Selective withdrawal and draining of a viscous liquid under air from a cylindrical tank through a tube imbedded in the liquid

摘要

Draining a viscous liquid from a partially filled, finite-size cylindrical tank through a tube imbedded in the liquid is viewed as selective withdrawal from the lower layer of viscous liquid in an identical tank, with the fluid of the upper layer being air or low-viscosity gas. Contrary to previous approaches that simplify the problem by considering a tank of infinite extent in the horizontal direction and approximating the withdrawal tube as a point mass sink, the model presented here employs a detailed flow geometry of a finite-size tank with a withdrawal tube of comparable radius. An Arbitrary Lagrangian-Eulerian (ALE) method is utilized in the numerical model to track the motion and deformation of the free surface. The results of simulations made with the present model show that the mean curvature at the tip of the free surface depends on the flow rate of drainage and the distance of the unperturbed free surface from the tube inlet; the mean curvature at the free surface tip is not influenced by the size of the tank when the tank-to-tube radius ratio exceeds a value of 30, in agreement with experimental results. The simulations reveal that a critical parameter for the system under investigation is the ratio of tube wall or tube support thickness or the horizontal distance of liquid from the tube inlet, at the level of the inlet, to the tube radius. When this parameter is correctly identified, results of simulations collapse on experimental results regarding the mean curvature of free surface at the tip. (C) 2015 Elsevier Ltd. All rights reserved.