Formation process of the vortex ring generated by an impulsively started circular disc

Abstract

AbstractWe present an experimental study on the axisymmetric vortex ring generated by a thin circular disc. The velocity and vorticity fields are measured by digital particle image velocimetry (DPIV). The finite-time Lyapunov exponent fields and the Lagrangian coherent structures (LCSs) of the vortex flow are computed in order to analyse the transport of the fluid during its formation and identify the boundary of the vortex ring. The volume, circulation and energy of the vortex ring are calculated. It is found that the formation of the vortex ring basically includes three phases: a rapid growth phase, a stable growth phase and a non-axisymmetric phase. In the rapid growth phase (dimensionless time $0\lt {T}_{n} \lt 0. 2$) during which Taylor’s inviscid estimation is valid, the circulation of the vortex ring grows and the translational velocity of the vortex ring decreases. In the stable growth phase ($0. 2\lt {T}_{n} \lt 4$), the growth rate of the circulation decreases gradually. In the non-axisymmetric phase (${T}_{n} \gt 4$), the ring loses axisymmetry due to instability. Compared with the vortex ring generated by the laminar flow from an orifice, the one generated by a circular disc always moves with the disc, and the entrained fluid decreases and the saturated circulation increases. The temporal impulse exerted by the moving disc on the fluid is estimated by DPIV measurements and is calculated using the direct momentum conservation method. The momentum of the control volume enclosing the LCS is found to occupy 64–68 % of the entire impulse exerted by the disc on the fluid.