Volume Of Fluid Technique Research Articles

Rise characteristics of gas bubbles in a 2D rectangular column: VOF simulations vs experiments

About five centuries ago, Leonardo da Vinci described the sinuous motion of gas bubbles rising in water. We have attempted to simulate the rise trajectories of bubbles of 4, 5, 7, 8, 9, 12 and 20 mm in diameter rising in a 2D rectangular column filled with water. The simulations were carried out using the volume-of-fluid (VOF) technique developed by Hirt and Nichols ( J. Computational Physics., 39, 201–225 (1981)). To solve the Navier-Stokes equations of motion we used a commercial solver, CFX 4.1c of AEA Technology, UK. We developed our own bubble-tracking algorithm to capture “sinuous” bubble motions. The 4 and 5 mm bubbles show large lateral motions observed by Da Vinci. The 7,8 and 9 mm bubble behave like jellyfish. The 12 mm bubble flaps its wings like a bird. The extent of lateral motion of the bubbles decreases with increasing bubble size. Bubbles larger than 20 mm in size assume a spherical cap form and simulations of the rise characteristics match experiments exactly. VOF simulations are powerful tools for a priori determination of the morphology and rise characteristics of bubbles rising in a liquid. Bubble-bubble interactions are also properly modelled by the VOF technique.

Numerical analysis of a single drop formation process under pressure pulse condition

In order to obtain the detailed information on mechanism of the motion of a single droplet formation process in the pulsed sieve-plate column, the numerical analysis for transient behavior is carried out by using VOF (volume of fluid) method, and their results are compared with the experimental results. On the assumption that the essential shape of the pressure pulse added to the system can be described numerically by a simple sine wave, the numerical results agree approximately with the real drop formation process. The mechanism of the fluid flow inside and outside a drop can be clear from the obtained numerical results, and it is found that there is a circulation flow inside a drop. Furthermore, it is confirmed that VOF technique is useful and efficient as the method for tracking boundary interfaces and can predict numerically well the transient behavior of the drop with liquid-liquid interfaces.

A hybrid finite‐element–volume‐of‐fluid method for simulating free surface flows and interfaces

AbstractA numerical technique is developed for the simulation of free surface flows and interfaces. This technique combines the strength on the finite element method (FEM) in calculating the field variables for a deforming boundary and the versatility of the volume‐of‐fluid (VOF) technique in advection of the fluid interfaces. The advantage of the VOF technique is that it allows the simulation of interfaces with large deformations, including surface merging and breaking. However, its disadantage is that is solving the flow equations, it cannot resolve interfaces smaller than the cell size, since information on the subgrid scale is lost. Therefore the accuracy of the interface reconstruction and the treatment of the boundary conditions (i.e. viscous stresses and surface tension forces) become grid‐size‐dependent. On the other hand, the FEM with deforming interface mesh allows accurate implementation of the boundary conditions, but it cannot handle large surface deformations occurring in breaking and merging of liquid regions. Combining the two methods into a hybrid FEM‐VOF method eliminates the major shortcomings of both. The outcome is a technique which can handle large surface deformations with accurate treatment of the boundary conditions. For illustration, two computational examples are presented, namely the instability and break‐up of a capillary jet and the coalescence collision of two liquid drops.

Numerical Calculations of the Breakup of Highly Loaded Slurry Jets

A complete numerical calculation procedure for predicting the effects of mass loading and particle diameter on laminar slurry jet breakup in a low velocity, coaxial gas stream has been developed. The method is based on the Volume of Fluid technique for the Navier-Stokes equations. The severe restrictions involved in earlier treatments have been relaxed. The influence of particle loading on liquid phase density and the influence of particle spacing on drag are included. The particular case considered is a slurry with a methanol liquid phase with aluminum oxide beads in order to compare with some related experimental results. The methanol liquid in the slurry is vaporized due to mass transfer in the gas stream. The variation of the instantaneous jet shape of the methanol slurry jet at low loadings is generally similar to that of an all-liquid methanol jet, but the final shapes at breakup are different. In the region of low mass loading (up to 20 percent), the effects of mass loading are to stabilize the interface and increase the breakup time of the slurry jet with increasing mass loading. Above that region of mass loading (more than 20 percent), the effects of mass loading are to destabilize the interface and decrease the breakup time of the slurry jet with increased mass loading. At the same mass loading condition, a slurry jet with large diameter particles has a more stabilizing effect than one with small diameter particles. Therefore, a slurry jet with higher mass loading and smaller diameter particles breaks up faster.

Curvature and the evolution of fronts

The evolution of a front propagating along its normal vector field with speedF dependent on curvatureK is considered. The change in total variation of the propagating front is shown to depend only ondF/dK only whereK changes sign. Analysis of the caseF(K)=1−εK, where ε is a constant, shows that curvature plays a role similar to that of viscosity in Burgers equation. For ε=0 and non-convex initial data, the curvature blows up, corners develop, and an entropy condition can be formulated to provide an explicit construction for a weak solution beyond the singularity. We then numerically show that the solution as ε goes to zero converges to the constructed weak solution. Numerical methods based on finite difference schemes for marker particles along the front are shown to be unstable in regions where the curvature builds. As a remedy, we show that front tracking based on volume of fluid techniques can be used together with the entropy condition to provide transition from the classical to weak solution.

A Computational Method for Free Surface Hydrodynamics

There are numerous flow phenomena in pressure vessel and piping systems that involve the dynamics of free fluid surfaces. For example, fluid interfaces must be considered during the draining or filling of tanks, in the formation and collapse of vapor bubbles, and in seismically shaken vessels that are partially filled. To aid in the analysis of these types of flow phenomena, a new technique has been developed for the computation of complicated free-surface motions. This technique is based on the concept of a local average volume of fluid (VOF) and is embodied in a computer program for two-dimensional, transient fluid flow called SOLA-VOF. The basic approach used in the VOF technique is briefly described, and compared to other free-surface methods. Specific capabilities of the SOLA-VOF program are illustrated by generic examples of bubble growth and collapse, flows of immiscible fluid mixtures, and the confinement of spilled liquids.

Volume of fluid (VOF) method for the dynamics of free boundaries

Several methods have been previously used to approximate free boundaries in finite-difference numerical simulations. A simple, but powerful, method is described that is based on the concept of a fractional volume of fluid (VOF). This method is shown to be more flexible and efficient than other methods for treating complicated free boundary configurations. To illustrate the method, a description is given for an incompressible hydrodynamics code, SOLA-VOF, that uses the VOF technique to track free fluid surfaces.