Particle Photon Monte Carlo Method for Simulating Atomic Radiation in Hypersonic Reentry Flows in DSMC

Transcription

1 4th Thermophysics Conference, June 28, Seattle, Washington Particle Photon Monte Carlo Method for Simulating Atomic Radiation in Hypersonic Reentry Flows in DSMC T. Ozawa, A. Wang, + D. A. Levin and M. Modest, + Department of Aerospace Engineering, + Department of Mechanical Engineering, The Pennsylvania State University, University Park, PA 1682 With a fast reentry speed, the Stardust reentry generates a strong shock region ahead of its blunt body with a temperature above 6, K, high enough to initiate gas ionization processes and thermal and chemical ablation processes. The generated charged particles affect nonequilibrium atomic and molecular energy distributions and shock layer radiation. In this work, we present the first loosely coupled direct simulation Monte Carlo (DSMC) simulations with the particle-based photon Monte Carlo (p-pmc) method to simulate Stardust reentry flows in the transitional flow regime. Eleven species including 5 ionization processes were modeled in DSMC, and the average ion velocity model was used to simulate electron motion. At these altitudes, the degree of ionization is predicted to be 3-7 % along the stagnation line, and the maximum translational and electron temperatures are approximately 6, K and 2, K, respectively. To efficiently capture high nonequilibrium effects, emission and absorption cross section databases using the Nonequilibrium Air Radiation (NEQAIR) were generated, and N and O radiation was calculated by the p-pmc method. It was found that the N emission is approximately one order of magnitude higher than the O emission along the stagnation line due to the higher concentration of N at this altitude. The radiation energy change calculated by the p-pmc method has been coupled in the DSMC calculations. It was found that while the N and O atomic radiation does not have impact on the flow field at 81 km, at 68.9 km, stronger radiation affected the flow filed and resulted in lowering temperatures and convective heat flux on the Stardust surface. Nomenclature B λ Planck function in W/cm 2 /sr/µ E abs,p Absorption energy per particle E abs Integrated absorption energy in W/cm 3 E emis,p Emission energy per particle E emis Integrated emission energy in W/cm 3 F num Number of particles represented by a simulated particle i Cell index in the x direction I λ Spectral intensity in W/cm 2 /sr/µ j Cell index in the r direction Postdoctoral fellow, Department of Aerospace Engineering; txo123@psu.edu. 135 Hammond Building, University Park, PA Member AIAA. Professor, Department of Aerospace Engineering; dalevin@psu.edu. 233 Hammond Building, University Park, PA Associate Fellow AIAA. Copyright c 28 by the American Institute of Aeronautics and Astronautics, Inc. The U.S. Government has a royalty-free license to exercise all rights under the copyright claimed herein for Governmental purposes. All other rights are reserved by the copyright owner. 1 of 22

2 n + n a N c n e Q emis,λ Q emis,l,k Q emis R c Ion number density Atom number density Number of paticles in a cell Electron number density Partially integrated emission cross section Accumulated atomic emission lines from i = 1 to k in order of increasing wavelength Integrated emission cross section Local cone radius of a ray Rn Uniform random number between and 1 T c Cell-averaged temperature T e Electron temperature T p Particle temperature T rot Rotational temperature T tr Translational temperature T vib Vibrational temperature Volume of a cell V c Symbols τ Contribution of a specific particle to the optical thickness λ hw Half width of the Doppler broadening ɛ λ Emission cross section at a wavelength ɛ L Emission cross section of a bound-bound transition centerline κ λ Absorption coefficient in cm 1 λ Wavelength in Å or µ λ L Wavelength of a bound-bound transition centerline in Å q Radiative energy change (=E emis E abs ) q par Radiation energy change per particle in W q R Radiative heat flux in W/cm 2 σ abs,λ Absorption cross section in cm 2 τ Optical thickness I. Introduction For high-speed reentry conditions, such as Stardust 1, 2 or Crew Exploration Vehicle, 3 radiation effects are significant for the prediction of heat shield design and efficiency. With the fast reentry speeds (e.g km/s), the vehicle can generate a strong shock region ahead of its blunt body with temperature above 1, K, high enough to initiate gas ionization processes 4, 5, 6 and thermal and chemical ablation processes. 7 The generated ions and electrons lead to complicated reactions among charged and neutral particles, which further affect nonequilibrium atomic and molecular energy distributions and radiation behavior. The ratio of radiative heat flux to convective heat flux for the Stardust reentry flows was found to be high for altitudes lower than 8 km, 8 and thus, coupling between flow field and radiation calculations is required. Olynick et al. 1 applied a continuum Navier-Stokes flow solver loosely coupled to radiation and material thermal ablation models to predict the Stardust reentry flows at altitudes of 43-8 km. Park 2 recently applied the viscous shock layer method to predict heat transfer rates for the Stardust at altitudes of km. However, for high altitudes such as higher than 6 km, continuum breakdown occurs and nonequilibrium effects need to be considered, and thus, continuum methods may not be applicable for prediction of these flow fields. Gallis and Harvey 9, 1 modeled nonequilibrium thermal radiation in DSMC as well as electronic excitation processes, and good agreement in terms of spectral intensity for an air shock-tube experiment was shown between computational and experimental results. However, for their method, accurate cross sections for electronic excitation and absorption are needed and the uncertainty in the cross sections is not well known for all the species. Also, the absorption of emitted radiation is limited within the cell, and one absorption cross section is used over all wavelengths. In our previous work, 4 ionization processes and charged species were modeled in the direct simulation Monte Carlo (DSMC) method. The effect of chemical reactions and charged species were discussed for the Stardust blunt body between 68.9 and 1 km altitudes. In addition, thermal and chemical ablation processes of the Stardust thermal protection layer were designed to prevent aerodynamic heating during the 2 of 22

