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# Vortex ring

A vortex ring, also called a toroidal vortex, is a region of rotating fluid moving through the same or different fluid where the flow pattern takes on a doughnut shape. The movement of the fluid is about the poloidal or circular axis of the doughnut, in a twisting vortex motion. An example of a this phenomenon is a smoke ring.

Vortex ring formation and structure

One way a vortex ring may be formed is by pushing a spherical mass of fast moving fluid (A) into a mass of stationary fluid (B). A and B may chemically be the same fluid. As B hits the ball of A it pushes the outer layers of A with it. The inner layers are less affected. The main mass of A forms a 'shadow' of lower pressure behind it, and the layer peeled off by B begins to curve round back into the main mass of A. This inward curving flow initiates the vortex, and splits it into a doughnut shape. Now B flows past both the inner and outer circumferences of the doughnut. The greater outer perimeter causes a net rolling the doughnut of A.

The leading edge of a plume, sometimes called the 'starting-plume', usually has a vortex-ring structure, as does a smoke ring. The motion of an isolated vortex ring and the interaction of two or more vortices are discussed in eg Batchelor's text book (ref 1).

For many purposes a ring vortex may be approximated as having a vortex-core of small cross-section. However a simple theoretical solution, called Hill's spherical vortex (ref 2), is known in which the vorticity is distributed within a sphere (the internal symmetry of the flow is however still annular). Such a structure or an electromagnetic equivalent has been suggested as an explanation for the internal structure of ball lightning.

Vortex ring effect in helicopters

In typical flight, the rotor disc directs the airflow downwards, creating lift. A vortex ring state (VRS), though, involves a toroid-shaped path of airflow circumscribing the blade disc, as the airflow moves down through the disc, then outward, and then down through the top again. This re-circulation of flow can negate much of the lifting force and cause a catastrophic loss of altitude.

Vortex ring state, also known as settling with power is a hazardous condition encountered in helicopter flight. It occurs when the helicopter has three things occurring; a rate of descent greater than 300 feet per minute, an airspeed slower than effective translational lift, and the helicopter is using more than 20% of its available power.Fact|date=September 2007 A helicopter typically induces a vortex ring state by descending into its own downwash. This condition can be corrected by moving the cyclic forward, which controls the pitch angle of the rotor blade, slightly pitching nose down, and establishing forward flight. The aircraft will fly into "clean air", and will be able to regain lift.

A clear understanding of this condition is essential for helicopter pilots to avoid danger.
*On a fast descent, no vortex will form because the vertical airspeed is faster than the recirculation speed - although rapid descent through one's own downwash is itself a highly dangerous maneuver.
*With high airspeed, no vortex will form because the translational airflow is faster than the recirculation speed.

In testing of the V-22 Osprey, the April 8, 2000 crash which killed 19 was attributed to VRS. The specific cause was officially determined to be due to a rate of descent of over 2000 feet per minute (600 m/min) of the aircraft while at slow horizontal speeds of around 30 knots (56 km/h). In addition, there were two planes descending in tandem, a possible risk factor for VRS. The military claims that subsequent testing has shown that the Osprey, and the tiltrotor in general, is less susceptible to VRS, that the conditions are easily recognized by and presented to the pilots, that recovery from VRS requires a more natural action by the pilot than for helicopters, and that the altitude loss is significantly less than for helicopters. They claim that with sufficient altitude (2000 feet or more), VRS recovery is relatively easy. [http://www.wired.com/wired/archive/13.07/osprey.html?pg=3&topic=osprey&topic_set=] They also claim that it is easy to train new pilots in the recognition of and recovery from VRS.

