When a spacecraft plunges back through the atmosphere, its heat shield does not simply sit and take the punishment. It burns away on purpose, sacrificing itself layer by layer in a process called ablation. For engineers designing thermal protection systems from lightweight porous carbon materials, predicting exactly how that burning surface recedes, roughens and reshapes itself has long been one of the hardest problems in aerospace simulation. A new study published in the journal Advances in Aerodynamics reports a hybrid micro-continuum scale modeling approach that tackles this problem in full three dimensions, reproducing experimentally observed ablation patterns and revealing why the recession of a porous carbon surface does not proceed at a steady pace.
The research, led by Jinyue Zhang, Jin Zhao, Guice Yao and Dongsheng Wen, focuses on carbon fibrous preform porous media, the skeletal architecture inside carbon/carbon composites. These materials are prized for atmospheric re-entry vehicles and rocket engine nozzles because they combine low density, high strength, a low thermal expansion coefficient and chemical stability at elevated temperatures. Under operational conditions they face high temperatures, high pressures and high-velocity gas flows, and their surface ablation acts as a self-protective mechanism: controlled consumption of the material shields the critical components behind it.
What makes porous materials so difficult to model is that ablation does not happen uniformly. Oxygen in the hot boundary layer reacts with carbon at the gas-solid interface, and as the surface recedes, diffusion channels open up that expose fibers and matrix to the flow. Because the microstructure of modern composites is increasingly complex, with varying fiber volume fractions and orientations, the recession pattern depends on pore-scale geometry. Prior experimental work has shown this vividly: ablation tests of carbon/carbon composites under propane flames in high-speed flows revealed two distinct fiber morphologies depending on fiber orientation, with fibers perpendicular to the flow ablating progressively from the surface toward the axis until they take on a needle-like shape. Other experiments found fiber thinning and pitting that alter porosity, permeability and surface roughness in competing ways.
Numerical approaches have chased this problem for years. Earlier tools solved coupled fluid transport and surface recession equations, and lattice Boltzmann methods became a mainstream route for pore-scale ablation evolution thanks to their high parallel efficiency, simple grid handling and convenient interface tracking. But the authors note limitations: some existing methods demand considerable computational resources and highly refined meshes, while lattice Boltzmann approaches do not always provide clear physical quantities that can be compared directly with experimental data. The new work builds on the micro-continuum approach of Soulaine and colleagues, re-developing the dbsFoam solver on the open-source OpenFOAM platform to strongly couple porous flow, heat transfer and heterogeneous chemical reactions with the energy equation in three dimensions.
The method deliberately simplifies the chemistry. The current framework incorporates only the dominant carbon monoxide-producing reaction pathway, in which solid carbon reacts with half a molecule of oxygen to produce CO, releasing about 110 kilojoules per mole. Processes such as oxygen dissociation, secondary reactions like CO oxidation, and multi-species effects under high-enthalpy conditions are neglected for now, with the authors citing prior demonstrations that CO is the dominant gaseous product when oxygen impinges on graphene sheets. More complex surface chemistry is planned for future versions of the model.
On the physics side, the model solves a Darcy-Brinkman-Stokes momentum equation throughout the computational domain, which behaves like the Navier-Stokes equation in pure gas regions and reduces to Darcy’s law in regions where gas and solid coexist and drag dominates. Porosity and permeability are updated at every time step as the heterogeneous reaction consumes the solid. Volume-averaged convection-diffusion equations track reactant and product species, fiber reactivity to molecular oxygen follows an Arrhenius-type temperature dependence, and an energy equation with a reaction heat source captures the exothermic nature of the oxidation. The simulated material is a three-dimensional carbon fibrous preform with randomly distributed fibers of 11 micrometer diameter, maximum fiber length of 100 micrometers and an initial porosity of 0.85, generated in the Abaqus environment.
Validation came in stages. A grid independence study compared eight mesh configurations ranging from 112,000 to nearly 21 million cells, and a grid of about 10.2 million cells was selected to balance accuracy and efficiency. The simulated ablation recession rate was then compared against the Lachaud model and the team’s own previously developed two-dimensional model, with the three-dimensional results showing better agreement with the Lachaud model while additionally resolving the morphological evolution of individual fibers. A comparison of average inlet temperature variation against experimental results from Panerai and colleagues supported the reliability of the temperature predictions.
The headline numerical result concerns the pace of recession. In the production simulations, the computational domain was initialized at a uniform 3000 kelvin, with high-temperature gas inflowing at 0.001 meters per second and an oxygen concentration of 2.713 moles per cubic meter. After 20 seconds of simulated reaction, less than 30 percent of the original solid volume remained. The ablation recession rate initially increased and then declined, reaching a maximum of 13.05 micrometers per second before falling gradually to 8.35 micrometers per second. The explanation lies in a competition of rates: under the high-temperature flow condition, the chemical reaction rate far exceeds the mass-transfer rate supplied by convection and diffusion, so incoming oxygen is consumed almost immediately at the flow-porous media interface. This fast consumption creates a low-oxygen-supply condition at the gas-solid interface, and the recession becomes constrained by what the authors call a diffusion limit.
The thermal fields tell a complementary story. Because the oxidation is exothermic, the temperature inside the porous medium rises as solid material is consumed, with a maximum temperature rise of 21.7 kelvin after 20 seconds. Temperature rise slopes were steepest near the initial gas-solid interface and the upstream region, where the reaction predominantly occurs, while downstream regions and the backface relied on slow heat conduction, with the backface warming by only about 5.5 kelvin. As solid reactants were consumed upstream, the exothermic effect there weakened, and over time the temperature distribution along the centerline became increasingly uniform, with the peak temperature position gradually migrating downstream.
Perhaps the most striking visual validation is morphological. The simulation reproduced the needle-like fiber shapes observed experimentally by Fan and colleagues, capturing the differential recession of the heterogeneous surface that generates surface roughness. The mechanism matches theory: the highest temperature occurs at the turning point between a fiber’s transverse section and its surface, driving ablation from the fiber surface toward its axis until the needle shape emerges. The flow fields also evolved in physically sensible ways, with preferential high-speed channels forming early through regions of locally elevated permeability, inlet pressure declining steadily as ablation reduced flow resistance, and the velocity field becoming increasingly uniform as the solid volume fraction dropped. The authors position the approach as a predictive tool for thermal protection system design, offering pore-scale insight into ablation behavior while acknowledging that its simplified single-reaction chemistry will need enrichment with oxygen dissociation, secondary reactions and multi-species effects to serve high-enthalpy flight conditions more fully.
Subject of Research: Three-dimensional pore-scale simulation of oxidation ablation and surface recession in porous carbon fibrous thermal protection materials
Article Title: Solving three-dimensional moving ablation interfaces between gas flow and porous thermal protection materials using a hybrid micro-continuum scale approach
Article References: Zhang, J., Zhao, J., Yao, G., & Wen, D. (2026). Solving three-dimensional moving ablation interfaces between gas flow and porous thermal protection materials using a hybrid micro-continuum scale approach. Advances in Aerodynamics, 8(1), Article 16. https://doi.org/10.1186/s42774-026-00257-4
Image Credits: AI Generated
DOI: 10.1186/s42774-026-00257-4
Keywords: ablation, thermal protection systems, carbon/carbon composites, porous media, micro-continuum modeling, OpenFOAM, oxidation, pore-scale simulation, aerodynamic heating, surface recession, lattice Boltzmann, heat transfer
News Source: Denise Maddox. (October 29, 2026). New 3D Simulation Tracks Moving Ablation Interfaces in Porous Heat Shields. Scienmag.
