Title: Heat flux estimation for materials with pyrolysis and ablation

Authors: S. Alestra, J. Collinet, F. Dubois

Addresses: Simulation Information Technology and Systems Engineering, EADS IW, 18 Rue Marius Terce, Campus Engineering, 31000 Toulouse, France. ' Re-entry Systems and Technologies, EADS Astrium, 66, route de Verneuil, BP2, 78133 Les Mureaux Cedex, France. ' Department of Mathematics, Conservatoire National des Arts et Metiers, 292, rue Saint Martin, F-75141 Paris Cedex 03, France

Abstract: In the development of future atmospheric re-entry vehicles, the heat shield (and its sizing) is one of the major challenges of the design. It is therefore important to know precisely aerothermal heat fluxes encountered during the re-entry, and the associated uncertainties. Identification of these stresses is possible only from indirect measurements, usually based on thermocouples located directly in the thermal protection. In this context, Astrium has developed since many years a one-dimensional tool to evaluate the heat loads on pyrolysable and ablative materials. An inverse problem is formulated to restore the heat flux encountered in re-entry problems, from temperature measurements made inside the material. We minimise the difference calculation/measurement with optimal control techniques (definition of a Lagrangian with adjoint and gradient techniques, with a quasi-Newton algorithm). On-ground and in-flight tests applications are presented, and first encouraging results using the automatic differentiation tool TAPENADE, developed at INRIA.

Keywords: inverse problem; ablation; pyrolysis; thermal protection; optimal control; adjoint; gradient; optimisation; automatic differentiation; heat flux estimation; atmospheric re-entry vehicles; heat shield; aerothermal heat fluxes; uncertainties.

DOI: 10.1504/IJESMS.2010.031876

International Journal of Engineering Systems Modelling and Simulation, 2010 Vol.2 No.1/2, pp.109 - 127

Published online: 27 Feb 2010 *

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