One of the most important aspects of space and planetary exploration is the ability to safely enter a planet's atmosphere, decelerate properly and land smoothly. Because entry vehicles travel long distances, they reach their destination with tremendous speed, which directly translates into a vast amount of kinetic energy. Although most of this energy dissipates into the surrounding atmosphere, a fraction still reaches the vehicle through convective heating and radiation. In order to protect the payload and ensure safe landing, it is critical to equip the vehicle with an appropriate Thermal Protection System (TPS).
The TPS of a entry vehicle is therefore one of the key components of its design. The material used for the TPS can be classified into two main categories: ablative materials, as in the one used on Apollo missions, and non-ablative materials, such as the ceramic tiles used on the space shuttle. The former can also be divided into two sub-categories: charring (also know as pyrolyzing) and non-charring ablators. The theory behind the use of ablators is quite simple; the energy absorbed by the removal of material from the surface is not used to heat the TPS, thus keeping the vehicle at a reasonably "cold" temperature. In the case of charring ablators, the ablative material is a resin that fills the pores of a carbon matrix. Although the matrix might ablate, it usually does not, thus preserving the original geometry of the aerodynamic surface during re-entry.
Modeling TPS is not a trivial task as it involves several physical phenomena in various scientific fields. First, the flow field needs to be modeled, which means solving an hypersonic flow with strong shocks, viscous effects, boundary layer effects, turbulence, radiation, thermo-chemical non-equilibrium, and much more. The surface must also be properly taken into account, as it involves surface chemical reactions, catalysis, ablation, recessing surfaces, surface roughness, etc. Finally, the TPS material must be modeled, which entails multi-layered material, multiphase flow, thermal stress, pressure stress, spallation, porous flow, chemical non-equilibrium, as well as other processes.