Bend Flow Calculational Methods Compared

Abstract

The two widely used methods of finite‐difference viscous‐flow calculation, the vorticity transport and primitive variable approaches, are applied to the analysis of flow through a plane short‐radius bend flanked by sections of straight conduit. Additionally, the vorticity transport method is employed in a direct (using combined rectangular and polar coordinates) and an indirect calculation (using a nonorthogonal coordinate transform). The solution for all three methods are found to be in essential agreement at a Reynolds number of 72. Because of the sharp curvature, the primitive variable method required pressure adjustment using a Poisson equation; velocities were adjusted by the divergence equation and advanced in time by the momentum equations. For the short‐radius bend, the matching procedures involved in the primitive variable approach were found to be crucial in developing smooth field transitions from one coordinate system to another. The adjustment of the coefficients in the transform vorticity transport method for the same regions (but not along the junction lines) were easily made and the comparisons with results from the other methods were excellent.