An inverse front tracking method for modeling solidification process in a smelting furnace

Abstract

An inverse process based on the conjugate gradient and adjoint problem is developed for predicting the time-varying bank thickness during the solidification/melting process in a smelting furnace. The direct problem rest on a single-phase moving boundary model to simulate the solid bank and refractory brick, simultaneously. The time-varying heat flux at solid/liquid interface, initial bank thickness and time-varying heat transfer coefficient at outer surface of the furnace are considered as the unknowns. Unlike the methods developed so far based on the enthalpy model, the current method does not require any prior information regarding the thermophysical properties of the liquid-phase and complex physical phenomena that occur in it. This improves the uniqueness of the solution that is inherent in the ill-posed inverse methods. To avoid the so-called “inverse crime”, a two-phase enthalpy method is used to generate the simulated measurement. These measurements are used in the present single-phase method for reconstruction of bank history. The model has shown good performance for non-intrusive temperature obtained from the outer surface of the furnace. The inverse model has been validated through an experiment conducted in a metallurgical reactor. A reasonable agreement between the estimated and measured molten salt bank indicates the existence and convergence of the inverse solution.