Inverse identification of temperature-dependent thermal conductivity coefficients in an orthotropic charring composite

Abstract

Charring composites are classified as orthotropic materials whose transport properties vary considerably with directions. Because of Exposure to the severe heating environment, these composites undergo internal chemical decomposition, which makes their thermophysical properties highly temperature-dependent. In this paper, a multidimensional inverse approach is proposed to simultaneously retrieve the thermal conductivity coefficients in both fiber in-plane and through-the-thickness directions. The thermal response of the material is obtained using a fully implicit axisymmetric solver with the ability to model several physical phenomena, including surface thermochemical ablation, decomposition of resin, and multidimensional pyrolysis gas transport. A comprehensive statistical analysis is performed to determine the optimal location and number of sensors to be installed. Accordingly, to obtain reasonable estimates, two sensors must be placed at locations where the applied heat flux is aligned with the in-plane and through-the-thickness directions. In the case involving noisy measurements of two sensors, results show that reconstructed thermal conductivities at the in-plane direction are more erroneous than the through-the-thickness one. However, utilizing the measurements of the third sensor reduces the average error of in-plane estimates from 13.4% to 2.7%. The sensitivity of the estimated parameters to ±10% perturbation in both surface heating rate and solid specific heat is also investigated. For both in-plane and through-the-thickness directions, it is demonstrated that perturbation in the surface heating rate has strongly affected the estimation of the material thermal conductivity at high temperature regions, where the material is in the char state.