Reconstruction of aerothermal heating for the thermal protection system of a reusable launch vehicle
Rafał Brociek, Edyta� Hetmaniok, Damian Słota
Abstract
The aim of this paper is to reconstruct the aerothermal heating profile for a three-layered thermal protection system of a reusable launch vehicle (RLV). Computational methods enable the simulation of such systems and contribute to understanding of their function, which is essential for safety. The mathematical model considered in this paper uses a one-dimensional heat conduction equation. The reconstructed heat flux on the outer surface is time-dependent. The implicit scheme of the finite difference method and the Levenberg–Marquardt methods are used to solve the direct and inverse problems, respectively. The developed algorithm is first tested on a benchmark example with a known analytical solution. Next, the algorithm is used for reconstructing the aerothermal heating profile for the thermal protection system of a RLV from known temperature values at a selected point of its thermal protection system. Input data for the inverse problem are obtained by solving the direct problem for the atmospheric entry heating profile on the surface of the RLV as measured by the NASA Langley Research Center. For the inverse problem of the main example, the aerothermal heat flux is reconstructed in the form of first- or third-order splines for various numbers of interpolating points. The model and algorithm produced a very good match between the reconstructed heat flux and the measured one. The best match is obtained for third-order splines and twenty interpolation nodes.