Analytical model of nonlinear thermo-acoustic effects in a matrix burner

Heckl, Maria A.

Abstract

This paper considers a fundamental thermo-acoustic test rig developed by Noiray (Linear and Nonlinear Analysis of Combustion Instabilities, Application to Multipoint Injection Systems and Control Strategies”, Ph.D. Thesis, École Centrale Paris, 2007) and models it with an entirely analytical approach. The measured flame describing function is represented by a surprisingly simple time-lag law, which is then used to derive the governing equation for a single acoustic mode in the test rig. This equation turns out to be that of a harmonic oscillator with a damping/amplification coefficient that depends on the velocity amplitude. On this basis we find analytically the pattern of the oscillation regimes in parameter space, in particular the frequency and amplitude of limit cycles at various tube lengths. There is good qualitative agreement with some, but not all, features of Noiray’s observations.

Citation

Heckl, M. A. (2013). Analytical model of nonlinear thermo-acoustic effects in a matrix burner. Journal of Sound and Vibration, 332(17), 4021-4036. https://doi.org/10.1016/j.jsv.2012.11.010

• Journal Article Type: Article
• Acceptance Date: Nov 8, 2012
• Online Publication Date: May 29, 2013
• Publication Date: Aug 19, 2013
• Deposit Date: Jun 14, 2023
• Journal: Journal of Sound and Vibration
• Print ISSN: 0022-460X
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 332
• Issue: 17
• Pages: 4021-4036
• DOI: https://doi.org/10.1016/j.jsv.2012.11.010
• Keywords: Mechanical Engineering; Mechanics of Materials; Acoustics and Ultrasonics; Condensed Matter Physics
• Additional Information: This article is maintained by: Elsevier; Article Title: Analytical model of nonlinear thermo-acoustic effects in a matrix burner; Journal Title: Journal of Sound and Vibration; CrossRef DOI link to publisher maintained version: https://doi.org/10.1016/j.jsv.2012.11.010; Content Type: article; Copyright: Copyright © 2012 Elsevier Ltd. All rights reserved.