Scalings for rectangular synthetic jet trajectory in a turbulent boundary layer

Synthetic jet actuators remain coveted components in flow control applications as the convection of vortex rings induces a redistribution of the momentum in a boundary layer although the net mass flux remains zero. The ability to predict the trajectory of these vortical structures, and subsequently the jet, is critical for efficient and targeted usage of such actuators. In this investigation, a synthetic jet is issued into a zero pressure gradient turbulent boundary layer from rectangular orifices with aspect ratios 3, 6 and 12 over a range of actuation frequencies and velocity ratios, with the flow field captured through particle image velocimetry measurements. An assessment of the trajectories culminates in scaling characteristics which encapsulate the aspect ratio, the momentum ratio between the jet and the cross-flow and the Strouhal number. However, the scaling mechanism is found to be sensitive to constraints which include the interaction between successive vortex pairs and the various regions of the flow field where the degree of interaction of the jet with the cross-flow changes. By redefining the threshold between the near-field, transitioning and far-field regions and accounting for vortex interaction, we observe the relevant non-dimensional parameters describing the scaling to vary. Additionally, together with cross-flow properties, variation in the orifice dimensions and actuation parameters enable the exact form of the Strouhal number for each combination of constraints to be determined. Under conditions of no vortex interaction, synthetic jets are found to follow identical trajectories provided the ratio of total momentum between the jet and the cross-flow remains the same, irrespective of the actuation frequency or Reynolds number of the incoming flow.