Passage-spectral method for turbomachinery long wave-length flow instabilities

Abstract

Numerical simulations of non-axisymmetric and unsteady flows are normally conducted using full-annulus geometries and U-RANS solvers. In general, nonlinear flow disturbances in time and/or space can be identified and represented by a discrete Fourier series as long as they are periodic. Single passage methods cannot capture this unsteady circumferential non-uniformities when the frequency is unknown. The identification and characterization of mechanisms related to flow instabilities with a reduction in computational resources should improve prediction methods and lead to more efficient control strategies, preserving the accuracy of a full domain solution. The proposed method presents for the first time an efficient means of approximating flows with spatial Fourier methods, extending the modeling to 3-D non-axisymmetrical unsteady flows without any assumed frequency in order to capture the long length-scale unsteady flow features of interest with a drastic reduction in number of reduced-passages to be required. Flow variables at the periodic boundaries are then continuously updated from the spatial Fourier coefficients of the uniformly spaced reduced-passage domains with the corresponding phase shift correction. An unsteady stall flow of a fan-stage at 50% (subsonic) of the design speed will be presented as a validation case to demonstrate effectiveness of the present method giving a comparison between the solution obtained with low number of harmonics against full-annulus solution. The stall unsteadiness is deterministic by higher frequency fluctuations caused by perturbations with a length-scale of the order of a blade pitch and long-wave rotating structures with length-scale of the order of the circumference domain. The present method accurately reproduces the unsteadiness associated to the large scales present in modal stall in a fan-stage with even one harmonic, capturing the characteristic features of a complex flow due to the tip leakage vortex with a propagation speed of approximately 70% to 80% of rotor speed counter to the rotation.