3 entry process, and the impact on the flow field and surface parameters was investigated in DSMC. 7 In this work, we further develop our DSMC flow field calculations loosely coupling with the particle-based photon Monte Carlo (p-pmc) method. 11 In the p-pmc method, absorption coefficient is calculated by the line-byline database, and the emitted photon can travel as far as possible until the photon energy is absorbed by particles. We simulate the radiation of Stardust hypersonic reentry flows between 68.9 and 81 km altitudes. In our previous work, the radiative heat flux was calculated in the stagnation region using the Boltzmann distribution for the electronic excitation population, and the contribution of radiative heat flux to the total heat flux was predicted to be about 4% at 81 km and about 18% at 68.9 km in the stagnation region in our previous work. 8 The advantage of the coupling between particle methods is that no continuum assumption is required. Therefore, for flows that breaks down, particle simulations provide us with more accurate flow field predictions. Also, between two particle simulations, we can easily transfer the DSMC particle properties to the p-pmc calculations. However, in order to utilize the particle information to calculate radiation on the particle base, accurate electronic excited state population needs to be modeled via collisions and relaxation in DSMC. In addition, flow field and radiation simulations need to be tightly coupled to represent different particle conditions for each time step. Currently, tightly coupled computations between DSMC and p-pmc is too expensive to be executed. Thus, in this work, a loosely coupled procedure has been selected between the DSMC and p-pmc methods. Using the DSMC steady state solution (e.g. number densities, temperatures), the electronic excited states are calculated by the quasi steady state (QSS) model, 12 and emission and absorption coefficients are calculated based on the electronic excited state populations. II. Modeling of Radiation The p-pmc methods were initially developed for turbulent combustion problems to evaluate the radiative 13, 14, 15, 16 source terms exactly. In this method, radiation transfer is modeled by allowing each particle to emit its emissive energy in the form of photon bundles (rays) into random directions, and tracing these rays until the ray s energy is depleted due to absorption by other particles or it escapes from the enclosure. Special 14, 15 schemes have been developed to simulate the ray-particle interaction and to minimize statistical errors. A line-by-line spectral Monte Carlo method has also been developed using a random number relationship, to treat the spectral variation of radiation exactly in PMC simulations. 16 In this work, a cone ray model with the point particle model is used. The particle information (e.g. position, velocity, energy, temperatures, number densities, and F num ) in DSMC can be transferred to the p-pmc method, and radiative energy change per particle due to the emission and absorption is calculated by the p-pmc method. In the 2D axisymmetric DSMC calculations, since radial weights are used, F num of each particle is based on its y coordinate (j = 1, N y ), F num (j) = F num, (2j 1)/(2N y 1), (1) where F num, is a number of atoms or molecules represented by a DSMC simulation particle. For the PMC method, the absorption and emission cross section databases are created using the Nonequilibrium Air Radiation (NEQAIR) 17 code. Since the NEQAIR code was developed for conditions that occur in nonequilibrium flows our database is considered to be more accurate than the conventional databases for equilibrium conditions. The details of the database can be found in the work of Sohn et al. 18 In the atomic species database, the excitation population was calculated using the QSS model as a function of electron temperature T e, electron number density n e, and the ratio of ion to neutral number density, n + /n a. The electronic excited state population is linearly proportional to the ratio of n + /n a. Atomic lines for N and O were also databased, and emission and absorption cross sections can be calculated as a function of T e, n e, n + /n a, and translational temperature T tr. The translational temperature is used to simulate Doppler line broadening in this paper for each atomic line. To perform the p-pmc calculation, a random number database based on emission cross sections is created from the emission and absorption database. 18 In the random number database, bound-bound (bb) transitions are separated from bound-free (bf) and free-free (ff) transitions. For bb transitions, the centerline wavelength λ L,k (Å) and accumulated emission cross section, Q emis,l,k (T e, n e, n + /n a ), are stored. The accumulated emission cross section is calculated as k Q emis,l,k = ɛ L,i (T e, n e, n + /n a ), (2) i=1 3 of 22

4 where ɛ L (T e, n e, n + /n a ) is an emission cross section in unit of W/sr of each atomic line. For N and O, 17 and 86 atomic lines are included in the databases, respectively. The atomic lines are sorted in order of increasing wavelength. From the initial investigation of the Stardust flow field, the range of each variable is selected as T e =1-28 K ( T e =1, K, 28 levels), n e = cm 3 ( 22 levels), and n + /n a =1 1 3 and.31 (2 levels). For bf transitions, partially integrated emission, λ λ min ɛ λ (T e, n e, n + /n a )dλ (W/sr) as a function of λ is stored for each condition. For the Stardust reentry cases considered here, 68.9 and 81 km, the contribution of ff transitions is negligible. For bf transitions, the wavelength range is λ=5-6 Å with a resolution of λ=1 Å. The size of the random number database is approximately 5 MB for each species. In the main p-pmc calculations, for both bb and bf transitions, an exponential