unsteady laminar flows
Example: Formation of a laminar ring-vortex
Vortex dynamics is a central theme within the research field of fluid dynamics. The formation process of viscid laminar ring vortices was calculated numerically applying a CFD (Computational-Fluid-Dynamics)-code. An experiment was simulated, where the vortices were produced by ejecting water from a pipe into a resting environment by means of a piston. The animation shows a typical result of the calculations (concentration field). The fluid emenating from the nozzle is coloured red, the surrounding fluid is coloured blue. The evolving line represents the trajectory of the vortex centre.
Parameters: nozzle diameter = 5 cm, velocity = 4.6 cm/s, ejection time = 1.522 s.
The two figures show the normalised axial position and the normalised radial position of the vortex centre versus normalised time. The results of the calculations coincide with the results obtained by the measurements (Didden 1979).
Additionally, the results of these calculations showed, that the formation laws given for plane inviscid vortices are also valid for the formation process of viscid ring vortices. This applies to the normalised axial and radial position of the vortex centre as well as for the normalised diameter of the vortex spiral.
The dependency of the radial position predicted by the similarity laws for the formation of laminar vortex rings can be reproduced by both, calculation and experiment.
References Matthias Hettel, (2006), Analytische und numerische Untersuchungen der Dynamik von Vormischflammen sowie deren Interaktion mit Ringwirbelstrukturen , Dissertation, Karlsruhe
Matthias Hettel, Frank Wetzel, Peter Habisreuther, Henning Bockhorn, (2007). Numerical Verification of the Similarity Laws for the Formation of Laminar Vortex Rings. Journal of Fluid Mechanics, 590, 35-60
Matthias Hettel, (2006), Analytische und numerische Untersuchungen der Dynamik von Vormischflammen sowie deren Interaktion mit Ringwirbelstrukturen , Dissertation, Karlsruhe