Publication Date:
2017-12-12
Description:
Vorticity distributions in axisymmetric vortex rings produced by a piston-pipe apparatus are numerically studied over a range of Reynolds numbers, Re, and stroke-to-diameter ratios, L=D. It is found that a state of advective balance, such that ς=ω/φ/r≈F(Ψ,t).is achieved within the region (called the vortex ring bubble) enclosed by the dividing streamline. Here ς=ω/φ/r is the ratio of azimuthal vorticity to cylindrical radius, and Ψ is the Stokes streamfunction in the frame of the ring. Some, but not all, of the Re dependence in the time evolution of F.(Ψ,t) can be captured by introducing a scaled time t, where v is the kinematic viscosity. When vt=D2 〉∼ 0:02, the shape of F. Ψ is dominated by the linear-in-Ψ component, the coefficient of the quadratic term being an order of magnitude smaller. An important feature is that, as the dividing streamline (Ψ=0) is approached, F.(Ψ) tends to a non-zero intercept which exhibits an extra Re dependence. This and other features are explained by a simple toy model consisting of the one-dimensional cylindrical diffusion equation. The key ingredient in the model responsible for the extra Re dependence is a Robin-type boundary condition, similar to Newton's law of cooling, that accounts for the edge layer at the dividing streamline. © 2017 Cambridge University Press.
Print ISSN:
0022-1120
Electronic ISSN:
1469-7645
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
,
Physics
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