A direct numerical simulation study of frequency and Lewis number effects on sound generation by two-dimensional forced laminar premixed flames

Abstract

This paper presents a numerical investigation of sound generation by two-dimensional laminar premixed flames. Direct numerical simulation (DNS) is used to study low Mach number flames with different Lewis numbers, namely Le=0.5, 1 and 2, excited by velocity perturbations at the inflow boundary for a range of frequencies. At intermediate forcing frequencies, ‘flame pinch-off’ and ‘flame island burn-out’ are observed as strong, monopolar sound sources for Le=1 and 2. However, these events produce almost no sound for Le=0.5.Dowling’s reformulation of Lighthill’s acoustic analogy is used to investigate the contribution of heat release rate fluctuations to the radiated sound. A comparison of direct calculation of heat release rate fluctuations and estimated values using a flamelet theory suggested by Clavin and Siggia [7], which assumes that heat release fluctuations are due to flame surface area fluctuations, shows good agreement for unity Lewis number when the forcing period is larger than the flame time. For forcing periods smaller than the flame time, flamelet theory does not succeed in describing the effects of heat release fluctuations, as expected. However, even for forcing periods greater than the flame time, the flamelet theory does not capture the observed trend with Lewis number. The pressure fluctuations due to heat release are always over-predicted by flamelet theory for Le=0.5 and under-predicted for Le=2.The flamelet model, intended for application to turbulent flames, assumes a constant consumption speed along the flame surface. The failure of this model in the case of non-unity Lewis number in the present unsteady laminar flames can be therefore due to the large modification of the consumption speed where large surface area fluctuation is present.