Propagation and generation of acoustic and entropy waves across a moving flame front

Chen, Lin Strobio; Bomberg, Sebastian; Polifke, Wolfgang

doi:10.1016/j.combustflame.2016.01.015

Cited by 71 publications

(31 citation statements)

References 27 publications

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“…However, downstream of the flame, the density contains the influence of both acoustic and entropy waves through Gibbs' relation (26). Small entropy inhomogeneities appear in the downstream region because the acoustic fluctuations change the temperature upstream, while the mean heat release is constant in this model [212]. The entropy spots are accelerated through the nozzle and converted into indirect acoustic waves.…”

Section: Sensitivity To Passive Devicesmentioning

confidence: 93%

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Adjoint Methods as Design Tools in Thermoacoustics

Magri

2019

Applied Mechanics Reviews

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In a thermoacoustic system, such as a flame in a combustor, heat release oscillations couple with acoustic pressure oscillations. If the heat release is sufficiently in phase with the pressure, these oscillations can grow, sometimes with catastrophic consequences. Thermoacoustic instabilities are still one of the most challenging problems faced by gas turbine and rocket motor manufacturers. Thermoacoustic systems are characterized by many parameters to which the stability may be extremely sensitive. However, often only few oscillation modes are unstable. Existing techniques examine how a change in one parameter affects all (calculated) oscillation modes, whether unstable or not. Adjoint techniques turn this around: They accurately and cheaply compute how each oscillation mode is affected by changes in all parameters. In a system with a million parameters, they calculate gradients a million times faster than finite difference methods. This review paper provides: (i) the methodology and theory of stability and adjoint analysis in thermoacoustics, which is characterized by degenerate and nondegenerate nonlinear eigenvalue problems; (ii) physical insight in the thermoacoustic spectrum, and its exceptional points; (iii) practical applications of adjoint sensitivity analysis to passive control of existing oscillations, and prevention of oscillations with ad hoc design modifications; (iv) accurate and efficient algorithms to perform uncertainty quantification of the stability calculations; (v) adjoint-based methods for optimization to suppress instabilities by placing acoustic dampers, and prevent instabilities by design modifications in the combustor's geometry; (vi) a methodology to gain physical insight in the stability mechanisms of thermoacoustic instability (intrinsic sensitivity); and (vii) in nonlinear periodic oscillations, the prediction of the amplitude of limit cycles with weakly nonlinear analysis, and the theoretical framework to calculate the sensitivity to design parameters of limit cycles with adjoint Floquet analysis. To show the robustness and versatility of adjoint methods, examples of applications are provided for different acoustic and flame models, both in longitudinal and annular combustors, with deterministic and probabilistic approaches. The successful application of adjoint sensitivity analysis to thermoacoustics opens up new possibilities for physical understanding, control and optimization to design safer, quieter, and cleaner aero-engines. The versatile methods proposed can be applied to other multiphysical and multiscale problems, such as fluid–structure interaction, with virtually no conceptual modification.

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Section: Sensitivity To Passive Devicesmentioning

confidence: 93%

“…Therefore, the heat source creates a discontinuity in the mean flow, and jump conditions can be derived by the integral form of the governing equations, accordingly. When linearized, the jump conditions at the nondimensional flame location x f read [212] ρ ū +ρu…”

Section: Helmholtz Equationmentioning

confidence: 99%

Adjoint Methods as Design Tools in Thermoacoustics

Magri

2019

Applied Mechanics Reviews

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“…Recent work for highly simplified (1-D planar and zero Mach number) flames has suggested that entropy disturbances are only generated in the presence of equivalence ratio fluctuations [25, 26]. This paper investigates the transport of entropy perturbations in realistic combustor flow-fields, and does not address the issue of entropy disturbance generation itself.…”

Section: Introductionmentioning

confidence: 99%

Dispersion of Entropy Perturbations Transporting through an Industrial Gas Turbine Combustor

Xia

Durán

Morgans

et al. 2017

Flow Turbulence Combust

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In the context of combustion noise and combustion instabilities, the transport of entropy perturbations through highly simplified turbulent flows has received much recent attention. This work performs the first systematic study into the transport of entropy perturbations through a realistic gas turbine combustor flow-field, exhibiting large-scale hydrodynamic flow features in the form of swirl, separation, recirculation zones and vortex cores, these being ubiquitous in real combustor flows. The reacting flow-field is simulated using low Mach number large eddy simulations, with simulations validated by comparison to available experimental data. A generic artificial entropy source, impulsive in time and spatially localized at the flame-front location, is injected. The conservation equation describing entropy transport is simulated, superimposed on the underlying flow-field simulation. It is found that the transport of entropy perturbations is dominated by advection, with both thermal diffusion and viscous production being negligible. It is furthermore found that both the mean flow-field and the large-scale unsteady flow features contribute significantly to advective dispersion — neither can be neglected. The time-variation of entropy perturbation amplitude at combustor exit is well-modelled by a Gaussian profile, whose dispersion exceeds that corresponding to a fully-developed pipe mean flow profile roughly by a factor of three. Finally, despite the attenuation in entropy perturbation amplitude caused by advective dispersion, sufficient entropy perturbation strength is likely to remain at combustor exit for entropy noise to make a meaningful contribution at low frequencies.

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“…We are thus left with the relation _ q / v, which substituted into equation (28) yields a source term analog to the classical Rayleigh source term @E=@t / _ q p F . The phenomenon of a flame at rest producing fluctuations in energy is referred to as ''the classical paradox of thermoacoustics'' by Bauerheim et al 54 and is also explained by Strobio Chen et al 55 The above described mechanism of creating fluctuations in heat release rate is fundamentally different from the fluctuations in heat release rate resulting from an active flame as described in The flame subsystem …”

Section: The Output Defines the Perspectivementioning

confidence: 99%

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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Propagation and generation of acoustic and entropy waves across a moving flame front

Cited by 71 publications

References 27 publications

Adjoint Methods as Design Tools in Thermoacoustics

Adjoint Methods as Design Tools in Thermoacoustics

Dispersion of Entropy Perturbations Transporting through an Industrial Gas Turbine Combustor

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

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