Vortex ring in the left ventricle of the heart

One of the most important fluid phenomena observed in the left ventricle during cardiac relaxation (diastole), is the vortex ring that develop with a strong jet entering through the mitral valve. The presence of these flow structures that develop during cardiac diastole was initially recognized by in-vitro visualization of the ventricular flow (ref.5 and ref.6) and subsequently strengthened by analyses based on color Doppler mapping (ref.7 and ref.8) and Magnetic Resonance Imaging (ref.9 and ref.10). Some recent studies (ref.11 and ref. 12) have also confirmed the presence of a vortex ring during rapid filling phase of diastole and implied that the process of vortex ring formation can influence on mitral annulus dynamics.

Instability

A kind of azimuthal radiant-symmetric structure was observed by Maxworthy (ref.3) when the vortex ring traveling around a critical velocity, which is between the turbulence and laminar states. Later Huang and Chan (ref.4) reported that if the initial states of the vortex ring is not perfect circular, another kind of instability would occur. e.g. As shown in the figure, a kind of oscillation occurs in an elliptical vortex ring. The two pictures were taken at different instants for the same vortex ring and it can be seen that the longer axis and shorter axis change to each other during the propagating process.

ee also

* Aeronautical engineering
* Autorotation
* Bubble ring
* Ground effect in aircraft
* Helicopter flight controls
* Helicopter pilotage
* Helicopter rotor
* Mushroom cloud
* Smoke ring
* Vortex ring toys

References

* Batchelor, G. K., (1967), "An Introduction to Fluid Dynamics", Cambridge UP (reprinted 2000)

* Hill, M. J. M. (1894), Phil. Trans. Roy. Soc. London, A, Vol. 185, p. 213

* Maxworthy, T. J. (1972) The structure and stability of vortex ring, Fluid Mech. Vol. 51, p. 15

* Huang, J., Chan, K.T. (2007) Dual-Wavelike Instability in Vortex Rings, Proc. 5th IASME/WSEAS Int. Conf. Fluid Mech. & Aerodyn., Greece

* Bellhouse, B.J., 1972. Fluid mechanics of a model mitral valve and left ventricle. Cardiovascular Research 6, 199–210.

* Reul, H., Talukder, N., Muller, W., 1981. Fluid mechanics of the natural mitral valve. Journal of Biomechanics 14, 361–372.

* Kim, W.Y., Bisgaard, T., Nielsen, S.L., Poulsen, J.K., Pedersen, E.M., Hasenkam, J.M., Yoganathan, A.P., 1994. Two-dimensional mitral flow velocity profiles in pig models using epicardial echo Doppler Cardiography. J Am Coll Cardiol 24, 532–545.

* Vierendeels, J. A., E. Dick, and P. R. Verdonck. Hydrodynamics of color M-mode Doppler flow wave propagation velocity V(p): A computer study, J. Am. Soc. Echocardiogr. 15:219–224, 2002.

* Kim, W.Y., Walker, P.G., Pedersen, E.M., Poulsen, J.K., Oyre, S., Houlind, K., Yoganathan, A.P., 1995. Left ventricular blood flow patterns in normal subjects: a quantitative analysis by three dimensional magnetic resonance velocity mapping. J Am Coll Cardiol 26, 224–238.

* Kilner, P.J., Yang, G.Z., Wilkes, A.J., Mohiaddin, R.H., Firmin, D.N., Yacoub, M.H., 2000. Asymmetric redirection of flow through the heart. Nature 404, 759–761.

* Kheradvar, A., Milano, M., Gharib, M. Correlation between vortex ring formation and mitral annulus dynamics during ventricular rapid filling, ASAIO Journal, Jan-Feb 2007 53(1): 8-16.

* Kheradvar, A., Gharib, M. Influence of ventricular pressure-drop on mitral annulus dynamics through the process of vortex ring formation. Ann Biomed Eng. 2007 Dec;35(12):2050-64.

* [http://www.enae.umd.edu/AGRC/Aero/vring.html Free-Vortex Wake Calculations of Helicopter Rotors and Tilt-Rotors Operating-In and Transitioning Through the Vortex Ring State]
* [http://www.liveleak.com/view?i=e87_1199375265 Video of possible vortex ring helicopter crash]

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