Two regimes of operation in a combustion chamber with a recirculation zone

Dubinkin, B. N.; Natanzon, M. S.; Cham'yan, A. É.

doi:10.1007/bf00786094

Cited by 8 publications

(7 citation statements)

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“…The bifurcation occurring in a dump combustor was confirmed by experiments in [10]. More recently, to understand fully the underlying mechanisms relevant to thermo-acoustic instability, nonlinear analysis has been employed in a more comprehensive manner [10][11][12][13][14]. Bifurcation of the steady combustion regimes induced by combustion in a dump combustor was pointed out in [10].…”

Section: Introductionmentioning

confidence: 90%

“…The limit cycle occurring in solid rocket motors was discussed using a numerical method by Levine and Baum [9]. The bifurcation occurring in a dump combustor was confirmed by experiments in [10]. More recently, to understand fully the underlying mechanisms relevant to thermo-acoustic instability, nonlinear analysis has been employed in a more comprehensive manner [10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 94%

“…More recently, to understand fully the underlying mechanisms relevant to thermo-acoustic instability, nonlinear analysis has been employed in a more comprehensive manner [10][11][12][13][14]. Bifurcation of the steady combustion regimes induced by combustion in a dump combustor was pointed out in [10]. Huang et al [11] argued that the heat transfer coefficient between the wall and the burned gas is an important bifurcation parameter for the combustion instability.…”

Section: Introductionmentioning

confidence: 99%

“…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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confidence: 99%

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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: 90%

Section: Introductionmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Nonlinear/chaotic behaviour in thermo-acoustic instability

Lei¹,

Turan²

2009

Combustion Theory and Modelling

View full text Add to dashboard Cite

show abstract

“…More recently, to fully understand the underlying mechanisms relevant to combustion instability, nonlinear analyses have been employed in a more comprehensive manner. Bifurcation of the steady combustion regimes induced by combustion in a dump combustor was pointed out by Dubinkin et al [11]. Huang et al [17] argued that the heat transfer coefficient between the wall and the burned gas is an important bifurcation parameter for the combustion instability.…”

Section: Introductionmentioning

confidence: 97%