## Solver: rhoCentralFoam Description

rhoCentralFoam is a density-based solver designed for transient simulations of compressible flow. It handles laminar and turbulent flow, and it is suitable for high-speed aerodynamic applications, considering transonic and supersonic flow.

The core of the solver is the central-upwind schemes for convective fluxes. This method is well-regarded for its balance between accuracy and robustness in capturing shock waves and other steep gradient phenomena inherent in compressible flows. This approach ensures reliable and precise simulations, particularly in scenarios involving complex shock interactions and rapid changes in flow properties. It supports Heat Transfer and allows easy integration of passive scalar transport equations.

The solver is used in industries where the dynamics of compressible flows are critical. This includes the aerospace sector for the analysis and design of high-speed aircraft, the automotive industry for studying the effects of airflow over high-speed vehicles, and the energy sector for the design and optimization of turbines and compressors. In the military industry, it can be used for high-speed bullets and missile analysis.

## Solver: rhoCentralFoam Features

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

- High-Speed Aerodynamics
- Transonic Flow
- Supersonic Flows
- Density-Based Solver
- Shock Waves Capturing

- Laminar and Turbulent (RANS, LES, DES)
- Equation of State Models
- Passive Scalar
- Heat Transfer
- Central Differencing Scheme
- Solution Limiters:
- Velocity Damping
- Temperature Limit

## Solver: rhoCentralFoam Application

**Aerospace**

- High-speed Aircraft Aerodynamics
- High-speed Airplanes Wing Profiles
- Rockets Entry to the Atmosphere

**Military**

- Bullets and Missiles
- Converging-diverging Nozzles in Engines

## Solver: rhoCentralFoam 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: rhoCentralFoam Tutorial

- A 2D analysis of supersonic flow through the tunnel with inclined wedge using a density-based solver (Rho Central) visualizes the resulting shock wave.

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