Efficient Passage-Spectral Method For Unsteady Flows Under Stall Conditions

Abstract

This paper presents an efficient method of approximating unsteady flows using a block-wise discrete spatial Fourier series for the modeling of three-dimensional non-axisymmetric flows without making any hypothesis about its temporal periodicity. The method aims at capturing the long wavelength flow patterns which are present in many unsteady problems of industrial interest. The method is intended to be used to compute flows exhibiting large-scale instabilities and where the fundamental frequency of the problem is not known beforehand. The approach discretizes the domain using a finite number of blocks or passages, where the flow variables at the supposedly periodic boundaries are continuously updated using the spatial Fourier coefficients of a uniformly spaced set of reduced-passage domains. The NASA rotor 67 under the effect of distorted inflow conditions has been used as verification case to demonstrate the effectiveness and viability of the method. The comparison between the Passage-Spectral Method and the full-annulus solution shows that accurate solutions can be obtained with a low number of harmonics. The new method has also been applied to investigate the rotating stall inception of the NASA rotor 67 for distorted inlet flows near stall operating conditions. The method is shown to accurately reproduce the full-annulus solution with a few spatial harmonics. The computational cost in this application has been reduced by a factor of between three and seven, although this number heavily depends on the ratio between the number of retained harmonics to the number of blades.

Impact of Downstream Potential Perturbations on the Nonlinear Stability of a Generic Fan

“…The existing parallel CFD code was modified and customized for this work to study the contribution of a given single spatial harmonic M efficiently, by approximating the solution with only three reduced-passages samples spanning over a sector of size 2π=M . Reader is referred to reference Romera and Corral (2020a) and Romera and Corral (2020b) for further details of the baseline flow solver and the implementation of the proposed method.…”

“…The Passage-Spectral naming is solely used a means of highlighting that the blocks coincide with the blade passages. This approach, which has been verified against full-annulus cases for rotating stall and force response cases in an isolated fan-stage (Romera and Corral, 2020a), has been further modified to deal efficiently with a single spatial harmonic and then applied to assess the effect of inlet distortion on fan stability (Romera and Corral, 2020b). Despite the number of struts or pylons and their geometrical complexity, any outlet static pressure distortion pattern can be Fourier decomposed.…”