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Detection of Precursors of Subcritical Hopf Bifurcations via Periodic Perturbations with Applications to Prediction of Rotating Stall in Axial Compressors

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Abstract:
Rotating stall is one type of aerodynamic instabilities that limit the performance of a jet engine. It is also a typical subcritical Hopf bifurcation with a hysteresis, which is very sensitive to small disturbances near the linear stability boundary due to shrinking region of attractions of the nominal operating point. Moreover, the transients to rotating stall are very abrupt and in the time scale of milliseconds. Hence, rotating stall poses a very challenging problem for control and avoidance. In this talk, we investigate the response of a nonlinear system to periodic perturbations as well as random disturbances near a subcritical Hopf bifurcation. There are two distinct response characteristics. The first one is the sensitivity of the amplitude of the periodic response to the bifurcation parameter approaches infinity, as the periodic orbits approach saddle-node instability. The other one is that the power spectra of the responses exhibit secondary peaks as the periodic orbits approaches the Neimark-Sacker bifurcations. We apply the general theory to the Moore-Greizter model for axial compressors, and compare the numerical simulations, the theoretic predictions, and the experiments on a single-stage low-speed compressor.

Type of Seminar:
IfA Seminar
Speaker:
Prof. Yong Wang
Department of Mechanics, Peking University, Beijing, China
Date/Time:
Jul 22, 2013   4:15 p.m.
Location:

ETZ E6, Gloriastrasse 35
Contact Person:

Manfred Morari
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Biographical Sketch:
Yong Wang received his B.S and M.S. degrees in the Department of Mechanics at Peking University in Beijing, China in 1991 and 1994, respectively. He received Ph.D in Control and Dynamical Systems at Caltech in 2000. He did Post-doctoral research in the Division of Applied Mathematics at Brown University, and in the Laboratory for Information and Decision Systems (LIDS) at MIT from 2000 to 2003. He went back to work in Peking University in 2003 and is currently a Professor in the Department of Mechanics and Aerospace Engineering. He was a visiting scholar in IFA at ETH from September 2007 to February 2008.