An inverse method for real-time estimation of aerothermal heating for thermal protection systems of space vehicles

Abstract

Space vehicles experience extremely high aerothermal heating during atmospheric entry which necessitates the use of appropriate thermal protection system (TPS). Effective design of TPS and the health monitoring systems (HMS) for space vehicles requires accurate flight data during atmospheric entry process. While direct measurement of the surface heat flux is a very challenging task, an alternative approach is to use the measured temperature values from the inner layers and solve the associated inverse heat conduction problem (IHCP) in order to estimate the surface heat flux. In the present paper, a solution approach is developed based on filter form of Tikhonov regularization method for near real-time calculation of surface heat flux in a one-dimensional medium consists of three layers that represents an integrated thermal protection system (ITPS). The solution is evaluated through numerical test cases developed in ANSYS and using experimental data from the literature. A parametric study is also conducted in order to understand the effect of sensor location (two layers and three layers models) as well as the effect of temperature dependent material properties on the performance of the solution. It is found that the developed solution estimates the surface heat flux with an average RMS error of about 1.96 and 3.44% for the two layer models with constant and temperature dependent material properties respectively. For the three layer model, the average RMS values are found for the constant and temperature dependent material properties as 2% and 4.44% respectively. It is also shown that the developed solution can evaluate the surface heat flux with 17 and 80 s delay for the two and three layers domain respectively, facilitating a near-real time operation for the inverse solution algorithm that can support the development of HMS for space vehicles or other industrial applications with the need for heat flux monitoring. The proposed solution technique is fast, accurate and very convenient to implement even for complex problems involving large temperature variations and temperature dependent material properties.