Abstract
Convective velocity perturbations (CVPs) are known to play an important role in the response of flames to acoustic perturbations and in thermoacoustic combustion instabilities. In order to elucidate the flow-physical origin of CVPs, the present study models the response of laminar premixed slit flames to low amplitude perturbations of the upstream flow velocity with a reduced order flow decomposition approach: A linearized G-equation represents the shape and heat release rate of the perturbed flame, while the velocity perturbation field is decomposed into irrotational and solenoidal contributions. The former are determined with a conformal mapping from geometry and boundary conditions, whereas the latter are governed by flame front curvature and flow expansion across the flame, which generates baroclinic vorticity. High-resolution CFD analysis provides values of model parameters and confirms the plausibility of model results. This flow decomposition approach makes it possible to explicitly evaluate and analyze the respective contributions of irrotational and solenoidal flows to the flame response, and conversely the effect of flame perturbations on the flow. The use of the popular ad hoc hypothesis of convected velocity perturbation is avoided. It is found that convected velocity perturbations do not result from immediate acoustic-to-hydrodynamic mode conversion, but are generated by flame-flow feedback. In this sense, models for flame dynamics that rely on ad-hoc models for CVPs do not respect causality. Furthermore, analysis of the flame impulse response reveals that for the configuration investigated, flame-flow feedback is also responsible for “excess gain” of the flame response, that is, the magnitude of the flame frequency response above unity.
Highlights
Publisher’s Note: MDPI stays neutralThermoacoustic instabilities are a cause for concern in combustion applications as diverse as rocket engines, gas turbines, or domestic heaters [1,2,3,4]
Flame frequency and impulse responses are computed with a model that relies on unidirectional flow/flame coupling
The response of confined, laminar, premixed slit flames to acoustic perturbations has been explored with a flow decomposition approach that allows us to judiciously “switch off” various mechanisms of acoustic/flow/flame interactions
Summary
Thermoacoustic instabilities are a cause for concern in combustion applications as diverse as rocket engines, gas turbines, or domestic heaters [1,2,3,4]. Such instabilities can lead to severe mechanical or thermal damage, even catastrophic failure of a combustor. The FTF relates variations of the heat release rate to those of velocity upstream of the flame. It may be represented in the frequency domain by the frequency response (FR) or in the time domain by the impulse response (IR) [10,11]. Several studies have proposed analytical expressions for the FTF of laminar Bunsen-type flames with regard to jurisdictional claims in published maps and institutional affiliations
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