## Solver: pimpleFoam Description

pimpleFoam is a pressure-based solver designed for transient simulations of incompressible flow. It handles laminar and turbulent, single-phase flows under isothermal conditions, accommodating both Newtonian and non-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 both Multiple Reference Frames (MRF) and porosity modeling and allows easy integration of passive scalar transport equations and source terms. The solver handles dynamic meshes.

The versatility of the solver is very wide and ranges from the automotive industry (vehicle aerodynamics) to the aerospace industry (wing optimization, aircraft aerodynamics). Internal flows can also be calculated which finds applications in the piping industry, chemical and food industry (mixers and stirring tanks). Dynamic mesh capabilities further increase the potential use of the solver, including the rotating machinery (compressors, turbines, fans) but also wind turbines, piston movements, and many others.

## Solver: pimpleFoam Features

**Transient****Incompressible****Single-Phase**

- Low-Speed Flows
- PIMPLE Algorithm
- Subsonic Flow (Ma < 0.3)
- Dynamic Mesh Motion

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

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

## Solver: pimpleFoam Application

**Automotive**

- Car Aerodynamics with Transient Effects (LES considered)
- Tire Aquaplaning

**Aerospace**

- Aircraft Aerodynamics
- Wing Optimization and Motion

**Biomedical**

- Heart Valves

**Rotating Machinery**

- Pumps
- Propellers
- Compressors
- Turbines, Fans

**HVAC**

- Fans and Pumps

**Pipping**

- Flows through the Pipe and Junctions
- Oscillating Inlets
- Valve Motion

**Pile Structures**

- Vortex Shedding on Bridges

## Solver: pimpleFoam Incompressible Solvers Comparison

Incompressible Solvers In this group, we have included single-phase, pressure-based solvers for **low-speed flows** with negligible variations in density, applicable for **external** and **internal aerodynamics** (**Ma < 0.3**) and **hydrodynamics**. These solvers use incompressibility features for stability and robustness.

**Incompressible, Stedy-State - Main Solvers**

- simpleFoam steady-state, SIMPLE algorithm
- overSimpleFoam extension of simpleFoam with Overset
- SRFSimpleFoam variant of simpleFoam resolved in SRF

**Incompressible, Transient - Main Solvers**

- pimpleFoam transient, PIMPLE algorithm, DyM
- overPimpleDyMFoam extension of pimpleFoam with Overset, DyM
- SRFPimpleFoam variant of pimpleFoam resolved in SRF

**Incompressible, Transient - Simplified Solvers***

- * Dedicated solvers for simplified scenarios, improve stability and computational efficiency
- ** The PISO algorithm is used for cases with a small Courant number Co < 1

- DyM - Dynamic Mesh
- MRF - Multiple Reference Frame
- SRF - Single Reference Frame
- Overset - also known as Chimera Grid (Method)
- SIMPLE - Semi-Implicit Method for Pressure-Linked Equations
- PIMPLE - merged PISO and SIMPLE
- PISO - Pressure-Implicit Split-Operator

## Solver: pimpleFoam 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.

- rhoPimpleFoam compressible version of
`pimpleFoam`

, small density changes - buoyantBoussinesqPimpleFoam extension of
`pimpleFoam`

with heat transfer and buoyancy using Boussinesq approximation

## Solver: pimpleFoam Tutorial

- Transient simulation of a static mixer, using a passive scalar to track fluid dispersion.

- Transient simulation of blood flow in a vessel, including the modeling of non-Newtonian fluid properties and time-variable boundary conditions.

## Solver: pimpleFoam 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 | \(P\) [\(Pa\)] |

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