spline interpolation scheme is used to determine the emission cross section at a given T e and n e. At a given n + /n a, a linear interpolation is used. For the exponential spline interpolations, the interpolated results were compared with the integrated emission energy obtained by NEQAIR, and resolution for T e and n e were determined. For bb transitions, the partially integrated emission is calculated as Q emis,λ = = λ ɛ λ (T e, n e, n + /n a )dλ λ min k 1 k 2 λ ɛ L,k + ɛ λ,k dλ λ λ hw,max k=1 = Q emis,l,k1 + k=k 1+1 k 2 k=k 1+1 λ λ λ hw,max ɛ λ,k dλ. (3) To evaluate Eq. (3), first, line indices, k 1 and k 2, are selected as follows. k 1 is selected using the bisection method by whether λ L < λ λ hw,max or not, where λ hw,max is the maximum half width of the Doppler broadening. In this work, it is set to.25 Å. k 2 is selected by whether λ L < λ + λ hw,max or not. The accumulated atomic line strength Q emis,l,k1 from k = 1 to k 1 is read from the database, and ɛ L,k is calculated as ɛ L,k = Q emis,l,k Q emis,l,k 1. If λ L λ < λ hw,max, the half width of the Doppler broadening is calculated, and the Doppler broadening is applied to evaluate the partial integration. Finally, the contributions of bb and bf transitions are summed up. The emission energy per PMC particle is calculated as λmax E emis,p = 4π ɛ λ dλ F num. (4) λ min The energy is emitted in the form of photon rays into random directions. To obtain an absorption cross section for a ray, a bisection method is used to select a wavelength by comparing a random number to Q emis,λ /Q emis = λ λ min ɛ λ (T e, n e, n + /n a )dλ/ λ max λ min ɛ λ dλ. Once a wavelength is selected, the absorption cross section, σ abs,λ (T e, n e, n + /n a, T tr ), is calculated from the database 18 on the fly. The rays are traced until the ray s energies are depleted due to absorption by other particles or it escapes from the enclosure. In this work, a cold Stardust body is used in the p-pmc calculations, and the ray s energy is absorbed by the body if a ray hits the Stardust body. Figure 1 shows an example of partially integrated emission as a function of wavelength for atomic oxygen. The translational and electron temperatures are 42, K and 27,5 K, respectively. The O number density and the degree of ionization (DOI) are cm 3 and 1 %. The bb only and bb+bf partially integrated emissions are compared with the results calculated directly from the database. It is seen that good agreement is obtained between the database of Sohn 18 and the random number database in the p-pmc method. Although the bf contribution can be observed for wavelength less than 1, Å, the bf contribution is small in Q emis,λ /Q emis. At the atomic lines the partially integrated emission is increased and most of random numbers will select the wavelength around 132 Å for O. Figure 2 shows a flow chart of DSMC and p-pmc coupling procedure. First, DSMC calculations are performed without radiation energies. Then, the DSMC particle information (e.g. position and F num ) and cell information (e.g. temperatures and number densities) in DSMC are transferred to the p-pmc method. In this work, instead of using the particle energies, cell-averaged temperatures and number densities are used in p-pmc. As shown in Fig. 3, the 2-D axisymmetric DSMC particle information is converted to the 3-D wedge to be used in the p-pmc method. Different radial weight functions can be used between DSMC and 4 of 22

5 p-pmc. If F num is different between DSMC and p-pmc in the cell, p-pmc particles are generated, and the location of the generated PMC particles are based on the following equations, x = x (i + Rn), r = r j 2 + (2j + 1)Rn, (5) where i (i=,n x 1) and j (j=,n y 1) are the cell index in x and r directions, and Rn is a random number. Radiative energy change per particle due to the emission and absorption is calculated by the p-pmc method. The radiative energy change in each cell is equally assigned into each DSMC particle and redistributed into the flow field translational and internal energy modes following the fraction of the number of degrees of freedom of the mode to the total number of degrees of freedom. A new flow field is calculated and the effect of radiation is considered in DSMC adding q par per particle every time step. (6) III. Numerical Flow Modeling Technique in DSMC In the flow modeling, 11 species (N, O, N +, O +, N 2, O 2, NO, N + 2, O+ 2, NO+, and e ) are considered for the Stardust blunt body. Figure 4 shows the Stardust blunt body geometry that is studied in this work. The free stream parameters at 68.9 and 81 km altitudes are listed in Table 1. The DSMC method is implemented in the Statistical Modeling In Low-density Environment (SMILE) 19 computational tool. In this work, a singletime step average ion velocity model 2 was used to model charged species in DSMC. The computational time step is the one associated with molecular collisions rather than with the electron collision frequency. For this model, the electron movement depends on the average velocity of ions per cell, and this model was found to maintain charge neutrality assumption. 4 Also, compared to the quasi-neutrality model of Bird, 21 this model is computationally more efficient. In this work, average ion velocities are calculated per cell and this is used for electron movement in the average ion velocity model. At the same time, the physical electron velocity (or energy) is stored per simulated electron. This is used for collision frequency, energy exchange, and chemical reaction rates between electrons and heavy particles. In DSMC, the majorant frequency scheme is employed for modeling the molecular collision frequency, 22 and the VHS model was used for modeling the interaction between particles. 