Application of the finite volume method to the radial conduction model of the CATHENA code

Abstract

The CATHENA code uses the finite element method (FEM) for the one-dimensional heat conduction model, which determines the temperature distribution from the fuel center to the cladding in the radial direction. However, it is shown that the finite element solutions in the heat source region such as a fuel pellet are converged to exact solutions with an increasing number of the mesh elements. Since the finite volume method (FVM) ensures local and global energy conservation due to an integral conservation over each control volume, the FVM is applied to the CATHENA wall conduction model to avoid the mesh size effect on the fuel temperature prediction. The accuracy and validity of the finite volume model in the CATHENA code are tested against two cases, a steady state and a transient heat conduction case, for which exact solutions are available. The constant temperature on the boundary surface and a uniform internal heat generation rate are assumed for the steady state problem. In the transient heat conduction problem, a cylinder is initially at a uniform temperature and suddenly its boundary surface is subjected to convection with a constant heat transfer coefficient into an ambient at a constant temperature. The steady state solutions by the FVM model are found to give almost the same results as the analytical solutions and consistent results with varying mesh sizes, while the original CATHENA with FEM over-predicts the center temperature with larger mesh sizes. The new model also closely follows the analytic solutions of the dimensionless transient heat conduction equation for a long cylinder.