Numerical Simulation of a Single Air Bubble Rising in Water with Various Models of Surface Tension Force

Abstract

Different numerical methods are employed and developed for simulating interfacial flows. A large range of applications belong to this group, e.g. two-phase flows of air bubbles in water or water drops in air. In such problems surface tension effects often play a dominant role. In this paper, various models of surface tension force for interfacial flows, the CSF, CSS, PCIL and SGIP models have been applied to simulate the motion of small air bubbles in water and the results were compared and reviewed. It has been pointed out that by using SGIP or PCIL models, we are able to simulate bubble rise and obtain results in close agreement with the experimental data. the advection equation, by a geometrically based calculation technique of the void fraction fluxes at the cell faces based on the reconstructed interface. A significant improvement of the interface representation was achieved by Youngs (1) by introducing a piecewise-linear method. The PLIC method approximate the interface is by a straight line of arbitrary orientation in each cell. Its orientation is found the distribution of one of the fluids in the neighbor cell. Given the volume fraction of one of the two fluids in each computational cell and an estimate of the normal vector to the interface, a plane surface is constructed within the cell having the same normal and dividing the cell into two parts each of which contains the proper volume of one of the two fluids. This has several advantages: the fluxes of F with which the phase field updated, can be determined more accurately, and essentially free of numerical diffusion. Fluid properties can be calculated accurately. In contrast to the interface representation methods, the methods for introducing surface tension effects at the interface into the physical model remain a problem. Generally, the influence of surface tension is incorporated into the momentum equation following the continuum surface force (CSF) model of Brackbill et al. (2). For doing so, the local curvature and the interface normal vector have to be calculated. This task is difficult, since the discontinuous void fraction function disallows the application of ordinary discretization schemes. An inconsistent calculation of the surface tension force can then result in the well-known phenomena of so-called spurious (11). Usually problems with parasitic currents arise when flows with high density ratios are considered. Unfortunately, a large range of applications belong to this group, e.g. two-phase flows of air bubbles in water. In such problems surface tension effects often play a dominant role. The behavior of each algorithm under surface tension-dominant problems is discussed in the next section.