Chapter 7 - Free Surface Flows

Abstract

This chapter is concerned with the modeling of free surface flows with the phases separated by a distinct interface. The phases are assumed to have different thermo-fluid properties. One reason for the designation of the term freearises from the prevalence of a large difference in the densities of the gas and the liquid. Free surfaces require the use of special methods to define their location, movement, and influence on a flow. Many numerical methods have been proposed to solve these interfacial flows in various frameworks. Lagrangian methods are employed when the deformation is not too large and when this domain does not result from topology changes. They are based on the displacement of a system of coordinates at each point of the free surface to track the movement of the interface between two phases. Generally, Eulerian methods are preferred for interfacial flows involving two immiscible fluids as they permit large topology changes and discontinuities, implicitly handling droplet coalescence and break-up. Two classes of methods can be distinguished for Eulerian methods. Such flows can be handled through the use of either surface methods (interface tracking) or volume methods (interface capturing) to compute the free surfaces and fluid interfaces. Furthermore, this chapter demonstrates the application of the fixed mesh approach based upon the use of volume methods (interface capturing) on an Eulerian mesh to predict the sharp free surfaces and fluid interfaces for a range of multiphase interfacial flows. The analysis of such flows is exemplified through relevant worked examples covering the rise of a bubble in a quiescent liquid, a Taylor bubble ascending through a denser stagnant liquid, collapse of a liquid column with and without an obstacle, and liquid sloshing at low-filling conditions in a tank.