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Vortex - Wikipedia
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A word with surprisingly literal origins.
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The direction of the vorticity vector is defined to be the direction of the axis of rotation of this imaginary ball according to the right-hand rule while its length is twice the ball's angular velocity. In theory, the speed u of the particles and, therefore, the vorticity in a vortex may vary with the distance r from the axis in many ways.
There are two important special cases, however:. In the absence of external forces, a vortex usually evolves fairly quickly toward the irrotational flow pattern [ citation needed ] , where the flow velocity u is inversely proportional to the distance r.
Irrotational vortices are also called free vortices. However, the ideal irrotational vortex flow is not physically realizable, since it would imply that the particle speed and hence the force needed to keep particles in their circular paths would grow without bound as one approaches the vortex axis. Indeed, in real vortices there is always a core region surrounding the axis where the particle velocity stops increasing and then decreases to zero as r goes to zero.
Within that region, the flow is no longer irrotational: The Rankine vortex is a model that assumes a rigid-body rotational flow where r is less than a fixed distance r 0 , and irrotational flow outside that core regions. The Lamb-Oseen vortex model is an exact solution of the Navier—Stokes equations governing fluid flows and assumes cylindrical symmetry, for which. A rotational vortex — one which has non-zero vorticity away from the core — can be maintained indefinitely in that state only through the application of some extra force, that is not generated by the fluid motion itself.
For example, if a water bucket is spun at constant angular speed w about its vertical axis, the water will eventually rotate in rigid-body fashion. The particles will then move along circles, with velocity u equal to wr. In this situation, the rigid rotating enclosure provides an extra force, namely an extra pressure gradient in the water, directed inwards, that prevents evolution of the rigid-body flow to the irrotational state. In a stationary vortex, the typical streamline a line that is everywhere tangent to the flow velocity vector is a closed loop surrounding the axis; and each vortex line a line that is everywhere tangent to the vorticity vector is roughly parallel to the axis.
A surface that is everywhere tangent to both flow velocity and vorticity is called a vortex tube. In general, vortex tubes are nested around the axis of rotation. The axis itself is one of the vortex lines, a limiting case of a vortex tube with zero diameter. According to Helmholtz's theorems , a vortex line cannot start or end in the fluid — except momentarily, in non-steady flow, while the vortex is forming or dissipating.
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In general, vortex lines in particular, the axis line are either closed loops or end at the boundary of the fluid. A whirlpool is an example of the latter, namely a vortex in a body of water whose axis ends at the free surface. A vortex tube whose vortex lines are all closed will be a closed torus -like surface. A newly created vortex will promptly extend and bend so as to eliminate any open-ended vortex lines. For example, when an airplane engine is started, a vortex usually forms ahead of each propeller , or the turbofan of each jet engine. One end of the vortex line is attached to the engine, while the other end usually stretches out and bends until it reaches the ground.
When vortices are made visible by smoke or ink trails, they may seem to have spiral pathlines or streamlines. However, this appearance is often an illusion and the fluid particles are moving in closed paths. The spiral streaks that are taken to be streamlines are in fact clouds of the marker fluid that originally spanned several vortex tubes and were stretched into spiral shapes by the non-uniform flow velocity distribution.
The fluid motion in a vortex creates a dynamic pressure in addition to any hydrostatic pressure that is lowest in the core region, closest to the axis, and increases as one moves away from it, in accordance with Bernoulli's Principle. One can say that it is the gradient of this pressure that forces the fluid to follow a curved path around the axis. In a rigid-body vortex flow of a fluid with constant density , the dynamic pressure is proportional to the square of the distance r from the axis. In a constant gravity field, the free surface of the liquid, if present, is a concave paraboloid.
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This formula provides another constraint for the extent of the core, since the pressure cannot be negative. Easy to install and operate. Designed for end customers, it works on grid, off grid and hybrid in combination with solar panels. Vortex scalability makes it perfect for on-site energy generation. Put it in your yard or over your roof and get clean energy from the wind! Nowadays, conventional wind turbines have shown that wind is an excellent source of energy.
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