# Modeling and simulation of radiation from hypersonic flows with Monte Carlo methods

vi Table of Contents List of Tables......................................x List of Figures.....................................xi Nomenclature......................................xx Acknowledgments...................................xxix Chapter 1.Introduction................................1 1.1 Background................................1 1.2 Objectives of This Work.........................7 1.3 Thesis Structure.............................9 Chapter 2.DSMC Simulation of Weakly Ionized Hypersonic Reentry Flows..13 2.1 Preface...................................13 2.2 Introduction to Rareﬁed Flow Modeling by DSMC..........13 2.3 DSMC Simulations for Hypersonic Reentry Flows around Stardust Sample Return Capsule Body......................15 2.3.1 Flow Simulations for Stardust Forebody at 71.9 and 61.8 km altitudes..............................17 2.3.2 Surface Catalytic Modeling in DSMC.............20 Chapter 3.Theory of Spectral Radiation Modeling in Hypersonic Reentry Flows 29

vii 3.1 Preface...................................29 3.2 Concepts of Radiation from Atomic Species..............31 3.2.1 Basic Relations of Radiation by Atomic Species........31 3.2.2 Calculation of Atomic Electronic Excited State Populations - Quasi Steady State Assumption.................35 3.3 Concepts of Radiation from Diatomic Species.............38 3.3.1 Basic Relations of Radiation by Diatomic Species.......38 3.3.2 Calculation of Excited Electronic State Population for Di- atomic Species..........................41 3.4 The One-Dimensional Tangent Slab Approximation,a Method for Radiative Transport...........................42 3.5 The Photon Monte Carlo (PMC) Ray Tracing Scheme,the Second Method for Radiative Transport.....................44 Chapter 4.Development of Databasing Schemes for Eﬃcient Radiation Calcula- tions of Hypersonic Reentry Flows...................52 4.1 Preface...................................52 4.2 Strategy for Generating Databases of Atomic Spectral Quantities..53 4.3 Strategy for Creating Databases of Spectral Quantities for Diatomic Emitters..................................57 4.4 Application of Radiation Databases to Reentry Flow Cases.....58 4.4.1 Investigation of the Accuracy of Spectral Coeﬃcients Gener- ated using the Database.....................58

viii 4.4.2 Investigation of Databasing Scheme Eﬃciencies........63 4.4.3 Application of Databasing Schemes to Radiation Calculations 65 Chapter 5.Coupled DSMC-Photon Monte Carlo Radiation Simulations....92 5.1 Preface...................................92 5.2 Finite Volume Photon Monte Carlo Method for Non-Gray Radiation 93 5.2.1 Wavelength Selection in the FV-PMC Procedure.......93 5.2.2 Validation.............................96 5.3 Coupled DSMC-PMC Simulation Results...............97 5.3.1 Coupled DSMC Calculations with PMC at 81,71.9 and 65.4 km altitudes............................97 5.3.2 Coupled DSMC Calculations with PMC at 61.8 km......100 5.3.3 Uncertainty Estimation of Radiative Heat Flux due to the Statistical Deviation of Flow Properties in DSMC......102 5.3.4 Discussion of Convective-Radiative Heating during the Star- dust Reentry Trajectory.....................105 Chapter 6.Eﬀect of Non-Local Vacuum UltraViolet (VUV) Radiation on a Hyper- sonic Non-equilibrium Flow.......................120 6.1 Preface...................................120 6.2 Entire Flowﬁeld Simulation of Stardust SRC at 81 km in DSMC..121 6.3 Derivation of the Escape Factor for Non-local Collisional-Radiative Modeling of N and O..........................125 6.3.1 Master equation for electronic state populations........125

ix 6.3.2 Calculation of escape factor coupled with non-local radiative transport.............................128 6.4 Comparison of Radiative Transport between PMC and TS Method.130 6.5 Coupled PMC - QSS Simulations using the Escape Factor......133 6.6 Eﬀect of the Escape Factor on Radiative Heating to the Surface...138 6.7 Simpliﬁcations to the Non-Local Escape Factor............140 Chapter 7.Conclusions................................166 References........................................170

