Efficient Passage-Spectral Method for Unsteady Flows Under Stall Conditions

Abstract

This paper presents an efficient method of approximating unsteady flows using a blockwise 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, such as compressor stability, with a drastic reduction in computational resources. 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 stall conditions has been used as verification validation case to demonstrate the effectiveness and viability of the proposed modeling strategy. The comparison between the solutions obtained with the discrete Fourier series and the full-annulus solution shows that accurate solutions can be obtained with a low number of harmonics. The new method has been applied to investigate the rotating stall inception of the NASA rotor 67 for clean and distorted inlet flow near stall operating conditions. The method is shown to accurately reproduce the full-annulus solution with a few spatial harmonics, capturing the characteristic features of the complex flow induced by the tip leakage vortex breakdown. 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 and the number of blades.

Nonlinear Stability Analysis of a Generic Fan With Distorted Inflow Using Passage-Spectral Method

“…However, the PSM, even with a single spatial harmonic, can reproduce the frequency spectrum quite decently with the corresponding reduction in computational resources. It has been previously demonstrated as well that the present method can reproduce fan transients caused by inlet distortion with a low number of spatial harmonics [28].…”

“…The proposed method has been previously described in [28] and the reader is referred to this reference for further details. This method has been modified and customized for this work to study…”

“…An existing parallel CFD code [26,27] has been modified and customized to study the aerodynamic response of turbomachinery rows due to distorted inlet flows by separating the contribution of each nodal diameter at the inlet. This approach, which has been verified against full-annulus cases for rotating stall and force response cases in an isolated fan-stage [28], has been further modified to deal efficiently with a single spatial harmonic and then applied to assess the effect of inlet distortion on the aerodynamic stability of the fan. In this model just three reduced-passages are retained.…”

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 2p/M. Reader is referred to reference (Romera and Corral, 2019) and (Romera and Corral, 2020) for further details of the baseline flow solver and the implementation of the proposed method.…”

“…A time-marching Passage-Spectral Method (PSM) is proposed in this study to reduce the computational cost of these unsteady and non-axisymmetric simulations and simplify the study of the fan rotor stability under the effect of a distorted exit static pressure without making any hypothesis about its temporal periodicity. 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, 2019), 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, 2020). Despite the number of struts or pylons and their geometrical complexity, any outlet static pressure distortion pattern can be Fourier decomposed.…”