Nonlinear/chaotic analysis, modelling and control of combustion instabilities due to vaporizing sprays

Lei, Shenghui; Turan, Ali

doi:10.1016/j.chaos.2009.03.081

Cited by 7 publications

(4 citation statements)

References 33 publications

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“…Table 1 shows the bifurcation parameter and the corresponding period at Hopf points under different coefficients as resolved by numerical and analytical methods. It is revealed that the analytical results are in good agreement with numerical values and the analytical formulae, (29) and (30), are reasonable to adopt. The slight difference between them is due to truncation errors during the numerical computations.…”

Section: Two-mode Dynamic Modelsupporting

confidence: 65%

“…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%

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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: Two-mode Dynamic Modelsupporting

confidence: 65%

Section: Introductionmentioning

confidence: 93%

Nonlinear/chaotic behaviour in thermo-acoustic instability

Lei¹,

Turan²

2009

Combustion Theory and Modelling

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“…Many studies have shown that the combustion process is a complex dynamic system, which is often greatly affected by initial conditions. There are nonlinear and chaotic characteristics in the combustion process [13–18]. Using the flame image to extract the flame combustion information and to analyze the data of the combustion information, the influence of initial conditions on the combustion process can be studied.…”

Section: Introductionmentioning

confidence: 99%

Chaotic Diagnostics in a Biodiesel Combustion System Using PLIF and Nonlinear Time Series Analysis^▴

Gao

Xiao

et al. 2020

Fuel Cells

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The combustion system of biodiesel has complex dynamic characteristics. In this paper, the combustion characteristics and flame stability of gutter oil biodiesel in a biodiesel evaporation combustion system are studied based on chaos identification theory. It aims to analyze the chaotic behavior of OH radical intensity on different equivalence ratio of laminar flame using OH‐PLIF technology with a specific focus on the use of 0–1 test. The results of 0–1 test are compared with those of phase space reconstruction, largest Lyapunov exponent and Fourier spectrum algorithm. The results show that the 0–1 test can be used as an efficient and reliable tool to diagnose the non‐linear dynamic characteristics of biodiesel combustion, and the combustion stability of flame is proportional to the chaotic intensity range. This method has a certain guiding value for identify the optimal combustion state and the most stable flame under different equivalence ratio.

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“…[1][2][3]. It arises from the interaction between the heat release and acoustic pressure or velocity oscillations within the combustion system.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation and nonlinear analysis of a time-delayed thermoacoustic system

Yang

Turan

Lei³

2017

Communications in Nonlinear Science and Numerical Simulation

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In this paper, of primary concern is a time-delayed thermoacoustic system, viz. a horizontal Rijke tube. A continuation approach is employed to capture the nonlinear behavior inherent to the system. Unlike the conventional approach by the Galerkin method, a dynamic system is naturally built up by discretizing the acoustic momentum and energy equations incorporating appropriate boundary conditions using a finite difference method. In addition, the interaction of Rijke tube velocity with oscillatory heat release is modeled using a modified form of King's law. A comparison of the numerical results with experimental data and the calculations reported reveals that the current approach can yield very good predictions. Moreover, subcritical Hopf bifurcations and fold bifurcations are captured with the evolution of dimensionless heat release coefficient, generic damping coefficient and time delay.Linear stability boundary, nonlinear stability boundary, bistable region and limit cycles are thus determined to gain an understanding of the intrinsic nonlinear behaviors.

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Nonlinear/chaotic analysis, modelling and control of combustion instabilities due to vaporizing sprays

Cited by 7 publications

References 33 publications

Nonlinear/chaotic behaviour in thermo-acoustic instability

Nonlinear/chaotic behaviour in thermo-acoustic instability

Chaotic Diagnostics in a Biodiesel Combustion System Using PLIF and Nonlinear Time Series Analysis^▴

Bifurcation and nonlinear analysis of a time-delayed thermoacoustic system

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Nonlinear/chaotic analysis, modelling and control of combustion instabilities due to vaporizing sprays

Cited by 7 publications

References 33 publications

Nonlinear/chaotic behaviour in thermo-acoustic instability

Nonlinear/chaotic behaviour in thermo-acoustic instability

Chaotic Diagnostics in a Biodiesel Combustion System Using PLIF and Nonlinear Time Series Analysis▴

Bifurcation and nonlinear analysis of a time-delayed thermoacoustic system

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Product

Resources

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Chaotic Diagnostics in a Biodiesel Combustion System Using PLIF and Nonlinear Time Series Analysis^▴