Vorticity in unsteady premixed flames: vortex pair–premixed flame interactions under imposed body forces and various degrees of heat release and laminar flame thickness

Abstract

The dynamics of vortical structures are investigated when a vortex pair propagates into a premixed flame under different imposed body forces in the direction of mean flame propagation and various degrees of heat release and laminar flame thicknesses. The direct numerical simulation assumes zero Mach number, adiabatic, simple chemistry equations, and constant diffusivities. Visual pictures of the qualitatively different behaviors of the vortical structures emerge. These range from destruction of the incoming vortex pair and flame generation of flame-attached counter-rotating (rotating in the opposite sense to the incoming vortex pair) vortical structures to amalgamation of the incoming vortex pair with flame-generated, flame-attached, co-rotating (rotating in the same sense as the incoming vortex pair) vortical structures. Understanding of the different qualitative behaviors is aided by examination of the vorticity transport equation in two dimensions. Baroclinic torque is found to scale more strongly with heat release and laminar flame thickness than dilatation. As a result, increasing values of heat release and decreasing values of laminar flame thickness significantly strengthen the intensity of the flame-attached vortical structures. For experimentally realizable values of heat release and laminar flame thickness the intensity of the flame-attached vortical structures can be significantly greater than the incoming wrinkle-inducing vortex pair, supporting baroclinic torque as a mechanism for the increase in the conditional burnt gas turbulence intensities observed experimentally (Cheng and Shepherd, 1987). With a positive mean pressure gradient from reactants to products, the pressure gradient in the unburnt gas in the flame finger formed by the incoming vortex pair is close to that in the burnt gas. For strong adverse body forces this results in streamwise velocities in the unburnt gas in the flame finger greater than in the burnt gas around the finger. This potentially creates a gradient transport mechanism for turbulent scalar fluxes through the Bray–Moss–Libby (BML) model of the turbulent scalar flux ρ ̄ u ″ ic″ ̃ = ρ̄ c̃(1 − c̃)( u ib − u iu ), where u iu and u ib are conditional mean velocities in unburnt and burnt gas, respectively.