A three-dimensional compressible flow stability model is presented in this paper, which focuses on stall inception of multi-stage axial flow compressors with a finite large radius annular duct configuration for the first time. It is shown that under some assumptions, the stability equation can be obtained yielding from a group of homogeneous equations. The stability can be judged by the non-dimensional imaginary part of the resultant complex frequency eigenvalue. Further more, based on the analysis of the unsteady phenomenon caused by casing treatment, the function of casing treatment has been modeled by a wall impedance condition which is included in the stability model through the eigenvalues and the corresponding eigenfunctions of the system. Finally, some experimental investigation and two numerical evaluation cases are conducted to validate this model and emphasis is placed on numerically studying the sensitivity of the setup of different boundary conditions on the stall inception of axial flow fan/compressors. A novel casing treatment which consists of a backchamber and a perforated plate is suggested, and it is noted that the open area ratio of the casing treatment is less than 10%, and is far smaller than conventional casing treatment with open area ratio of over 50%, which could result in stall margin improvement without obvious efficiency loss of fan/compressors.
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