## Solver: rhoPimpleFoam Description

rhoPimpleFoam is a pressure-based solver designed for transient simulations of compressible flow. It handles laminar and turbulent, single-phase flows with temperature and density variations (it solves the energy equation).

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 Frame (MRF) and porosity modeling and allows easy integration of passive scalar transport equations and source terms. The solver handles dynamic meshes.

The application of the solver is very wide and allows utilization in time-dependent problems with high-density variation. An example can be jet engines and propulsion studies, and subsonic and supersonic flows with shock waves investigations. The solver can also be used in heat exchangers and cooling systems analysis or HVAC studies. Its dynamic mesh capabilities further increase applications for high-speed moving objects.

## Solver: rhoPimpleFoam Features

**Transient****Compressible****Single-Phase**

- High-Speed Aerodynamics
- Subsonic Flow
- Transonic Flow
- Pressure-Based Solver
- Dynamic Mesh Motion

- Laminar and Turbulent (RANS, LES, DES)
- Equation of State Models
- Rotating Objects:
- Multiple Reference Frames (MRF)
- Rotating Mesh Motion

- Passive Scalar
- Porosity Modeling
- Heat Transfer
- Heat Source
- Source Term (explicit/implicit)
- PIMPLE Algorithm
- Solution Limiters:
- Velocity Damping
- Pressure Limit
- Temperature Limit

## Solver: rhoPimpleFoam Application

**Aerospace Industry**

- Jet Engines & Propulsion
- Supersonic Flows

- Shock Waves and Expansion Waves around Supersonic Aircraft
- Supersonic Nozzles and Diffusers

**Automotive**

- High-Speed Vehicles - Race Cars Components

**Explosions and Blast Waves**

- Studying the propagation of shock waves in the air or any other medium due to explosions.

**Heat Transfer**

- Heat Exchangers
- Cooling Systems

**HVAC**

- Venturi Systems or Ejectors
- Rapid Depressurization
- Choked Flows in Valves or Orifices

**Rotating Machinery**

- Turbines
- Compressors

## Solver: rhoPimpleFoam Compressible Solvers Comparison

Compressible Solvers In this group, we have included single-phase, pressure and density-based solvers that can handle flows with significant variations in density, mostly applicable for and **high-speed aerodynamics** (**Ma > 0.3**)

**Subsonic / Transonic, Steady-State, Ma < 1**

- rhoSimpleFoam steady-state, pressure-based, small density changes
- overRhoSimpleFoam extension of rhoSimpleFoam with Overset

**Subsonic / Transonic, Transient, Ma < 1**

- rhoPimpleFoam transient, pressure-based, small density changes, DyM
- overRhoPimpleDyMFoam extension of rhoPimpleFoam with Overset, DyM

**Transonic / Supersonic, Pressure-Based, Ma > 1**

- sonicFoam transient, pressure-based, shock waves
- sonicDyMFoam extension of sonicFoam with DyM

**Transonic / Supersonic, Density-Based, Ma > 1**

- rhoCentralFoam transient, density-based, shock waves
- rhoCentralDyMFoam extension of rhoCentralFoam with DyM

- Ma - Mach Number
- DyM - Dynamic Mesh
- Overset - also known as Chimera Grid (Method)

## Solver: rhoPimpleFoam 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.

- pimpleFoam incompressible version of
`rhoPimpleFoam`

, constant density - buoyantPimpleFoam variant of
`rhoPimpleFoam`

solver for buoyancy-driven flow

## Solver: rhoPimpleFoam Validation Cases

- Analysis of the rarefaction wave propagation speed, contact discontinuity, and shock discontinuity, this scenario is commonly used as a validation benchmark for compressible solvers.

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

Pressure | \(p\) [\(Pa\)] |

Temperature | \(T\) [\(K\)] |

**Derivative Results**

Density | \(\rho\) [\(\frac{kg}{m^{3}}\)] |

Vorticity | \(\omega\) [\(\frac{1}{s}\)] |

Mach Number | \(Ma\) [\(-\)] |

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 | \(WSS\) [\(Pa\)] |

Wall Heat Flux | \(\phi_q\) [\(W/m^2\)] |

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