## Solver: buoyantBoussinesqPimpleFoam Description

buoyantBoussinesqPimpleFoam is a pressure-based solver designed for transient simulations of incompressible flows. It handles laminar and turbulent, single-phase flows. The unique feature of the solver is its use of the Boussinesq approximation, which simplifies the computations related to buoyancy by linearly relating the density changes in the fluid to temperature changes, based on a reference temperature. The solver is particularly accurate and efficient when the changes in density compared to a reference density are small.

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 Frames (MRF) and porosity modeling and allows easy integration of passive scalar transport equations and source terms.

The solver can be applied in time-dependent problems, where incompressible flow is affected by temperature changes within a small range of variations. The example can be found in the HVAC (Heating, Ventilation, and Air Conditioning) field, for room ventilation or chimney effects in buildings. Another application is related to the study of the thermal load in electronic systems.

## Solver: buoyantBoussinesqPimpleFoam Features

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

- Buoyancy using Boussinesq Approximation
- Heat Transfer
- Heat Source (temperature source therm)
- Radiation

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

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

## Solver: buoyantBoussinesqPimpleFoam Application

**HVAC**

- Natural Convection
- Room Ventilation
- Chimney Effect in Buildings

**Electronics**

- Electronic Cooling

**Meteorology**

- Lake and Ocean Thermal Stratification

## Solver: buoyantBoussinesqPimpleFoam Heat Transfer Solvers

Heat Transfer Solvers In this group, we have included solvers that are designed to model: **Heat Transfer**, **Radiation**, **Natural** and **Forced Convection**, **Conjugate Heat Transfer (CHT)**.

**Heat Transfer, Single Fluid**

- buoyantSimpleFoam steady-state, compressible, buoyancy-driven flow
- buoyantPimpleFoam transient, compressible, buoyancy-driven flow

**Heat Transfer, Single Fluid - Boussinesq**

- buoyantBoussinesqSimpleFoam steady-state, incompressible, buoyancy using Boussinesq approximation
- buoyantBoussinesqPimpleFoam transient, incompressible, buoyancy using Boussinesq approximation

**Heat Transfer, Single Solid**

- laplacianFoam steady-state and transient, thermal conduction in solid
- overLaplacianDyMFoam extension of laplacianFoam with Overset

**CHT, Multiple Fluids / Solids**

- chtMultiRegionSimpleFoam steady-state, compressible, arbitrary fluid and solid regions
- chtMultiRegionFoam transient, compressible, arbitrary fluid and solid regions

- CHT - Conjugate Heat Transfer
- MRF - Multiple Reference Frame
- Overset - also known as Chimera Grid (Method)

## Solver: buoyantBoussinesqPimpleFoam 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 base version of
`buoyantBoussinesqPimpleFoam`

without buoyancy and heat transfer

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

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

Kinematic Pressure \(p/\rho\) | \(p\) [\(\frac{m^{2}}{s^{2}}\)] |

Kinematic Hydrostatic Perturbation Pressure | \(p - \rho gh\) [\(\frac{m^{2}}{s^{2}}\)] |

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

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