line is calculated using the heat diffusion equation. Conditions in the core flow behind the incident shock are T 5 =340K and P 5 =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. 97

118 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. 98

119 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 99

120 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 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 roomtemperature, mean measurement error is only 0.4%. The error slightly increased to about 100

121 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 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 101

122 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 nonuniform 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 M bl, for simplicity. Due to its vicinity to walls and their temperature (T 1, room temperature), M bl is considered to be a function of M 1 (Mach speed prior to the arrival of incident shocks) and as such, the stagnation pressure of the boundary layer (P bl,stag ) also becomes a function of M 1 and γ. For a given M 1 and γ, two phenomena can take place when boundary layer and reflected shock (P 5 ) interact. First, if P 5 <P bl,stag, the boundary layer is expected to pass continuously under the foot of the shock wave and 102

123 into region 5. The boundary layer continues to grow in thickness. More interestingly, if P 5 >P bl,stag (for γ = 1.4, 1.33 < M 1 < 6.45), the boundary layer flow cannot overcome P 5 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. 103

124 104

125 Appen ndix A. BSDF of samples transmitting Surface scatter is a complicated phenomenon that can fill the entire hemisphere centered about the sample. The distribution of light within the hemisphere is a function of incident angle, wavelength, and power, as well as sample parameters (orientation, transmittance, reflectance, absorptance, surface finish, index of refraction, bulk homogeneity, contamination, etc.). Bidirectional l scatter distribution function (BSDF) is commonly used to describe scattered light aboutt a surface. Geometry for defining BSDF according to Nicodemus [118] is shown in Figuree A.1. Figure A.1: Geometry for defining BSDF. Subscript i and s refer to incident and scatter component. Using the notation given in Figure A..1, BSDF is expressed as: 105

126 Ω Equation A.1 The distribution is bidirectional in that it depends both on the incident (θ i,ϕ i ) and scattered (θ s,ϕ s ) 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 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 Ω P 16, Ω Equation A.2 The left hand side of Equation A.2 is the power scattered in the s direction through dω s per unit incident power. Also, it is the product of cosine corrected BSDF and differential solid angle dω s, 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(f x,f y ) is the two-sided, two-dimensional surface PSD function in terms of the sample spatial frequencies f x and f y. 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. 106

127 Appen ndix B. PLIF test section design The aluminum base plate connects to the extension section via four screws and is sealed with an o-ring (Parker 2-259) ). Each window frame sits on the base plate and is guided into place with two positioning rods and attached with three screws. The vacuum seal between the base plate is a combination of o-rings and RTV adhesive (Momentive RTV159). Grooves are etched into the window frames so that excess RTV adhesive can easily penetrate the seams and provide air tight seals. A total of four aluminum window frames are required to hold the three side windows and a sensor array plate. Each window frame is designed so that it provides normal loads support and vibration isolation for the window. A close up of the side windoww frame and side windows are shown in Figure B.3. The window w float on top of the frame and is held in place with RTV adhesive, and not with a mechanical fastener, to isolate the window from vibrations that may occur during shock tube operation. Figure B.1: Cross-section of the window frame assembly, shown heree with two adjoining windows and window frames. 107

128 The windows are designed in the shape of isosceles trapezoid. This is to enable edge-to-edge visualization, and provide air-tighinto windoww design andd assembly because fused silica is seals between the window-to-window interfaces. Great attention went brittle and catastrophic failure may occur when silica-silica interfaces are not properly treated. In order to avoid failure, a thin strip of Teflon, 0.005inch thick, is placed between the window-to-window interfaces. An even thinner stripp of RTV is sandwichedd between the fused silica and Teflon to improve vacuum seals. A cross-section of the end wall with end wall window is shown in Figure B.4. The end walll window is also fused silica and shares the similar trapezoidal cross sectional design to evenly distribute the load on to the end wall section. Figure B.2: Cross-section of the end wall window side wall windows and frames. assembly, shown here with An o-ring encompasses the end wall window and helps to keep a tight vacuum seal between the edge of the side windows and the end wall. The end wall window is affixed to the end wall section using RTV adhesive. Thee end wall is connected to the side window frames via 16 screws. 4 additional support rods connectt the end wall to the extensionn section. This is done to minimize the load created by the end wall and prevent additional stress to the side windows and frames. 108