## Solver: multiphaseEulerFoam Description

multiphaseEulerFoam is a solver designed for transient simulations of multiple incompressible fluid phases, whether dispersed or resolved. This solver supports the Eulerian-Eulerian approach, treating each phase as a continuous fluid with separate volume fractions for each phase. It is particularly useful for modeling and analyzing complex fluid interactions in scenarios such as gas-liquid flows or liquid-liquid flows. It supports any number of fluid phases, each having its distinct properties but sharing a common pressure field. It handles laminar and turbulent, accommodating Newtonian fluids.

The solver uses the **PIMPLE** (merged **PISO-SIMPLE**) algorithm for pressure-momentum coupling. This algorithm leverages the strengths of both PISO and SIMPLE methods for pressure-velocity coupling, ensuring robustness in handling transient flows with large time steps. This approach is supplemented by under-relaxation techniques to secure convergence stability. It supports Multiple Reference Frames (MRF) and allows easy integration of passive scalar transport equations.

The solver’s capability to analyze multiphase flow makes it suitable for modeling various applications such as bubble columns, fluidized bed combustion, cyclone separators, and mixing processes involving high concentration droplets, bubbles or particles like dust. These applications span across industries including chemistry, energy, and the oil and gas sector.

## Solver: multiphaseEulerFoam Features

**Transient****Incompressible****Multiphase - Dispersed Phase (Eulerian)**

- Dispersed Phase
- Multiple Miscible Fluids
- Euler-Euler Approach

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

- Passive Scalar
- Buoyancy
- PIMPLE Algorithm
- Solution Limiters:
- Velocity Damping

## Solver: multiphaseEulerFoam Application

**Energy**

- Fluidized Bed Combustion
- Pneumatic Conveying Systems for Coal and Limestone
- Feeding Systems

**Piping**

- Bubble Columns
- Mixing in Pipelines

**Agriculture/cement industry**

- Cyclone Separator

**Manufacturing**

- Hoppers with high concentrated droplets, bubbles or particles

## Solver: multiphaseEulerFoam 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: multiphaseEulerFoam Alternative Solvers

In this section, we propose alternative solvers from different categories, distinct from the current solver. While they may fulfill similar purposes, they diverge significantly in approach and certain features.

- multiphaseInterFoam multiple immiscible fluids, VoF approach
- reactingFoam compressible, multicomponent mixture, species transport

## Solver: multiphaseEulerFoam 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 | \(U\) [\(\frac{m}{s}\)] |

Phase Volume Fraction | \(\alpha\) [\(-\)] |

Hydrostatic Perturbation Pressure | \(p - \rho gh\) [\(Pa\)] |

**Hydrostatic Perturbation Pressure** This value represents the pressure without the hydrostatic component (minus gravitational potential). Read More: Hydrostatic Pressure Effects

**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 | \(Avg\) \(Min\) \(Max\) |