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# Multiphase flow

Flows in technology and nature are not limited to a single phase of a fluid, but often comprise two or more phases. In this context, the term phase not only includes the different physical states solid, liquid and gaseous, but also includes the different areas of immiscible liquids. The definition of fluid is also broader here. In addition to liquids and gases, mobile solid particles are also referred to. The particle flow is therefore to be regarded as a sub-area of the two- or multiphase flow.

Two- or multiphase flows occur in a wide variety of combinations: Two physical states of a substance up to the same or different physical states of different substances. An example of a one-component two-phase flow is the bubble flow during a boiling process. If the volume fraction of a phase is dominant, this phase is described as continuous and the other phase as discontinuous or dispersive. The smaller the proportion of the disperse phase, the less it usually affects the continuous phase. For example, smoke, understood as a few small solid particles in a gas flow, hardly influences the continuous phase, whereas in a stratified flow, gas and liquid are separated, a strong interaction is present. However, there are also exceptions, such as chemical reactions or combustion processes. In these cases even a few parts of the disperse phase can strongly influence the continuous flow.

This brief outline of two- or multiphase flows alone shows how complicated and physically complex this topic is. As with turbulence, two- or multiphase flows often have microscopically small structures, which make a direct solution of the Navier-Stokes equations impossible in everyday engineering work. For this reason, working with temporally averaged values is also indispensable here.

## two-fluid formulation

A general approach to describe two-phase or multiphase flow is based on the Euler-Euler model or the two-fluid formulation. Here, each phase is regarded as a continuous fluid, which means that there is a separate set of state variables for each phase in the flow area at each location and at each point in time. Averaging must be performed separately in each control volume, element or cell, for each phase and each size. To couple the two phases, additional conservation equations for pulse, energy and mass are introduced, taking into account the respective local volume fraction. Turbulence can be represented by a common or by individual turbulence models.

It is obvious that this formulation considerably increases the numerical effort compared to single-phase flow. For this reason, other simplified models have been developed for different classes of two-phase and multiphase flows. Among others for:

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