Numerical investigation and correlations for heat diffusion through planar ablative thermal protection systems

• Published in: Thermal science and engineering progress Vol. 7; pp. 279 - 287
• Main Authors: Kannan, Srinivasa Ramanujam, Katte, Subrahmanya S.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.09.2018
• ISSN: 2451-9049; 2451-9049
• DOI: 10.1016/j.tsep.2018.07.008

•Heat diffusion through a planar ablative Thermal Protection System is considered.•Landau type coordinate transformation is used to immobilize moving boundary.•Onset time of ablation is captured using an adjustable time step scheme.•Correlations are developed to predict ablated material thickness. In the present study, heat diffusion through a planar ablative Thermal Protection System (TPS) is numerically investigated by modeling the problem as one-dimensional transient heat conduction equation in Cartesian coordinates subject to the adiabatic back wall and aerodynamic heating on the other surface. The surface exposed to aerodynamic heating undergoes sensible heating until the surface temperature reaches an ablative temperature of the material. Further exposure of the material to heat flux results in material getting ablated. Ablation is modeled as Stefan-type wherein layers of material are immediately removed upon melt after reaching ablative temperature. Boundary immobilization method is used to fix the moving boundary and the governing equations are solved using finite difference scheme in space and Crank-Nicolson semi-implicit scheme in time, after expressing them in non-dimensional form. A FORTRAN code is developed to solve the set of equations using Tri-Diagonal Matrix Algorithm (TDMA). Parametric studies are conducted and new correlations are developed for predicting the amount of material ablated as a function of non-dimensional heat flux, Stefan number and non-dimensional time. Correlations are also developed to predict the non-dimensional time when back-wall that protects the vehicle interiors from extreme heat flux environment attains non-dimensional temperature 0.1. Results show that the developed correlations predict the parameter very well and errors are within acceptable limits.