Vortex self-similarity in an impinging synthetic jet and its three-stage evolution. (November 2020) - Silva-Llanca, Luis; d'Alençon, Jean Paul
Highlights: Direct Numerical Simulations of an Impinging Synthetic Jet Three distinguishable stages during the vortex pair evolution The vortex pair is self-similar during the "free-flight" stage The vortex-intensity-based Re is a better definition than the traditional Re Convective heat transfer is proportional to the vortex-intensity-based Re Graphical abstract: Abstract: The periodic ejection of fluid from a cavity or channel generates a train of counter-rotating vortex pairs that synthesizes a coherent fluctuating flow, known as a Synthetic Jet. In recent years, such flows found applications in the electronics cooling industry by impinging the flow onto heated surfaces, and in aerodynamics for boundary layer control. This paper intends to simplify the fluid dynamics of Synthetic Jets using the Lamb-Oseen solution to deepen the fundamental understanding of these flows. We used experimentally validated Direct Numerical Simulations to compare those data with the analytical approach. The numerical experiments were carried using the Finite Volume Method through the commercial software ANSYS Fluent. The analytical approach showed excellent agreement with the DNS data, except early in the jet cycle due to channel effects, and late in the cycle because of merging and viscous dissipation of vorticity. Appropriate non-dimensionalization of the data demonstrated that the vortices are self-similar and depend on the vortex-distance-to-radius ratio, regardless of time or the case studied. The evolution of the vortex radius evidenced the existence of three stages: (1) Actuation as the vortices emerge from the channel, (2) separation from the channel and free-flight toward the wall, and (3) convection as a remnant stationary vortex induces extra translational velocity on the primary vortex.