## Solver: MPPICDyMFoam Description

mppicDyMFoam is a solver designed for transient simulations involving a single kinematic cloud within a continuous phase. The acronym MPPIC denotes the Multi-Phase Particle in Cell method. This solver is equipped to manage both laminar and turbulent flows and is compatible with Newtonian and non-Newtonian fluids. It is an extension of the mppicFoam solver, additionally supporting the functionality of dynamic mesh motion.

This solver is categorized under the Eulerian-Lagrangian solvers, distinguishing between a continuous fluid phase and a discrete solid phase. The fluid phase’s behavior is described by the time-averaged Navier-Stokes equations. The progression of the dispersed phase is dictated by the Liouville equation, which pertains to the particle distribution function. This function details various particle attributes, such as their location, velocity, and mass. In the solver, particles are amalgamated into parcels, a strategy that significantly reduces computational time.

In contrast to other methods such as those employed by DPMFoam, this solver does not explicitly simulate particle collisions. Rather, it models the force of particle collisions as a spatial gradient. A particle stress model, based on this concept, is utilized to characterize the collisions. This approach enables the accurate simulation of gas-solid flows, even at the dense and close-packed limits, with a reasonable demand on computational resources by avoiding direct calculation of collisions. The technique is capable of managing systems with over \(1⋅10^(15)\) particles. Furthermore, the solver is adept at handling a complete particle size spectrum, efficiently operating across a broad spectrum of particle volume fractions, ranging from dilute flows (less than 0.1%) to dense flows (greater than 60%).

Applications of the solver are very similar to mppicFoam. However, with the additional capabilities of dynamic mesh, the movable components can be considered. For example, the solver can be used to examine the aerodynamic wake after the rotating wind turbine in a sandy environment.

## Solver: MPPICDyMFoam Features

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

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

- MP-PIC method
- 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: MPPICDyMFoam Application

**Energy**

- Wind Turbine - Aerodynamic Wake Behind in Sandy Environment

**Industrial Chemistry**

- Reactors Columns with Oscillatory Motion

## Solver: MPPICDyMFoam 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: MPPICDyMFoam 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 | \(Avg\) \(Min\) \(Max\) |