Cascade viscous flow analysis using the Navier-Stokes equations

A previously developed explicit, multiple-grid, time-marching Navier-Stokes solution procedure has been modified and extended for the calculation of steady-state high Reynolds number turbulent flows in cascades. Particular attention has been given to the solution accuracy of this procedure as compared with boundary-layer theory and experimental data. A new compact discretization scheme has been implemented for the viscous terms which has the same finite-difference molecule as the inviscid terms of the Navier-Stokes equations. This compact operator has been found to yield accurate and stable solutions in regions of the flow where the gradients are large and the computational mesh is relatively sparse. A modified C grid generation procedure has been developed for cascades that greatly reduces grid skewing in the midgap region. As a result, numerical errors associated with the use of numerical smoothing on skewed grids are reduced considerably. In addition, a body normal grid system has also been generated for accurately determining the eddy viscosity distribution based on an algebraic turbulence model and for comparing the results directly with boundary-layer theory. A combined second and fourth difference numerical smoothing operation has been carefully constructed to prevent oscillations in the solution for the flow over complicated geometries without contaminating the velocity profiles near the wall. Results from turbine and compressor applications are presented to demonstrate the accuracy of the present scheme through comparisons with experimental data and attached boundary-layer theory.