## Solver: MPPICFoam Description

mppicFoam is a solver designed for transient simulations of a single kinematic cloud carried by the continuous phase. MPPIC stands for Multiphase Particle in Cell method. It handles laminar and turbulent, accommodating both Newtonian and non-Newtonian fluids.

The solver belongs to the Eulerian-Lagrangian group of solvers, where the fluid phase is continuous, while the solid phase is treated as a discrete phase. The fluid phase is modeled with time-averaged Navier-Stokes equations.

The evolution of the dispersed phase is governed by a Liouville equation for the particle distribution function. The particle distribution function contains particle properties such as particle location, velocity, mass, etc. In this solver, particles are grouped into parcels that allow significant calculation time reduction.

The collisions between particles are not considered explicitly as in other similar approaches, (e.g. DPMFoam). Instead, this solver assumes the particle’s collision force as a spatial gradient. A particle stress model developed on this principle is used to describe collisions. Gas-solid flows of dense and close-pack limits can be accurately modeled with reasonable computational time because collisions are not calculated explicitly. The method can handle systems with particle count over \(1⋅10^(15)\) particles. Moreover, this solver can model full particle size distribution and works well in a wide range of particle volume fractions: from dilute flows (< 0.1%) up to dense flows (> 60%).

The solver can be used in industrial chemistry for modeling coal gasification. It can be applied for modeling cyclone separators when we want to separate particles from the continuous phase.

## Solver: MPPICFoam Features

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

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

- MP-PIC method

- 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: MPPICFoam Application

**Energy**

- Biomass Gasifiers
- Fluidized Bed Combustion

**Industrial Chemistry**

- Coal Gasification

**Agriculture/Cement Industry**

- Cyclone Separator - (e.g. Cyclone Separator Tutorial)

**Pharmaceutical Industry**

- Particle Jets

**Metallurgy**

- Metal Spray Coating

## Solver: MPPICFoam 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: MPPICFoam Tutorial

- Discrete particle modeling in a cyclone separator simulation. Particles enter through the inlet boundary with air, and due to gravity, they separate and escape.

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