An investigation is made into the mechanism of pinch-off for turbulent vortex rings formed by a synthetic jet using time resolved particle image velocimetry measurements in air. During formation, measurements of the material acceleration field show a trailing pressure maximum (TPM) forms behind the vortex core. The adverse pressure gradient behind this TPM inhibits vorticity transport into the ring and the TPM is spatially coincident with the termination of vorticity flux into a control volume moving with the ring. A Lagrangian Coherent Structures (LCS) analysis is shown to be in agreement with the role of the TPM in pinch-off and in identifying the vortex ring before separation. The LCS analysis provides physical insights which form the basis of a revised model of pinch-off, based on kinematics, which predicts the time of formation (formation number) well for the present dataset. The delivery of impulse to the vortex ring is also considered. Two equally important mechanisms are shown to play a role: a material flux and a vortex force. In the case of long maximum stroke ratio, it is demonstrated that a vortex force continues to deliver impulse to the ring after the material flux is terminated at pinch-off and that this contribution may be substantial. This shows that the pinch-off and separation process cannot be considered impulse invariant, which has important implications for unsteady propulsion, present models of vortex ring formation, and existing explanations for vortex ring pinch-off.

The formation of turbulent vortex rings by synthetic jets

Impulsively started, low-aspect-ratio elliptical and rectangular flat plates were investigated to determine the role of geometric asymmetries on vortex evolution. Dye visualizations, force measurements, and particle image velocimetry were used throughout to characterize the variation between shapes. For all the shapes studied, aspect ratio was observed to have the largest influence on force production and vortex evolution. Non-uniform curvature and edge discontinuities characteristic of ellipses (with aspect ratios other than one) and rectangles, respectively, play a secondary role. Furthermore, it was shown that stably attached vortex rings form behind the circular and square flat plates, which reduce the instantaneous drag force of each plate until the vortex rings break down. In contrast, all flat plates with aspect ratios other than one are subjected to fast-modulating elliptical vortex rings in the wake. These vortex rings increase the drag force of each plate until pinch-off occurs. Finally, pinch-off was identified with the streamwise pressure-gradient field and compared with formation numbers calculated using the circulation-based methodology, yielding good agreement for all plates with aspect ratios greater than one.

On vortex evolution in the wake of axisymmetric and non-axisymmetric low-aspect-ratio accelerating plates

The propagation of periodically generated vortex rings (period generates a train of vortices in the quasi-steady state.

On the scaling of propagation of periodically generated vortex rings

Effects of swirl on flow and mixing of acoustically excited swirling double-concentric jets

Characteristic flow modes, flow evolution processes, jet spread width, turbulence properties, and dispersion characteristics of swirling double-concentric jets were studied experimentally. Jet pulsations were induced by means of acoustic excitation. Streak pictures of smoke flow patterns, illuminated by a laser-light sheet, were recorded by a high-speed digital camera. A hot-wire anemometer was used to digitize instantaneous velocity instabilities in the flow. Jet spread width was obtained through a binary edge identification technique. Tracer-gas concentrations were measured for information on jet dispersions. Two characteristic flow patterns were observed: (1) synchronized vortex rings appeared in the low excitation intensity regime (the excitation intensity less than one) and (2) synchronized puffing turbulent jets appeared in the high excitation intensity regime (the excitation intensity greater than one). In the high excitation intensity regime, the “suction back” phenomenon occurred and therefore induced in-tube mixing. The jet spread width and turbulent fluctuation intensity exhibited particularly large values in the high excitation intensity regime at the excitation Strouhal numbers smaller than 0.85. At the excitation Strouhal numbers >0.85, the high-frequency effect caused significant decay of jet breakup and dispersion—the jet spread width and fluctuation intensity decreased sharply and may, at very high Strouhal numbers, asymptotically approach values almost the same as the values associated with unexcited jets. Exciting the jets at the high excitation intensity regime, the effects of puffing motion and in-tube mixing caused breakup of the jet in the near field and therefore resulted in a small Lagrangian integral time and small length scales of fluctuating eddies. This effect, in turn, caused drastic dispersion of the central jet fluids. It is possible that the excited jets can attain 90 % more improvements than the unexcited jets. We provide a domain regarding excitation intensity and Strouhal number to facilitate identification of characteristic flow modes.

Flow and mixing characteristics of swirling double-concentric jets subject to acoustic excitation

The periodic formation of vortex rings in the developing region of a round jet subjected to high-amplitude acoustic forcing is investigated with High-Speed Particle Image Velocimetry. Harmonic velocity oscillations ranging from 20 to 120% of the mean exit velocity of the jet was achieved at several forcing frequencies determined by the acoustic response of the system. The time-resolved history of the formation process and circulation of the vortex rings are evaluated as a function of the forcing conditions. Overall, high-amplitude forcing causes the shear layers of the jet to breakup into a train of large-scale vortex rings, which share many of the features of starting jets. Features of the jet breakup such as the roll-up location and vortex size were found to be both amplitude and frequency dependent. A limiting time-scale of t/T ≈ 0.33 based on the normalized forcing period was found to restrict the growth of a vortex ring in terms of its circulation for any given arrangement of jet forcing conditions. In sinusoidally forced jets, this time-scale corresponds to a kinematic constraint where the translational velocity of the vortex ring exceeds the shear layer velocity that imposes pinch-off. This kinematic constraint results from the change in sign in the jet acceleration between t = 0 and t = 0.33T. However, some vortex rings were observed to pinch-off before t = 0.33T suggesting that they had acquired their maximum circulation. By invoking the slug model approximations and defining the slug parameters based on the experimentally obtained time- and length-scales, an analytical model based on the slug and ring energies revealed that the formation number for a sinusoidally forced jet is L/D ≈ 4 in agreement with the results of Gharib et al. (J Fluid Mech 360:121–140, 1998).

E. Aydemir

Papers

The formation of vortex rings in a strongly forced round jet