Vortex breakdown in swirling Burke–Schumann flames

Abstract

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 ambient-temperature fuel jet in solid-body rotation emerges into quiescent air. A critical value of the swirl number S for the onset of the bubble (SB*) and the cone (SC*) is determined as the jet fuel-feed mass fraction YF,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 SB*=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 quasi-cylindrical approximation. Variation in the critical swirl number SC*, characterizing the second transition from the bubble to the cone, is relatively small (1.80≤SC*≤1.83) in the range 0.1≤YF,j≤1, but the resulting flow and flame shape for conical breakdown is found to depend critically on YF,j. For realistic values of dilution (YF,j≥0.2), the bubble transitions to a steady compact cone at SC* with a flame sheet that passes around the recirculation region, maintaining a jet-like flame. In the extreme dilution case (YF,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 SC*). The reduced viscosity associated with the lower adiabatic flame temperature leads to an enlarged unsteady conical breakdown with the flame sheet stabilized near the inlet.