## Solver: rhoSimpleFoam Description

rhoSimpleFoam is a pressure-based solver designed for steady-state 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 **SIMPLE** (Semi-Implicit Method for Pressure-Linked Equations) algorithm for pressure-momentum coupling, augmented by under-relaxation techniques to enhance convergence. It supports Multiple Reference Frame (MRF), porosity modeling and allows easy integration of passive scalar transport equations and source terms.

It finds extensive use in fields where the effects of compressibility are non-negligible. This includes high-speed aerodynamics in the automotive and aerospace industries for applications like engine inlets and exhaust systems, supersonic flow over airframes, and HVAC systems dealing with high-temperature gradients.

## Solver: rhoSimpleFoam Features

**Steady-State****Compressible****Single-Phase**

- High-Speed Aerodynamics
- Subsonic Flow
- Transonic Flow
- Pressure-Based Solver

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

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

## Solver: rhoSimpleFoam Application

**Aerospace**

- Aircraft Aerodynamics
- Wing Optimization and Motion
- Jet Engines
- High-Speed Aerodynamics
- Supersonic Flow

**Automotive**

- Airflow Ducts
- Intercooler Flows

**Spacecrafts**

- Rocket Engine
- Propulsion Systems

**Energy**

- Steam Turbines

**Manufacturing**

- Supersonic Cold Spray - Additive Manufacturing Process

**Rotating Machinery**

- Centrifugal Pumps

## Solver: rhoSimpleFoam 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: rhoSimpleFoam 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.

- simpleFoam incompressible version of
`rhoSimpleFoam`

, constant density - buoyantSimpleFoam variant of
`rhoSimpleFoam`

solver for buoyancy-driven flow

## Solver: rhoSimpleFoam 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 | \(Ma\) [\(-\)] |

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