“…Afterwards, the velocities stayed at nearly constant values depending on the wall-normal position. Similar temporal and spatial velocity evolutions were observed during an impulsively movement of a piston to discharge fluid through an orifice (Limbourg & Nedic 2021). Small velocity oscillations were seen as the speaker diaphragm moved back when control was switched off, which were followed by a slow but long suction phase as the speaker diaphragm returns back until the next control phase starts.…”
Section: Experimental Set-upsupporting
confidence: 67%
“…Control was then switched off until the next turbulent spot appeared. (Limbourg & Nedic 2021). Small velocity oscillations were seen as the speaker diaphragm moved back when control was switched off, which were followed by a slow but long suction phase as the speaker diaphragm returns back until the next control phase starts.…”
Opposition control of artificially initiated turbulent spots in a laminar boundary layer was carried out in a low-turbulence wind tunnel with the aim to delay transition to turbulence by modifying the turbulent structure within the turbulent spots. The timing and duration of control, which was carried out using wall-normal jets from a spanwise slot, were pre-determined based on the baseline measurements of the transitional boundary layer. The results indicated that the high-speed region of the turbulent spots was cancelled by opposition control, which was replaced by a carpet of low-speed fluid. The application of the variable-interval time-averaging technique on the velocity fluctuation signals demonstrated a reduction in both the burst duration and intensity within the turbulent spots, but the burst frequency was increased.
“…Afterwards, the velocities stayed at nearly constant values depending on the wall-normal position. Similar temporal and spatial velocity evolutions were observed during an impulsively movement of a piston to discharge fluid through an orifice (Limbourg & Nedic 2021). Small velocity oscillations were seen as the speaker diaphragm moved back when control was switched off, which were followed by a slow but long suction phase as the speaker diaphragm returns back until the next control phase starts.…”
Section: Experimental Set-upsupporting
confidence: 67%
“…Control was then switched off until the next turbulent spot appeared. (Limbourg & Nedic 2021). Small velocity oscillations were seen as the speaker diaphragm moved back when control was switched off, which were followed by a slow but long suction phase as the speaker diaphragm returns back until the next control phase starts.…”
Opposition control of artificially initiated turbulent spots in a laminar boundary layer was carried out in a low-turbulence wind tunnel with the aim to delay transition to turbulence by modifying the turbulent structure within the turbulent spots. The timing and duration of control, which was carried out using wall-normal jets from a spanwise slot, were pre-determined based on the baseline measurements of the transitional boundary layer. The results indicated that the high-speed region of the turbulent spots was cancelled by opposition control, which was replaced by a carpet of low-speed fluid. The application of the variable-interval time-averaging technique on the velocity fluctuation signals demonstrated a reduction in both the burst duration and intensity within the turbulent spots, but the burst frequency was increased.
“…After the initial decrease, the non-dimensional energy of 0.26 is maintained for the remainder of the vortex merging process while other quantities, such as the circulation and diameter of the vortex ring (figure 6 b – d ), continue to evolve. The continued evolution of the circulation and size of vortex rings after their pinch-off or for formation times beyond the formation number has been observed by Lawson and Dawson (2013) and Limbourg and Nedić (2021b). Figure 7.Temporal evolution of ( a ) the non-dimensional energy of the vortex and ( b ) the translational velocity of the experimentally observed vortex according to and based on the tracking of the vortex centre locations.…”
Section: Resultsmentioning
confidence: 79%
“…The additional volume and associated vorticity that is added to the main vortex ring due to merging does not significantly alter the non-dimensional circulation based on the vortex size, but primarily leads to an increase in the vortex core diameter (figure 6 d ). The increase in the vortex diameter during the merging process is confirmed for vortex rings generated in different configurations, such as orifice-generated vortex rings (Limbourg & Nedić, 2021b). After merging, the vortex core diameter converges to at the same time as the non-dimensional circulation converges.…”
Pulsatile jet propulsion is a highly energy-efficient swimming mode used by various species of aquatic animals that continues to inspire engineers of underwater vehicles. Here, we present a bio-inspired jet propulsor that combines the flexible hull of a jellyfish with the compression motion of a scallop to create individual vortex rings for thrust generation. Similar to the biological jetters, our propulsor generates a nonlinear time-varying exit velocity profile and has a finite volume capacity. The formation process of the vortices generated by this jet profile is analysed using time-resolved velocity field measurements. The transient development of the vortex properties is characterised based on the evolution of ridges in the finite-time Lyapunov exponent field and on local extrema in the pressure field derived from the velocity data. Special attention is directed toward the vortex merging observed in the trailing shear layer. During vortex merging, the Lagrangian vortex boundaries first contract in the streamwise direction before expanding in the normal direction to keep the non-dimensional energy at its minimum value, in agreement with the Kelvin–Benjamin variational principle. The circulation, diameter and translational velocity of the vortex increase due to merging. The vortex merging takes place because the velocity of the trailing vortex is higher than the velocity of the main vortex ring prior to merging. The comparison of the temporal evolution of the Lagrangian vortex boundaries and the pressure-based vortex delimiters confirms that features in the pressure field serve as accurate and robust observables for the vortex formation process.
“…Vortex rings are often produced by ejecting a volume of fluid through a circular nozzle. If the ejection velocity is constant, the non-dimensional energy of the generated vortex converges to values ranging from 0.27 to 0.35 (Gharib, Rambod & Shariff 1998; Mohseni, Ran & Colonius 2001; Danaila & Hélie 2008; Limbourg & Nedić 2021 a ). The non-dimensional energy of vortex rings that are produced in the wake of disks or cones translating at a constant speed also converges towards (Yang, Jia & Yin 2012; de Guyon & Mulleners 2021).…”
The non-dimensional energy of starting vortex rings typically converges to values around 0.33 when they are created by a piston-cylinder or a bluff body translating at a constant speed. To explore the limits of the universality of this value and to analyse the variations that occur outside of those limits, we present an alternative approach to the slug-flow model to predict the non-dimensional energy of a vortex ring. Our approach is based on the self-similar vortex sheet roll-up described by Pullin (J. Fluid Mech., vol. 88, 1978, pp. 401–430). We derive the vorticity distribution for the vortex core resulting from a spiralling shear layer roll-up and compute the associated non-dimensional energy. To demonstrate the validity of our model for vortex rings generated through circular nozzles and in the wake of disks, we consider different velocity profiles of the vortex generator that follow a power law with a variable time exponent
$m$
. Higher values of
$m$
indicate a more uniform vorticity distribution. For a constant velocity (
$m=0$
), our model yields a non-dimensional energy of
${{E}^{{*}}}=0.33$
. For a constant acceleration (
$m=1$
), we find
${{E}^{{*}}}=0.19$
. The limiting value
$m \rightarrow \infty$
corresponds to a uniform vorticity distribution and leads to
${{E}^{{*}}}=0.16$
, which is close to values found in the literature for Hill's spherical vortex. The radial diffusion of the vorticity within the vortex core results in the decrease of the non-dimensional energy. For a constant velocity, we obtain realistic vorticity distributions by radially diffusing the vorticity distribution of the Pullin spiral and predict a decrease of the non-dimensional energy from 0.33 to 0.28, in accordance with experimental results. Our proposed model offers a practical alternative to the existing slug flow model to predict the minimum non-dimensional energy of a vortex ring. The model is applicable to piston-generated and wake vortex rings and only requires the kinematics of the vortex generator as input.
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