x List of Tables 2.1 Freestream and DSMC Numerical Parameters...............22 4.1 Datasets for ε c λ and κ c λ of atomic O.....................68 4.2 Datasets for ε c λ and κ c λ of atomic N.....................68 4.3 Electronic transitions of diatomic species in NEQAIR..........69 4.4 Dataset example for N + 2 1st negative transition..............69 4.5 Dataset example for N + 2 1st negative transition-Continued........70 4.6 Comparison of computation time for narrow spectral region from 500 to 2,000 ˚ A....................................70 4.7 Comparison of computation time for wide spectral region from 500 to 10,000 ˚ A....................................70 4.8 Freestream conditions of Stardust reentry ﬂow..............71 5.1 Uncertainty in stagnation-point radiative heat ﬂux due to the statistical variation of DSMC ﬂows...........................110 6.1 DSMC Numerical Parameters for the entire ﬂowﬁeld around Stardust blunt body at 81 km.............................145 6.2 Electronic transitions aﬀected by escape factor..............145

xi List of Figures 2.1 Stardust geometric conﬁguration.......................23 2.2 Variation of translational temperature along the stagnation streamline from transitional to peak heating regime..................23 2.3 Distributions of temperatures (top) and number densities (bottom) along the stagnation streamline at 71.9 km altitude................24 2.4 Contours of the electron number density (top) and electron temperature (bottom) at 71.9 km altitude.........................25 2.5 Distributions of temperatures (top) and number densities (bottom) along the stagnation streamline at 61.8 km altitude................26 2.6 Contours of the electron number density (top) and electron temperature (bottom) at 61.8 km altitude.........................27 2.7 Comparison of mole fraction of atomic N and O species (top) and con- vective heat ﬂux along the Stardust forebody surface (bottom) due to surface catalytic recombination at 71.9 km altitude............28 3.1 Schematic diagram of ray tracing in one cell on X-Y (top) and Y-Z plane (bottom)....................................51 4.1 Cutoﬀ range of the Voigt line shape to satisfy 99.9 % integrated line for atomic line with respect to the ratio of Lorentzian to Voigt width which is less than 0.024................................71

xii 4.2 Comparison of emission (top) and absorption (bottom) coeﬃcients of atomic O from 500 to 2,000 ˚ A between the database and NEQAIR for n a = 1.1513×10 15 cm −3 ,n + = 3.8214×10 12 cm −3 ,n e = 1.2667×10 14 cm −3 ,T trn = 24,187 K and T e = 17,485 K.................72 4.3 Comparison of emission (top) and absorption (bottom) coeﬃcients of atomic O from 2,000 to 7,000 ˚ A between the database and NEQAIR for n a = 1.1513×10 15 cm −3 ,n + = 3.8214×10 12 cm −3 ,n e = 1.2667×10 14 cm −3 ,T trn = 24,187 K and T e = 17,485 K.................73 4.4 Comparison of emission (top) and absorption (bottom) coeﬃcients of atomic N from 500 to 2,000 ˚ A between the database and NEQAIR for n a = 3.1609×10 15 cm −3 ,n + = 5.5472×10 12 cm −3 ,n e = 1.2667×10 14 cm −3 ,T trn = 24,187 K and T e = 17,485 K.................74 4.5 Comparison of emission (top) and absorption (bottom) coeﬃcients of atomic N from 2,000 to 7,000 ˚ A between the database and NEQAIR for n a = 3.1609×10 15 cm −3 ,n + = 5.5472×10 12 cm −3 ,n e = 1.2667×10 14 cm −3 ,T trn = 24,187 K and T e = 17,485 K.................75 4.6 Maximum diﬀerence of emission (top) and absorption (bottom) bound- bound line strength of atomic Nand Obetween the database and NEQAIR for the entire n e and T e conditions......................76 4.7 Averaged diﬀerence of bound-free emission (top) and absorption (bot- tom) coeﬃcient of atomic N and O between the database and NEQAIR for the entire n e and T e conditions......................77

