Vortex Roll-Up Criterion for Synthetic Jets

Abstract

In this paper, both theoretical analysis and numerical simulations are undertaken to study the parameters that affect the strength of vortex roll-up of synthetic jets. A dimensional analysis reveals that the dimensionless vorticity of vortex roll-up produced by an orifice flow depends on the dimensionless stroke length, Stokes number, and the ratio between the orifice diameter and the thickness of the Stokes layer. Based on the results from a fully developed oscillating laminar pipe flow, the Stokes number is found to play an important role in determining the thickness ofthe Stokes layer inside the orifice and hence the shape of the velocity profile. Results from the numerical simulations confirm that the Stokes number also determines the strength of vortex roll-up of a synthetic jet issued from an orifice of a finite depth, for the same reason. Finally, a parameter map, which marks the three different regimes of synthetic jets (classified as no jet, jet formation without vortex roll-up, and jet formation with vortex roll-up) is produced based on the numerical simulation results. It is shown that for the synthetic jet actuator used in the present study, a minimum Stokes number of about 8.5 is required to ensure the occurrence of an appreciable vortex roll-up at a dimensionless stroke length greater than 4. In addition, a very low Stokes number can also suppress the formation of synthetic jets. This study provides a further understanding of the behavior of synthetic jets in quiescent conditions, which will be useful for designing more effective synthetic jet actuators in which vortex roll-up is desired.