Method of simulating unsteady turbomachinery flows with multiple perturbations

Currently time-marching methods for unsteady turbomachinery flow calculations suffer from the inability to deal with multiple perturbations in a single-passage solution. A new periodic boundary condition method has been proposed, in which one can perform a single-passage solution with multiple perturbations. At the periodic boundaries, all of the perturbations are identified by their own phase-shifted periodicities and approximated by Fourier series. A combined parameter is chosen for the Fourier transform so that the Fourier coefficients can be efficiently updated. Corrections on both the variables at a current time level and on the Fourier coefficients are carried out repeatedly until a periodic state is reached. Numerical examples for oscillating cascade flows subject to inlet/outlet perturbations have demonstrated the validity of the present method and its ability to deal with situations of practical interest.