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.Copyright © 2015 by ASME

[1]  Nigel Peake,et al.  Resonant acoustic frequencies of a tandem cascade. Part 1. Zero relative motion , 1999 .

[2]  E. M. Greitzer,et al.  A Computational Model for Short-Wavelength Stall Inception and Development in Multistage Compressors , 1999 .

[3]  J. P. Longley.  Calculating the Flowfield Behaviour of High-Speed Multi-Stage Compressors , 1997 .

[4]  Sanford Fleeter,et al.  Instability Pathology of a High Speed Centrifugal Compressor , 1999 .

[5]  C. Peskin.  The immersed boundary method , 2002, Acta Numerica.

[6]  R. A. Van den Braembussche,et al.  Distinction Between Different Types of Impeller and Diffuser Rotating Stall in a Centrifugal Compressor With Vaneless Diffuser , 1984 .

[7]  Sanford Fleeter,et al.  Rotating Stall Acoustic Signature in a Low-Speed Centrifugal Compressor: Part 1—Vaneless Diffuser , 1995 .

[8]  L. Kovasznay,et al.  Non-linear interactions in a viscous heat-conducting compressible gas , 1958, Journal of Fluid Mechanics.

[9]  Xiaohua Liu,et al.  Basic Studies of Flow-Instability Inception in Axial Compressors Using Eigenvalue Method , 2014 .

[10]  L. Kovasznay.  Turbulence in Supersonic Flow , 1953 .

[11]  Nigel Peake,et al.  Acoustic Resonance in Aeroengine Intake Ducts , 2004 .

[12]  C. R. Peterson,et al.  Mechanics And Thermodynamics Of Propulsion , 1965 .

[13]  Lawrence Sirovich,et al.  Initial and Boundary Value Problems in Dissipative Gas Dynamics , 1967 .

[14]  Z. S. Spakovszky,et al.  Spike and Modal Stall Inception in an Advanced Turbocharger Centrifugal Compressor , 2009 .

[15]  Alex Solomonoff,et al.  Accuracy and Speed in Computing the Chebyshev Collocation Derivative , 1995, SIAM J. Sci. Comput..

[16]  Georg Gyarmathy,et al.  The Operational Stability of a Centrifugal Compressor and Its Dependence on the Characteristics of the Subcomponents , 1994 .

[17]  Björn Benneke.  A methodology for centrifugal compressor stability prediction , 2009 .

[18]  Xiaohua Liu,et al.  A General Theory of Flow-Instability Inception in Turbomachinery , 2013 .

[19]  Zoltán S. Spakovszky,et al.  Applications of axial and radial compressor dynamic system modeling , 2000 .

[20]  Lawrence Sirovich,et al.  Steady Gasdynamic Flows , 1968 .

[21]  Lawrence Sirovich,et al.  Boundary‐Value Problems in Compressible Magnetohydrodynamics , 1967 .

[22]  L. Sirovich,et al.  Modeling a no-slip flow boundary with an external force field , 1993 .

[23]  Lakshmi N. Sankar,et al.  Computational Analysis of Stall and Separation Control in Centrifugal Compressors , 2000 .

[24]  Rodrick V. Chima,et al.  A Three-Dimensional Unsteady CFD Model of Compressor Stability , 2013 .