Designing the Thermal Protection System of an Apollo Type Vehicle under Uncertainty

A multi-disciplinary optimization under uncertainty (MDO-U) capability has been developed in order to solve optimization problems with multiple sets of objectives and constraints originating from different design disciplines while simultaneously accounting for uncertainty during the optimization process. Uncertainties are introduced in the optimization process by considering the constraints which depend on any random variables and any random parameters as probabilistic. Satisfying the probabilistic constraints in the presence of uncertainty introduces sufficient conservatism in the solution and eliminates the need for further application of safety factors. The MDO-U capability is applied for performing design optimization for the TPS of an Apollo type vehicle. The Traj and FIAT codes of NASA Ames are employed during this design process for trajectory and for thermal analyses, respectively. Five different types of TPS material are considered to be applied over different sections of the vehicle. The trajectory bank angle schedule and thicknesses of the five different TPS are adjusted within the MDO-U environment in order to reduce the overall weight of the TPS while satisfying the imposed constraints. Uncertainties are considered in the entry angle, the TPS densities, the heat transfer coefficient, and the thermal conductivity. The results from the MDO-U analysis are validated through comparison with Monte Carlo simulations. Finally, a comparison between the performance of the deterministic and the probabilistic optimum is made.