Experimental investigation on the impingement of synthetic jet vortex rings on a spherical wall

An experimental study was conducted to investigate the influence of sphere diameter and Reynolds number on synthetic jet vortex rings impinging on a spherical wall. Laser-induced fluorescence and two-dimensional particle image velocimetry techniques were applied to visualize flow and measure flow velocity, respectively. In this experiment, the stroke length was kept constant $(L=3.6)$, and different diameters ($d/D=1$, 6, and 16) and Reynolds numbers (${\mathrm{Re}}_{sj}=227$ and 682) were analyzed. In addition to flow visualization images and phase-averaged ${\lambda }_{ci}$ fields, the vortex ring trajectories and circulation are presented to reveal the evolution features of the vortex rings. The results demonstrated that the Reynolds number mainly determined the strength and induced ability of the primary vortex ring (PVR) and the sphere-diameter effect was reflected by the expansion distance of the PVR and its separation from the wall boundary layer. It was found that only a secondary vortex ring (SVR) was induced in the case of a small diameter or a low Reynolds number. As the diameter and Reynolds number increased, the PVR expanded continuously along the wall and induced a SVR and tertiary vortex ring. In particular, driven by the curve, the strength of the induced vortex ring decreased with the increase in the sphere diameter.

Figure 1

(a) Three-dimensional schematic of experimental setup and (b) side view of the configuration of the experimental setup.

Figure 2

Flow images of synthetic jet vortex rings impingement on a $d/D=1$ sphere surface. (a) ${\mathrm{Re}}_{sj}=227$ and (b) ${\mathrm{Re}}_{sj}=682$.

Figure 3

Flow images of synthetic jet vortex rings impingement on a $d/D=6$ sphere surface. (a) ${\mathrm{Re}}_{sj}=227$ and (b) ${\mathrm{Re}}_{sj}=682$.

Figure 4

Flow images of synthetic jet vortex rings impingement on a $d/D=16$ sphere surface. (a) ${\mathrm{Re}}_{sj}=227$ and (b) ${\mathrm{Re}}_{sj}=682$.

Figure 5

Phase-averaged ${\lambda }_{ci}$ fields of vortex ring impingement on a $d/D=1$ sphere surface for all Reynolds numbers. (a) ${\mathrm{Re}}_{sj}=227$ and (b) ${\mathrm{Re}}_{sj}=682$.

Figure 6

Phase-averaged ${\lambda }_{ci}$ fields of vortex ring impingement on a $d/D=6$ sphere surface for all Reynolds numbers. (a) ${\mathrm{Re}}_{sj}=227$ and (b) ${\mathrm{Re}}_{sj}=682$.

Figure 7

Phase-averaged ${\lambda }_{ci}$ fields of vortex ring impingement on a $d/D=16$ sphere surface for all Reynolds numbers. (a) ${\mathrm{Re}}_{sj}=227$ and (b) ${\mathrm{Re}}_{sj}=682$.

Figure 8

Trajectories of the primary and induced vortex rings near the wall for all cases. (a) $d/D=1$, (b) $d/D=6$, and (c) $d/D=16$.

Figure 9

Vortex ring behavior along the sphere surface, (a)–(d) correspond to stages 1–4 of vortex ring motion, respectively.

Figure 10

Trajectories of the PVR upstream. (a) all cases, (b) ${\mathrm{Re}}_{sj}=227$, and (c) ${\mathrm{Re}}_{sj}=682$.

Figure 11

Circulation variations of (a) PVR at ${\mathrm{Re}}_{sj}=227$, (b) the induced vortex ring at ${\mathrm{Re}}_{sj}=227$, (c) PVR at ${\mathrm{Re}}_{sj}=682$, and (d) the induced vortex ring at ${\mathrm{Re}}_{sj}=682$.