Effects of vortex-induced velocity on the development of a synthetic jet issuing into a turbulent boundary layer

A synthetic jet issuing into a cross-flow influences the local velocity of the cross-flow. At the jet exit the jet is oriented in the wall-normal direction while the cross-flow is oriented in the streamwise direction, leading to a momentum transfer between the jet and the cross-flow. Streamwise momentum transferred from the cross-flow to the jet accelerates the pulses created by the jet. This momentum transfer continuous up to some point downstream where these pulses have the same velocity as the surrounding flow and are no longer blocking the cross-flow. The momentum transfer from the cross-flow to the jet leads to a momentum deficit in the cross-flow far downstream of the viscous near field of the jet. In the literature this momentum-flux deficit is often attributed to viscous blockage or to up-wash of low-momentum fluid. The present paper proposes and quantifies a third source of momentum deficit: a velocity induced opposite to the cross-flow by the vortical structures created by the synthetic jet. These vortical structures are reconstructed from measured data and their induced velocity is calculated using the Biot-Savart law. The three-dimensional three-component induced velocity fields show great similarity to the measured velocity fields, suggesting that this induced velocity is the main contributor to the velocity field around the synthetic jet and viscous effects have only a small influence. The momentum-flux deficit induced by the vortical structures is compared to the measured momentum-flux deficit, showing that the main part of this deficit is caused by the induced velocity. Variations with Strouhal number (frequency of the jet) and velocity ratio (velocity of the jet) are observed and discussed. An inviscid-flow model is developed, which represents the downstream evolution of the jet in cross-flow. Using the measured data as an input, this model is able to predict the deformation, (wall-normal) evolution and qualitative velocity field of the jet. The present study presents evidence that the velocity induced by the vortical structures forming a synthetic jet plays an important role in the development of and the velocity field around the jet.