Effect of density ratio on flame propagation along a vortex tube

Abstract

Propagation of a premixed flame along a vortex tube perpendicular to the flame is numerically simulated to study the effect of the density ratio of the flame, on the propagation velocity and to clarify the mechanism of propagation. The vortex tube is assumed to be a Burgers vortex with an initial circumferential velocity ranging from 1.7 to 36 times the laminar burning velocity and with an initial core diameter ranging from 0.15 to 1.71 times the flame thickness. The density ratios of the flame are assumed to be 7.53 and 2.63. It is found that the flame propagation velocity along the vortex tube has an inverse relation with the density ratio and depends on the power of the maximum circumferential velocity and on the diameter of the vortex tube. It is also observed that the baroclinic torque produces vorticity in the flame zone and that this vorticity can provoke the flame to accelerate along the vortex tube with a velocity similar to the observed one. The theory on the basis of the pressure difference across the flame does not explain the inverse dependency on the density ratio—neither the dependency on the power of the circumferential velocity nor on the diameter of the vortex tube. On the other hand, the theory on the basis of the baroclinic torque better explains the inverse dependency on the density ratio, as well as the dependency on almost the second power of the circumferential velocity and on the diameter of the vortex tube.