23 Note that collisions are modeled between electrons and neutrals and ions, but not between electrons and electrons in DSMC. The viscosity index of the electron species was set to.1 if not specified. The Borgnakke-Larsen (BL) 24 model with temperature-dependent rotational and vibrational relaxation numbers was used for modeling rotation-translation (R-T) and vibration-translation (V-T) energy transfer between neutral species, and 51 chemical reactions including 5 ionization processes are considered 12, 25 for the full set of calculations. The Millikan and White (MW) 26 form of the relaxation time are used for V-T rates, and Parker s rates 27 for the R-T rates. For high temperature, it is known that the vibration-rotation coupling is so important that both vibrational and rotational collision numbers become a similar constant number. However, without any corrections, as temperature increases (e.g. T > 2, K), the MW vibrational collision number becomes smaller than rotational collision number. Thus, in this work, a constant correction term of σ v = 1. Å 2 is used for V-T collision numbers to be consistent with the 28, 29 rotational collision numbers. 3, 31 In addition, electron-vibration (e-v) relaxation is modeled using the Lee s relaxation time for N2. From his solution he found that the maximum value of the rate coefficient for each vibrational state lies around 16, K, 3 and that the minimum relaxation time lies around 7, K, due to the strong shape resonance effect. More accurate parameters for VHS model were obtained for e +N, e +N 2, e +O, e +O 2, and e +NO collisions (see the reference of Ozawa 4 ). The TCE model 32 was used for chemical reactions for both charged and neutral species. The electric force was not included because charge neutrality was assumed. The gas-surface interaction was modeled using the Maxwell model with total energy and momentum accommodation. A surface wall temperature changes between 5 and 2,8 K (see Ref. 7 ). The full charge recombination is assumed at the wall. The time step, cell size, computational domain, and total number of simulated molecules were investigated to obtain results that are independent of these DSMC numerical parameters. At 68.9 and 81 km, approximately 3.1 and 2.7 million particles were simulated in the computational domain, respectively. The total numbers of collision(macroparameter) cells were 15,(1,) and 9,(6,), respectively. The total number of time steps was about 1, with a time step of and s for 68.9 and 81 km altitudes, 5 of 22

6 respectively. Macroparameter sampling was started after a time step that is sufficient to reach the steady state. Table 1. Free stream parameters Parameter 68.9 km 81 km Temperature, K Number density, molec/m Speed, km/s O 2 mole fraction, % N 2 mole fraction, % K n, (L =.23 m) IV. Results and Discussion Since this is the first application of the p-pmc method for a shock high gradient, rarefied gas condition, several test cases were used to validate the p-pmc numerical parameters and the accuracy of random number databases. Two test cases, a 1% atomic oxygen gas of uniform flow field and 1% O with 5 km/s speed shock, were performed with the DSMC and p-pmc methods. In addition, the atomic nitrogen and oxygen radiation from Stardust reentry flow fields at 68.9 and 81 km were calculated in the DSMC and p-pmc method. For the 5 km/s, 1% O test case and 81 km Stardust flow fields, tangent-slab, 1D disk flow fields were created using the flow field information along the stagnation in order to compare with the tangentslab NEQAIR results. The p-pmc emission and absorption results are compared with NEQAIR along the stagnation line for each case. The NEQAIR code was also modified to calculate E emis, E abs, and q for each cell as a tangent-slab approximation solution. In NEQAIR, the spectral intensity, I λ is calculated by I λ (i) = B λ (i) + [I λ (i 1) B λ (i)] exp( κ λ x/ cos θ), (7) where i denotes a cell index and κ λ is an absorption coefficient. The vehicle surface is assumed to be a blackbody radiation, on I λ () = B λ. Using the I λ value, q R (i) in W/cm 2 is obtained by q R (i) = (I λ (i) I λ (i 1))dλ cos θ sin θdθdφ = π φ θ λ π/2 λ (I λ (i) I λ (i 1))dλ sin 2θdθ. (8) Using Simpson s rule, the radiative energy transfer equation is integrated with respect to θ from to π/2 in two directions, x= to free stream and back to the body. The energy change in a cell is calculated by Then, the absorption energy is calculated by q(i) = q R(i). (9) x E abs (i) = E emis (i) q(i) (1) Note that the absorption and q energies may not be accurate if the flow field is in thermally nonequilibrium because the Planck function that is used in Eq. 7 may not be accurate in nonequilibrium conditions. In the p-pmc method, E emis,p, E abs,p, and q p can be calculated per particle in unit of W. In order to compare with NEQAIR, the particle energies are averaged in each cell by the following equation, N c E cell [W/cm 3 ] = E p,k [W]/F num n a /N c, (11) k=1 where n a is the number density of the atomic species in the cell, and N c is the number of particles in the cell. 6 of 22

7 A. Ray Energy Investigation In the p-pmc method, a cone ray model with the point particle model is used. The absorption energy removed from a ray by particle absorption is evaluated as, E abs,p = E ray [ 1 exp( τ) ], (12) where τ is the contribution of a specific particle to the optical thickness. In the p-pmc calculations, τ is calculated as W 2D (r/r c ) τ = σ abs,λ F num πrc 2, (13) where R c is the local cone radius of the ray, r is a radius between the cone center to a particle, σ abs,λ is the absorption cross section, and W 2D is a spatial weighting function. 