Flame Front Geometry and Stretch During Interactions of Premixed Flames with Vortices

Abstract

Flame front geometry and flame stretch during interactions of premixed flames with vortices at various configurations are computationally investigated using a kinematical relationship between vortex-induced velocity and flame propagation velocity, in conjunction with Lagrangian coordinates to represent the flame front. The maximum flame stretch that can occur during an interaction with a single vortex is found to be very close to Uθ/r_m + S_L/2r_m, while the mean flame stretch has a maximum that asymptotes to 18-23% of this value for vortex radii between 1.25 and 5.0 mm as UθS_L is increased to 2. For flames interacting with a counter-rotating vortex pair, the flame stretch near the flow symmetry axis increases when the spacing between the vortices increase to align the velocity vectors with the flame front; while the flame stretch away from this region is relatively independent of the action of the opposite vortex and is determined primarily by the vortex velocity and length scale similar to the single vortex case. For flame contours caused by vortex arrays, the flame curvature scales more strongly with vortex size than vortex velocity; and the mean flame curvatures for both vortex arrays and a single vortex are bounded between 1/d_m and 1/(2d_m) except in an instance where the vortex produces negligible wrinkles on the flame front. The effect of decreasing the tangential spacing in the vortex array is to increase the coupling of actions of adjacent vortices which leads to an increase in flame area and a positive shift in the flame curvature pdf; while variations of normal vortex spacing have less effect on the flame front geometry. The maximum flame stretch for flames interacting with vortex arrays is found to be close to the value caused by a single vortex, whereas the mean flame stretch and higher statistical moments are significantly different due to the additional strains caused by the coupling of actions of adjacent vortices.