Estimation of a source term in a quasi steady two-dimensional heat transfer problem: application to an electron beam welding

Abstract

In previous work, we have analyzed the feasibility of the estimation for a source term S(x, y, z) in a transversal section. The present study is concerned with a two-dimensional inverse phase change problem. The goal is the estimation of the dissipated heat flux in the liquid zone (reconstruction of a source term in the energy equation) from experimentally measured temperatures in the solid zone. This work has an application in the electron beam welding of steels of thickness about 8 cm. The direct thermo-metallurgical problem is treated in a quasi steady two-dimensional longitudinal section (x, y). The beam displacement is normally in the y direction. But in the quasi steady simulation, the beam is steady in the study section. The sample is divided in the axial direction z in few sections. At each section, a source term is defined with a part of the beam and creates a vaporized zone and a fused zone. The goal of this work is the rebuilding of the complete source term with the estimations at each section. In this paper, we analyze the feasibility of the estimation. For this work, we use only the simulated measurements without noise.

Keywords

estimation / source term / quasi steady / the iterative regularization method