xiii 4.8 Comparison of emission (top) and absorption (bottom) coeﬃcients of N + 2 from 3,000 to 6,000 ˚ A between the database and NEQAIR for N N + 2 = 6.4529 × 10 13 cm −3 ,N N = 3.9464 × 10 15 cm −3 ,n e = 1.1607 × 10 14 cm −3 ,T trn = 34,469 K and T e = 16,511 K.................78 4.9 Comparison of emission (top) and absorption (bottom) coeﬃcients of NO from 2,000 to 7,000 ˚ A between the database and NEQAIR for N NO = 2.5624 × 10 13 cm −3 ,N N = 3.9464 × 10 15 cm −3 ,N O = 1.2829 × 10 15 cm −3 ,n e = 1.1607 ×10 14 cm −3 ,T trn = 34,469 K and T e = 16,511 K.79 4.10 Comparison of emission (top) and absorption (bottom) coeﬃcients of N 2 from 1,000 to 6,000 ˚ A between the database and NEQAIR for N N 2 = 2.5624 × 10 13 cm −3 ,N N = 3.9464 × 10 15 cm −3 ,n e = 1.1607 × 10 14 cm −3 ,T trn = 34,469 K and T e = 16,511 K.................80 4.11 Comparison of emission (top) and absorption (bottom) coeﬃcients of O 2 from 2,000 to 3,500 ˚ A between the database and NEQAIR for N O 2 = 6.8349 × 10 12 cm −3 ,N O = 1.2829 × 10 15 cm −3 ,n e = 1.1607 × 10 14 cm −3 ,T trn = 34,469 K and T e = 16,511 K.................81 4.12 Comparison of total emission energy error using ﬁxed and variable cutoﬀ ranges for atomic bound-bound radiation along the stagnation streamline of Stardust at 68.9 km altitude........................82 4.13 Stagnation and shoulder line location of Stardust body for radiation cal- culations....................................82 4.14 Number density (top) and temperature (bottom) proﬁle along stagnation streamline of DPLR ﬂowﬁeld.........................83

xiv 4.15 Number density (top) and temperature (bottom) proﬁle along shoulder line of DPLR ﬂowﬁeld.............................84 4.16 Comparison of ∇ q R (top) and total emission (bottom) of 6 radiating species between the database and NEQAIR along the stagnation line and shoulder line of Stardust DPLR ﬂow ﬁeld..................85 4.17 Number density (top) and temperature (bottom) proﬁle along stagnation streamline of DSMC ﬂowﬁeld at 68.9 km altitude.............86 4.18 Number density (top) and temperature (bottom) proﬁle along shoulder line of DSMC ﬂowﬁeld at 68.9 km altitude.................87 4.19 Comparison of ∇ q R (top) and total emission (bottom) of 6 radiating species between the database and NEQAIR along the stagnation stream- line and shoulder line of Stardust DSMC ﬂowﬁeld at 68.9 km altitude..88 4.20 Number density (top) and temperature (bottom) proﬁle along stagnation streamline of DSMC ﬂowﬁeld at 81 km altitude..............89 4.21 Number density (top) and temperature (bottom) proﬁle along shoulder line of DSMC ﬂowﬁeld at 81 km altitude..................90 4.22 Comparison of ∇ q R (top) and total emission (bottom) of 6 radiating species between the database and NEQAIR along the stagnation stream- line and shoulder line of Stardust DSMC ﬂowﬁeld at 81 km altitude...91 5.1 Comparison of ∇q R along the stagnation streamline among the PMC 1-D disk,PMC Stardust geometry and 1D-TS at 71.9 km (top) and 61.8 km (bottom) altitudes...............................111

xv 5.2 Comparison of distributions of the translational (top) and rotational,vi- brational,electron (bottom) temperatures along the stagnation stream- line between cases with and without radiation at 81 km altitude.....112 5.3 Comparison of heat ﬂux to the surface between cases with and without radiation along the forebody surface (top) and heat ﬂux at the stagnation point for each iteration of the DSMC-PMC coupling (bottom) at 81 km altitude.Here and in subsequent ﬁgures S = 0 and 0.436 represent the stagnation point and shoulder of the vehicle,respectively.........113 5.4 Comparison of distributions of the translational (top) and rotational,vi- brational,electron (bottom) temperatures along the stagnation stream- line between cases with and without radiation at 71.9 km altitude....114 5.5 Comparison of heat ﬂux to the surface between cases with and without radiation along the forebody surface (top) and heat ﬂux at the stagnation point for each iteration of the DSMC-PMC coupling (bottom) at 71.9 km altitude.....................................115 5.6 Comparison of distributions of the translational (top) and rotational,vi- brational,electron (bottom) temperatures along the stagnation stream- line between cases with and without radiation at 61.8 km altitude....116 5.7 Comparison of heat ﬂux along the forebody surface for cases with and without radiation (top) and heat ﬂux at the stagnation point as a function of DSMC-PMC coupling iterations (bottom) for the Stardust body at 61.8 km altitude................................117