15 σ abs,λ is calculated as σ abs,λ = κ λ n a. (14) In this work, a Gaussian weight function is used. Using the random number database, a wavelength is chosen for a ray, and σ abs in each cell is calculated by the line-by-line database. The total optical thickness τ is τ. Figures 5 and 6 show comparisons of ray s energy as a function of the traveling distance between F num = and F num = 1 1 1, respectively. In the comparison, the absorption coefficient, κ, is fixed as 1 m 1, and the number density is set to m 3. In the figures, 1 sampled rays are shown for each case, and compared with the theoretical results. It is shown that for the case of F num = , the deviation from the theoretical optical thickness is larger than the case of F num = If the deviation is high, some rays can escape from the high emission region without being absorbed by particles, and this may results in lower absorption prediction. As the number of particles increases (i.e. a simulated particle represents less number of particles), τ represented by a simulated particle decreases. More particles result in more intersections for each ray, and the increase of number of intersections per ray reduces the deviation. Therefore, it is important to have sufficient number of intersections per ray especially in high gradient region. B. Atomic Oxygen for a Free Stream Velocity of 5 km/s Case First, we performed the p-pmc method for 1 % atomic oxygen, uniform flow field. The number density is m 3, the DOI is set to 1 %, and the temperature is 1, K. The wall temperature is set to 1, K, and a black surface is assumed. The p-pmc calculations were performed for both gray and non-gray cases. For the gray case, the absorption coefficient κ is set to 1. cm 1. For the non-gray case, λ is selected using the random number database, and κ λ is calculated by the NEQAIR-based database. Good agreement of E emis and E abs was obtained between p-pmc and theoretical solution for both gray and non-gray cases. Second, 1 % atomic oxygen is used with a free stream speed of 5 km/s. The free stream number density is m 3 and the temperature is 217 K, which corresponds to the condition at 81 km altitude. Chemical reactions are not included. The DOI is assumed to be 1 % in the radiation calculations. The Stardust geometric configuration is used (see Fig. 4). Figure 7 presents the distribution of translational temperature and O number density along the stagnation line for the Stardust blunt body for free stream velocity of 5 km/s. In the shock, the maximum temperature is approximately 1, K, and the number density is more than one order of magnitude higher than the value of free stream. Using the stagnation line flow field in Fig. 7, a tangent-slab, 1D disk flow field was created and the p- PMC calculations were tested for O radiation. Good agreement was obtained between p-pmc and NEQAIR tangent-slab results in terms of emission and absorption energies. The p-pmc calculations were also performed using the 2D axisymmetric DSMC flow field. Figures 8 and 9 show comparisons of emission and absorption energies of O, respectively, between p-pmc and NEQAIR along the stagnation line for the 5km/s, 2D axisymmetric flow field. The maximum emission energy is approximately.5 W/cm 3 in the shock. Since the flow field is approximately the same in the stagnation region, the p-pmc results are averaged over the cells between y = and 1 cm to reduce the statistical noise. The cone angle of 2 degree is used in the calculations, and a F num is changed between and Since the ratio of shock thickness to the stardust blunt body radius is approximately 1/4, in the stagnation region, similar results to the tangent-slab case were obtained. Therefore, good agreement is obtained between the p-pmc and tangent-slab NEQAIR results along the stagnation line, and as the number of particle increases, the statistical noise is more reduced and the shock gradient is captured better. 7 of 22

8 C. Stardust flow field at 68.9 and 81 km without Radiation The DSMC calculations have been performed for the Stardust reentry flow field at 68.9 and 81 km altitude. Eleven species (N, O, N +, O +, N 2, O 2, NO, N + 2, O+ 2, NO+, and e ) including 5 ionization processes are modeled and we discuss the effect of radiation for the Stardust blunt body at 68.9 and 81 km. The free stream speed is 11.9 and 12.4 km/s at 68.9 and 81 km altitude. From our previous work, 4 N, O, N + 2, and NO were found to be strongly radiating molecules. In this work, we calculate radiation of atomic species, N and O, by the p-pmc method. Figures 1 and 11 show a contour of the electron number density and electron temperature for the Stardust blunt body at two altitudes, respectively. It may be seen that the shock standoff distance increases as the altitude becomes higher. The maximum total number density and electron number density are observed at the shoulder of the Stardust body. At 81 km, the maximum electron temperature is also observed at the shoulder of the body, and thus, the maximum emission may be off the stagnation point. Note that in the modeling of the flow around the blunt body shape of the Aeroassist Flight Experiment, 33, 34 a similar feature was observed. The discussion of the reason why a peak in the degree of ionization and thermal excitation occurs off the stagnation point can be found in Ref. 4. The majority of the gas particles pass through a strong shock wave, and flow around the body without being cooled by collisions with the surface. Since they travel a greater distance through the shock layer than those particles that flow along the stagnation streamline, they experience a greater number of collisions that result in thermal excitation and chemical reactions. Due to the nonequilibrium nature of the flow, the peak number of reactions can occur, not on the stagnation streamline, but on the shoulder of the body at 81 km. At 68.9 km, the flow is more continuumlike, and there is a sufficient number of collisions that results in thermal excitation and ionization reactions in the stagnation region. The maximum degree of freedom is approximately 7 % and 3 % at 68.9 and 81 km, respectively. The maximum electron temperature is about 2, K and 16, K at 68.9 and 81 km, respectively. Figure 12 shows distributions of total, ion, and electron number densities along the stagnation line for the Stardust blunt body at 68.9 and 81 km altitudes. As shown in the figure, the density gradient at 68.9 km is much higher than the one at 81 km. The maximum degree of freedom is approximately 7 % and 3 % along the stagnation line at 68.9 and 81 km, respectively. Both ions and electrons are produced within x=-.3 m at both altitudes, and the charge neutrality implementation scheme is validated to hold in the shock region. Figure 13 shows distributions of N, O, N +, O +, NO, and N + 2 number densities along the stagnation line for the Stardust blunt body at 68.9 and 81 km altitudes. It is shown that at 68.9 km, due to the high dissiciation rates, atomic neutrals and ions are dominant in the shock. In Fig. 