The present study developed a three-dimensional compressible analytical model for predicting the rotating stall boundary in turbomachinery. Based on the small perturbation theory and the inviscid Euler equation. Using the perturbation wave dispersion theory and boundary conditions, the problem of stall prediction in turbomachinery can be regarded as the solution of the matrix eigenvalue problem. To validate the feasibility and accuracy of the developed analytical model. After that, the NASA Rotor 67 and NASA Stage 35, which have been disclosed in detail, are selected to validate the 3D analytical model. Results has been successfully verified the accuracy of the developed prediction model. Meanwhile, the advantages of the 3D analytical model, which considers the radial mainstream velocity and disturbance velocity are also demonstrated in comparison with the 2D model developed by Ludwig et al. Finally, the three-dimensional analytical model is used to predict the stall boundary of a contra-rotating compressor test rig. Results show that the downstream rotor encounters rotating stall firstly, and the stall mass flow is about 5.871kg/ s. A good agreement has been also revealed from the unsteady numerical simulation and thus again evidence the ability of the developed three-dimensional analytical model in terms of accuracy and efficiency.

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