Rapid Prediction of Compressor Rotating Stall Inception Using Arnoldi Eigenvalue Algorithm

This paper presents a stability model that can make a rapid prediction of the rotating stall inception in turbomachinery and provide the spatial distribution of the corresponding instability mode. In addition, this model can take the three-dimensional geometry of blades and complex flow details in the compressor into consideration, and the solution of the development process of small perturbations can be converted to a nonlinear eigenvalue problem. We propose a solution method by converting the nonlinear eigenvalue problem into a generalized one; then, it can be solved by the Arnoldi algorithm. The proposed method can shorten the elapsed time from hundreds of hours to a few minutes, as compared with the methods adopted in previous works, substantially reducing the computational cost. Furthermore, the spatial distribution of eigenvectors can be obtained to investigate the characteristics of the perturbation mode, which can be applied as a foundation to set the inlet/outlet boundary conditions and select the eigenvalue representing the rotating stall inception. In the cases of a transonic isolated rotor and a subsonic one-stage compressor, the results are in accordance with those measured in experiments, verifying the accuracy and effectiveness of the stability model. Therefore, the model can be applied to evaluate the flow stability in the design stage of compressors with low computational cost.