The accurate modeling of hypersonic environments, including coupled ablation, is a challenging problem due to the complex flow physics, numerical accuracy, and robustness required for these simulations. The simulation mesh needs to be designed carefully, and structured high-aspect ratio stretched grids are typically used to properly capture the high wall-normal gradients. The mesh generation process proves to be a cumbersome and time-consuming process for realistic and complex vehicles, creating a severe bottleneck to the current CFD workflow. This work highlights the development of the Cartesian Higher-Order Adaptive Multi-Physics Solver (CHAMPS) near-body Cartesian grid solver, capable of automatic volume mesh generation, and its accurate and robust use in simulating coupled ablation for steady-state graphite ablation by interfacing with the Kentucky Aerothermodynamics and Thermal Response System Material Response (KATS-MR) solver. Validation on a Mach 8.7 cylinder and a Mach 22.88 axisymmetric Mars 2020 capsule showcases the challenges associated with shock-capturing on non-shock-aligned Cartesian grids. A verification study of the CHAMPS–KATS coupled ablation framework is performed for steady-state graphite ablation on a Mach 25.2, 9 deg blunt cone, followed by the validation of the solver for a blunt cone in the NASA Ames Interaction Heating Facility arcjet.

References

[1] Slotnick J., Khodadoust A., Alonso J., Darmofal D., Gropp W., Lurie E. and Mavriplis D., “CFD Vision 2030 Study: A Path to Revolutionary Computational Aerosciences,” NASA CR 2014-218178, Washington, D.C., March 2014. Google Scholar
[2] Meakin R. L., Wissink A. M., Chan W. M., Pandya S. A. and Sitaraman J., “On Strand Grids for Complex Flows,” 18th AIAA Computational Fluid Dynamics Conference, AIAA Paper 2007-3834, 2007. https://doi.org/10.2514/6.2007-3834 Link Google Scholar
[3] McQuaid J. A. and Brehm C., “Heat Flux Predictions for Hypersonic Flows with an Overset Near Body Solver on an Adaptive Block-Structured Cartesian Off-Body Grid,” Computers and Fluids, Vol. 269, 2023, Paper 106121. https://doi.org/10.1016/j.compfluid.2023.106121 Google Scholar
[4] Brahmachary S., Natarajan G., Kulkarni V. and Sahoo N., A Sharp-Interface Immersed Boundary Method for High-Speed Compressible Flows, Springer, Berlin, 2020, pp. 251–275 Chap. 9. https://doi.org/10.1007/978-981-15-3940-4_9 Crossref Google Scholar
[5] Arslanbekov R., Kolobov V. and Frolova A., “Analysis of Compressible Viscous Flow Solvers with Adaptive Cartesian Mesh,” 20th AIAA Computational Fluid Dynamics Conference, AIAA Paper 2011-3381, 2011. https://doi.org/10.2514/6.2011-3381 Link Google Scholar
[6] Sekhar S. K. and Ruffin S. M., “Predictions of Convective Heat Transfer Using a Cartesian Grid Solver for Hypersonic Flows,” Fluid Dynamics and Co-Located Conferences, AIAA Paper 2013-2645, 2013. https://doi.org/10.2514/6.2013-2645 Google Scholar
[7] McQuaid J. A., Zibitsker L. A., Martin A. and Brehm C., “An Immersed Boundary Method for Hypersonic Viscous Flows,” AIAA Science and Technology Forum and Exposition Forum, Virtual Event, AIAA Paper 2021-0926, 2021. https://doi.org/10.2514/6.2021-0926 Google Scholar
[8] Baskaya A. O., Capriati M. C., Ninni D., Bonelli F., Pascazio G., Turchi A., Magin T. and Hickel S., “Assessment of Immersed Boundary Methods for Hypersonic Flows with Gas-Surface Interactions,” Computers and Fluids, Vol. 270, 2024, pp. 1–15. https://doi.org/10.1016/j.compfluid.2023.106134 Google Scholar
[9] van Noordt W., Ganju S. and Brehm C., “An Immersed Boundary Method for Wall-Modeled Large-Eddy Simulation of Turbulent High-Mach-Number Flows,” Journal of Computational Physics, Vol. 470, 2022, pp. 1–30. https://doi.org/10.1016/j.jcp.2022.111583 Google Scholar
