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Improved VOF Scheme for FLOW-3D

FLOW-3D VOF Simulation

Normal vector in each cell
Figure 1

Volume fluid in the computational domain
Figure 2

mean kinetic energy from standard VOF method
Figure 3

Figure 4: Fluid volume and volume error
Figure 4

In its continuing quest to ensure that FLOW-3D users have the best possible methods for predicting fluid flows in all circumstances, Flow Science will introduce a new volume of fluid (VOF) option with Version 9.1 called the Split Lagrangian method. This method has several advantages over the existing VOF options in FLOW-3D.

In the new VOF scheme, given a function of fluid fraction, F, the free surface is reconstructed using a piecewise linear interface representation, often called PLIC. The key to this construction is to accurately find a normal vector in each cell in question, as shown in Figure 1. A newly developed scheme based on the least-square method developed earlier was adopted for this purpose. After free surface reconstruction, the fluid volume passing between adjacent cells in all three directions in the computational domain can be then calculated, as shown in Figure 2.

To illustrate the strengths of the new VOF scheme, two example simulations are shown here.

The first example involves the simulation of a classic two-dimensional circular droplet of water 1.0 mm in diameter. The surface tension model is turned on, but gravity is not, so the fluid should be at rest with the uniform pressure distribution determined by theconstant curvature of the free surface. In practice, it is difficult to achieve these conditions in a numerical model because of the discrete nature of the approximations. Truncation errors in determining the surface curvature and in tracking the minute changes in the VOF function at the interface result in small variations in pressure and velocities. These variations are often called “parasitic currents.” The accuracy of a numerical method can be measured by the amplitude of these perturbations – smaller amplitude for better accuracy. In the worst cases, the amplitude grows significantly with time.

Figure 3 shows the evolution of the mean kinetic energy obtained with the standard VOF method, IFVOF=4, (red curve) and with the new method, IFVOF=6,(black curve). The time scale is 50 ms. Not only do the maximum values of the two curves differ by a factor of 50.0, but at the end of the time segment the new VOF method predicts almost three orders of magnitude smaller perturbations of the equilibrium solution. Both simulations also include new improvements to the surface tension model in FLOW-3D Version 9.1 that help keep the solution well-behaved.

The second example is a simulation of a sloshing tank. The simulation time was set to 15 seconds, which includes seven sloshing cycles. Because of the nature of the three-dimensional sloshing flow, it is a challenge for any VOF method to conserve fluid volume to an acceptable degree. In FLOW-3D, the volume error is usually small over one wave period, but when multiple wave periods are modeled, the error may accumulate and reach several percent of the initial value. This in turn may significantly affect the solution. The new Split Lagrangian method helps to alleviate these problems. For this test volume error and fluid volume are shown in Figure 4, while an animation of the results is shown at the top of the page. Almost constant fluid volume in the tank and small volume error, less than 0.02%, were observed. These results confirm the superior fluid volume conservation properties of the new VOF scheme.

The new features described here will be available with the release of FLOW-3D Version 9.1.