## Solver: DPMFoam Description

DPMFoam is a transient solver that considers the effect of the particle volume fraction on the continuous phase, suitable for dense particle flows. The solver takes into account four-way coupling: fluid to particles, particles to fluid, and particle-particle collisions. It handles both laminar and turbulent flows, encompassing Newtonian and non-Newtonian fluids.

The solver is a part of the Eulerian-Lagrangian solver category, treating the fluid phase as continuous and the solid phase as discrete. The fluid phase dynamics are captured using the time-averaged Navier-Stokes equations and solved using the PIMPLE algorithm. Calculating isothermal particle motions requires a solution of the set of ordinary differential equations. All relevant forces acting on the particle, e.g., drag, gravitational and buoyancy, and pressure forces are considered.

For particle-particle interactions, the solver employs the soft sphere model, also known as the Cundall and Strack model. The model assumes that the collision between two particles can be represented by a spring and a dash-pot. The spring represents the elastic deformation and the dash-pot considers the viscous dissipation. The contact force between particles is split into the normal component (according to Hertzian contact theory) and tangential force. In complete analogy, the contact force between a particle and a wall is expressed in the same way.

Applications of the DPM model are very numerous. In the agriculture industry, the solver can be used to predict the interaction of particles (representing, for example, seeds of barley) with the transport and distribution systems used in modern agriculture machines. In industries such as food and pharmaceuticals, particle modeling facilitates process optimization. Other applications can be found in chemical manufacturing, oil and gas, energy, environmental engineering and biological systems.

## Solver: DPMFoam Features

**Transient****Incompressible****Multiphase - Lagrangian Particles**

- 1 Fluid and Particles
- Lagrangian Particles:
- Dense Cloud/Particle Bed

- Laminar and Turbulent (RANS, LES - limited set)
- Newtonian and Non-Newtonian Fluid
- Pressure-Based Solver
- Rotating Objects:
- Multiple Reference Frames (MRF)

- Passive Scalar
- Porosity Modeling
- Buoyancy
- Source Term (explicit/implicit)
- Erosion
- PIMPLE Algorithm
- Solution Limiters:
- Velocity Damping

## Solver: DPMFoam Application

**Chemical Industry**

- Fluidized Bed Reactors

**Energy Industry**

- CFD Combustors - Circulating Fluidized Bed Combustors

**Mining Industry**

- Transporting Systems
- Crushing Systems
- Milling Systems

**Piping Industry**

- Slurry Pipelines
- Sediment Transport

## Solver: DPMFoam Multiphase - Dispersed Solvers Comparison

Dispersed Solvers In this group, we have included solvers implementing the **Eulerian** or **Lagrangian** approach to handle multiple fluids and particle clouds considering **Dispersed Phases** or **Fluid-Particle interactions**.

**Dispersed - Euler**

- multiphaseEulerFoam multiple miscible fluids, Euler-Euler approach

**Dispersed - Lagrangian**

- DPMDyMFoam extension of DPMFoam with DyM
- MPPICDyMFoam extension of MPPICFoam with DyM

**Dispersed - Drift-Flux**

- driftFluxFoam 1 fluid and slurry or plastic dispersed phase, drift flux approximation for relative phase motion

- DPM - Discrete Phase Model
- MP-PIC - multiphase particle-in-cell method
- DyM - Dynamic Mesh

## Solver: DPMFoam Results Fields

This solver provides the following results fields:

**Primary Results Fields**- quantities produced by the solver as default outputs**Derivative Results**- quantities that can be computed based on primary results and supplementary models. They are not initially produced by the solver as default outputs.

**Primary Results Fields**

Velocity | \(U\) [\(\frac{m}{s}\)] |

Kinematic Pressure \(p/\rho\) | \(p\) [\(\frac{m^{2}}{s^{2}}\)] |

**Kinematic Pressure** It is a pressure normalized by density. To obtain pressure in Pascals [Pa], multiply kinematic pressure by the fluid’s reference density. Read More: Kinematic Fluid Properties

**Derivative Results**

Pressure | \(P\) [\(Pa\)] |

Density | \(\rho\) [\(\frac{kg}{m^{3}}\)] |

Vorticity | \(\omega\) [\(\frac{1}{s}\)] |

Courant Number | \(Co\) [\(-\)] |

Peclet Number | \(Pe\) [\(-\)] |

Stream Function | \(\psi\) [\(\frac{m^2}{s}\)] |

Q Criterion | \(Q\) [\(-\)] |

Wall Functions (for RANS/LES turbulence) | \(y^+\) [\(-\)] |

Wall Shear Stress | \(WSS\) [\(Pa\)] |

Turbulent Fields (for RANS/LES turbulence) | \(k\) \(\epsilon\) \(\omega\) \(R\) \(L\) \(I\) \(\nu_t\) \(\alpha_t\) |

Volumetric Stream | \(\phi\) [\(\frac{m^{3}}{s}\)] |

Passive Scalar | \(scalar_i\) [\(-\)] |

Forces and Torque acting on the Boundary | \(F\) [\(N\)] \(M\) [\(-\)] |

Force Coefficients | \(C_l\) [\(-\)] \(C_d\) [\(-\)] \(C_m\) [\(-\)] |

Average, Minimum or Maximum in Volume from any Result Field | \(Avg\) \(Min\) \(Max\) |