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Description
Background of the study
When a vehicle travels through Earth’s atmosphere at hypersonic speeds, the temperature in the shock layer rises significantly. This causes air molecules to dissociate. For higher enthalpies flow regions may experience chemical nonequilibrium, ionization, and thermal nonequilibrium. In addition, transitions between bound-bound, and, for a partially ionized gas, bound-free and free-free states contribute toward thermal radiation. At sufficiently high enthalpies, e.g. for the FIRE II experiment, thermal radiation from the gas phase travelling toward the vehicle makes up a significant portion of the heat load on the vehicle surface. In [1], at the peak heating point of the FIRE II trajectory (1643s), 27% of the total heat flux on the wall was caused by radiation. Thermal radiation travelling outwards to a sensor becomes the radiation signature of the vehicle. This signature can be estimated from surface radiation of the vehicle. To improve this estimation, radiation from the gas phase leaving toward the sensor can be included.
The method of choice for this work to compute gas radiation is the photon Monte Carlo method [2]. A high-order variation of the method was developed by Wu et al. in 2006 [3]. In 2012 a version was presented by Feldick et al. which exploits 2-D axial symmetry to reduce computation time significantly [4]. Karl et al. integrated the method into the DLR TAU code and computed radiation for the FIRE II capsule in 2015 [1]. In 2019 an implementation of the photon Monte Carlo method called StaRad has been applied at the 8th iteration of this workshop to Martian reentry by Bonin et al. [5]. They also computed radiation for the FIRE II 1642s flight point and a generic triple cone configuration [6]. The method has also been integrated into the open-source DSMC software SPARTA to compute the radiation in the flow field of the Huygens probe by Oblapenko et al. in 2023 [7]. Recent work by Swenson et al. from 2024 implemented a voxelized version into DART where they validated the method using a 2-D cylinder [8].
In this work we focus on computing the radiation signature as seen by a sensor. 2-D axisymmetric CFD computations in thermo-chemical nonequilibrium for a generic hypersonic glide vehicle and the FIRE II capsule have already been performed.
Methodology
The first step in the radiation analysis is determining the emission and absorption coefficients. Given the species densities and temperatures from CFD, these spectral properties can be computed e.g. from the plasma radiation database PARADE [9]. The next step is solving the radiative transfer equation [2]. This equation describes propagation of directional radiation intensity in a medium along a line of sight. Unfortunately, solving for the radiative heat flux leads to an integrodifferential equation that is challenging to solve. 1-D approximate methods such as the infinite slab method have been developed.
More accurate and more computationally demanding are 3-D methods that transfer the problem into a set of PDEs. The method of spherical harmonics (P_N) approximates the radiative intensity in a certain direction with a generalized series. P_1 is a well-known version of this method. The P_N method suffers from low accuracy in optically thin media as they are encountered during the initial part of reentry. Another popular 3-D method is the method of discrete ordinates (S_N) which discretizes the range of solid angles with a fixed number N of directions and then solves the radiative transfer equation along each of those lines. Due to the discretization, it can produce unphysical geometrical radiation patterns in the solution.
The photon Monte Carlo method solves the radiative transfer equation by directly simulating it for a statistically large number of photon bundles. Hence, it will produce the exact solution in the limit of infinitely many bundles. This makes the method attractive for reentry applications. By discretizing radiation into photon bundles, radiative energy is not treated as a continuous quantity anymore. This allows high flexibility regarding the spatial and spectral resolution. Ray tracing of these photon bundles is computationally expensive but very suitable for parallel computing as all bundles are independent of each other. Due to statistical sampling, results from this method are noisy. The higher the number of simulated photon bundles, the lower the noise level.
Tallying the photon bundles that are emitted or absorbed by the vehicle wall then gives the radiative surface heat load. Similarly, the radiative heat flux in the gas phase is determined. These results can then be fed back to the CFD tool as a source term in the energy equation to achieve loose coupling.
