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research-article

THERMOACOUSTIC MODES OF QUASI-1D COMBUSTORS IN THE REGION OF MARGINAL STABILITY

[+] Author and Article Information
Camilo F. Silva

Professur für Thermofluiddynamik, Technische Universität München
silva@tfd.mw.tum.de

Kah Joon Yong

Professur für Thermofluiddynamik, Technische Universität München
kah-joon.yong@tum.de

Luca Magri

University of Cambridge, Engineering Department, Cambridge, UK
lm547@cam.ac.uk

1Corresponding author.

ASME doi:10.1115/1.4041118 History: Received July 04, 2018; Revised July 17, 2018

Abstract

The purpose of this study is twofold. In the first part, we show that the resonance frequencies of two premixed combustors with fully acoustically reflecting boundary conditions in the region of marginal stability depend only on the parameters of the flame dynamics, but do not depend on the combustor's geometry. This is shown by means of a parametric study, where the time delay and the interaction index of the flame response are varied and the resulting complex eigenfrequency locus is shown. Assuming longitudinal acoustics and a low Mach number, a quasi-1D Helmholtz solver is utilized. The time delay and interaction index of the flame response are parametrically varied to calculate the complex eigenfrequency locus. It is found that all the eigenfrequency trajectories cross the real axis at a resonance frequency that depends only on the time delay. Such marginally stable frequencies are independent of the resonant cavity modes of the two combustors, i.e. the passive thermoacoustic modes. In the second part, we exploit the aforementioned observation to evaluate the critical flame gain required for the systems to become unstable at four eigenfrequencies located in the marginally stable region. A computationally-efficient method is proposed. The key ingredient is to consider both direct and adjoint eigenvectors associated with the four eigenfrequencies. Hence, the sensitivity of the eigenfrequencies to changes in the gain at the region of marginal stability is evaluated with cheap and accurate calculations.

Copyright (c) 2018 by ASME
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