xvi 5.8 Comparison of the stagnation-point convective heat ﬂux versus freestream correlation during the Stardust reentry trajectory.............118 5.9 Comparison of the stagnation-point radiative heat ﬂux versus freestream correlation during the Stardust reentry trajectory.............119 6.1 Mach number distribution and streamlines around Stardust SRC body at 81 km....................................146 6.2 Mole fractions of atomic N (top) and O (bottom) at 81 km altitude...147 6.3 Mole fractions of N 2 ,O 2 ,N and O along the stagnation streamline at 81 km altitude...................................147 6.4 Contours of the electron number density at 81 km altitude........148 6.5 Contours of the electron temperature at 81 km altitude..........148 6.6 Distributions of atomic nitrogen translational temperature and temper- ature of total electrons and newly produced electrons from ionization reaction (N + O −→NO + + e) along the nornal line to the side surface (line (2) of Fig.6.5)..............................149 6.7 Distributions of electron,atomic and molecular nitrogen concentration along the nornal line to the side surface (line (2) of Fig.6.5).......149 6.8 Distributions of electron temperature along the nornal line to the side surface (line (2) of Fig.6.5) with and without relaxation with N 2 ....150 6.9 Comparison of electron temperature (LHS) and atomic Nnumber density (RHS) along the nornal line to the side surface (line (2) of Fig.6.5) with and without surface recombination of atomic N species..........150

xvii 6.10 Contours of the electron temperature considering surface recombination of atomic N species at 81 km altitude....................151 6.11 Proﬁles of electron temperature along the vertical lines starting from the vehicle surface at diﬀerent horizontal locations...............151 6.12 Iterative procedure for the calculation of escape factor and electronic state populations using PMC and QSS model................152 6.13 Divergence of radiative heat ﬂux (∇ q R ) calculated by PMC (Top) and diﬀerence of ∇ q R between PMC and TS method (Bottom).......153 6.14 Number densities of electron and atomic species and electron tempera- ture along a normal line to the surface located in the afterbody as shown in Fig.6.13..................................154 6.15 Local emission and divergence of radiative heat ﬂux along a normal line to the surface located in the afterbody as shown in Fig.6.13.......154 6.16 Upper electronic state populations of atomic Nand Oduring the iterative coupling process with the escape factor calculations along the stagnation streamline...................................155 6.17 Escape factor of atomic N (Top) and O (Bottom) during the iterative coupling process along the stagnation streamline..............156 6.18 Number of transitions by the non-local absorption from the ground to the 4th electronic state of atomic N (Top) and from the ground to the 5th electronic state of atomic O (Bottom) during the iterative coupling process along the stagnation streamline...................157

xviii 6.19 Upper electronic state populations of atomic Nand Oduring the iterative coupling process with the escape factor calculations along the line normal to the shoulder surface.( line (1) of Fig.6.5 )...............158 6.20 Escape factor of atomic N (Top) and O (Bottom) during the iterative coupling process along the line normal to the shoulder surface.( line (1) of Fig.6.5 )..................................159 6.21 Upper electronic state populations of atomic Nand Oduring the iterative coupling process with the escape factor calculations along the line normal to the side surface.( line (2) of Fig.6.5 ).................160 6.22 Upper electronic state populations of atomic Nand Oduring the iterative coupling process with the escape factor calculations along the line normal to the side surface.( line (3) of Fig.6.5 ).................161 6.23 Distribution of escape factor for atomic N (top,4th to ground) and O (bottom,5th to ground) transitions around the Stardust SRC body...162 6.24 Convective-radiative heat ﬂuxes to the vehicle surface at 81 km......163 6.25 Comparison of escape factor of transition from the 4th to ground (Top) and the 4th electronic state population (Bottom) of atomic N along the stagnation streamline between non-local and local way...........164 6.26 Distribution of the 4th electronic state population along the shoulder line (line (1) of Fig.6.5) calculated by using non-local escape factor and zero escape factor and Boltzmann relation....................165

