Computation of Multistage Flows Using a Fourier Approach

Abstract

This paper presents efficient procedures to model multistage flows using Fourier-based methods. The Favre-averaged nonlinear harmonic method is extended to compute multistage flows by introducing rotor–rotor or stator–stator interactions. A unified treatment to transfer disturbances through blade–row interfaces is also formulated. The performance of the proposed method is demonstrated in a multistage compressor and turbine with different levels of flow nonlinearity. The computed solutions using the proposed method matches well with unsteady Reynolds-averaged Navier–Stokes (RANS) simulations but require far smaller computational resources. A method is proposed to reduce the computational cost of clocking studies even further by building reduced models from existing Fourier modes. The method allows the flowfield for a required clocking position to be constructed by postprocessing the Fourier modes computed for a single arbitrary clocking configuration. This technique is demonstrated by predicting compressor efficiency variation with respect to rotor blade clocking and wall temperature distributions in a turbine hot streak migration problem. Excellent agreement with unsteady RANS simulations is found. The proposed methods become less accurate in the presence of large flow nonuniformity but the produced solutions still show significant improvement over mixing plane solutions.