To determine the radiation signature as seen from a sensor, running the photon Monte Carlo method in reverse is more efficient. A satellite-based sensor can be many kilometres away from the vehicle of interest and thus only a very small portion of the solid angle is of interest. Reverse means the calculation starts at the sensor. Absorbed photon bundles are traced backward to their point of origin. From that origin, the associated energy and wavelength can be determined. This ensures that only photon bundles of interest are simulated.
Results
CFD results are already generated for the 1648s and 1636s flight points of the FIRE II capsule, and also for a generic hypersonic glide vehicle. The CFD tool is the in-house code KEGNI (see e.g. [10] and [11]) which splits the flow field into an inviscid Euler region and a viscid boundary layer. KEGNI is a shock-fitting finite difference method which uses flux vector splitting to discretize spatially with a third-order upwind scheme. To reach a steady-state solution it integrates in artificial time with a second-order low-storage Runge Kutta algorithm.
Special emphasis is placed on the sensor-based radiation signature calculations. The reverse photon Monte Carlo method and gas radiation will be discussed.
References
[1] S. Karl, D. Potter, M. Lambert, K. Hannemann: Computational Analysis of Radiative Heat Loading on Hypervelocity Reentry Vehicles, Journal of Spacecraft and Rockets, vol. 52, No.1, 2015, https://doi.org/10.2514/1.A32791
[2] Modest, M. F., Radiative Heat Transfer, Academic Press, New York, 2003, pp. 295–569.
[3] Y. Wu, M. F. Modest, D.C. Haworth, A high-order photon Monte Carlo method for radiative transfer in direct numerical simulation, Journal of Computational Physics 223 (2007) pages 898-922, https://doi.org/10.1016/j.jcp.2006.10.014
[4] A. M. Feldick, M. F. Modest, A Spectrally Accurate Two-Dimensional Axisymmetric, Tightly Coupled Photon Monte Carlo Radiative Transfer Equation Solver for Hypersonic Entry Flows, Journal of Heat Transfer 134(12): 122701 (2012), https://doi.org/10.1115/1.4007069
[5] J. Bonin, Ch. Mundt: 3d Monte Carlo radiative transport computation for Martian atmospheric entry, 8th Int. workshop on Radiation of high temperature gases for space missions, Madrid, 2019.
[6] J. Bonin, Ch. Mundt: Full 3D Monte Carlo radiative transport for hypersonic entry vehicles, AIAA Journal of Spacecraft and Rockets, vol. 56, pp. 44-52, 2019, https://arc.aiaa.org/doi/10.2514/1.A34179
[7] G. Oblapenko, T. Ecker, S. Fechter, T. Horchler, S. Karl, Development of a photon Monte Carlo radiative heat transfer solver for CFD applications, Aerospace Europe Conference 2023 10th EUCASS - 9th CEAS 2023, DOI: 10.13009/EUCASS2023-423
[8] S. J. Swenson, B. M. Agrow, C. P. Turansky, The voxelized photon Monte Carlo method for hypersonic radiation modeling, Computers & Fluids, Vol. 271 106168 (2024), https://doi.org/10.1016/j.compfluid.2023.106168
[9] A. Smith, J. Beck, M. Fertig, H. Liebhart, and L. Marrafa: Plasma Radiation Database PARADE V3.1, ESA Contract Rept. TR28/96 No. 8, Fluid Gravity Engineering, Ltd., 6 June 2011.
[10] F. Monnoyer, Ch. Mundt, M. Pfitzner: Calculation of the hypersonic viscous flow past reentry vehicles with an Euler-boundary layer coupling method, AIAA-paper 90-417, 1990. https://arc.aiaa.org/doi/pdf/10.2514/6.1990-417
[11] Ch. Mundt: Calculation of hypersonic, viscous non-equilibrium flows around reentry bodies using a coupled Euler/boundary layer method, AIAA-paper 92-2856, 1992. https://arc.aiaa.org/doi/10.2514/6.1992-2856
Summary
A reverse photon Monte Carlo method is applied to hypersonic flow as experienced during Earth reentry to compute the radiation signature as seen from a sensor many kilometers away from the reentry object.