14, distributions of translational, rotational, vibrational, and electron temperatures along the stagnation line are shown. Although the maximum translational temperature is as high as 6, K, other temperatures are lower than 2, K. The maximum electron temperature is as high as 2, K at 68.9 km and 16, K at 81 km in the stagnation region. At 68.9 km, the overshoot phenomenon can be seen between x=-.3 and -.2 m, and the difference between translational and other temperatures is less than 1, K between x=-.2 and m. The flow at 81 km is thermally high degree of nonequilibrium, and therefore, nonequilibrium effect needs to be considered. Using the DSMC Stardust flow field, the NEQAIR/new database 18 calculations were performed to calculate for N, O, N + 2, N 2, O 2, and NO species. Figure 15 presents distributions of N, O, N + 2, N 2, O 2, and NO emission energies along the stagnation line for the Stardust blunt body at 68.9 and 81 km altitudes. It is shown that molecular radiation is more than two orders of magnitude lower than N radiation inside the shock. NO radiation cannot be seen in the figure because the the emission energy is too low. Far from the body, the magnitude of radiation between atoms and molecules is approximately the same, but the magnitude is too low to impact the flow field. Therefore, in this work, we focus on the atomic N and O radiation calculations. D. Atomic Oxygen Radiation at 81 km First, atomic oxygen radiation was calculated by the p-pmc method and compared with NEQAIR. Atomic oxygen was used as a test species because the number of lines are about half of N. For the first time, the p-pmc method is applied for the high gradient, rarefied gas conditions. Thus, using the stagnation line flow field information at 81 km, a tangent-slab, 1D disk Stardust flow field was created to validate the p- PMC calculations by comparing with the tangent-slab NEQAIR results. Figure 16 shows comparisons of O 8 of 22

9 emission and absorption energies between p-pmc and NEQAIR for the tangent-slab, 1D disk Stardust flow field at 81 km along the stagnation line. For this high gradient and various number density and temperature case, the interpolated emission using the database was found to agree well with the NEQAIR results. It is also shown that with regard to the O absorption, good agreement is obtained between p-pmc and NEQAIR for the tangent-slab, 1D disk case. Secondly, the p-pmc calculations were performed for the 2D axisymmetric Stardust flow field at 81 km. Figure 17 shows comparisons of O emission and absorption energies between p-pmc and NEQAIR along the stagnation line. In the comparison, the p-pmc results is averaged over cells between y= and 1 cm. The shock is much thinner than the 5 km/s test case, and thus, as expected, the p-pmc results show good agreement with the NEQAIR tangent-slab solution in the stagnation region. E. N and O Radiation at 68.9 and 81 km In this subsection, the p-pmc method were performed for gas mixture cases. Atomic N and O radiation energies were calculated by the p-pmc method using the 2D axisymmetric Stardust flow field at 68.9 and 81 km. The difference between translational and electron temperatures is higher than 4, K in the shock at 81 km, and thus, the high nonequilibrium effects are important for both altitudes. At 81 km, F num = , and a radial weight function is used with y = 2 cm. The cone angle is set to 2 degree. Figure 18 shows comparisons of the N and O emission energies between p-pmc and NEQAIR for the Stardust flow field at 81 km along the stagnation line. The p-pmc results are averaged over cells between y = and 1 cm in the figure. The NEQAIR calculations were performed for each species, separately. It is shown that good agreement is obtained for both N and O emission energies between p-pmc and NEQAIR. The maximum of N emission is approximately one order of magnitude is higher than O emission because of the higher concentration of N and N+ than O and O+ in the shock. In Fig. 19, comparisons of the absorption energies between p-pmc and NEQAIR are shown, and the p-pmc results agreed well with NEQAIR for each species. It is also found that correlations between N and O are not significant because the important atomic lines for each species do not overlap each other. At 68.9 km, comparisons of the N and O emission and absorption energies between p-pmc and NEQAIR for the 2D axisymmetric Stardust flow field along the stagnation line are shown in Fig. 2 and 21, respectively. At 68.9 km, F num = , and a radial weight function is used with y = 2.5 cm. The cone angle is set to 2 degree. Since the p-pmc results are averaged over several cells in the r-direction between and 1 cm, the p-pmc results are slightly different from the NEQAIR. Finally, in Figs. 22 and 23, contours of the N emission energy in W/cm 3 calculated by p-pmc are shown for the Stardust blunt body at 68.9 km and 81 km altitudes, respectively. It is found that although the radiation peak is in the stagnation region at 68.9 km, the radiation peak is on the shoulder of the body at 81 km. The maximum emission energy is approximately 85, and 4, W/cm 3 at 68.9 and 81 km altitudes, respectively. F. Stardust Flow Field at 68.9 km with Atomic Radiation The p-pmc results of q (=E emis E abs ) was considered in the DSMC calculations at two altitudes, and the effect of energy change due to atomic radiation was investigated. q c in each cell is assigned into DSMC particles equally as q par = q cv c. (15) N c F num,c If the DSMC flow field changes, N c also changes. Thus, N c is averaged over 1 time steps, and q par in each cell in W is updated every 1 time steps. The energy change q par t is added to each DSMC particle in the cell every time step. In this work, q of N and O are assigned into all the energy modes of all the species in DSMC. In this model, we assumed that the energy exchange rates between electronic energies of N and O and translational and internal energies of other species in the cell via collisions are so high that the electronic energy change is redistributed into all the particles simultaneously during a time step. q par is assigned into each energy modes following the fraction of the number of degrees of freedom of the mode to the total number of degrees of freedom. At 81 km altitude, since the intensity of radiation energy is not high, it was found that the radiation did not impact the overall flow field. However, this energy change due to radiation is more important for lower altitude, and calculations were performed at 68.9 km altitude. Figure 24 shows a comparison of contour plots of electron temperature between cases of first iteration with q (top) and second iteration with q (bottom) 9 of 22

