Hopf-Hopf Interactions of Surge and Rotating Stall

[+] Author and Article Information
B. D. Coller

Department of Mechanical Engineering, Northern Illinois University, DeKalb, IL 60115

J. Comput. Nonlinear Dynam 1(4), 320-327 (Jun 06, 2006) (8 pages) doi:10.1115/1.2338324 History: Received November 15, 2005; Revised June 06, 2006

In this paper, we examine the interaction of two instabilities that occur in axial compressors using the Hopf-Hopf normal form. As a result, we illuminate some gaps in understanding the dynamics of standard compressor models. We find a possible dynamic mechanism, which explains certain “curious” behavior observed in experiments, and are able to predict and explain failure mechanisms in previously proposed control strategies.

Copyright © 2006 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.



Grahic Jump Location
Figure 1

Schematic diagram of compression system

Grahic Jump Location
Figure 2

(a) Compressor and throttle characteristics. (b) Creating an “effective” throttle characteristic via feedback.

Grahic Jump Location
Figure 3

Stability of the nominal operating point

Grahic Jump Location
Figure 4

Partial parameter space for the Hopf-Hopf normal form 9. Dotted lines separate different degenerate behaviors (solid letters). Solid lines separate nondegenerate classes (open Roman numerals). Dashed lines serve the dual purpose.

Grahic Jump Location
Figure 5

Phase portraits for two interacting Hopf bifurcations. Sixty-six additional cases are obtained by reversing the sense of the arrows.

Grahic Jump Location
Figure 6

Compressor characteristic and throttle curves for a variety of settings. As one continuously varies the throttle setting, one traverses a one-dimensional curve through a normal form parameter space.

Grahic Jump Location
Figure 7

Sequence of phase portraits for the normal form as one varies the throttle setting

Grahic Jump Location
Figure 8

Branches of rotating stall amplitudes

Grahic Jump Location
Figure 9

Simulation of Moore-Greitzer model with KT=0.873. Variables x1 and y1 are the sine and cosine components of the first Fourier mode of the stall cell. Two slightly different initial conditions lead to dramatically different results.

Grahic Jump Location
Figure 10

(a) Simulation of Moore-Greitzer model with and without feedback control. With β, small surge dynamics are highly damped and the Liaw-Abed-type controller works. For larger β as in (b), however, the controller fails.

Grahic Jump Location
Figure 11

Eveker ’s (4)Φ̇ feedback successfully controls the system with larger β

Grahic Jump Location
Figure 12

Portraits corresponding to normal form dynamics of controlled systems

Grahic Jump Location
Figure 13

Phase portraits showing an example of a tertiary Hopf bifurcation

Grahic Jump Location
Figure 14

Simulation depicting three-frequency behavior in compression system



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In