Turbulence-Induced Noise Effects on High-Frequency Combustion Instabilities

Clavin, Paul; Kim, J. S.; Williams, Forman A.

doi:10.1080/00102209408935347

Cited by 75 publications

(42 citation statements)

References 11 publications

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“…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.…”

Section: Figurementioning

confidence: 99%

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Triggering in a Thermoacoustic System with Stochastic Noise

Waugh

Juniper

2011

International Journal of Spray and Combustion Dynamics

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This paper explores the mechanism of triggering in a simple thermoacoustic system, the Rijke tube. It is demonstrated that additive stochastic perturbations can cause triggering before the linear stability limit of a thermoacoustic system. When triggering from low noise amplitudes, the system is seen to evolve to self-sustained oscillations via an unstable periodic solution of the governing equations. Practical stability is introduced as a measure of the stability of a linearly stable state when finite perturbations are present. The concept of a stochastic stability map is used to demonstrate the change in practical stability limits for a system with a subcritical bifurcation, once stochastic terms are included. The practical stability limits are found to be strongly dependent on the strength of noise.

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Section: Figurementioning

confidence: 99%

“…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].…”

Section: Figurementioning

confidence: 99%

Triggering in a Thermoacoustic System with Stochastic Noise

Waugh

Juniper

2011

International Journal of Spray and Combustion Dynamics

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“…When more acoustic modes are considered,this may not be the case, as demonstrated by Yang et al 1 for third-order gasdynamics. Therefore, the results of Clavin et al 11 may not be applicable in general.…”

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confidence: 68%

“…In addition,the formulation was awed, and the form of the resultingnoise terms is not quite correct. Clavin et al 11 studied the in uence of turbulence on instabilities in liquid rocket motors. Using only one mode in the analysis and thirdorder nonlinearities, it was reported that the inclusion of noise can lead to the possibilityof pulsed oscillations.It is a well-known result that a single third-order equation may produce a subcritical bifurcation.…”

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confidence: 99%

Influence of Random Excitations on Acoustic Instabilities in Combustion Chambers

Burnley

Culick

2000

AIAA Journal

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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.

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“…In addition, the formulation was flawed, and the form of the resulting noise terms is not quite correct. Clavin et al 21 studied the influence of turbulence on instabilities in liquid rocket motors. Using only one mode in the analysis and third-order nonlinearities, it was reported that the inclusion of noise can lead to the possibility of triggering.…”

Section: The Influence Of Combustion Noisementioning

confidence: 99%

Some Dynamics of Acoustic Oscillations With Nonlinear Combustion and Noise

Burnley¹,

Culick

1997

Int J Energetic Materials Chem Prop

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The results given in this paper constitute a continuation of progress with nonlinear analysis of coherent oscillations in combustion chambers. We are currently focusing attention on two general problems of nonlinear behavior important to practical applications: the conditions under which a linearly unstable system will execute stable periodic limit cycles; and the conditions under which a linearly stable system is unstable to a sufficiently large disturbance. The first of these is often called 'soft' excitation, or supercritical bifurcation; the second is called 'hard' excitation, 'triggering,' or subcritical bifurcation and is the focus of this paper. Previous works extending over more than a decade have established beyond serious doubt (although no formal proof exists) that nonlinear gasdynamics alone does not contain subcritical bifurcations. The present work has shown that nonlinear combustion alone also does not contain subcritical bifurcations, but the combination of nonlinear gasdynamics and combustion does. Some examples are given for simple models of nonlinear combustion of a solid propellant but the broad conclusion just mentioned is valid for any combustion system. Although flows in combustors contain considerable noise, arising from several kinds of sources, there is 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 here a few results of power spectral densities of acoustic amplitudes in the presence of a sub critical bifurcation associated with nonlinear combustion and gasdynamics.

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Turbulence-Induced Noise Effects on High-Frequency Combustion Instabilities

Cited by 75 publications

References 11 publications

Triggering in a Thermoacoustic System with Stochastic Noise

Triggering in a Thermoacoustic System with Stochastic Noise

Influence of Random Excitations on Acoustic Instabilities in Combustion Chambers

Some Dynamics of Acoustic Oscillations With Nonlinear Combustion and Noise

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