A finite element‐finite difference solution of three‐dimensional viscous‐inviscid interaction

Abstract

AbstractBased on the concept of viscous‐inviscid interaction, a hybrid solution technique in studying external flow past three‐dimensional bodies is developed. The finite element method is employed to solve the inviscid part of the flow and the finite difference technique is utilized in solving the viscous part of the flow. This hybrid technique is applied to study the flow past a swept bump on a circular cylinder. The 8‐noded trilinear brick elements are used for the finite element formulation of the problem where the flow is considered potential. In the viscous part, however, three‐dimensional boundary‐layer equations simplified with small cross‐flow assumption and expressed in the surface co‐ordinates are solved utilizing the finite difference method. Numerical studies are made for both the laminar and the turbulent flow cases using the boundary‐layer edge velocity distribution obtained through inviscid solution. The results are compared with the available experimental data. The boundary‐layer edge velocity distribution is in good agreement with the experimental data; the prediction of the separation point for the laminar case is the same. For the turbulent flow case, the velocity profiles in the flow direction when compared to the measurements are overall in reasonably good agreement, and the discrepancies are due to small cross‐flow assumption. However, the agreement concerning the wall shear stress component in the flow direction is more satisfactory.