On Steady Solutions of a PDE Model of Compressor Stall

Proceedings of the IEEE Conference on Decision and Control

Volumn 2, Issue , 2003, Pages 1848-1853

  Hagen, Gregory ^a   Mehta, Prashant G ^a  

^a UNITED TECHNOLOGIES RESEARCH CENTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; BIFURCATION (MATHEMATICS); BOUNDARY CONDITIONS; CONTROL SYSTEM ANALYSIS; FLOW OF FLUIDS; FUNCTIONS; LYAPUNOV METHODS; MATHEMATICAL MODELS; PARTIAL DIFFERENTIAL EQUATIONS;

AXIAL COMPRESSORS; IRROTATIONAL FLOW;

COMPRESSORS;

EID: 1542350324     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (23)

1. R. A. Adomaitis and E. H. Abed. Bifurcation analysis of nonuniform flow patterns in axial-flow gas compressors. 1st World Congress of Nonlinear Analysis, Tampa, Florida, 1992.
2. A. Banaszuk, H. A. Hauksson, and I. Mezić. A back-stepping controller for a nonlinear partial differential equation model of compression system instabilities. SIAM Journal on Control and Optimization, 37(5), 1999.
3. B. Birnir and H. A. Hauksson. A finite dimensional attractor of the moore-greitzer PDE model. SIAM Journal on Applied Mathematics, 59(2), 1998.
4. T. R. Camp and I. J. Day. A study of spike and modal stall phenomena in a low-speed axial compressor. Transactions ASME Paper No. 97-GT-526, 1997.
5. R. G. Casten and C. J. Holland. Instability results for reaction diffusion equations with neumann boundary conditions. Journal of Differential Equations, 27:266-273, 1978.
6. L. C. Evans. Partial Differential Equations. American Mathematical Societry, 1998.
7. W. H. Fleming. A selection-migration model in population genetics. Journal of Mathematical Biology, 2:219-234, 1975.
8. Y. Gong, C., S. Tan, K. A. Gordon, and E. M. Greitzer. A computational model for short-wavelength stall inception and development in multistage compressors. Transactions ASME Journal of Turbomachinery, 121, 1999.
9. G. Hagen. Large Scale Flow Phenomena in Axial Compressors: Modeling, Analysis, and Control with Air Injectors. PhD thesis, University of California, Santa Barbara, 2001.
10. G. Hagen and I. Mezić. Spillover stabilization in finite dimensional control and observer design for dissipative evolution equations. SIAM Journal on Control and Optimization, 42(2):746-768, 2003.
11. G. Hagen, I. Mezić, and B. Bamieh. Distributed control design for parabolic evolution equations; application to compressor stall control. Accepted to IEEE Transactions on Automatic Control, 2002.
12. L. He. Computational study of rotating-stall inception in axial compressors. Journal of Propulsion and Power, 13(1), 1997.
13. F. E. McCaughan. Bifurcation analysis of axial flow compressor stability. SIAM Journal on Applied Mathematics, 50:1232-1253, 1990.
14. N. M. McDougal, N. A. Cumpsty, and T. P. Hynes. Stall inception in axial compressors. Transactions ASME Journal of Turbomachinery, 1990.
15. P. G. Mehta. Nonbifurcating solutions of parallel flows. PhD thesis, Cornell University, 2003.
16. I. Mezić. A large-scale theory of axial compression system dynamics. Preprint, 2000.
17. L. Modica. The gradient theory of phase transition and the minimal interface criterion. Archive for Rational Mechanics and Analysis, 98:123-142, 1987.
18. F. K. Moore and E. M. Greitzer. A theory of post-stall transients in axial compression systems:Part 1 - Development of equations. Transactions ASME Journal of Engineering for Gas Turbines and Power, 108:68-76, 1986.
19. N. C. Owen, J. Rubinstein, and P. Sternberg. Minimizers and gradient flows for singularly perturbed bi-stable potentials with a dirichlet condition. Proceedings of the Royal Society of London A, 429:505-532, 1990.
20. R. C. Pampreen. Compressor Surge and Stall. Concepts ETI, Inc., 1998.
21. P. H. Rabinowitz. Minimax Methods in Critical Point Theory with Applications to Differential Equations. American Mathematical Society, 1984.
22. R. Temam. Infinite-Dimensional Dynamical Systems in Mechanics and Physics. Springer-Verlag, New York, 1997.
23. M. Q. Xiao and T. Basar. Center manifold of the viscous moore-greitzer PDE model. SIAM Journal on Applied Mathematics, 61(3), 2000.