Convective Heat Transfer in an Impinging Synthetic Jet: A Numerical Investigation of a Canonical Geometry

Synthetic jets are generated by an equivalent inflow and outflow of fluid into a system. Even though such a jet creates no net mass flux, net positive momentum can be produced because the outflow momentum during the first half of the cycle is contained primarily in a vigorous vortex pair created at the orifice edges; whereas in the backstroke, the backflow momentum is weaker, despite the fact that mass is conserved. As a consequence of this, the approach can be potentially utilized for the impingement of a cooling fluid onto a heated surface. In previous studies, little attention has been given to the influence of the jet's origins; hence it has been difficult to find reproducible results that are independent of the jet apparatus or actuators utilized to create the jet. Furthermore, because of restrictions of the resonators used in typical actuators, previous investigations have not been able to independently isolate effects of jet frequency, amplitude, and Reynolds number. In the present study, a canonical geometry is presented, in order to study the flow and heat transfer of a purely oscillatory jet that is not influenced by the manner in which it is produced. The unsteady Navier–Stokes equations and the convection–diffusion equation were solved using a fully unsteady, two-dimensional finite volume approach in order to capture the complex time dependent flow field. A detailed analysis was performed on the correlation between the complex velocity field and the observed wall heat transfer. Scaling analysis of the governing equations was utilized to identify nondimensional groups and propose a correlation for the space-averaged and time-averaged Nusselt number. A fundamental frequency, in addition to the jet forcing frequency, was found, and was attributed to the coalescence of consecutive vortex pairs. In terms of time-averaged data, the merging of vortices led to lower heat transfer. Point to point correlations showed that the instantaneous local Nusselt number strongly correlates with the vertical velocity v although the spatial-temporal dependencies are not yet fully understood.