Block Spectral Method Analysis for Turbomachinery Applications

Abstract

The block-wise spectral reconstruction of turbomachinery flows has been successfully used in the past to reduce the computational cost of full-annulus turbomachinery simulations. The rationale of the method is based on an explicit representation of the long-wavelengths of the problem using a Fourier expansion of the blocks, which in turn contain the short-wavelength content of the spectrum. This work analyzes the accuracy of this approach and shows that this approximation retains not only the explicit Fourier representation of the long wavelengths and finite volume approximation of the short wavelengths but their interaction as well. This interaction due to the scattering associated with the nonuniformity of the flow is referred to as Tyler–Sofrin modes by turbomachinery practitioners and is highly relevant for many practical applications. The solution’s harmonic content is illustrated by resorting to the linear wave equation with varying propagation speed and the NASA rotor 67 fan.