Fractal modeling and numerical simulation of ablative surfaces under non-uniform diffusion in carbon fiber materials

During atmospheric reentry, spacecrafts are subjected to intense aerodynamic heating, necessitating ablative thermal protection systems (TPS) as a primary safeguard. Although severe ablation typically occurs in continuum or near-continuum flow regimes, many advanced TPS materials under development feature carbon fiber-based porous microstructures. In such cases, gas diffusion can still be dominated by Knudsen diffusion, where the diffusion coefficient depends strongly on the pore diameter. Traditional models often neglect the non-uniformity of pore distribution within fiber preforms, leading to errors in ablation rate prediction. In this study, fractal theory is employed to characterize the mesoscale pore structure of random carbon fiber materials, and a fractal-based diffusion model is developed that accounts for the non-uniform distribution of pores. Analysis reveals that the pore distribution plays a critical role in accurate diffusion modeling. Assuming uniform pore distribution can severely overestimate the diffusion coefficient—by up to 1.8 times compared to the fractal model. Furthermore, the Weierstrass–Mandelbrot function is employed to reconstruct the rough ablation surface induced by non-uniform diffusion in a fractal manner, and an analytical expression for the surface area is derived. Based on the reconstructed surface, the ablation process of a reentry spacecraft with a rough wall is simulated using the direct simulation Monte Carlo (DSMC) method. This approach provides an efficient means of incorporating mesoscale roughness into DSMC simulations, avoiding the excessive computational cost associated with mesh refinement down to the roughness scale.