Numerical prediction of stall inception in centrifugal compreßor using eigenvalue method

This paper is concerned with the prediction of stability inception of centrifugal compreßor based on eigenvalue theory. A body force model has been developed to simulate the impellers of the compreßor by applying the effect of the blade force on momentum change and energy loß and geometries of blades. Using spectrum method, the stability equations can be precisely transformed into a very large matrix equation due to the compreßor configuration. Before computing with spectrum method, it is available to use Jacobi Transform when making a transformation between physical and computational regions. Afterwards, the Singular Value Decomposition is adopted to solve the resultant eigenvalue matrix, the roots of which can conveniently predict whether the flow is stable or not. It is found that the relative error of the computational model is smaller in comparison with CFD steady results, which indicates that the model can be used as a practical and reliable theoretical criterion during the compreßor design phase without requiring any experiential formulas and data.