Stratified flow

Flows in open channels are flows with a free surface. Looking closely, however, this free surface is not free, but describes the boundary or contact surface to another phase. From the point of view of numerical fluid mechanics, the channel flow can therefore also be regarded more generally as stratified flow between two phases that are not mixed.

A simplified possibility for the numerical formulation of stratified flows is the Volume-of-Fluid method, VOF method for short. This is based on the consideration that a control volume can never be completely filled by both phases at the same time, which means that the sum of the respective volume proportions can never be greater than 1. Numerically the flow is therefore described with the Euler formulation as a single-phase flow. In addition, however, the respective phase fraction is introduced. With its help, the physical properties such as density or viscosity can be derived volumetrically for each element or cell. Elements that contain more than one phase represent an interface between the phases. The exchange of impulse, energy and mass takes place only at this interface or in the corresponding cells. The interface moves according to the flow velocity and can thus continuously change both its shape and its topology. The Volume-of-Fluid method provides additional models for the often necessary consideration of surface tension.

Applications of the VOF model include the already mentioned open channel flow as a special case of layered flows, the filling or sloshing of a liquid as well as the movement of large bubbles in a liquid.