xix 6.27 Distribution of the 4th electronic state population along the line normal to the side face (a line of Fig.6.13) calculated by using non-local escape factor and zero escape factor and Boltzmann relation...........165

xx Nomenclature A Einstein coeﬃcient for spontaneous emission,s −1 , or a chemical species symbol A(i,j) Einstein coeﬃcient for spontaneous emission from state i to state j,s −1 A(c,i) Einstein coeﬃcient for spontaneous emission from continuum state to state i,cm 3 s −1 A(i,c) Einstein coeﬃcient for photoionization from state i to continuum state,s −1 a 0 Bohr radius,5.29167 ×10 −9 cm B Einstein coeﬃcient for stimulated emission and absorption,(cm 3 -m)/(J-s), or a chemical species symbol BP breakdown parameter B V U rotational constant,cm −1 b exponent,dimensionless b hw line half width, ˚ A c speed of light,2.9979 ×10 10 cm s −1 ¯ C, ¯ D vector assembled by excitation rate coeﬃcients of atom ¯ C m , ¯ D m vector assembled by excitation and dissociation rate coeﬃcients of molecule D a photon traveling distance,cm d parameter in the Voigt width,dimensionless (See Eq.(4.4)) d ﬀ correction factor for free-free radiation,dimensionless D w Doppler line half width,cm e electron charge,4.8030 ×10 −10 statcoul

xxi E radiative energy,W E abs radiative energy absorbed by cell,W E bundle radiative energy carried by photon bundle,W E emis total emission energy,W/cm 3 E i electronic term energy for atomic level i,cm −1 E k kinetic energy of free electron,cm −1 E trans transmitted radiative energy,W E ∞ ionization energy of an atom,cm −1 ∆E net kinetic energy of a free electron,cm −1 F rotational term energy for a molecule,cm −1 F i assembled collisional and radiative coeﬃcient of electronic state i,dimensionless G vibrational term energy for a molecule,cm −1 G i assembled collisional and radiative coeﬃcient of electronic state i,dimensionless G λ incoming radiative intensity integrated over all directions,W/cm 2 -m GF Gaunt factor for bound-free radiation,dimensionless g degeneracy,dimensionless H data points of electron number density and electron temperature ∆H data point interval h Planck’s constant,6.6262 ×10 −34 Js I H ionization potential of atomic hydrogen,109,679 cm −1 I λ radiative intensity,W/cm 2 -m-sr J rotational quantum number,dimensionless

xxii j data point index K n Knudsen number,dimensionless K e (i,j) excitation rate coeﬃcient of collisional transition from state i to state j by electron impact,cm 3 s −1 K(i,c) excitation rate coeﬃcient of collisional transition from state i to continuum state,cm 3 s −1 K(c,i) recombination rate coeﬃcient of collisional transition from continuum state to state i,cm 6 s −1 K Wi heavy particle induced recombination rate coeﬃcient,cm 3 s −1 K e ci electron induced recombination rate coeﬃcient,cm 3 s −1 K W (i,j) heavy particle induced molecular excitation rate coeﬃcient from state i to state j,cm 3 s −1 k B Boltzmann’s constant,1.3806 ×10 −23 JK −1 k,k 1 ,k 2 line-center index,dimensionless L nose radius of the Stardust blunt body,m l number of electronic states for bound-free transition, l 1,2 ratio between face endpoints,m l m number of electronic state energy levels for diatomic QSS,dimensionless Ma Mach number,dimensionless M matrix assembled excitation rate coeﬃcients of atom, or a chemical species symbol M m matrix assembled excitation and dissociation rate coeﬃcients of molecule

