Extending Inverse Heat Conduction Method to Estimate Flight Trajectory of a Reentry Capsule

Document Type : Research Article


1 Amirkabir University of Technology, 15875-4413 Tehran, Iran

2 صنعتی امیرکبیر*مهندسی هوافضا


This study is dedicated to the solution of inverse heat conduction problem for estimation of time-varying velocity and altitude profiles regarding the flight trajectory of an earth-entry capsule. Four tungsten-rhenium sensors are supposed to be embedded inside the ablative heat shield of the probe, three of which cannot tolerate high-temperature condition and burn out during entry and the other one remained intact until the end of the simulation. The conventional Levenberg-Marquardt method is reinforced by a relaxation scheme to prevent unfavorable severe oscillations encountered in the inverse iterations. To keep generality of the method, no prior knowledge on the thermal condition and surface recession of ablative insulator is utilized in the current estimation. Therefore, in the associated direct problem, velocity and altitude profiles are given and temperature field inside the heat shield is determined. Accordingly, a solution of the direct problem consists of (i) bow shock calculations in dissociated air (ii) boundary layer solver to compute stagnation heating rate (iii) identification of the thermal response of charring ablative heat shield. It is shown that if the standard deviation of the temperature measurement error is 5 K, estimation of altitude and velocity are associated with approximately 10 and 5 percent normalized error, respectively.


Main Subjects