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In order to analyze the flow stability of compressors rapidly in the design stage, a fast analysis method is developed in this paper. This method takes the baseflow on each streamline at different spanwise locations as the research object, and characterizes the effect of blade rows on the internal flow by establishing a body force model. Therefore, it is capable to take the complex three-dimensional blade geometry and the abundant flow details into account, and what’s more, it has a significantly high computational efficiency, which makes it available to engineering practice. Based on the eigenvalue theory, the flow stability problem is transformed into the eigenvalue problem, and the system stability is determined by the eigenvalue obtained by utilizing the singular value decomposition (SVD) method. The flow stability of NASA Rotor 37 is analyzed to validate the reliability of the developed approach, and results show that this analysis method is able to capture the process of stability deterioration with throttling and identify the blade tip region as the most unstable area. In order to further study the influence of blade geometry on compressor stability, a number of swept rotors are designed by modifying the stacking line of NASA Rotor 37. The assessment results via the developed method indicate that the forward sweep defined in this work can significantly improve the stability of the flow field in the tip region, while the backward sweep has the opposite effect.

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.