Formation and scaling of a coherent large-scale vortex from the impingement of a laminar synthetic jet

Most previous studies have focused on the vortical structure formed from a transient wall jet created by a steady or quasi-steady external forcing, such as the junction vortex from a moving belt and the starting vortex from a kHz-level dielectric barrier discharge (DBD) plasma. There is little knowledge on the vortex formed from the wall jet through a periodic forcing. Therefore, in this study, a laminar synthetic jet is employed to impinge onto a solid wall to induce a radial wall jet under the action of a periodic forcing. It is found that a coherent large-scale vortex is generated from the impingement of the synthetic jet. Both the size and location of this large-scale vortex exhibit good collapse features, indicating self-similar behavior. The similarity laws derived from Euler’s equations provide a universal description of this large-scale vortex, and its temporal growth prediction attains a reasonable agreement with the experimental measurements. Accounting for the measuring uncertainty, the temporal growth of this laminar large-scale vortex is determined as t^0.33, the average of the predicted and measured values, and thus the velocity field scales as t^−0.67. Based on the derived similarity laws, the forcing-type parameter is calculated as n ≈ 1.32 in this study, which suggests that the applied force produced by the impingement of periodic vortex rings of a laminar synthetic jet decreases with time gradually, and thus lies between an impulse and a step forcing. Graphical abstract: [Figure not available: see fulltext.].