Characterization of critical eigenvalues of axial flow engine compressor PDE model

Abstract

In this article, we study the spectrum of axial flow engine compressor PDE model and show that there are three types of critical eigenvalues which determine the stability of the steady solution of the system depending on the compressor geometry. All of these critical eigenvalues cross the imaginary axis with nonzero speeds as the throttle coefficient increases, leading to Hopf bifurcations of the system.

†Dedicated to Professor Wei Lin on the occasion of his 70th birthday.

Keywords:

• Moore–Greitzer PDE model
• Spectrum of linear operator
• Linearized system

Keywords:

• Mathematics Subject Classifications 2000:
• 34D45
• 34K15
• 35B40
• 35K55

Acknowledgement

This research was supported in part by the Summer Faculty Fellowship from Air Force Office of Scientific Research, 2001–2002. This work is submitted to the special issue of Applicable Analysis for Professor Wei Lin's 70th birthday.

Notes

†Dedicated to Professor Wei Lin on the occasion of his 70th birthday.