Development of a comprehensive flame transfer function and its application to predict combustion instabilities in a dump combustor

ABSTRACT

In combustion instability analysis, a flame transfer function (FTF) is used to describe the response of a premixed flame to incident acoustic oscillations. A comprehensive FTF is developed that relates the fluctuations in flame heat-release rate to those in density, heat of reaction, turbulent flame speed, and the flame surface area. Each of these four contributions is eventually expressed in terms of the fluctuations in acoustic pressure and velocity through the respective response functions. The flame surface-area response to acoustic oscillations is incorporated into the FTF through the -equation level-set method. In this method, we directly solve for the level-set fluctuations in terms of the velocity fluctuations and then relate the flame surface-area oscillations to . In the absence of turbulent flame-speed fluctuations, the response functions from the present -equation approach are in good agreement with those from the conventional -equation approach (where one writes ). However, when the turbulent flame-speed fluctuations are included, the two approaches differ, principally in the flame response to axial velocity fluctuations. The current FTF, generalized for any mean flame shape, is applied to analyze the response of a V-shaped mean flame located at the cross-sectional interface of a 2D dump combustor. For this flame, the effects of variation in acoustic frequency, mean Mach number, mean temperature, and mean equivalence ratio on the FTF magnitude and phase are investigated. Both axial and mixed mode acoustic perturbations are considered. For the purely axial modes, the response-function amplitudes of density and heat of reaction are seen to be independent of frequency, while those of flame speed and axial velocity exhibit harmonic-like oscillations as a function of frequency. For the mixed-mode fluctuations, the response-function amplitude of density decays monotonically with frequency, whereas the response-function amplitudes of the heat of reaction, turbulent flame speed, and velocity components show decaying oscillatory behavior in frequency. Further, it is observed that the flame-speed response function contributes the most to the overall FTF. Phase analysis of the FTF shows that the transverse velocity response is nearly in phase with the heat-release fluctuations. In addition, density and transverse velocity fluctuations always show constructive interference with pressure fluctuations. The current FTF is also incorporated into a linear modal analysis framework to predict the combustion instabilities in a 2D dump combustor, and the model predictions validated against experiments. Three mean velocity profiles—uniform, parabolic, and turbulent power law—are considered. For the three flames, the first three longitudinal and fundamental transverse unstable modes are predicted.

KEYWORDS:

• Flame transfer function
• Combustion instability
• G-equation
• Turbulent premixed flames
• Turbulent flame speed

Nomenclature

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