Efficient analysis of unsteady flows within multi-stage turbomachines using the coupled time and passage spectral method

A coupled time and passage spectral method has been proposed very recently for tracking blade wakes penetrating the immediate downstream blade row and reaching far downstream blade rows. To achieve an efficient numerical analysis, the number of time and space modes to be retained has to be limited, as the computational cost of such an analysis is at least proportional to the number of modes. In this study, time and space modes related to downstream propagation of blade wakes reaching beyond their immediate downstream blade row are ranked according to their amplitudes of flow quantities through a time domain harmonic balance analysis using a domain consisting of multiple blade passages for the third row to capture the wakes of the first row of a two-stage fan. Modes with significant amplitudes are identified and they are really sparse. This sparsity of significant modes provides the premise for an efficient analysis using the coupled time and passage spectral method. A guideline for a priori selection of time and space modes has been developed by analyzing the frequencies and nodal diameters of those significant modes. The guideline is subsequently verified through four different coupled time and passage spectral analyses with different levels of accuracy by including different time and space modes.