The domain of influence of flame instabilities in turbulent premixed combustion

Abstract

Although a number of experiments and numerical simulations indicate persistence of flame instability effects in turbulent premixed flames, the exact domain of influence of these instabilities remains unknown. In this study, a simple estimate of that domain is obtained by comparing a characteristic flame stretch due to flame instabilities, Ki, with a characteristic flame stretch due to turbulent eddies, Kt. The resulting criterion, (Kt/Ki)≤1, shows that instability effects are promoted by: small values of the ratio of turbulence intensity divided by the laminar flame speed (u′/sL): large values of the ratio of integral length scale divided by the laminar flame thickness (lt/lF) (given that (lt/lF)>10): large values of the heat release factor τ: large positive values of the flame Richardson number Ri (Ri measures buoyancy effects and is positive when the corresponding flow acceleration is directed from the fresh mixture to the burnt gas): small values (below one) of the flame Lewis number Le. Direct numerical simulations (DNS) are used to test the validity of the theoretical criterion. The numerical configuration corresponds to three-dimensional premixed flames propagating into a temporally decaying turbulent flow. The simulations are limited by DNS constraints to small length scale ratios, (lt/lF)≤10; they use Le=1 and correspond to different values of (u′/sL), τ and Ri. Due to the turbulence decay, all simulated flames with τ≠0 and Ri≥0 undergo a transition from turbulent to unstable flame surface dynamics. The DNS values of (Kt/Ki) at transition time are found to be of order one and are in good agreement with the theoretical predictions.