Flutter Computation of Turbomachinery Cascades Using a Parallel Unsteady Navier-Stokes Code

Aquasi-three-dimensional multigrid Navier–Stokes solver on single- andmultiple-passage domains is presented for solving unsteady ows around oscillating turbine and compressor blades. The conventional direct store method is used for applying the phase-shifted periodic boundary condition over a single blade passage. A parallel version of the solver using the message passing interface standard is developed for multiple-passage computations. In parallel multiple-passage computations, the phase-shifted periodic boundary condition is converted to a simple in-phase periodic condition. Euler and Navier–Stokes solutions are obtained for unsteady ows through an oscillating turbine cascade blade row with both the sequential and the parallel codes. It is found that the parallel code offers almost linear speedup with a slope close to 1 on multiple CPUs. In addition, signi cant improvement is achieved in convergence of the computation to a periodic unsteady state in the parallel multiple-passage computations due to the use of the in-phase periodic boundary conditions compared with that in the single-passage computations with phase-shifted periodic boundary conditions via the direct store method. The parallel Navier–Stokes code is also used to calculate the ow through an oscillating compressor cascade. Results are compared with experimental data and computations by other authors. Nomenclature Cp1 = rst harmonic unsteady pressure coef cient