Vortex breakdown in swirling Burke-Schumann flames

Unsteady axisymmetric numerical simulations are used to determine the transition to bubble and conical vortex breakdown in low-Mach-number laminar swirling Burke-Schumann flames, for which an ambienttemperature fuel jet in solid-body rotation emerges into quiescent air. A critical value of the swirl number S for the onset of the bubble (S *B ) and the cone (S *C ) is determined as the jet fuel-feed mass fraction Y F ,j is varied for fixed Re = 800 , assuming typical conditions for methane combustion with air. During the first transition from pre-breakdown to the bubble, the jet core is relatively unaffected by the flame in the surrounding shear layer, and S *B = 1 . 36 is constant for all values of dilution. This transition to the jet-like bubble breakdown flame is found to be in agreement with theoretical predictions based on the criterion of failure of the slender quasicylindrical approximation. Variation in the critical swirl number S *C , characterizing the second transition from the bubble to the cone, is relatively small ( 1 . 80 < S *C < 1 . 83 ) in the range 0 . 1 < Y F ,j < 1 , but the resulting flow and flame shape for conical breakdown is found to depend critically on Y F ,j . For realistic values of dilution (Y F ,j & GE; 0 . 2) , the bubble transitions to a steady compact cone at S *C with a flame sheet that passes around the recirculation region, maintaining a jet-like flame. In the extreme dilution case (Y F ,j = 0 . 1) , the reaction sheet occurs closer to the fuel jet axis, increasing the radial velocities through thermal expansion and accelerating the transition to the cone (lower S *C ). The reduced viscosity associated with the lower adiabatic flame temperature leads to an enlarged unsteady conical breakdown with the flame sheet stabilized near the & COPY; 2022 The Author(s). Published by Elsevier Inc. on behalf of The Combustion Institute. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )