Vortex Simulation of Unsteady Wrinkled Laminar Flames

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Abstract
A discrete vortex dynamics time-dependent simulation of a premixed wrinkled laminar flame shows that the computed turbulent shear stress in the flame brush region based on unconditioned velocities is substantial. By comparison, the computed shear stresses in the burnt and in the unburnt flow are negligible. Thus, it is the intermittent flame motion that gives the appearance of counter-gradient fluxes in a turbulence model based on unconditioned velocities. The flame is considered to be of zero thickness and the flame location is described in terms of arc length from the flame holder. Two-dimensional V-shaped and bunsen burner flames have been simulated in planar geometry. A flame speed relation is used which depends on flame curvature and in some calculations on flame stretch. Discrete volume sources are distributed along the flame location to represent the volume expansion at constant pressure combustion in this open system. The estimated vorticity production due to fluctuating pressure gradients combined with an assumed flame density gradient is small compared to the freestream turbulence level of five percent, and hence was neglected in this simulation. At fixed locations in the middle of the flame brush, the passage time distribution indicates the geometrical nature of the flame sheet in that the cusps that point towards the burnt fluid produce an increased probability at short durations for unburned fluid in comparison with the burnt passage times.