Simulation and validation of Mach number effects on secondary flow in a transonic turbine cascade using a multigrid, k-ε solver

The existing three-dimensional Navier-Stokes flow solver with an explicit Runge-Kutta algorithm and a low-Reynolds-number k-epsilon turbulence model has been modified in order to simulate turbomachinery flows in a more efficient manner. The solver has been made to converge more rapidly through use of the multigrid technique. Stability problems associated with the use multigrid in conjunction with two-equation turbulence models are addressed and techniques to alleviate instability are investigated. Validation for the new code was performed with a transonic turbine cascade tested by Perdichizzi. In the fully three-dimensional turbulent cascade, real convergence (i.e., CPU time) was improved nearly two times the original code. Robustness was enhanced with the full multigrid initialization procedure. The same test case was then used to perform a series of simulations that investigated the effect of different exit Mach numbers on secondary flow features. This permitted an in-depth study into the mechanisms of secondary flow formation and secondary losses at high Mach numbers. In this cascade, it was found that secondary losses and secondary poly deviation, which are fairly constant in incompressible flows with similar geometries, underwent a large reduction in the compressible poly range. The structure of the trailing edge shock system and the reduced endwall boundary layer at supersonic exit conditions were shown to be very significant in reducing the amount of secondary flow and losses.