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# Polydisperse 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 a previous article, we briefly introduced disperse multiphase flows and their simulation with CFD in OpenFOAM using multiphaseEulerFoam. One important aspect of disperse multiphase flows is particle size. It influences the exchange processes between the particles and the continuous phase, including the transfer of momentum (e.g. drag, lift) as well as heat and mass (e.g. boiling, condensation, species diffusion).

Particle size can vary considerably (for the same particle type), e.g. ranging from nano- to micrometers for powder produced in flame reactors, or milli- to centimeters for gas bubbles in an industrial bubble column. Where the particle size distribution is significant, we describe the flow as “polydisperse”. (“Monodisperse” describes the case of uniform particle size.) Polydisperse flows can involve significant changes in particle size due to: collisions, causing particles to agglomerate or coalesce into larger ones; and, shear forces, causing breakup into smaller ones.

Reproduced with permission from the Institute of Fluid Dynamics Helmholtz-Zentrum Dresden – Rossendorf (HZDR).

## Modelling Particle Size in OpenFOAM

In multiphaseEulerFoam, the models for momentum, mass and energy exchange between the continuous phase and particles are dependent on particle size. Models for the particle diameter can be selected, including:

• assuming a constant value (monodisperse);
• calculating the isothermal expansion of bubbles due to variation in pressure;
• in case of phase change, computing the bubble diameter as a function of the liquid phase sub-cooling;
• coalescence, breakup, dilatation, as well phase change, using an additional transport equation for the interfacial curvature per unit volume.

These models provide a localized mean particle diameter but do not describe any size distribution.

## Particle Size Distribution in OpenFOAM

In December 2017, a population balance model was added to multiphaseEulerFoam which describes a size distribution for particles and tracks its evolution during the flow. The modelling approach, also commonly known as the method of classes, derives its name from its way of solving the population balance equation. The particle population is split into a series of size groups, each representing a characteristic particle size. A set of coupled transport equations is solved for the corresponding particle concentrations. The equations include source terms describing the change of the respective particle concentrations resulting from phase or density changes as well as coalescence and breakup.

Calculations which use the method of classes provide information about the particle size distribution function, which can be  compared relatively easily to a particle size distribution measured in experiments. Repeated calculations and comparisons enable rapid development and calibration of models for coalescence or breakup.

Helmholtz-Zentrum Dresden – Rossendorf has developed code in OpenFOAM to solve the population balance equation with models for coalescence and breakup, in collaboration with VTT Finland. The code is integrated into multiphaseEulerFoam with help in software design from Will Bainbridge and Henry Weller at CFD Direct. It is continuously maintained within the development version of OpenFOAM (OpenFOAM-dev), enabling the latest modelling capability to reach to the general public quickly. The modelling is later available in the following version release of OpenFOAM, supported by the dedicated core maintenance team at CFD Direct.

Basic elements of the model and its usage in OpenFOAM are presented in subsequent articles.