[10] Baskaya A., Dungan S. D., Hickel S. and Brehm C., “Fluid Ablation Interactions on a Compression Ramp at Mach 8,” AIAA Science and Technology Forum and Exposition, AIAA Paper 2024-0501, 2024.https://doi.org/10.2514/6.2024-0501 Google Scholar
[11] Dungan S. D., McQuaid J. A., Zibitsker A. L., Martin A. and Brehm C., “Numerical Investigation of Fluid-Ablation Interactions for a Mach 5.3 Transitional Boundary Layer Flow over a 13 Degree Cone,” AIAA Paper 2023-0476, 2023. https://doi.org/10.2514/6.2023-0476 Link Google Scholar
[12] Wissink A. M., Katz A. J., Chan W. M. and Meakin R. L., “Validation of the Strand Grid Approach,” 19th AIAA Computational Fluid Dynamics Conference, AIAA Paper 2009-3792, 2020. https://doi.org/10.2514/6.2009-3792 Google Scholar
[13] Wissink A. M., Sitaraman J., Katz A. J. and Roget B., “Application of 3D Strand Mesh Technology to Rotorcraft Hover,” 53rd AIAA Aerospace Sciences Meeting, AIAA Paper 2015-0044, 2015. https://doi.org/10.2514/6.2015-0044 Link Google Scholar
[14] Weng H. and Martin A., “Multi-Dimensional Modeling of Pyrolysis Gas Transport Inside Charring Ablative Materials,” Journal of Thermophysics and Heat Transfer, Vol. 28, No. 4, 2014, pp. 583–597. https://doi.org/10.2514/1.T4434 Google Scholar
[15] Weng H. and Martin A., “Numerical Investigation of Pyrolysis Gas Blowing Pattern and Thermal Response Using Orthotropic Charring Ablative Material,” 11th AIAA/ASME Joint Thermophysics and Heat Transfer Conference, AIAA Paper 2014-2121, 2014. https://doi.org/10.2514/6.2014-2121 Link Google Scholar
[16] Weng H. and Martin A., “Numerical Investigation of Geometric Effects of Stardust Return Capsule Heat Shield,” 53rd AIAA Aerospace Sciences Meeting, AIAA Paper 2015-0211, 2015. https://doi.org/10.2514/6.2015-0211 Link Google Scholar
[17] Weng H., Bailey S. C. C. and Martin A., “Numerical Study of iso-Q Sample Geometric Effects on Charring Ablative Materials,” International Journal of Heat and Mass Transfer, Vol. 80, 2015, pp. 570–596. https://doi.org/10.1016/j.ijheatmasstransfer.2014.09.040 Crossref Google Scholar
[18] Park C., “Assessment of Two-Temperature Kinetic Model for Ionizing Air,” Journal of Thermophysics and Heat Transfer, Vol. 3, No. 3, 1989, pp. 233–244. https://doi.org/10.2514/3.28771 Link Google Scholar
[19] Blottner F. G., Johnson M. and Ellis M., “Chemically Reacting Viscous Flow Program for Multi-Component Gas Mixtures,” Sandia Labs., Albuquerque, NM, Jan. 1971. Google Scholar
[20] Wilke C., “A Viscosity Equation for Gas Mixtures,” Journal of Chemical Physics, Vol. 18, No. 4, 1950, pp. 517–519. https://doi.org/10.1063/1.1747673 Crossref Google Scholar
[21] Sozer E., Brehm C. and Kiris C. C., “Gradient Calculation Methods on Arbitrary Polyhedral Unstructured Meshes for Cell-Centered CFD Solvers,” AIAA Science and Technology Forum and Exposition, AIAA Paper 2014-1440, 2014. https://doi.org/10.2514/6.2014.1440 Google Scholar
[22] Work D., Tong O., Workman R., Katz A. and Wissink A. M., “Strand-Grid-Solution Procedures for Sharp Corners,” AIAA Journal, Vol. 52, No. 7, 2014, pp. 1528–1541. https://doi.org/10.2514/1.J052607 Link Google Scholar
[23] Zihao Z., “HAMSTRAN, An Indirect Method to Create All-Quadrilateral Grids for the HAMSTR Flow Solver,” Univ. of Maryland, College Park, MD, 2017. Google Scholar
[24] Lakshminarayan V. K., Sitaraman J. and Roget B., “Development and Validation of a Multi-Strand Solver for Complex Aerodynamic Flows,” Computers and Fluids, Vol. 147, 2017, pp. 41–62. https://doi.org/10.1016/j.compfluid.2017.02.002 Crossref Google Scholar
[25] Secco N. R., Kenway G. K. W., He P., Mader C. A. and Martins J. R. R. A., “Efficient Mesh Generation and Deformation for Aerodynamic Shape Optimization,” AIAA Journal, Vol. 59, No. 4, 2021, pp. 1151–1168. https://doi.org/10.2514/1.J059491 Link Google Scholar