10 for the Stardust blunt body at 68.9 km altitudes. Comparing with Fig. 11, the high electron temperature region became smaller and moved slightly in the upstream direction with radiation because near the body radiation energy loss resulted in lowering temperatures. The second iteration result shows a slightly smaller high electron temperature region than the first iteration case. Figure 25 shows comparisons of distributions of the translational, rotational, and vibrational temperatures, and electron temperature among cases, (1) without radiation, (2) first iteration with q, and (3) second iteration with q, for the Stardust blunt body at 68.9 km altitudes along the stagnation line. For the first iteration, it is shown that for both models, the temperatures are decreased between x = and -.15 m near the body due to radiation energy loss. The translational temperature is decreased by 3, - 5, K and rotational, vibrational, and electron temperatures are decreased by approximately 1, - 3, K. For the second iteration, the emission peak is slightly shifted toward upstream around x =.13 m, and the emission energy is decreased near the body. In the high emission region around x =.13 m, the temperatures are decreased, but regions around x =.2 m and near the body, temperatures are increased due to absorption. The radiation energy also slightly affected the chemistry in the flow field. As shown in Fig. 26, N and O number densities are slightly higher than the case without radiation, and the gradient of concentration is slightly lower near the body for the first iteration. Due to the decrease of temperatures between x = and -.15 m, the pressure is lower in this region and this resulted in the diffusion of particles toward upstream. It was also found that the O + number density was slightly increased inside the shock with radiation due to the increase of the O number density. On the other hand, the N + 2 number density was decreased slightly near x =.13 m because the lower translational temperature became the lower ionization rate for N+N e +N + 2. In contrast, for the second iteration, the temperature increase near the body resulted in higher pressure and lower number densities. Similar to the first iteration, the O + number density was slightly increased inside the shock with radiation due to the increase of the O number density, but decreased near the body. The N + 2 number density was decreased slightly near x =.13 m because of the lower ionization rate for N+N e +N + 2, but near the body, it was slightly increased. The convective heat flux on the wall was calculated and compared between cases with and without radiation. The convective heat flux on the stagnation point was approximately W/m 2 without radiation. With radiation for the first iteration, it was approximately W/m 2. The lower temperature and lower gradient near the body resulted in lower convective heat flux on the wall. The inclusion of radiation affected the convective heat flux by approximately 2 %. On the contrary, for the second iteration, the convective heat flux is increased by approximately 2 % compared to the case without radiation because of the higher temperature and the higher gradient near the wall. The radiative heat flux calculated by the p-pmc method was also approximately 2 % compared to the convective heat flux at this altitude. V. Conclusions The Stardust reentry flows were simulated at 68.9 and 81 km altitudes. Atomic radiation energies were calculated by the p-pmc method, and we succeeded to loosely couple the DSMC method with the p-pmc method. Eleven species including 5 ionization processes are modeled in DSMC, and electron impact ionization processes produce atomic ions near the body. The average ion velocity model was used for electron movement, and the DOI is predicted to be 7 and 3 % along the stagnation line at 68.9 and 81 km, respectively. While the translational temperature is as high as 6, K, the maximum electron temperature is approximately 2, K at 68.9 km. To capture this high nonequilibrium effect, the NEQAIR-based emission cross section databases for N and O were generated, and N and O radiation was calculated by the p-pmc method. The molecular radiation was not considered in this work because the contribution of molecules to radiation is less than.1 %. It was found that the N emission is approximately one order of magnitude higher than the O emission along the stagnation line. Along the stagnation line, the p-pmc results agreed well with the tangent-slab NEQAIR results because the shock is so thin that the shock curvature may not influence the stagnation region. In the p-pmc method, the maximum radiation energy was found to be on the shoulder of the body at 81 km where the electron temperature is the maximum. However, the maximum radiation energy was found to be in the stagnation region at 68.9 km. The energy change due to radiation in p-pmc was taken into account in the DSMC calculations. It was found that at 81 km altitude, the atomic radiation does not have impact on the flow field significantly. At 68.9 km, the coupling the p-pmc atomic radiation with DSMC resulted in lower temperatures inside the shock, but the temperatures are slightly increased in 1 of 22

