Analytical modeling of the steady state ablation of a 3D C/C composite

Abstract

Following an analysis of surface roughness features that develop on a 3D C/C composite during ablation, i.e. wall recession by oxidation and/or sublimation, a modeling strategy is set up in order to predict the composite behavior from that of its components. It relies on two changes of scale: (i) microscopic scale (fiber, matrix) to mesoscopic scale (bundle) and (ii) mesoscopic scale (bundle, matrix) to macroscopic scale (composite). The physical basis is a general model for receding surfaces under a gasification process coupled to mass transfer. At each scale, the 3D surface equation is analytically solved in steady state considering a 1D mass transfer perpendicular to the overall surface. The models are validated by comparison to experimental data.

Analytical modeling of the transient ablation of a 3D C/C composite

“…In this case, fibers take ogival shapes rather than needle shapes [4], we have shown, as pictured in figure 2-b. When diffusion is fully limiting, then no surface roughness should be observed in theory, as represented in figure 2-c, but to our knowledge, no observation of flat ablated surfaces has been reported so far for C/C composites.…”

“…The mechanism leading to the typical pointed fiber shape has previously been modeled and explained [4,27,32]. In figure 2-a, we propose an illustration with a fiber embedded in a more reactive weak carbon phase.…”

“…heat shields of space vehicles, nozzles of rocket thrusters, aircraft and formula one brake disks, diverters of nuclear fusion reactors [4]. They are made of porous carbon fiber reinforcements densified with carbon matrix.…”

“…A rigorous mathematical derivation is provided in reference [4]. Another interesting fact is that the exact fiber shape slightly varies from one application to another.…”

“…We previously developed and validated a multiscale analytical model to predict the steady-state surface roughness and effective oxidation rate of a 3D C/C composite from the intrinsic reactivity of its components [4]. In this work, we extend the steady-state model to the transient regime (section 2), …”