Coordinate Systems and Integration Limits for Global Flame Transfer Function Calculations

Humphrey, Luke; Acharya, Vishal; Shin, Dong-Hyuk; Lieuwen, Tim

doi:10.1260/1756-8277.6.4.411

Cited by 8 publications

(3 citation statements)

References 16 publications

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“…7(a) and 7(b) show that the entropy generation has a low-pass filter behavior. This result agrees qualitatively with the analytical derivations of F H in the G-equation framework made by Lieuwen [26], Cho et al [27] and Humphrey et al [28].…”

Section: Entropy Production By a Non-perfectly Pre-mixed Flamesupporting

confidence: 91%

On Generation of Entropy Waves by a Premixed Flame

Chen

Steinbacher

Silva

et al. 2016

Volume 4A: Combustion, Fuels and Emissions

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It is understood that so-called “entropy waves” can contribute to combustion noise and play a role in thermoacoustic instabilities in combustion chambers. The prevalent description of entropy waves generation regards the flame front as a source of heat at rest. Such a model leads — in its simplest form — to an entropy source term that depends exclusively on the unsteady response of the heat release rate and upstream velocity perturbations. However, in the case of a perfectly premixed flame, which has a constant and homogeneous fuel / air ratio and thus constant temperature of combustion products, generation of entropy waves (i.e. temperature inhomogeneities) across the flame is not expected. The present study analyzes and resolves this inconsistency, and proposes a modified version of the quasi 1-D jump relations, which regards the flame as a moving discontinuity, instead of a source at rest. It is shown that by giving up the hypothesis of a flame at rest, the entropy source term is related upto leading order in Mach number to changes in equivalence ratio only. To supplement the analytical results, numerical simulations of a Bunsen-type 2D premixed flame are analysed, with a focus on the correlations between surface area, heat release and position of the flame on the one hand, and entropy fluctuations downstream of the flame on the other. Both perfectly premixed as well as flames with fluctuating equivalence ratio are considered.

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Section: Entropy Production By a Non-perfectly Pre-mixed Flamesupporting

confidence: 91%

On Generation of Entropy Waves by a Premixed Flame

Chen

Steinbacher

Silva

et al. 2016

Volume 4A: Combustion, Fuels and Emissions

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“…*As noted in Humphrey et al (2014), multiple definitions for the spatially integrated heat release exist, depending upon one's assumptions of the potentially oscillating integration limits. We will assume here that flames are confined and spread to the wall and so the transverse integration limits are fixed, implying that the axial integration limits oscillate.…”

Section: Introductionmentioning

confidence: 99%

Modeling the Response of Turbulent Flames to Harmonic Forcing

Humphrey

Acharya

Shin

et al. 2016

Combustion Science and Technology

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This paper analyzes the response of a turbulent, premixed flame to harmonic forcing. This problem has been worked extensively for laminar flames, and the key parameters influencing the flame transfer function are well understood. For turbulent flames, several prior studies have utilized a "quasi-laminar" approach, by utilizing the time-averaged flame position, and ensemble-averaged disturbance field, as inputs to what is otherwise identical to the laminar problem. More generally, the manner in which turbulent flames respond to harmonic disturbances is not amenable to analytical solutions because of the nonlinear interactions between stochastic flow disturbances and harmonic flame wrinkling. We utilize a turbulent burning velocity closure proposed by Shin and Lieuwen (2013), who showed that the ensembleaveraged turbulent burning rate for a harmonically forced flame is proportional to the ensemble-Downloaded by [Georgia Tech Library], [Luke Humphrey] at 07:15 23 June 2016 2 averaged flame curvature. Shin and Lieuwen (2013) previously used it to analyze the ensembleaveraged space-time flame wrinkle characteristics. Here we extend these results to analyze the spatial variation of ensemble-averaged flame surface area and burning rate and then compare these results to computations. These results show that, for low stochastic forcing amplitudes, wrinkling of the front exerts quantitative differences between those predicted by a quasi-laminar and the actual flame response (e.g., reducing peak values of the flame transfer function, and eliminating nodes), but does not change the key qualitative features. While this result needs to be considered for strongly turbulent flames, it does suggest why good agreement has been observed between quasi-laminar approaches and experimental data for harmonically excited, turbulent flames. Two results for model problems showing the linearized flame transfer functions are also presented, which explicitly demonstrate qualitative turbulence effects on harmonically excited flames.

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“…The conical flame is single valued also in the axial direction. However, to work with a function which hasx as an independent variable is an unfortunate choice, because the flame tip moves along this direction and the domain of existence of the flame front becomes time dependent, [0,xend(t)], unnecessarily complicating the formulation[26].…”

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confidence: 99%

Linear stability and adjoint sensitivity analysis of thermoacoustic networks with premixed flames

Orchini

Juniper

2016

Combustion and Flame

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We analyse the linear response of laminar conical premixed flames modelled with the linearised front-track kinematic G-equation. We start by considering the case in which the flame speed is fixed, and travelling wave velocity perturbations are advected at a speed different from the mean flow velocity. A previous study of this case contains a small error in the Flame Transfer Function (FTF), which we correct. We then allow the flame speed to depend on curvature. No analytical solutions for the FTF exist for this case so the FTF has to be calculated numerically as its parameters -aspect ratio, convection speed and Markstein length -are varied. Then we consider the stability and sensitivity of thermoacoustic systems containing these flames. Traditionally, the stability of a thermoacoustic system is found by embedding the FTF within an acoustic network model. This can be expensive, however, because the FTF must be re-calculated whenever a flame parameter is varied. Instead, we couple the linearised G-equation directly with an acoustic network model, creating a linear eigenvalue problem without explicit knowledge of the FTF. This provides a simple and quick way to analyse the stability of thermoacoustic networks. It also allows us to use adjoint sensitivity analysis to examine, at little extra cost, how the system's stability is affected by every parameter of the system.

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Coordinate Systems and Integration Limits for Global Flame Transfer Function Calculations

Cited by 8 publications

References 16 publications

On Generation of Entropy Waves by a Premixed Flame

On Generation of Entropy Waves by a Premixed Flame

Modeling the Response of Turbulent Flames to Harmonic Forcing

Linear stability and adjoint sensitivity analysis of thermoacoustic networks with premixed flames

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