vortex ring formation at the edge of a circular tube
This simulation was motivated by a laboratory experiment of
which appears in Van Dyke's
"An Album of Fluid Motion" (p. 43).
At time t=0,
a piston begins pushing fluid through the open end of a
The boundary layer
rolls up to form a vortex ring which propagates downstream.
The piston stops moving at t=1.6
a counter-rotating ring forms
at the tube opening.
In the simulation results shown below,
the shear layer is represented by a free vortex sheet
and the circular tube by a bound vortex sheet.
Axisymmetry is imposed.
Prandtl's slip-flow model
is applied to simulate
separation at the edge of the tube.
On the formation of vortex rings:
rolling-up and production of circulation,
Z. Angew. Math. Phys. 30, 101
Nitsche, M. & Krasny, R.
A numerical study of vortex ring formation at the
edge of a circular tube,
J. Fluid Mech. 276, 139-161
Van Dyke, M.
An album of fluid motion,
The Parabolic Press, 43