Similarity parameter for synthetic jet vortex rings impinging onto porous walls

Previous studies have shown that vortex rings impinging onto porous walls will pass through the wall more easily as the vortex ring strength, wall porosity, and pore size increase and the wall thickness decreases. Thus, there should exist a similarity parameter formed from these factors that will allow determination of the dynamics of the vortex rings/porous wall interaction. To find this similarity parameter, the effects of the Reynolds number Re_sj (309–1238) and pore size d_h (0.07–0.20) on the vortex rings/porous wall interaction are investigated by laser-induced fluorescence and particle image velocimetry (PIV) techniques. By dimensional analysis and quantitative investigation of PIV data, a similarity parameter Re²sj^dh³ is proposed to effectively characterize the losses in jet dynamical parameters, such as momentum flux, kinetic energy, and vortex ring circulation, due to impingement onto a porous wall. Physically, Re²sj^dh³ reflects the relative importance of the forces due to the momentum relative to the viscous forces, and the drag forces associated with the porous wall geometry. Finally, the results of the flow visualization validate that the near-wall flow structure during the interaction is qualitatively similar at the closest matching Re²sj^dh^3..