Bifurcation of steady combustion regimes and their influence on the onset of high-frequency oscillations in combustion chambers

Natanzon, M. S.; Men'shikova, O. M.

doi:10.1007/bf00789947

Cited by 5 publications

(4 citation statements)

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“…It makes sense to study the nonlinear behaviour inherent in thermo-acoustic instability using tools that can explore the variation of certain parameters covering the entire operational conditions. Such considerations also pointed out by Culick [30,32,33] and Lei and Turan [29], enforce the notion that each numerical (CFD) simulation is, in general, only one particular case and it is, to some extent, difficult to generalise limited results to gain a fundamental understanding of thermo-acoustic instability in totality.…”

Section: Introductionmentioning

confidence: 93%

Nonlinear/chaotic behaviour in thermo-acoustic instability

Lei¹,

Turan²

2009

Combustion Theory and Modelling

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This paper is concerned with the dynamic system nonlinear behaviour encountered in classical thermo-acoustic instability. The Poincaré map is adopted to analyse the stability of a simple non-autonomous system considering a harmonic oscillation behaviour for the combustion environment. The bifurcation diagram of a one-mode model is obtained where the analysis reveals a variety of chaotic behaviours for some select ranges of the bifurcation parameter. The bifurcation parameter and the corresponding period of a two-mode dynamic model are calculated using both analytical and numerical methods. The results computed by different methods are in good agreement. In addition, the dependence of the bifurcation parameter and the period on all the relevant coefficients in the model is investigated in depth. IntroductionVarious devices including aerospace propulsion, gas turbines, domestic boilers and radiant heaters, frequently suffer from combustion instability. It is widely recognised that the thermo-acoustic instability results from the interaction of heat release within a combustion chamber with pressure/velocity oscillations related to the chamber acoustics. Generally, the amplitude of pressure oscillation within a chamber will increase if the heat-release energy is transferred with the appropriate phase to an acoustic field, as illustrated in Rayleigh's seminal work on thermo-acoustic instability known as Rayleigh's Criterion [1]. Chu [2] proposed a more comprehensive criterion, as a generalised form of Rayleigh's criterion, considering the effect of boundary conditions and viscous dissipation, in addition to the exchange of energy between combustion and the acoustic waves. Chu's criterion reveals that thermo-acoustic instability occurs if the net energy gain from combustion exceeds the sum of the energy losses across the boundary and due to dissipation. Consequently, the amplitude of pressure fluctuations increase initially and then reach a plateau, viz., the limit cycle, owing to nonlinear effects. Therefore, it is of paramount importance to pay attention to system nonlinearities resulting in thermo-acoustic instability.In the past, the various nonlinear behaviours concerning thermo-acoustic instability have been investigated experimentally, analytically and computationally by a number of authors [3][4][5][6][7][8][9][10][11][12][13][14]. Culick [3,4] put forward a second-order nonlinear dynamic model using

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Section: Introductionmentioning

confidence: 93%

Nonlinear/chaotic behaviour in thermo-acoustic instability

Lei¹,

Turan²

2009

Combustion Theory and Modelling

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“…The content of this part of the chapter was presented in Ref. [71], where not only the bifurcation of steady-state regimes of combustion was examined, but also the changes of stability of the combustion processes due to those bifurcations.…”

Section: Bifurcations Of Steady Combustion Regimes Andmentioning

confidence: 99%

Combustion Instability

Natanzon¹

2008

Self Cite

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“…Its significance probably depends on the geometry and flow conditions in the combustor. Another example has been discussed by Dubinkin, Natanzon and Cham'yan (1978) and Natanzon and Men'shikova (1992) for a liquid jet injector of the sort used in liquid rocket engines. Presently work is progressing to determine more precisely the physical.,processes responsible for the hysteresis.…”

Section: Concludinv Remarksmentioning

confidence: 99%

“…Its existence in the combustor used in this work was implied by data reported by Sterling and Zukoski (1987) but the results found here are the first defining its character and demonstrating the possibility of controlled transitions from the 'unstable' to the 'stable' state described above. Previous work in Russia on liquid rocket combustors (Natanzon and Men'shikova, 1992) has appealed explicitly to the presence of hysteresis to explain some otherwise puzzling behavior of instabilities. However, those researchers did not recognize the phenomenon as a possible basis for active control.…”

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confidence: 99%