Influence of random excitations on acoustic instabilities in combustion chambers

Abstract

Although ows in combustors contain considerable noise, arising from several kinds of sources, there is a sound basis for treating organized oscillations as distinct motions. That has been an essential assumption incorporated in virtually all treatments of combustion instabilities. However, certain characteristics of the organized or deterministic motions seem to have the nature of stochastic processes. For example, the amplitudes in limit cycles always exhibit a random character, and even the occurrence of instabilities seems occasionally to possess some statistical features. Analysis of nonlinear coherent motions in the presence of stochastic sources is, therefore, an important part of the theory. We report a few results for organized oscillations in the presence of noise. The most signi cant de ciency is that, because of the low level of current understanding, the stochastic sources of noise are modeled in ad hoc fashion and are not founded on a solid physical basis appropriate to combustion chambers.

Triggering in a Thermoacoustic System with Stochastic Noise

“…When stochastic forcing is present, probability density functions (PDFs) have been used to describe the response of thermoacoustic systems in both experiments and theory [2,15,[18][19][20]. These papers show that a single periodic solution creates a bimodal PDF, and that the addition of other stable solutions creates additional peaks.…”

“…Various types of noise have been shown to destabilise systems that are linearly stable when noiseless [2,[13][14][15] . Noise resulting from entropy and vorticity has also been shown to play a part in the process [2].…”

“…Various types of noise have been shown to destabilise systems that are linearly stable when noiseless [2,[13][14][15] . Noise resulting from entropy and vorticity has also been shown to play a part in the process [2]. Non-normality has been highlighted as a key factor in the amplification of noise [16], and the susceptibility of a system to to be pushed out of the basin of attraction of the stable zero solution.…”

“…This is known as triggering, or pulsed oscillation [2,3]. An analogy has been suggested with bypass transition to turbulence in hydrodynamics [1,Ch1 §IV] [4].…”

Modeling and Dynamics of Nonlinear Acoustic Waves in a Combustion Chamber

“…Experiments by Ma et al [20] have suggested that the velocity coupling function has a threshold nature, i.e., there is a threshold value of the acoustic velocity below which the effects of nonlinear combustion are not felt. In a recent paper, using a four-mode truncation and an ad hoc threshold velocity coupling model, Burnley and Culick [21] have computed a bifurcation diagram which shows triggered limit cycles. Additional results are available in the thesis by Burnley [22].…”