Radiative equilibrium boundary condition and correlation analysis on catalytic surfaces in DSMC

Abstract: This study integrates radiative equilibrium boundary conditions on a catalytic surface within the Direct Simulation Monte Carlo (DSMC) method. The radiative equilibrium boundary condition is based on the principle of energy conservation at each surface element, enabling the accurate capture of spatially varying surface temperatures and heat fluxes encountered during atmospheric re-entry. The surface catalycity is represented through the finite-rate surface chemistry (FRSC) model, specifically focusing on the heterogeneous recombination of atomic oxygen on silica surfaces. Both the FRSC model and the radiative equilibrium boundary conditions within the DSMC framework are validated through comparison to analytical solutions. Numerical simulations are conducted for rarefied hypersonic flow around a two-dimensional cylinder under representative re-entry conditions for both non-catalytic and catalytic surfaces. The results demonstrate significant discrepancies in computed surface properties between the radiative equilibrium and conventional isothermal boundary conditions. Furthermore, linear interpolation between results from two independent isothermal boundary conditions is shown to be inadequate for accurately predicting surface heat flux, particularly when surface reactions are considered. The observed discrepancies originate from a non-linear correlation between surface temperature and heat flux, influenced by factors such as surface catalycity and local geometric variations along the cylinder. These findings highlight the necessity of implementing radiative equilibrium boundary conditions within DSMC to ensure physically accurate aerothermodynamic computations.