SIMULATION AND VALIDATION OF MACH NUMBER EFFECTS ON SECONDARY FLOW INA TRANSONIC TURBINE CASCADE USING A MULTIGRID, K-EPSILON SOLVER

The existing three-dimensional Navier-Stokes flow solver with an expli cit Runge-Kutta algorithm and a low-Reynolds-number k-epsilon turbulen ce model has been modified in order to simulate turbomachinery flows i n a more efficient manner. The solver has been made to converge more r apidly through use of the multigrid technique. Stability problems asso ciated with the use multigrid in conjunction with two-equation turbule nce models are addressed and techniques to alleviate instability are i nvestigated. Validation for the new code was performed with a transoni c turbine cascade tested by Perdichizzi. In the fully three-dimensiona l turbulent cascade, real convergence (i.e., CPU time) was improved ne arly two times the original code. Robustness was enhanced with the ful l multigrid initialization procedure. The same test case was then used to perform a series of simulations that investigated the effect of di fferent exit Mach numbers on secondary flow features. This permitted a n in-depth study into the mechanisms of secondary flow formation and s econdary losses at high Mach numbers. In this cascade, it was found th at secondary losses and secondary poly deviation, which are fairly con stant in incompressible flows with similar geometries, underwent a lar ge reduction in the compressible poly range. The structure of the trai ling edge shock system and the reduced endwall boundary layer at super sonic exit conditions were shown to be very significant in reducing th e amount of secondary flow and losses.