xxiii m mass,kg max maximum value of vibrational or rotational line,dimensionless N number density,cm −3 N i number density of electronic state i,m −3 N rays per cell number of rays emitted from one cell N total rays initial total number of rays n principal quantum number,dimensionless n a atom number density,m −3 n e electron number density,m −3 n + ion number density,m −3 P number of data points Q partition function,dimensionless Q emis total integrated emission coeﬃcient,W/cm 3 -sr Q emis,k accumulated atomic emission lines from i = 1 to k,W/cm 3 -sr Q emis,λ partially integrated emission coeﬃcient,W/cm 3 -sr q V U V L Franck Condon factor,dimensionless q c convective heat ﬂux,W/m 2 q R radiative heat ﬂux,W/m 2 R transition moment,statcoul-cm R random number,dimensionless R c radius of curvature,m Re electronic transition moment for a vibrational band (V U ,V L )

xxiv normalized by ea 0 ,dimensionless r radial component of photon travel distance in a cell,m r c internuclear distance,unit of length,not explicitly evaluated S distance from stagnation point,m S J U J L rotational line strength factor,dimensionless S c source function,W/cm 2 -m-sr S d distance from emission point to cell face intersection point,m s x ,s y ,s z unit directional cosines in a Cartesian coordinate system T trn translational temperature,K T rot rotational temperature,K T vib vibrational temperature,K T e electron temperature,K T eU upper state electronic energy of the term symbol for molecular radiation,cm −1 T eL lower state electronic energy of the term symbol for molecular radiation,cm −1 t time,s V vibrational quantum number,dimensionless V cell cell volume,m 3 V ∞ freestream velocity,m/s w l Lorentzian width, ˚ A w g Gaussian width, ˚ A w s Stark width, ˚ A w s,0 reference Stark width, ˚ A

xxv w v Voigt width, ˚ A X horizontal coordinate of DSMC computational domain for the Stardust geometry,m x i ,y i ,z i intersection points of a photon bundle with a cell face,m x e ,y e emission locations,m x 1 ,x 2 coordinates of cell boundary along X-axis,m X i,data emission or absorption coeﬃcients from the database at the i-th wavelength data point X i,NEQ emission or absorption coeﬃcients from NEQAIR at the i-th wavelength data point Y vertical coordinate of DSMC computational domain for the Stardust geometry,m y 1 ,y 2 coordinates of cell boundary along Y-axis,m α optical length,dimensionless ε i emission coeﬃcient of a bound-bound transition at the line-center wavelength,W/cm 3 -sr ε λ emission coeﬃcient,W/cm 3 -m-sr ε c λ assembled parameter for emission coeﬃcient,W/sr θ polar angle,radian κ λ absorption coeﬃcient,cm −1 κ c λ assembled parameter for absorption coeﬃcient,cm 3 λ wavelength, ˚ A λ 1 wavelength where line broadening starts, ˚ A λ 2 wavelength where line broadening ends, ˚ A

xxvi λ k 1 wavelength at line-center index k 1 , ˚ A λ k 2 wavelength at line-center index k 2 , ˚ A ν frequency,s −1 ¯ν transition energy of emitted photon,cm −1 Ω solid angle,sr ∆λ distance from line center, ˚ A ˜ν wavenumber,cm −1 ρ mass density,kg/m 3 ρ i ratio of non-equilibrium to equilibrium populaion of electronic state i,dimensionless ρ ij escape factor of transition from state i to state j,dimensionless ρ ∞ freestream mass density,kg/m 3 ̺ collision rate σ standard deviation σ λH ionization cross-section of hydrogen atom,cm 2 σ bf λ bound-free absorption cross-section,cm 2 σ ﬀ H hydrogenic free-free cross-section,cm 5 τ λ optical thickness,dimensionless φ λ line broadening function,m −1 χ ratio of summation of non-equilibrium electronic state populations to that of equilibrium state,dimensionless Ψ vibrational wave function,units of length −1/2 ,not explicitly evaluated

xxvii ϕ cell face intersection angle,radian ψ azimuthal angle,radian Subscripts a atom b blackbody c line-center cell computational cell cross section cell cross-section e electron emis emission end ending data E equilibrium state H hydrogenic i,j index of electronic state,or index of cell init initial data k kinetic L lower state LU lower to upper state W heavy particle m molecule max maximum value min minimum value

