Synthetic jet vortex rings impinging onto a porous wall: Reynolds number effect

The interaction of synthetic jet vortex rings with a porous wall was investigated using laser-induced fluorescence (LIF) and particle image velocimetry (PIV) techniques. The synthetic jet Reynolds number (Re_sj) varied from 309 to 1238, where the vortex rings underwent transition from laminar to turbulent flow. For the lowest Reynolds number (Re_sj = 309), the flow is almost laminar; the primary vortex ring (VR1) induces and pairs with a well coherent secondary vortex ring (VR2) in the upstream side of the porous wall, leading to a conventional “rebound” and “reversal” in VR1's trajectory. As Re_sj increases, the induced VR2 becomes weaker and loses coherence quickly after rolling up; even at Re_sj = 1238, VR2 becomes indistinguishable. During the vortex ring interacting with the porous wall, some fluid penetrates through the wall to form a transmitted vortex ring (VRT) in the downstream region. The circulation of VRT increases with the growth of Re_sj. In particular, for a higher Re_sj, the synthetic jet tends to pass through a porous wall more easily with less losses in both vortex ring circulation and jet momentum. Velocity triple decomposition shows that VRT for all tested cases has lost coherence completely before it moves out of the field of view. Moreover, for Re_sj = 309, the incoherence of VRT is caused by the vorticity diffusion and viscous dissipation since both the upstream and downstream flow are almost laminar. But for the high Re_sj (619, 928 and 1238), VRT lost coherence is mainly due to the transition, which results in a relatively large ratio of the fluctuation kinetic energy (FKE) to the total flow kinetic energy (KE). In particular, for Re_sj = 928 and 1238, it is observed that some small-scale Kelvin-Helmholtz vortices are formed in the trailing jet, and entrained into the primary vortex core, which accelerates the loss of coherence for the primary vortex ring. This observation can explain why the vortex ring at high Reynolds number is less coherent.