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The main physical phenomenon of the vortex tube is the temperature separation between the cold vortex core and the warm vortex periphery. The "vortex tube effect" is fully explained with the work equation of Euler, [ 3 ] also known as Euler's turbine equation, which can be written in its most general vectorial form as: [ 4 ]
More simply, vortex lines move with the fluid. Also vortex lines and tubes must appear as a closed loop, extend to infinity or start/end at solid boundaries. Fluid elements initially free of vorticity remain free of vorticity. Helmholtz's theorems have application in understanding: Generation of lift on an airfoil; Starting vortex; Horseshoe vortex
A vortex tube is the surface in the continuum formed by all vortex lines passing through a given (reducible) closed curve in the continuum. The 'strength' of a vortex tube (also called vortex flux) [10] is the integral of the vorticity across a cross-section of the tube, and is the same everywhere along the tube (because vorticity has zero ...
The vorticity equation of fluid dynamics describes the evolution of the vorticity ω of a particle of a fluid as it moves with its flow; that is, the local rotation of the fluid (in terms of vector calculus this is the curl of the flow velocity). The governing equation is:
For a single knotted vortex tube with circulation , then, as shown by Moffatt & Ricca (1992), the helicity is given by = (+), where and are the writhe and twist of the tube; the sum + is known to be invariant under continuous deformation of the tube.
The unsimplified equations do not have a general closed-form solution, so they are primarily of use in computational fluid dynamics. The equations can be simplified in several ways, all of which make them easier to solve. Some of the simplifications allow some simple fluid dynamics problems to be solved in closed form. [citation needed]
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 ...
The parameter is named after Vincenc Strouhal, a Czech physicist who experimented in 1878 with wires experiencing vortex shedding and singing in the wind. [1] [2] The Strouhal number is an integral part of the fundamentals of fluid mechanics. The Strouhal number is often given as =,