Speaker
Description
Background of the study
During atmospheric entry, the interaction of the dissociated, thermochemically non-equilibrium boundary-layer gas with the vehicle surface strongly influences the wall composition, the surface heat flux, and both the convective and radiative heating experienced by the thermal protection system (TPS). Surface catalycity governs the recombination of atomic species such as $N$ and $O$ and, in the fully catalytic limit, can increase the wall heat flux several-fold relative to a non-catalytic surface. Historically, computational tools have treated gas–surface interaction (GSI) with two largely disjoint families of models: phenomenological catalytic-wall models based on specified reaction efficiencies (the $\gamma$ model, or specified-reaction-efficiency1, SRE, models), and detailed finite-rate surface chemistry (FRSC) models that resolve adsorption, desorption, Eley–Rideal and Langmuir–Hinshelwood steps, sublimation and ablation. In many production solvers these families are implemented independently, and even inconsistently across different wall boundary conditions (isothermal, adiabatic, radiative-equilibrium), leading to duplicated logic, divergent physics between wall types, and no clean pathway from a simple catalytic wall to a fully finite-rate mechanism. The present work removes this artificial separation by developing a single, general boundary-condition model that treats catalytic recombination and finite-rate surface chemistry as limiting cases of one unified formulation, implemented in the CFD++ solver [1].
Methodology
Both model families are recast within a common surface mass balance (SMB) framework following Marschall and MacLean [2,3]. At the gas–solid interface the wall composition is obtained by balancing the diffusive and convective species fluxes against the net surface chemical production:
\begin{equation}
\mathbf{J}_i\cdot\mathbf{n} + \rho v\, y_i = \dot{w}_i, \qquad \rho v = \sum_i \dot{w}_i = \dot{m} \tag{1}
\end{equation}
where $\mathbf{J}_i$ is the (corrected Fickian) diffusion flux, $y_i$ the wall mass fraction, $v$ the blowing velocity set by the net mass rate $\dot{m}$, and $\dot{w}_i$ the surface source term. Adsorbed (surface-phase) species are closed by their own coverage balance together with a site-conservation constraint, while bulk-phase species account for ablation and deposition. The gas mass fractions (or partial densities), surface coverages, and blowing velocity are solved simultaneously with a fully coupled Newton method using analytically derived Jacobians.
The unification relies on expressing every GSI process as a reaction contributing to the species chemistry source term $\dot{w}_i$. The FRSC model involves reactions using the mass-action law, whereas the catalytic reactions based on the SRE model use a rate model based on the first-order Knudsen–Langmuir flux, with an optional Motz–Wise correction. Because both reaction types contribute to $\dot{w}_i$ through the same net-stoichiometry operator, surface mechanisms of arbitrary complexity are handled by a single solver invoked identically from every wall boundary condition. The SRE model is thereby recovered as the macroscopic, steady-state limit of the finite-rate adsorption and recombination kinetics. A further contribution is a generalized evaluation of the backward-rate coefficients, in which the equilibrium constants are reconstructed by combining gas-phase thermodynamic properties with adsorption and sublimation rate data. This removes the need for the (generally unavailable) thermodynamic data of surface- and bulk-phase species and eliminates reaction-specific hard-coded expressions, so that arbitrary reaction types can be treated within the same framework. The formulation also supports partially ionized boundary layers: ion–wall recombination reactions of the form $X^+ + e^- \rightarrow X$ are solved together with the neutral surface chemistry, while the electron mass fraction is obtained from a charge quasi-neutrality condition rather than from a separate wall balance.
Results
The non-equilibrium reactive boundary-condition framework has been verified on a graphite sphere-cone model in a high-enthalpy (about $27$ MJ/kg) arc-jet air flow, reproducing the stagnation heat flux and pressure and the coupled surface response, with the predicted heating lying between the non-catalytic and fully catalytic limits. The unified catalytic capability is verified against the legacy SRE model walls: for homonuclear recombination ($2N \rightarrow N_2$, $2O \rightarrow O_2$) the SMB solver reproduces the reaction-limited Knudsen–Langmuir flux to Newton-solver tolerance, and the generalized backward-rate formulation recovers the same equilibrium as the original Zhluktov–Abe treatment [4] while extending it to arbitrary reaction types. Representative entry-relevant catalytic and multi-reaction cases will be presented to demonstrate the consistency and generality of the model across the different wall boundary-condition types and its impact on the predicted near-wall composition and surface heating.
Conclusion
A single generalized boundary-condition model has been developed that unifies phenomenological catalytic recombination and detailed finite-rate surface chemistry within one surface mass balance formulation, solved by a coupled Newton method with analytical Jacobians in CFD++. By expressing the SRE catalytic model as a limiting reaction type of the finite-rate framework, and by generalizing the backward-rate computation to avoid surface- and bulk-phase thermodynamic data, the model delivers consistent, extensible, and thermodynamically sound GSI predictions across all wall boundary conditions. The framework also broadens the catalytic modeling capability already available in CFD++: whereas the earlier catalytic wall was designed around a predefined set of recombination reactions, the unified formulation allows surface mechanisms to be specified freely, and it further improves the consistency of the species-diffusion treatment at the wall. This unified surface treatment enables the accurate prediction of near-wall composition and surface heating in non-equilibrium entry environments, and provides a modular basis for incorporating new catalytic and ablative mechanisms. The framework has furthermore been designed with future coupling to a material-response code in mind.
References
[1] Lopez, B., "Finite-Rate Surface Chemistry Modeling for High-Temperature Gas–Surface Interactions in CFD++," AIAA SciTech Forum, 2026.
[2] Marschall, J., and MacLean, M., "Finite-Rate Surface Chemistry Model, I: Formulation and Reaction System Examples," AIAA Paper 2011-3783, 42nd AIAA Thermophysics Conference, Honolulu, HI, 2011.
[3] MacLean, M., Marschall, J., and Driver, D. M., "Finite-Rate Surface Chemistry Model, II: Coupling to Viscous Navier–Stokes Code," AIAA Paper 2011-3784, 42nd AIAA Thermophysics Conference, Honolulu, HI, 2011.
[4] Zhluktov, S. V., and Abe, T., "Viscous Shock-Layer Simulation of Airflow past Ablating Blunt Body with Carbon Surface," Journal of Thermophysics and Heat Transfer, Vol. 13, No. 1, 1999, pp. 50–59.
Summary
This work presents a general gas–surface interaction boundary condition for the CFD++ solver that unifies phenomenological catalytic recombination (SRE / $\gamma$ models) and detailed finite-rate surface chemistry within one surface-mass-balance formulation. Every surface process is expressed as a reaction feeding a common source term, and the resulting system is solved by a coupled Newton method with analytical Jacobians. A generalized backward-rate procedure removes the need for surface- and bulk-phase thermodynamic data, the SRE model is recovered as the steady-state limit of the finite-rate kinetics, and partially ionized boundary layers are handled through a charge quasi-neutrality closure. The framework is verified on a graphite arc-jet case and against legacy catalytic walls, broadens CFD++'s existing catalytic capability to arbitrary user-specified mechanisms with a more consistent species-diffusion treatment, and is designed to also provide an equilibrium reactive boundary condition for future coupling with a material-response code.