During an atmospheric reentry, the heat shield protecting the body will undergo very high temperature (> 2000 K) and pressure (> 100 bars) on its surface. This is why thermal protection systems (TPS) are used, especially composed of 3D carbon/carbon composites. Numerous phenomena will occur on the surface, in particular heterogeneous chemical reactions between the carbon and the surrounding air (oxidation, nitruration) and, at higher temperatures, sublimation; these reactions will cause the recession of the surface of the composite heat shield.

All along the reentry phase, the flow around the body will evolve, with in each regime characteristic surface roughness features caused by the ablation of the composite material. The laminar flow is associated with a microscopic roughness dimension, due to the flow-material interaction. Then the weaving of the material will favour the transition to turbulence on located spots on the surface, and will give birth to macroscopic patterns with a centimetre scale. The flow will finally become fully turbulent, with the development of a new type of patterns of a millimetre scale, no more localised this time but generalised to the whole surface. These characteristic patterns are known as ”scallops”.

The stability of these morphological features is studied, considering the coupled viscous boundary-layer equations, the convection-diffusion of an oxidant, the Hamilton-Jacobi equation for the surface recession and the heterogeneous reaction on the surface. A model leading to the amplification of a surface perturbation is given, involving the surface roughness and the pressure gradient within the flow. A linear stability analysis is carried out to determine the unstable regimes. The parameters upon which the stability depend are the Reynolds number (inertial/viscous effects), Damköhler number (reaction/diffusion), Schmidt number (viscous/diffusion) and surface roughness.

A numerical approach is also carried out, in order to retrieve the results of the theoretical work. A strong coupling between the turbulent flow and the surface recession is performed using the open-source toolbox OpenFoam. The simulation is incompressible, and because the matter here is the interaction between the turbulence and the surface recession, the simulation only one oxidizing species taken into account, without thermal effects. A Reynolds-Averaged Navier-Stokes (RANS) method is considered, with the two-equation turbulence model k − ω SST. The flow is solved with a finite-volume scheme, and the evolution of the surface with a level-set method. To perform an efficient coupling between these two phenomena occurring at very different time scales, the PIMPLE algorithm is considered allowing Courant numbers much greater than 1.