Study on three-dimensional transient heat flow in circumferential GTA welding of pipes using periodicity conditions

A transient three-dimensional finite difference mode (FDM) of the heat flow in the circumferential GTA welding of pipes was developed and applied to calculate the temperature distribution in the workpiece. In order to minimize the computing time required for solving the FDM equations as much as possible, the alternating direction implicit (ADI) scheme which makes use of the tridiagonal matrix algorithm efficiently was adopted. Based on the characteristics of the pipe welding process, the periodic boundary condition was applied to calculate the temperature distribution in the θ direction. For treating the moving heat source effectively, the grid meshes with variable spacings were regenerated at each time step. In order to decrease the interpolating error by grid remeshing, the temperature values at new meshes were interpolated from those at old meshes by using the periodic spline function. The temperature-dependent thermal properties, the latent heat and the convective and radiative boundary conditions were included in the model. The calculated sizes of the fusion and heat-affected zone were compared with the observed values after experiments.