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.
The purpose of this paper is to construct a general broadband impedance model, which is suited for predicting acoustic propagation problems in time domain. A multi-freedom broadband impedance model for sound propagation over impedance surfaces is proposed and the corresponding time domain impedance boundary condition is presented. Basing on the extended Helmholtz resonator, the multi-freedom impedance model is constructed through combing with a sum of rational functions in the form of general complex-conjugate pole-residue pairs and it is proved that the impedance model is well posed. The impedance boundary condition can be implemented into a computational aeroacoustics solver by a rectlrsive convolution technique, which results in a fast and computationally efficient algorithm. The two dimensional and three dimensional benchmark problems are selected to validate the accuracy of the proposed impedance model and time domain simulations. The numerical results are in good agreement with the reference solutions. It is demonstrated that the proposed impedance model can be used to describe the broadband characteristics of acoustic liners, and the corresponding time domain impedance boundary condition is viable and accurate for the prediction of sound propagation over broadband impedance surfaces.
