SINOPSIS

A synthetic jet issued in a cross flow creates a momentum deficit in the cross flow downstream of the jet. In the literature, this deficit is ascribed to viscous blockage by the jet and the up wash of low-momentum fluid caused by the vortical structures of the jet. This paper proposes and quantifies a third effect contributing to the momentum deficit: a velocity induced by the vortical structures in the direction opposite to the cross flow. A reconstruction technique − quantifying the vortex-induced velocity − is developed to determine the momentum deficit caused by the proposed effect. This is applied to a test case of a rectangular synthetic jet (AR = 13, St = 0.5, r = 0.88) issuing into a turbulent boundary layer (Re_τ = 1220, U_∞ = 10 m/s, δ = 45 mm). The shape of the created vortical structures is reconstructed using a combination of planar- (two-dimensional two-component) PIV in the streamwise−wall-normal plane and stereo- (two-dimensional three-component) PIV in the spanwise−wall-normal plane. The reconstructed shape consists of overlapping clockwise- and counterclockwise hairpins. With this (constant) shape known, the distribution of hairpins can be determined using the spanwise-vorticity field only. From this distribution of vortical structures the induced velocity is calculated using Biot-Savart's law. Qualitatively the induced velocity components are very similar to the equivalent measured velocity components. The streamwise momentum flux deficit per unit width at the centerline is calculated for both the induced and the measured case. After some start-up behaviour the momentum deficit for both cases becomes relatively constant. In this constant regime (x/δ > 1) the momentum deficit induced by the vortical structures accounts for 90% of the measured momentum deficit. It is reasoned that the other 10% is most likely to be caused by an increase in skin friction resulting from the up wash of low-momentum fluid (and consequential down wash of high-momentum fluid).