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Center Manifold of a Nonlinear Partial Differential Equation that models Compressor Systems
Student-Run Research| Speaker: | MingQing Xiao, Mathematics, UC Davis |
| Location: | 593 Kerr |
| Start time: | Wed, Apr 28 1999, 4:10PM |
Description
A commonly used mathematical model that captures the flow behavior of a
compression system, due to Moore and Greitzer, consists of a PDE and two
ODEs. The PDE describes the behavior of disturbances in the inlet region
of compression system, and the two ODEs describe the coupling of the
disturbances with the mean flow.
In this talk I will first introduce this model, and then show that the PDE
system features a local center manifold. The significance of this result
is that a study of the behavior of the local flow in the compressor can
thus be translated into a study of the flow of two scalar differential
equations on the center manifold. The result is obtained by converting the
original PDE system into an evolution equation on a Hilbert space, and
showing that this equation and its linearized version (around a desired
equilibrium) are not topologically equivalent. I will further discuss the
stability of the flow, using the reduced two dimensional system.
The talk will conclude with a discussion of some control issues that arise
in the stabilization of the flow through compressor systems, and some
underlying mathematical challenges.