Vortex ring
Visible vortex rings can also be formed by the firing of certain artillery, in mushroom clouds, in microbursts,[1][2] and rarely in volcanic eruptions.
[citation needed] Unlike a sea wave, whose motion is only apparent, a moving vortex ring actually carries the spinning fluid along.
Just as a rotating wheel lessens friction between a car and the ground, the poloidal flow of the vortex lessens the friction between the core and the surrounding stationary fluid, allowing it to travel a long distance with relatively little loss of mass and kinetic energy, and little change in size or shape.
A method proposed by G. I. Taylor[7] to generate a vortex ring is to impulsively start a disk from rest.
In a laboratory, vortex rings are formed by impulsively discharging fluid through a sharp-edged nozzle or orifice.
The impulsive motion of the piston/cylinder system is either triggered by an electric actuator or by a pressurized vessel connected to a control valve.
In order to satisfy the Kutta condition, the flow is forced to detach, curl and roll-up in the form of a vortex sheet.
[8] Later, the vortex sheet detaches from the feeding jet and propagates freely downstream due to its self-induced kinematics.
For instance, a mushroom cloud formed by a nuclear explosion or volcanic eruption, has a vortex ring-like structure.
[10] Finally, for more industrial applications, the synthetic jet which consists in periodically-formed vortex rings, was proved to be an appealing technology for flow control, heat and mass transfer and thrust generation[11] Prior to Gharib et al. (1998),[12] few studies had focused on the formation of vortex rings generated with long stroke-to-diameter ratios
For short stroke ratios, only one isolated vortex ring is generated and no fluid is left behind in the formation process.
For long stroke ratios, however, the vortex ring is followed by some energetic fluid, referred as the trailing jet.
[16][17] For instance, it was shown that biological systems such as the human heart or swimming and flying animals generate vortex rings with a stroke-to-diameter ratio close to the formation number of about 4, hence giving ground to the existence of an optimal vortex ring formation process in terms of propulsion, thrust generation and mass transport.
[18] In particular, the squid lolliguncula brevis was shown to propel itself by periodically emitting vortex rings at a stroke-ratio close to 4.
[19][17] Moreover, in another study by Gharib et al (2006),[9] the formation number was used as an indicator to monitor the health of the human heart and identify patients with dilated cardiomyopathy.
Air vortices can form around the main rotor of a helicopter, causing a dangerous condition known as vortex ring state (VRS) or "settling with power".
Applying more power (increasing collective pitch) serves to further accelerate the downwash through which the main-rotor is descending, exacerbating the condition.
A vortex ring is formed in the left ventricle of the human heart during cardiac relaxation (diastole), as a jet of blood enters through the mitral valve.
This phenomenon was initially observed in vitro[20][21] and subsequently strengthened by analyses based on color Doppler mapping[22][23] and magnetic resonance imaging.
[3][29] Though a rare phenomenon, several volcanoes have been observed emitting massive vortex rings as erupting steam and gas condense, forming visible toroidal clouds: There has been research and experiments on the existence of separated vortex rings (SVR) such as those formed in the wake of the pappus of a dandelion.
[43][44] Compared to a standard vortex ring, which is propelled downstream, the axially symmetric SVR remains attached to the pappus for the duration of its flight and uses drag to enhance the travel.
[44][45] These dandelion seed structures have been used to create tiny battery-free wireless sensors that can float in the wind and be dispersed across a large area.
[citation needed] Vortex rings were first mathematically analyzed by the German physicist Hermann von Helmholtz, in his 1858 paper On Integrals of the Hydrodynamical Equations which Express Vortex-motion.
The discontinuity introduced by the Dirac delta function prevents the computation of the speed and the kinetic energy of a circular vortex line.
which finally results in the well-known expression found by Kelvin and published in the English translation by Tait of von Helmholtz's paper:[48][49][51]
For example, Shafranov [citation needed] used a magnetohydrodynamic (MHD) analogy to Hill's stationary fluid mechanical vortex to consider the equilibrium conditions of axially symmetric MHD configurations, reducing the problem to the theory of stationary flow of an incompressible fluid.
[citation needed] The Fraenkel-Norbury model of isolated vortex ring, sometimes referred as the standard model, refers to the class of steady vortex rings having a linear distribution of vorticity in the core and parametrised by the mean core radius
In addition, the circulation, the hydrodynamic impulse and the kinetic energy of such steady vortex rings were computed and presented in non-dimensional form.
A kind of azimuthal radiant-symmetric structure was observed by Maxworthy[57] when the vortex ring traveled around a critical velocity, which is between the turbulence and laminar states.
Later Huang and Chan[58] reported that if the initial state of the vortex ring is not perfectly circular, another kind of instability would occur.
