The role of hydrodynamic shear in the thermoacoustic response of slit flames

Short wavelength hydrodynamic perturbations excited by long wavelength acoustics can wrinkle the front of acoustically compact flames, perturb the heat release rate, and generate sound, thereby closing a thermoacoustic feedback loop. One important conversion mechanism in this context is the generation of vortical perturbations by acoustic waves impinging on a sharp corner. Such excitation may directly disturb the flame base or trigger vortex shedding in regions of high flow shear located upstream of the flame. These upstream perturbations, our main focus here, offer at least two mechanisms to drive excess gain of the flame transfer function (FTF). First, the convective time delay between the generation of upstream perturbations and their arrival at the flame may result in constructive interference with other perturbations generated at the flame base. Second, the burner geometry may allow upstream perturbations to be convectively amplified by hydrodynamic shear on their way to the flame. Leveraging linear frequency domain analysis of the compressible reactive flow equations, the present article demonstrates that both mechanisms contribute to the response of two-dimensional premixed laminar slit flames. The FTF is computed over a range of Reynolds numbers Re and slit lengths L in order to vary convective time delays and convective amplification and study their respective influences on the flame response. Analysis of the discrete impulse response reveals two amplification mechanisms for slit flame perturbations with independent delay times. The potential role of convective amplification of upstream disturbances on thermoacoustic feedback is further highlighted by means of resolvent analysis, which indicates that the optimal gain increases with the non-normality of the linearised reactive flow operator. These findings suggest passive thermoacoustic control strategies such as designing the burner geometry to avoid internal flow separation and minimise hydrodynamic disturbance amplification, and tuning the slit length to achieve destructive interference for problematic frequencies.