NUMERICAL METHOD FOR THE COMPUTATION OF FLOW AND SCALAR TRANSPORT USING NONORTHOGONAL BOUNDARY-FITTED COORDINATES

Abstract

Transport processes in most engineering applications occur in complex geometries. A control volume method is presented, based on generalized nonorthogonal curvilinear coordinates for the prediction of incompressible flow and related transport processes in complex geometries, The primitive variable formulation is adopted and a staggered grid, with contravariant velocities used as the primary unknowns in the momentum equations, is utilized. A method for the discretization of the scalar transport equation, which accounts for possible discontinuities in the diffusivities, is described. A local coordinate approach is used to obtain the momentum source terms that arise due to the grid curvature. Subtle details of the discretization of the pressure gradient term in the momentum equations for nonorthogonal grids, in the presence of discontinuities in the flow resistance, are described. The SIMPLER algorithm is used for handling the velocity-pressure coupling. A discussion on the derivation and the solution of the pressure correction equation is presented. The consistency and accuracy of the proposed method are ascertained by comparing the results for shear-driven flow in a trapezoidal cavity with a fine grid solution available in the literature. The relevance of the method for computing the pressure force in the momentum equations is demonstrated by solving a flow problem that incorporates discontinuities in flow resistance. The utility of the present method is then demonstrated by its application to two illustrative problems for which experimental data are available.