Dependency of Finite Difference Solutions on Grid Structures and Turbulence Models for Cascade Flows.

Abstract

For cascade with a high turning and a large camber, it is difficult to impose grid orthogonality as well as point-to-point periodicity simultaneously on a single structured grid. In this study, the effects of periodic and non-periodic grids on finite difference solutions are investigated for twodimensional transonic flows about rotor blades. The spatial derivatives of the Reynolds-averaged Navier-Stokes equations are discretized with central difference approximations and matrix dissipation models. The resulting system of equations is integrated in time with an explicit 2-stage Rational Runge-Kutta scheme. For turbulence closure, Baldwin-Lomax model, Baldwin-Barth model, and Spalart-Allmaras model are compared. The non-periodic grids have favorable resolutions for the shock system and the wase. The shock-induced production of the eddy-viscosity is remarkable in the Baldwin-Barth model. The Spalart-Allmaras model works well, even on the periodic grids, in comparison with the other models.