Fourier modeling of steady and unsteady nonaxisymmetrical flows

A Fourier transform based approach is developed in various forms for efficient computation of unsteady turbomachinery flows. The purpose of using the Fourier approximation is to reduce the computing resource required by a direct calculation of the whole domain of 360-deg circumference. The present work is aimed at extending the Fourier modeling methodology to nonaxisymmetrical steady and unsteady flows. The method has been implemented in a multiblock structured-mesh Reynolds-averaged Navier-Stokes (RANS) solver. It is found that the method is accurate and effective leading to a significant computational speed over direct whole annulus solution.