Wave nature in vortex-bursting initiation

Abstract

A new mechanism responsible for rapid flame propagation in a flammable vortex tube (vortex bursting) has been previously proposed by one of the authors. (1) The vortex tube is radially expanded due to thermal expansion at the flame surface. (2) For the conservation of angular momentum, vortex filaments which constitute the original vortex tube are deformed into spiral form, thus producing a torus of azimuthal-vorticity distribution of the shoulder part of the parabola-like flame surface. (3) By Biot-Savart's law, the azimuthal-vorticity distribution induces an axial velocity at the flame-tip location, so that the flame is convected forth with a speed corresponding to the maximum rotational speed of the vortex tube. In the present study, this theory is extended to examine the transient behavior of a flame propagating in a vortex tube. The most important findings are a wavelike nature of the azimuthal-vorticity distribution, which is produced by the spiraling of axial filaments, and its effect on flame extinction. The azimuthal-vorticity distribution propagates as a wave with its own speed, which is determined from its circulation and form. When the rotational speed of vortex tube is too high relative to the flame heat-release rate, the azimuthal-vorticity torus passes the flame tip, and the burned gas region is immersed in a straining flow which is produced by the circulating flow around the azimuthal-vorticity torus. Thus, the elongated burned gas region is rapidly cooled by the surrounding cold gas, and the tapered flame front suffers from the danger of extinction. The steady flame propagation state is established when the propagation speed of the azimuthal-vorticity wave coincides with the flame-tip propagation speed, which is consistent with the previously proposed expression for steady flame propagation speed.