Measurement of a Circulation of the Vortex Ring induced by Pulsatile Jet flow in a Pipe

The method for measuring the circulation of vortex ring induced by pulsatile jet flow in a stenosed pipe is studied using Hierarchical Recursive PIV. In this method, relative velocity vectors are initially estimated by deducting a propagation velocity of vortex ring from phase mean velocity vectors. A propagation velocity of vortex ring is regarded to be equal to a propagation velocity of vorticity peak point. Because the vorticity profile in vortex region is similar to the laminar vortex ring with the Gaussian vorticity profile and with peak vorticity at the center of vortex. In deciding the vortex core region inside the vortex region defined by closing streamline, the threshold level of vorticity defined at the maximum point of circumference velocity around the vortex center. The vortex core region, similar to the forced vortex flow in the Rankine-Vortex, is defined as the region where the vorticity is higher than the threshold level. The circulation of vortex ring is estimated by the integrated vorticity in the vortex core region.