Application of Levenberg–Marquardt Method for Estimation of the Thermophysical Properties and Thermal Boundary Conditions of Decomposing Materials

Abstract

This study is devoted to inversely estimating the thermophysical properties and thermal boundary conditions of a carbon-phenolic composite, which is one of the widely used charring ablator. Conventional and modified Levenberg–Marquardt methods are applied to determine the unknown parameters and functions, respectively. The unknown parameters include specific heat and thermal conductivity over a wide temperature range, and the unknown functions are the time-varying cold-wall heat flux and surface temperature. Before inverting the data, a correlation analysis is performed to demonstrate the dependency of the unknown quantities and also to determine the number and locations of sensors. An in-house version of charring material ablation code is used to both compute the sensor measurements and invert the data. The current study pursues three scenarios, including avoiding crime in the inversion, adding random errors to the simulated measurements and using different decomposition models to generate the measurement temperatures and invert the data. The obtained results demonstrate the efficiency of the proposed method in retrieving the boundary conditions at the receding surface of charring composites, as well as, the temperature dependent thermophysical properties.