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

ProQuest Dissertations and Theses, 2011
Dissertation
Author: Ilyoup Sohn
Abstract:
During extreme-Mach number reentry into Earth's atmosphere, spacecraft experience hypersonic non-equilibrium flow conditions that dissociate molecules and ionize atoms. Such situations occur behind a shock wave leading to high temperatures, which have an adverse effect on the thermal protection system and radar communications. Since the electronic energy levels of gaseous species are strongly excited for high Mach number conditions, the radiative contribution to the total heat load can be significant. In addition, radiative heat source within the shock layer may affect the internal energy distribution of dissociated and weakly ionized gas species and the number density of ablative species 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 tolerances. Therefore, in the design process of spacecrafts the effect of radiation must be considered and radiation analyses coupled with flow solvers have to be implemented to improve the reliability during the vehicle design stage. To perform the first stage for radiation analyses coupled with gas-dynamics, efficient databasing schemes for emission and absorption coefficients were developed to model radiation from hypersonic, non-equilibrium flows. For bound-bound transitions, spectral information including the line-center wavelength and assembled parameters for efficient calculations of emission and absorption coefficients are stored for typical air plasma species. Since the flow is non-equilibrium, a rate equation approach including both collisional and radiatively induced transitions was used to calculate the electronic state populations, assuming quasi-steady-state (QSS). The Voigt line shape function was assumed for modeling the line broadening effect. The accuracy and efficiency of the databasing scheme was examined by comparing results of the databasing scheme with those of NEQAIR for the Stardust flowfield. An accuracy of approximately 1 % was achieved with an efficiency about three times faster than the NEQAIR code. To perform accurate and efficient analyses of chemically reacting flowfield - radiation interactions, the direct simulation Monte Carlo (DSMC) and the photon Monte Carlo (PMC) radiative transport methods are used to simulate flowfield - radiation coupling from transitional to peak heating freestream conditions. The non-catalytic and fully catalytic surface conditions were modeled and good agreement of the stagnation-point convective heating between DSMC and continuum fluid dynamics (CFD) calculation under the assumption of fully catalytic surface was achieved. Stagnation-point radiative heating, however, was found to be very different. To simulate three-dimensional radiative transport, the finite-volume based PMC (FV-PMC) method was employed. DSMC - FV-PMC simulations with the goal of understanding the effect of radiation on the flow structure for different degrees of hypersonic non-equilibrium are presented. It is found that except for the highest altitudes, the coupling of radiation influences the flowfield, leading to a decrease in both heavy particle translational and internal temperatures and a decrease in the convective heat flux to the vehicle body. The DSMC - FV-PMC coupled simulations are compared with the previous coupled simulations and correlations obtained using continuum flow modeling and one-dimensional radiative transport. The modeling of radiative transport is further complicated by radiative transitions occurring during the excitation process of the same radiating gas species. This interaction affects the distribution of electronic state populations and, in turn, the radiative transport. The radiative transition rate in the excitation/de-excitation processes and the radiative transport equation (RTE) must be coupled simultaneously to account for non-local effects. The QSS model is presented to predict the electronic state populations of radiating gas species taking into account non-local radiation. The definition of the escape factor which is dependent on the incoming radiative intensity from over all directions is presented. The effect of the escape factor on the distribution of electronic state populations of the atomic N and O radiating species is examined in a highly non-equilibrium flow condition using DSMC and PMC methods and the corresponding change of the radiative heat flux due to the non-local radiation is also investigated.

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

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Abstract: During extreme-Mach number reentry into Earth's atmosphere, spacecraft experience hypersonic non-equilibrium flow conditions that dissociate molecules and ionize atoms. Such situations occur behind a shock wave leading to high temperatures, which have an adverse effect on the thermal protection system and radar communications. Since the electronic energy levels of gaseous species are strongly excited for high Mach number conditions, the radiative contribution to the total heat load can be significant. In addition, radiative heat source within the shock layer may affect the internal energy distribution of dissociated and weakly ionized gas species and the number density of ablative species 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 tolerances. Therefore, in the design process of spacecrafts the effect of radiation must be considered and radiation analyses coupled with flow solvers have to be implemented to improve the reliability during the vehicle design stage. To perform the first stage for radiation analyses coupled with gas-dynamics, efficient databasing schemes for emission and absorption coefficients were developed to model radiation from hypersonic, non-equilibrium flows. For bound-bound transitions, spectral information including the line-center wavelength and assembled parameters for efficient calculations of emission and absorption coefficients are stored for typical air plasma species. Since the flow is non-equilibrium, a rate equation approach including both collisional and radiatively induced transitions was used to calculate the electronic state populations, assuming quasi-steady-state (QSS). The Voigt line shape function was assumed for modeling the line broadening effect. The accuracy and efficiency of the databasing scheme was examined by comparing results of the databasing scheme with those of NEQAIR for the Stardust flowfield. An accuracy of approximately 1 % was achieved with an efficiency about three times faster than the NEQAIR code. To perform accurate and efficient analyses of chemically reacting flowfield - radiation interactions, the direct simulation Monte Carlo (DSMC) and the photon Monte Carlo (PMC) radiative transport methods are used to simulate flowfield - radiation coupling from transitional to peak heating freestream conditions. The non-catalytic and fully catalytic surface conditions were modeled and good agreement of the stagnation-point convective heating between DSMC and continuum fluid dynamics (CFD) calculation under the assumption of fully catalytic surface was achieved. Stagnation-point radiative heating, however, was found to be very different. To simulate three-dimensional radiative transport, the finite-volume based PMC (FV-PMC) method was employed. DSMC - FV-PMC simulations with the goal of understanding the effect of radiation on the flow structure for different degrees of hypersonic non-equilibrium are presented. It is found that except for the highest altitudes, the coupling of radiation influences the flowfield, leading to a decrease in both heavy particle translational and internal temperatures and a decrease in the convective heat flux to the vehicle body. The DSMC - FV-PMC coupled simulations are compared with the previous coupled simulations and correlations obtained using continuum flow modeling and one-dimensional radiative transport. The modeling of radiative transport is further complicated by radiative transitions occurring during the excitation process of the same radiating gas species. This interaction affects the distribution of electronic state populations and, in turn, the radiative transport. The radiative transition rate in the excitation/de-excitation processes and the radiative transport equation (RTE) must be coupled simultaneously to account for non-local effects. The QSS model is presented to predict the electronic state populations of radiating gas species taking into account non-local radiation. The definition of the escape factor which is dependent on the incoming radiative intensity from over all directions is presented. The effect of the escape factor on the distribution of electronic state populations of the atomic N and O radiating species is examined in a highly non-equilibrium flow condition using DSMC and PMC methods and the corresponding change of the radiative heat flux due to the non-local radiation is also investigated.