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# Disperse Multiphase Flows in OpenFOAM

#### Guide to CFD for Polydisperse Flows

1. Disperse Multiphase Flows
2. Polydisperse Multiphase Flows
3. Population Balance Modelling
4. Population Balance Modelling in OpenFOAM

In engineering and physics, multiphase flows describe a variety of problems that involve the combined flow of several phases — gas, liquid or solid. The phases may be clearly separated, e.g. when air blows over ocean water and generates waves. The phases may also mix, e.g. when waves break to form a foam of water and air bubbles.

A lot of engineering problems involve mixing of phases, where gas, solid, or liquid particles (i.e. droplets, bubbles, etc) are dispersed in a continuous phase. These disperse multiphase flows are particularly common in the process and energy industries, but extend to most disciplines of engineering. For example, in power generation, water is boiled which forms bubbles of vapour that eventually drives a steam turbine. In aerosol flame reactors, solid particles are synthesized from a vapour phase by a chemical reaction; the resulting powders are used as pigments or filler materials. Combustion engines rely on a dispersed phase of liquid fuel, in the form of a spray, which evaporates.

## Multiphase Flows with CFD

Multiphase flows can be simulated using computational fluid dynamics (CFD) with suitable methods to account for multiple phases. A popular approach — the volume of fluid (VoF) method — defines the phase(s) occupying a region of space by a phase fraction. A fraction of 1 indicates a region fully occupied by a given phase; 0 indicates none of that phase. Where phases are separate, e.g. air and ocean water, there is a sharp transition of the phase fraction from 0 to 1 across the interface between the phases. When the interface is at a large scale, its position can be tracked efficiently during the simulation. Exchanges of mass, momentum and energy are governed by equations which apply across, and between, all phases.

For a dispersed phase, it becomes very costly to track the interface of a large number of small particles. However, the concept of phase fraction can still be used to indicate the average volume of particles, as a fraction of the overall volume. In this so-called Euler-Euler model of multiphase flow, the governing equations of mass, momentum and energy are applied to each phase individually so no exchanges across interfaces between phases are calculated. Instead additional models are required for exchanges between phases, e.g. the drag force acting on a particle. The models need to cover a range of observed behaviour, e.g. particles experiencing lift due to shear and dispersing further due to turbulence.  These exchange processes are dependent on particle size.

## Multiphase Flows in OpenFOAM

OpenFOAM includes multiphaseEulerFoam, a versatile solver that computes the flow of multiple compressible phases. The solver is the result of more than a decade of development work appearing in a collection of former solvers in OpenFOAM, including bubbleFoam, twoPhaseEulerFoam and reactingEulerFoam solvers. In OpenFOAM 8, the entire functionality was consolidated and made available within multiphaseEulerFoam.

multiphaseEulerFoam offers a wealth of modelling possibilities, with the flexibility that the phase fraction can be used both to indicate an interface resolved by an abrupt 0 – 1 transition and the fractional volume of particles with the Euler-Euler approach. The solver covers a wide range of applications and can model phenomena such as phase change, diffusive species mass transfer and chemical reactions. The user can choose from a large number of turbulence models and interactions between particles under dense conditions can be modelled using kinetic theory applied to granular flows.