xxviii min cutoﬀ limit NEQ NEQAIR n principal quantum number R rotational state total all cells of computational domain U upper state UL upper to lower state V vibrational state θ polar angle λ wavelength ψ azimuthal angle + ion ∞ ionization,or freestream Superscripts bf bound-free c constant e electronic state ﬀ free-free rad radiative transition ∗ normalized quantity

xxix Acknowledgments I would like to thank my advisor,Dr.Deborah A.Levin,for her guidance and encouragement she has shown me during my time at Penn State. I also would like to thank my other committee members,Dr.Cengiz C.Camci and Dr.Michael M.Micci,for their insightful commentaries on my work.Special thanks are to Dr.Michael F.Modest for guidance and enlightening discussions about radiation. I am grateful to Dr.Zheng Li and Dr.Takashi Ozawa for their help to my disser- tation research. I would like to acknowledge support from NASA grant NNX07AC47A for my graduate research. Finally,I am grateful to my family,3J (Jueun,Jiyeon and Jiwoo),for their con- stant love,support and encouragement and to my friends and colleagues in Penn State.

1 Chapter 1 Introduction 1.1 Background For high-speed reentry into Earth’s atmosphere,spacecraft such as Stardust[1, 2,3,4,5,6],Crew Exploration Vehicle[7],or MUSES-C[8] experience hypersonic non- equilibrium ﬂow conditions where molecules are dissociated and atoms are weakly ion- ized.These complex phenomena occurring behind the shock wave lead to high temper- ature ﬂows and ionization that generate a severe heating load on the thermal protection system (TPS) and cause radar communications blackout to the vehicle.[9] Since the internal energy states of atomic species are strongly excited for high Mach number con- ditions,the radiative contribution to the total heat load becomes signiﬁcant.[10] In fact, the radiative heating to the stagnation region can readily exceed the convective heat- ing rates at superorbital reentry velocities.[11] In addition,radiative energy within the shock layer may aﬀect the macroscopic ﬂow properties and internal energy distribution of dissociated and weakly ionized air species and ablative products released from the surface of vehicles.Due to the radiation total heat load to the heat shield surface of the vehicle may be altered beyond mission constraints.Therefore,the eﬀect of radiation on the ﬂowﬁeld and TPS must be taken into account and radiation analyses coupled with ﬂow solvers have to be implemented to improve the reliability of the vehicle design stage.

2 The radiative heat loads resulting from high temperature gases have been an area of signiﬁcant research over the past ﬁfty years with the goal of developing spacecraft TPS,that can withstand the severe ﬂow conditions such as high temperature and air plasma.The ﬁeld has progressed by developing accurate numerical and experimental methods for aerodynamics and chemistry modeling to predict chemical reactions in high temperature gas dynamics.Zhigulev et al.[12] carried out a systematic examination of the eﬀect of radiation under a high temperature gas ﬂow past a vehicle body by a theoretical approach.It was veriﬁed that radiation contributed to the change of the characteristics of hypersonic ﬂows around the vehicle - especially at the temperature and the species concentration of the radiating gas ﬂow.The inﬂuence of radiation to convective heating was studied by Goulard[13] using approximate inviscid ﬂowﬁelds with transparent or gray-gas radiation,estimating that the ﬂowﬁeld temperature decreased and the convective heat transfer was also reduced as a result of radiative cooling eﬀects. Viscous ﬂowﬁelds coupled with equilibrium gas radiation were studied to examine the eﬀect of radiation cooling and contribution of the convective and radiative heating to an ablating body[14].In that work,only the absorption coeﬃcients of continuum radiation were employed for atomic radiation and the smeared band model was used for evaluating the molecular line absorption coeﬃcients. In the 1970s,non-gray equilibriumradiation models were adopted to the radiative heating problem for the entry into Earth and other planetary atmospheres.Moss[15] performed radiative viscous shock layer calculations with a coupled ablation injection model in the Earth reentry equilibriumﬂowﬁelds surrounding axisymmetric blunt bodies. A non-gray radiation model including atomic line and continuumtransitions were used in