An adaptive Cartesian cut-cell method for conjugate heat transfer on arbitrarily moving fluid-solid interfaces

Abstract

This study developed and validated a numerical method to handle two-dimensional mixed-convection conjugate heat transfer (CHT) over arbitrarily moving/deforming fluid-solid interfaces. We will base the development on the finite-volume adaptive Cartesian grid method with the cut cell approach developed and matured previously. Few studies in literature tackled the issue of CHT across moving/deforming interfaces, especially in the community of Cartesian grid methods. The present work benefited from the merit of the cut cell approach, i.e., adapting to various types of boundary condition in a unified manner, to implement the boundary conditions required of the CHT. A temperal discretization scheme near moving interfaces is proposed aiming to achieve nominally second-order accuracy in time. Some cases were simulated to demonstrate the validity and spatial/temperal order of accuracy of the numerical method. Results show that the method has a globally second-order accuracy in space if the time step size varies in some fashion with the mesh size and, in a local sense (i.e., near the interface), both the spatial and temperal accuracies are superior or equal to first order for all the considered flow and thermal variables except that the temperal accuracy of pressure is mildly worse than first order for complicated moving-interface problems.