[26] Brehm C., Barad M. and Kiris C. C., “Development of Immersed Boundary Computational Aeroacoustic Prediction Capabilities for Open-Rotor Noise,” Journal of Computational Physics, Vol. 388, 2019, pp. 690–716. https://doi.org/10.1016/j.jcp.2019.02.011 Crossref Google Scholar
[27] Brehm C., Hader C. and Fasel H. F., “A Locally Stablilized Immersed Boundary Method for the Compressible Navier-Stokes Equations,” Journal of Computational Physics, Vol. 295, 2015, pp. 475–504. https://doi.org/10.1016/j.jcp.2015.04.023 Crossref Google Scholar
[28] Brehm C. and Fasel H., “A Novel Concept for the Design of Immersed Interface Methods,” Journal of Computational Physics, Vol. 242, 2013, pp. 234–267. https://doi.org/10.1016/j.jcp.2013.01.027 Crossref Google Scholar
[29] Brehm C., Barad M. F., Housman J. A. and Kiris C. C., “A Comparison of Higher-Order Finite-Difference Shock Capturing Schemes,” Computers & Fluids, Vol. 122, 2015, pp. 184–208. https://doi.org/10.1016/j.compfluid.2015.08.023 Crossref Google Scholar
[30] Jiang G.-S. and Shu C.-W., “Efficient Implementation of Weighted ENO Schemes,” Journal of Computational Physics, Vol. 126, 1996, pp. 202–228. https://doi.org/10.1006/jcph.1996.0130 Crossref Google Scholar
[31] Liu X.-D., Osher S. and Chan T., “Weighted Essentially Non-Oscillatory Schemes,” Journal of Computational Physics, Vol. 115, No. 1, 1994, pp. 200–212. https://doi.org/10.1006/jcph.1994.1187 Crossref Google Scholar
[32] Ducros F., Ferrand V., Nicoud F., Weber C., Darracq D., Gacherieu C. and Poinsot T., “Large-Eddy Simulation of the Shock/Turbulence Interaction,” Journal of Computational Physics, Vol. 152, No. 2, 1999, pp. 517–549. https://doi.org/10.1006/jcph.1999.6238 Crossref Google Scholar
[33] Wright M. J., Candler G. V. and Bose D., “Data-Parallel Line Relaxation Method for the Navier-Stokes Equations,” AIAA Journal, Vol. 36, No. 9, 1998, pp. 1603–1609. https://doi.org/10.2514/2.586 Link Google Scholar
[34] Zibitsker A. L., McQuaid J. A., Stern E. C., Palmer G. E., Libben B., Brehm C. and Martin A., “Finite-Rate and Equilibrium Study of Graphite Ablation under Arc-Jet Conditions,” Computers and Fluids, Vol. 267, 2023, Paper 106069. https://doi.org/10.1016/j.compfluid.2023.106069 Crossref Google Scholar
[35] Prata K. S., Schwartzentruber T. E. and Minton T. K., “Air-Carbon Ablation Model for Hypersonic Flight from Molecular-Beam Data,” AIAA Journal, Vol. 60, No. 2, 2022, pp. 627–640. https://doi.org/10.2514/1.J060516 Link Google Scholar
[36] Park C., “Effects of Atomic Oxygen on Graphite Ablation,” AIAA Journal, Vol. 14, No. 11, 1976, pp. 1640–1642. https://doi.org/10.2514/3.7267 Link Google Scholar
[37] Murray V. J., Recio P., Caracciolo A., Miossec C., Balucani N., Casavecchia P. and Minton T. K., “Oxidation and Nitridation of Vitreous Carbon at High Temperatures,” Carbon, Vol. 167, 2020, pp. 388–402. https://doi.org/10.1016/j.carbon.2020.05.076 Crossref Google Scholar
[38] Baker R., “Graphite Sublimation Chemistry Nonequilibrium Effects,” AIAA Journal, Vol. 15, No. 10, 1977, pp. 1391–1397. https://doi.org/10.2514/3.60806 Link Google Scholar
[39] Keenan J. A. and Candler G. V., “Simulation of Graphite Sublimation and Oxidation under Re-Entry Conditions,” 6th AIAA/ASME Joint Thermophysics and Heat Transfer Conference, AIAA Paper 1994-2083, 1994. https://doi.org/10.2514/6.1994-2083 Link Google Scholar
[40] Taylor R., “Thermal Diffusivity of Poco Graphite and Stainless Steel SRM 735-S,” Thermal Conductivity, Vol. 17, 1983, pp. 753–762. Crossref Google Scholar
[41] Karl S., Schramm J. M. and Hannemann K., “High Enthalpy Cylinder Flow in HEG: A Basis for CFD Validation,” 33rd AIAA Fluid Dynamics Conference and Exhibit, AIAA Paper 2003-4252, 2003, pp. 1–8. https://doi.org/10.2514/6.2003-4252 Link Google Scholar
