Turbomachinery Applications with the Time Spectral Method

This paper presents the Time Spectral Method, which is capable of significantly reducing the CPU requirements for time periodic flows. Here the main focus is turbomachinery computations for which the standard formulation must be adapted to take sector periodicity into account if the problem is solved in the Cartesian frame. Odd-even decoupling is avoided by choosing an odd number of time intervals in a period. Results are presented for the NASA Stage 35 compressor test case and these show that engineering accuracy is obtained with 11 time intervals per blade passing. Especially for high RPM applications, like the Stage 35, the Time Spectral Method leads to a reduction of an order of magnitude in CPUtime compared to a standard second order backward difference time integration scheme.