Inverse Conduction in a System Undergoing Charring and Ablation

ABSTRACT

A one-dimensional (axisymmetric) system undergoing charring and ablation is considered. The direct problem is solved for and the temperature profile at an interior point is stored. This is given as the input for the inverse problem and taken as equivalent to the experimental value. The flux variation is chosen so that the error(norm) between the experimental and the computed temperatures is a minimum. The heat flux is assumed to be piecewise linear in time. Powell optimization method is used for error minimization. The number of linear intervals is taken as one initially and the number of linear intervals is increased, using the previous predicted values as the initial guess. This results in faster convergence. As the number of linear intervals increases, the predicted flux becomes closer to the actual one. The variation of charring and ablation fronts is also compared against the actual ones. It is seen that the predicted variation of charring fronts is close to the actual one, while there is a minor deviation in the case of ablation front. Thus, the inverse conduction algorithm predicts the movement of charring-ablation fronts in addition to the heat flux.

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