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Axisymmetric draining of a cylindrical tank with a free surface

Published online by Cambridge University Press:  26 April 2006

Qiao-Nian Zhou  and
W. P. Graebel
Qiao-Nian Zhou
Affiliation:
Department of Mechanical Engineering and Applied Mechanics, The University of Michigan, Ann Arbor, MI 48109, USA
W. P. Graebel
Affiliation:
Department of Mechanical Engineering and Applied Mechanics, The University of Michigan, Ann Arbor, MI 48109, USA
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Abstract

The withdrawal of layered fluids from an open tank through a hole centred on the bottom is investigated numerically under the assumption of potential flow. A fully cubic-spline nonlinear axisymmetric boundary-integral-method scheme with the built-in boundary conditions, which effectively reduces the numerical errors at the intersection lines where the tank wall and the density interfaces meet, is used. Two cases are studied: (i) the tank contains only one fluid with a free surface; (ii) the tank contains two fluids having different densities with a distinct interface and a free surface

The numerical results show two different phenomena, depending upon the drain rate and initial conditions. When the tank is rapidly drained, a dip forms at the centre of the lower interface and extends into the hole very quickly, as observed by Lubin & Springer (1967). For a slowly draining tank, a jet forms in the centre of the depression region. This jet can either shoot up or move down, depending on the initial conditions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 221 , December 1990 , pp. 511 - 532
Copyright
© 1990 Cambridge University Press

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References

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