Volume of fluid method

About: Volume of fluid method is a research topic. Over the lifetime, 5338 publications have been published within this topic receiving 116760 citations.

The development of a bubble rising in a viscous liquid

Abstract: The rise and deformation of a gas bubble in an otherwise stationary liquid contained in a closed, right vertical cylinder is investigated using a modified volume-of-fluid (VOF) method incorporating surface tension stresses. Starting from a perfectly spherical bubble which is initially at rest, the upward motion of the bubble in a gravitational field is studied by tracking the liquid–gas interface. The gas in the bubble can be treated as incompressible. The problem is simulated using primitive variables in a control-volume formulation in conjunction with a pressure–velocity coupling based on the SIMPLE algorithm. The modified VOF method used in this study is able to identify and physically treat features such as bubble deformation, cusp formation, breakup and joining. Results in a two-dimensional as well as a three-dimensional coordinate framework are presented. The bubble deformation and its motion are characterized by the Reynolds number, the Bond number, the density ratio, and the viscosity ratio. The effects of these parameters on the bubble rise are demonstrated. Physical mechanisms are discussed for the computational results obtained, especially the formation of a toroidal bubble. The results agree with experiments reported in the literature.

Turbulent fountains in an open chamber

Abstract: The flow and density distribution produced by injecting dense fluid upwards at the bottom of a homogeneous fluid have been investigated experimentally and theoretically. Both axisymmetric and line sources have been studied using small-scale laboratory experiments in which salt water is injected into a tank of fresh water. The turbulent fountain formed in this way rises to a maximum height which can be related to the Froude number of the inflow, and then falls back and spreads out along the floor. Continuing the inflow builds up a stable stratification in a similar manner to that discussed earlier for the ‘plume filling box model’ of Baines & Turner (1969) which is complementary to the present work. The fountain flows considered here have the important new feature that the volume of the inflow is significant, so the total volume of fluid in the ‘open’ container increases with time. The evolution is determined by the rate of entrainment into the fountain from its surroundings, which is found directly by experiment. Re-entrainment of fluid into the fountain continually changes the density profile in the mixed fluid collecting at the bottom of the chamber below the level of the fountain top, and controls the rate of rise of a ‘front’ of marked fluid. The top of the fountain rises linearly in time, at a rate which, for axisymmetric fountains, has been shown both experimentally and theoretically to be close to half the rate of rise of the free surface due to the inflow. Thus at a certain time the front rises above the top of the fountain. Once the mixed fluid at the bottom of the chamber has risen above the fountain its density profile remains unchanged. The front velocity, the fountain height and the density profile have all been obtained as functions of time using a theory which is in good agreement with the experimental results for a large range of input Froude numbers. For line fountains the results are less precise owing to an instability which causes the flow to switch irregularly from a symmetrical state to one in which the downflow occurs on one side only, and with a smaller maximum height. In concluding we discuss the applications which motivated the work, particularly the development of a stratified hybrid layer in magma chambers replenished from below, and the dynamically identical, but inverted problem of heating large buildings through ducts located near the roof.