[42] Nastac G., Walden A., Nielsen E. and Frendi A., “Implicit Thermochemical Nonequilibrium Flow Simulations on Unstructured Grids Using GPUs,” AIAA Science and Technology Forum and Exposition, Virtual Event, AIAA Paper 2021-0159, 2021. https://doi.org/10.2514/6.2021-0159 Google Scholar
[43] Knight D., Longo J., Drikakis D., Gaitonde D., Lani A., Nompelis I., Reimann B. and Walpot L., “Assessment of CFD Capability for Prediction of Hypersonic Shock Interactions,” Progress in Aerospace Sciences, Vols. 48–49, 2012, pp. 8–26. https://doi.org/10.1016/j.paerosci.2011.10.001 Crossref Google Scholar
[44] Nompelis I., Candler G. V., MacLean M., Wadhams T. P. and Holden M. S., “Numerical Investigation of Double-Cone Flow Experiments with High-Enthalpy Effects,” 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, AIAA Paper 2010-1283, 2010. https://doi.org/10.2514/6.2010-1283 Link Google Scholar
[45] Gupta R. N., Yos J. M., Thompson R. A. and Lee K.-P., “A Review of Reaction Rates and Thermodynamic and Transport Properties for an 11-Species Air Model for Chemical and Thermal Nonequilibrium Calculations to 30,000 K,” NASA TR-RP-12, Aug. 1990. Google Scholar
[46] Park C., “On Convergence of Computation of Chemically Reacting Flows,” 23rd Aerospace Sciences Meeting, AIAA Paper 1985-247, 1985. https://doi.org/10.2514/6.1985-247 Google Scholar
[47] Schoenenberger M., Van Norman J., Karlgaard C., Kutty P. and Way D., “Assessment of the Reconstructed Aerodynamics of the Mars Science Laboratory Entry Vehicle,” Journal of Spacecraft and Rockets, Vol. 51, No. 4, 2014, pp. 1076–1093. https://doi.org/10.2514/1.A32794 Link Google Scholar
[48] Wise A. J., Prabhu D. K., Saunders D. A., Johnston C. O. and Edquist K. T., “Computational Aerothermodynamic Environments for the Mars 2020 Entry Capsule,” AIAA Aviation Forum, AIAA Paper 2018-3116, 2018. https://doi.org/10.2514/6.2018-3116 Google Scholar
[49] Keenan J. A., Thermo-Chemical Ablation of Heat-Shields under Earth Re-Entry Conditions, Ph.D. Thesis, North Carolina State Univ., Raleigh, NC, 1994. Google Scholar
[50] Chen Y.-K., Milos F., Reda D. and Stewart D., “Graphite Ablation and Thermal Response Simulation Under Arc-Jet Flow Conditions,” 36th AIAA Thermophysics Conference, AIAA Paper 2003-4042, 2003. https://doi.org/10.2514/6.2003-4042 Link Google Scholar
[51] Chen Y.-K. and Milos F. S., “Navier-Stokes Solutions with Finite Rate Ablation for Planetary Mission Earth Reentries,” Journal of Spacecraft and Rockets, Vol. 42, No. 6, 2005, pp. 961–970. https://doi.org/10.2514/1.12248 Link Google Scholar
[52] Zibitsker A. L., McQuaid J. A., Brehm C. and Martin A., “Validation and Analysis of a Coupled Fluid-Ablation Framework for Modeling Low-Temperature Ablator,” International Journal of Heat and Mass Transfer, Vol. 218, 2024, Paper 124728. https://doi.org/10.1016/j.ijheatmasstransfer.2023.124728 Crossref Google Scholar
[53] Park C., Jaffe R. L. and Partridge H., “Chemical-Kinetic Parameters of Hyperbolic Earth Entry,” Journal of Thermophysics and Heat Transfer, Vol. 15, No. 1, 2001, pp. 76–90. https://doi.org/10.2514/2.6582 Link Google Scholar
[54] Park C., Howe J. T. and Jaffe R. L., “Chemical-Kinetic Problems of Future NASA Missions,” 29th Aerospace Sciences Meeting, 1991, pp. 1–33. https://doi.org/10.2514/6.1991-464 Google Scholar
[55] Mitcheltree R. A. and Gnoffo P. A., “Wake Flow About a MESUR Mars Entry Vehicle,” 6th AIAA/ASME Joint Thermophysics and Heat Transfer Conference, AIAA Paper 1994-1958, 1994. https://doi.org/10.2514/6.1994-1958 Link Google Scholar
[56] Johnston C. O., Brandis A. M. and Sutton K., “Shock Layer Radiation Modeling and Uncertainty for Mars Entry,” 43rd AIAA Thermophysics Conference, AIAA Paper 2012-2866, 2012. https://doi.org/10.2514/6.2012-2866 Link Google Scholar
