Synthetic jet vortex rings impinging onto porous walls: a more comprehensive similarity parameter

By combining the effects of synthetic jet Reynolds number (Re_sj), porous wall porosity (ϕ) and porous wall hole diameter (d_h*), Li et al. (AIAA J 58:722–732, 2020) and Xu et al. (Phys Fluids 33:035140, 2021) presented a dimensionless similarity parameter [(Re_sj²d* _h³)^ϕ] to characterize the interaction between synthetic jet vortex rings and a porous wall. To futher incorporate the jet-exit-to-wall distance (H^*) into this similarity parameter, an experimental study was conducted to inverstigate the effect of the jet-exit-to-wall distance (H^* = 2, 4, 6, and 8) on the impingement of synthetic jet vortex rings onto a porous wall under three Reynolds numbers (Re_sj = 300, 600, and 900). By establishing the relationship between the loss of jet momentum flux and the jet-exit-to-wall distance (H^*) at different Re_sj, a more comprehensive similarity parameter [(Re_sj²d_h^*3H^*−0.64)^ϕ] was derived to characterize this vortex rings-porous wall interaction. Given the substantial impact of H^* on the vortex ring strength upon the impingement, an effective interaction velocity (V_j,eff = V_j/H^*0.32±0.045, V_j is the characteristic velocity of the synthetic jet) was introduced, so that [(Re_sj²d_h^*3H^*−0.64)^ϕ] was transformed as [(Re_eff²d_h^*)^ϕ], where Re_eff was the Reynolds number based on V_j,eff. This new similarity parameter effectively characterized both the losses of the momentum flux and kinetic energy transport due to impinging onto a porous wall in over 50 cases from current and previous experiments, thus verifying its validity at least in the range of [(Re_eff²d_h^*)^ϕ] ≤ 1000.