On the dynamics of anchored flames

Boyer, L.; Quinard, Joel

doi:10.1016/0010-2180(90)90077-5

Cited by 118 publications

(62 citation statements)

References 8 publications

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“…32,[43][44][45] It has been reported that this low-order model is capable of reproducing fairly realistic flame behavior observed for laminar wedge flames in both the linear 46 and nonlinear regime. 47 However, in general, the formulation of _ q in equation (17) allows for any linear filter deduced from experiments or numerical simulations.…”

Section: The Flame Subsystemmentioning

confidence: 86%

A systems perspective on non-normality in low-order thermoacoustic models: Full norms, semi-norms and transient growth

Blumenthal

Tangirala

Sujith

et al. 2016

International Journal of Spray and Combustion Dynamics

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Non-normal transient growth of energy is a feature encountered in many physical systems. Its observation is intimately related to the norm used to describe the system dynamics. For a multi-physics problem such as thermoacoustics, where a heat source is in feedback with acoustic waves and a flow field, the appropriate metric is an ongoing matter of debate. Adopting a systemic perspective, it is argued in the present paper that an energy norm is, in principle, a matter of choice, but one that is critically tied to the dynamics described by the system model. To illustrate our arguments, it is shown that different norms exhibit the non-normal dynamics of thermoacoustic systems differently, but that this difference is fully explicable by the energy flux and source terms related to the formulation of the model. The non-normal dynamics as such is unaffected by the choice of norm, and transient growth merely results from a maximization of the flux and source terms governing the energy balance associated with the specific model formulation. Investigating transient growth for arbitrary energy norms requires the capability to handle semi-norm optimization problems. In the present study, we propose an approach to do so using the singular value decomposition. Non-normal transient growth around a stable fix point is then investigated for a low-order model of a simple thermoacoustic configuration of a premixed flame enclosed in a duct with non-zero mean temperature jump and bulk mean flow. The corresponding optimal mode shapes and pertinent parameters leading to transient growth are identified and discussed. For transient growth resulting from the interaction of the flame with the acoustic field, it is found that heat sources with a fast response lead to more transient growth than slow heat sources, because the system can bear a larger source term before becoming linearly unstable. Furthermore, the amount of transient energy growth does not increase monotonically with the amplitude of the initial perturbation of the flame.

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Section: The Flame Subsystemmentioning

confidence: 86%

A systems perspective on non-normality in low-order thermoacoustic models: Full norms, semi-norms and transient growth

Blumenthal

Tangirala

Sujith

et al. 2016

International Journal of Spray and Combustion Dynamics

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show abstract

“…A new stage in modeling was initiated by the idea to describe the kinematics of the excited flame front by the so-called G-equation [20]. The fundamentally new idea in this approach is that the flame front perturbations are not prescribed a priori, but naturally arise as the flame front responds to an applied flow perturbation.…”

Section: The Genesis Of Thermo-acoustic Models Of Premixed Bunsen-typmentioning

confidence: 99%

Experimental and numerical investigation of the acoustic response of multi-slit Bunsen burners

Kornilov

Rook

Boonkkamp

et al. 2009

Combustion and Flame

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“…This work is motivated by recent work to model both the local space-time dynamics of the flame, as well as its globally integrated heat release, in response to flow and mixture property variations [1][2][3][4][5][6][7][8][9]. The front tracking approach forms the basis of the flame response modeling used here, where the flame position is the zero contour of the implicit function, , whose dynamics are described by [1,2,[10][11][12], (1) where is the flow velocity at the flame front, and s f denotes the normal propagation front speed.…”

mentioning

confidence: 99%

Coordinate Systems and Integration Limits for Global Flame Transfer Function Calculations

Humphrey

Acharya

Shin

et al. 2014

International Journal of Spray and Combustion Dynamics

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On the dynamics of anchored flames

Cited by 118 publications

References 8 publications

A systems perspective on non-normality in low-order thermoacoustic models: Full norms, semi-norms and transient growth

A systems perspective on non-normality in low-order thermoacoustic models: Full norms, semi-norms and transient growth

Experimental and numerical investigation of the acoustic response of multi-slit Bunsen burners

Coordinate Systems and Integration Limits for Global Flame Transfer Function Calculations

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