# Vortex ring: Wikis

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# Encyclopedia

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 toroidal (doughnut) shape. The movement of the fluid is about the poloidal or circular axis of the doughnut, in a twisting vortex motion. Examples of this phenomenon is a smoke ring or a microburst, [1], [2].

## Vortex ring formation and structure

Vortex ring of a microburst

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.[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 [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

The curved arrows indicate airflow circulation about the rotor disc. The helicopter shown is the RAH-66 Comanche.
The V-22 Osprey in flight.

Vortex ring state (VRS), also known as settling with power, is a hazardous condition encountered in helicopter flight. It occurs when the helicopter has three things occurring: A high rate of descent, an airspeed slower than effective translational lift, and the helicopter is using a large portion of its available power. A helicopter typically induces a vortex ring state by descending into its own downwash. In typical flight, the rotor disc directs the airflow downwards, creating lift. During VRS, a toroid-shaped path of airflow circumscribes 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. Specific to vortex ring state is that the helicopter operating in its own downwash is descending through descending air. Applying more power (increasing collective pitch) serves to further accelerate the downwash through which the main-rotor is descending, exacerbating the condition. A particularly deadly example occurred on April 8, 2000, when a V22 Osprey suffered VRS as a result of a classic high descent and low forward airspeed. The fully-laden aircraft stalled its right wing, rolled over, and crashed, killing all 19 aboard.

In single rotor helicopters, a VRS 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. In tandem-rotor helicopters, recovery is accomplished through lateral cyclic or pedal input. The aircraft will fly into "clean air", and will be able to regain lift.

## 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[3][4] and subsequently strengthened by analyses based on color Doppler mapping[5][6] and Magnetic Resonance Imaging[7][8]. Some recent studies[9][10] 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[11] when the vortex ring traveled around a critical velocity, which is between the turbulence and laminar states. Later Huang and Chan[12] reported that if the initial state of the vortex ring is not perfectly 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.

## References

### Inline notes

1. ^ An Introduction to Fluid Dynamics, Batchelor, G. K., 1967, Cambridge UP
2. ^ Hill, M. J. M. (1894), Phil. Trans. Roy. Soc. London, A, Vol. 185, p. 213
3. ^ Bellhouse, B.J., 1972, Fluid mechanics of a model mitral valve and left ventricle, Cardiovascular Research 6, 199–210.
4. ^ Reul, H., Talukder, N., Muller, W., 1981, Fluid mechanics of the natural mitral valve, Journal of Biomechanics 14, 361–372.
5. ^ 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.
6. ^ 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.
7. ^ 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.
8. ^ 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.
9. ^ 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.
10. ^ 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.
11. ^ Maxworthy, T. J. (1972) The structure and stability of vortex ring, Fluid Mech. Vol. 51, p. 15
12. ^ Huang, J., Chan, K.T. (2007) Dual-Wavelike Instability in Vortex Rings, Proc. 5th IASME/WSEAS Int. Conf. Fluid Mech. & Aerodyn., Greece