Numerical simulation of motion and bubble entrainment of vortex ring

In present paper a three-dimensional discrete vortex filament method is put forward to simulate the motion and bubble entrainment of an inviscid, incompressible vortex ring. In this method the circular or elliptical vortex ring is discreted into a number of individual elements with finite spherical cores placed on the centerline of the ring and the induced velocity can be obtained by summing up the contribution of each element. The vorticity across the section of the ring is approximated by a second-order Gaussian distribution and second order predictor-corrector algorithm is adopted in the simulation of vortex ring evolution. First this model is verified by the motion of circular vortex ring through the comparison with theoretical solution. Then a parametric study of the influences of circulations, core-to-radius ratios and long-to-short axis ratios on the evolution of elliptical ring is carried out. The periodical exchange of major and minor axis is numerically reproduced and evolution rule of a single elliptical vortex ring is obtained. Finally bubble dynamic equation is introduced into the three-dimensional discrete vortex model to simulate the bubble entrainment of the vortex ring. The resemblance between calculated bubble trajectory and experiment also validate our two-phase model.