## Solver: DPMDyMFoam Description

DPMDyMFoam is a transient solver designed for dense particle flows, focusing on the influence of particle volume fraction on the continuous phase. It incorporates a comprehensive four-way coupling mechanism, covering fluid-particle interactions, particle-fluid effects, and particle-particle collisions. The solver is versatile, capable of managing both laminar and turbulent flow regimes, and supports both Newtonian and non-Newtonian fluid types. It is an extension of the DPMFoam solver additionally supporting the functionality of dynamic mesh motion.

Within the Eulerian-Lagrangian solver framework, this solver differentiates between the continuous fluid phase and the discrete solid phase. Fluid dynamics are delineated through the time-averaged Navier-Stokes equations, with the PIMPLE algorithm facilitating their resolution. The computation of isothermal particle movement hinges on solving ordinary differential equations, incorporating forces like drag, gravity, buoyancy, and pressure that influence particle behavior.

The solver utilizes the soft sphere model, also referred to as the Cundall and Strack model, for simulating particle-particle interactions. This model conceptualizes collisions using a spring (for elastic deformation) and a dash-pot (for viscous dissipation). Forces during contact are divided into normal (based on Hertzian contact theory) and tangential components, a concept that is similarly applied to interactions between particles and walls.

Applications of the solver are very similar as to DPMFoam. However, with the additional capabilities of dynamic mesh, the movable components can be considered. For example, rotating transporting systems in the mining and agriculture industries or crushing components of the transport system.

## Solver: DPMDyMFoam Features

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

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

- Dynamic Mesh Motion

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

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

## Solver: DPMDyMFoam Application

**Chemical Industry**

- Reacting Columns with Oscillatory Motion

**Mining Industry**

- Transporting Systems with Motion
- Crushing Systems with Moving Components
- Milling Systems with Moving Components

## Solver: DPMDyMFoam Multiphase - Dispersed Solvers

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: DPMDyMFoam 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 | \(Avg\) \(Min\) \(Max\) |