11 the regions around x =.2 m and near the body due to absorption. At this altitude, the radiative heat flux in the stagnation region on the surface was calculated by the p-pmc method and it is approximately 2 % of convective heat flux. The consideration of radiation resulted in higher gradient of both temperatures and concentration near the body, and the convective heat flux was increased by approximately 2 % in the stagnation region compared to the case without radiation. Acknowledgments The research performed at the Pennsylvania State University was supported by the NASA through the grant No. NNX7AC47A. I would like to acknowledge Prof. M. Ivanov of the Institute of Theoretical and Applied Mechanics, Russia for the use of the original SMILE code. References 1 Olynick, D., Chen, Y.-K., and Tauber, M. E., Aerothermodynamics of the Stardust Sample Return Capsule, Journal of Spacecraft and Rockets, Vol. 36, No. 3, 1999, pp Park, C., Calculations of Stagnation-Point Heating Rates Associated with Stardust Vehicle, AIAA paper 25-19, Jan Johnson, E. J., Starkey, R. P., and Lewis, M. J., Aerodynamic Stability of Reentry Heat Shield Shapes for a Crew Exploration Vehicle, Journal of Spacecraft and Rockets, Vol. 43, No. 4, 26, pp Ozawa, T., Levin, D. A., and Wysong, I. J., Chemical Reaction Modeling for Hypervelocity Collisions between O and HCl, Physics of Fluids, Vol. 19, No. 5, 27, Ozawa, T., Nompelis, I., Levin, D. A., Barnhardt, M., and Candler, G. V., DSMC-CFD Comparison of a High Altitude, Extreme-Mach Number Reentry Flow, AIAA paper , Jan Zhong, J., Ozawa, T., and Levin, D. A., Modeling of Hypersonic Wake Flows of Slender and Blunt Bodies, AIAA paper , Jan Zhong, J., Ozawa, T., and Levin, D. A., Modeling of Stardust Reentry Reacting Thermal and Chemical Ablation Flow, AIAA paper , June Ozawa, T., Improved Chemistry Models for DSMC Simulations of Ionized Rarefied Hypersonic Flows, Ph.D. thesis, The Pennsylvania State University, Gallis, M. A. and Harvey, J. K., Nonequilibrium Thermal Radiation from Air Shock Layers Modeled with Direct Simulation Monte Carlo, Journal of Thermophysics and Heat Transfer, Vol. 8, No. 4, 1994, pp Gallis, M. A. and Harvey, J. K., Atomic Species Radiation from Air Modeled with Direct Simulation Monte Carlo Method, Journal of Thermophysics and Heat Transfer, Vol. 9, No. 3, 1995, pp Wang, A., Investigation of Turbulence-Radiation Interactions in Turbulent Flames Using a Hybrid Finite Volume/Monte Carlo Approach, Ph.D. thesis, The Pennsylvania State University, Park, C., Nonequilibrium Hypersonic Aerothermodynamics, John Wiley & Sons, Inc., New York, Wang, A., Modest, M. F., Haworth, D. C., and Wang, L., Monte Carlo Simulation of Radiative Heat Transfer and Turbulence Interactions in Methane/Air Jet Flames, Journal of Quantitative Spectroscopy and Radiative Transfer, Aug Wang, A. and Modest, M. F., An Adaptive Emission Model for Monte Carlo Simulations in Highly Inhomogeneous Media Represented by Stochastic Particle Fields, Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 14, No. 2, 27, pp Wang, A. and Modest, M. F., Investigation of Radiative Transfer by Photon Monte Carlo Methods in Discrete Particle Fields, ASME Journal of Heat Transfer, Vol. 128, No. 1, 26, pp Wang, A. and Modest, M. F., Spectral Monte Carlo Methods for Nongray Analyses of Radiative Heat Transfer in Inhomogeneous Participating Media, International Journal of Heat and Mass Transfer, Vol. 5, No. 19-2, 27, pp Park, C., Nonequilibrium Air Radiation (NEQAIR) Program: Users Manual, Ames research center, NASA, Sohn, I., A., L. D., and Modest, M., Improved Radiation Calculations For Hypersonic Reentry Flows Using Efficient Databasing Schemes, CHT-8-282, Marrakech, Morocco, May Ivanov, M. S., Markelov, G. N., and Gimelshein, S. F., Statistical Simulation of Reactive Rarefied Flows: Numerical Approach and Applications, AIAA paper , June Boyd, I. D., Monte Carlo Simulation of Nonequilibrium Flow in a Low-Power Hydrogen Arcjet, Physics of Fluids, Vol. 9, No. 1, 1997, pp Bird, G. A., Direct Simulation of Typical AOTV Entry Flows, AIAA paper , June Ivanov, M. S. and Rogasinsky, S. V., Analysis of the Numerical Techniques of the Direct Simulation Monte Carlo Method in the Rarefied Gas Dynamics, Soviet Journal of Numerical Analysis and Mathematical Modeling, Vol. 3, No. 6, 1988, pp Bird, G. A., Monte-Carlo Simulation in an Engineering Context, Rarefied Gas Dynamics, edited by S. Fisher, Vol. 74, AIAA, New York, 1981, pp Borgnakke, C. and Larsen, P. S., Statistical Collision Model for Monte Carlo Simulation of Polyatomic Gas Mixture, Journal of Computational Physics, Vol. 18, No. 4, 1975, pp Bird, G. A., Nonequilibrium Radiation During Re-Entry at 1 km/s, AIAA paper , June of 22

12 26 Millikan, R. C. and White, D. R., Systematics of Vibrational Relaxation, Journal of Chemical Physics, Vol. 39, No. 12, 1963, pp Parker, J. G., Rotational and Vibrational Relaxation in Diatomic Gases, Physics of Fluids, Vol. 2, No. 4, 1959, pp Park, C., Problems of Rate Chemistry in the Flight Regimes of Aeroassisted Orbital Transfer Vehicles, Thermal Design of Aeroasisted Orbital Transfer Vehicles, edited by H. F. Nelson, Vol. 96, AIAA, New York, 1985, pp Park, C., Assessment of Two-Temperature Kinetic Model for Ionizing Air, Journal of Thermophysics and Heat Transfer, Vol. 3, No. 3, 1989, pp Lee, J. H., Electron-Impact Vibrational Excitation Rates in the Flowfield of Aeroassisted Orbital Transfer Vehicles, Thermophysical Aspects of Reentry Flows, edited by J. N. Moss and C. D. Scott, Vol. 13, AIAA, New York, 1986, pp Lee, J. H., Electron-Impact Vibrational Relaxation in High-Temperature Nitrogen, Journal of Thermophysics and Heat Transfer, Vol. 7, No. 3, Sept. 1993, pp Bird, G. A., Simulation of Multi-Dimensional and Chemically Reacting Flows, Rarefied Gas Dynamics, edited by R. Campargue, AIAA, Paris, 1979, pp Candler, G. and Park, C., The Computation of Radiation from Nonequilibrium Hypersonic Flows, AIAA paper , NASA Ames Research Center, June Candler, G. V., The Computation of Weakly Ionized Hypersonic Flows in Thermo-Chemical Nonequilibrium, Ph.D. thesis, Stanford University, of 22

13 1-12 Partially integrated emission [W/sr] DATABASE PPMC (bb only) PPMC (bb+bf) Wavelength, Å Figure 1. Partially integrated emission as a function of wavelength for O. Figure 3. Conversion from 2-D DSMC particle information to the 3-D wedge in the p-pmc method. Figure 2. coupling. A flow chart of DSMC and p-pmc Free Stream R =.2 m 6 6 S.19 m.46 m R =.23 m.557 m Figure 4. Stardust Geometric Configuration. 13 of 22