Efficient computation of heat distribution of processed workpiece with coupling to bottom water vapor in water-jet guided laser machining

Abstract

In this paper, we present a novel approach for calculating the heat distribution within a processed workpiece subjected to laser irradiation while accounting for the influence of bottom water vapor. A comprehensive mathematical model is introduced and numerical techniques using difference approximation are employed. Initially, the three-dimensional heat equation, originally defined in the rectangular coordinate system, is transformed into a corresponding model within the cylindrical coordinate system, incorporating a nonlinear boundary condition to account for coupling effects. Subsequently, leveraging the axial symmetry of the heat distribution, the three-dimensional model is simplified into a two-dimensional one. This simplified model is solved using the alternating direction implicit scheme coupled with the Crank-Nicolson method. Moreover, we develop a high-precision numerical treatment for the nonlinear boundary condition within the cylindrical coordinate system. To validate our methodology, simulation experiments are conducted on three distinct samples. Our comparative results demonstrate the feasibility and efficiency of the proposed approach in the context of water-jet guided laser processing.