[57] Beck W. H. and Mackie J. C., “Formation and Dissociation of $C_{2}$ from High Temperature Pyrolysis of Acetylene,” Journal of Chemical Society, Faraday Transactions I: Physical Chemistry in Condensed Phases, Vol. 71, No. 0, 1975, Paper 1363. https://doi.org/10.1039/F19757101363 Google Scholar
[58] Mozzhukhin E., Burmeister M. and Roth P., “High Temperature Dissociation of Cyanogen Radical,” Berichte Bunsengesellschaft für Physikalische Chemie, Vol. 93, No. 1, 1989, pp. 70–75. Google Scholar
[59] Bose D. and Candler G. V., “Thermal Rate Constants of the $O_{2} + N \to NO + O$ Reaction Based on the A2’ and A4’ Potential-Energy Surfaces,” Journal of Chemical Physics, Vol. 107, No. 16, 1997, pp. 6136–6145. https://doi.org/10.1063/1.475132 Google Scholar
[60] Fujita K., Yamada T. and Ishii N., “Impacts of Ablation Gas Kinetics on Hyperbolic Earth Entry Radiative Heating,” 44th AIAA Aerospace Sciences Meeting and Exhibit, AIAA Paper 2006-1185, 2006. https://doi.org/10.2514/6.2006-1185 Link Google Scholar
[61] Park C., Howe J. T. and Jaffe R. L., “Review of Chemical-Kinetic Problems of Future NASA Missions, II: Mars Entries,” Journal of Thermophysics and Heat Transfer, Vol. 8, No. 1, 1994, pp. 9–23. https://doi.org/10.2514/3.496 Link Google Scholar
[62] Ibragimova L. B., “Recommended Rate Constants of CO + O2—Reversible—CO2 + O Reactions,” Khimicheskaya Fizika, Vol. 10, 1991, pp. 307–310. Google Scholar
[63] Park C. S., Studies of Radiation Emission from the Simulated Shock Layer of the Huygens Probe, Ph.D. Thesis, Stanford Univ., Stanford, CA, 1991. Google Scholar
[64] Tunder R., Mayer S., Cook E. and Schieler L., “A Compilation of Reaction Rate Data for Nonequilibrium Performance and Reentry Calculation Programs,” Aerodynamics and Propulsion Research Labs. SSD-TR-67-45, Jan. 1967. Google Scholar
[65] Bortner M. H., “A Review of Rate Constants of Reactions in Re-Entry Flow Fields,” TIS TR R68SD13, General Electric Co., Boston, June 1968. Google Scholar
[66] Mortensen C., Effects of Thermochemical Nonequilibrium on Hypersonic Boundary-Layer Instability in the Presence of Surface Ablation or Isolated Two-Dimensional Roughness, Ph.D. Thesis, Univ. of California, Los Angeles, CA, 2015. Google Scholar

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The authors would like to recognize and show appreciation for the financial support provided by NASA Kentucky EPSCoR RA Award No. 80NSSC19M0144 with E. Stern as the technical monitor, NASA EPSCoR R3 Award No. 80NSSC19M0084 with M. Barnhardt as the technical monitor, and from the NASA ACCESS program Award No. 80NSSC21K1117. The authors would also like to thank the collaborators from NASA Ames Research Center, NASA Langley Research Center, and the NASA Johnson Space Center. The funding support provided by the DoD HPC Modernization Program under contract FA700-19-2-0002 with Dr. Russ Cummings (Director of Hypersonic Vehicle Simulation Institute (HVSI)) as program manager is also gratefully acknowledged. Computational time was provided by the University of Kentucky on the Lipscomb Compute Cluster (LCC) HPC system for the completion of this work. The authors would also like to thank Mateus Braga and Dr. Robyn Macdonald from the University of Colorado Boulder for providing results on the Mars 2020 capsule with US3D as an additional validation test case in this work. The authors would also like to thank Mateus Braga and Dr. Robyn Macdonald from the University of Colorado Boulder for providing results on the Mars2020 capsule with US3D as an additional validation test case in this work.

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Received26 July 2024
Accepted19 February 2025
Published online19 April 2025

Development of an Overset Near-Body Cartesian Solver for Graphite Ablation Simulations

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