ChtMultiRegionFoam
ChtMultiRegionFoam
Solver for steady or transient fluid flow and solid heat conduction, with conjugate heat transfer between regions, buoyancy effects, turbulence, reactions and radiation modelling.
Contents
1 Equations
For each region defined as fluid, the according equation for the fluid is solved and the same is done for each solid region. The regions are coupled by a thermal boundary condition.
1.1 Equations Fluid
For each fluid region the compressible Navier Stokes equation are solved.
1.1.1 Mass conservation
The variable-density continuity equation is
| (1) |
The source code can be found in src/finiteVolume/cfdTools/compressible/rhoEqn.H:
{ fvScalarMatrix rhoEqn ( fvm::ddt(rho) + fvc::div(phi) == fvOptions(rho) ); fvOptions.constrain(rhoEqn); rhoEqn.solve(); fvOptions.correct(rho); }
1.1.2 Momentum conservation
| (2) |
represent the velocity, the gravitational acceleration, the pressure minus the hydrostatic pressure and and are the viscose and turbulent stresses.
The source code can be found in Ueqn.H:
// Solve the Momentum equation MRF.correctBoundaryVelocity(U); tmp<fvVectorMatrix> tUEqn ( fvm::ddt(rho, U) + fvm::div(phi, U) + MRF.DDt(rho, U) + turbulence.divDevRhoReff(U) == fvOptions(rho, U) ); fvVectorMatrix& UEqn = tUEqn.ref(); UEqn.relax(); fvOptions.constrain(UEqn); if (pimple.momentumPredictor()) { solve ( UEqn == fvc::reconstruct ( ( - ghf*fvc::snGrad(rho) - fvc::snGrad(p_rgh) )*mesh.magSf() ) ); fvOptions.correct(U); K = 0.5*magSqr(U); } fvOptions.correct(U);
1.1.3 Energy conservation
The energy equation can be found in: https://cfd.direct/openfoam/energy-equation/
The total energy of a fluid element can be seen as the sum of kinetic energy and internal energy . The rate of change of the kinetic energy within a fluid element is the work done on this fluid element by the viscous forces, the pressure and eternal volume forces like the gravity:
| (3) |
The rate of change of the internal energy of a fluid element is the heat transferred to this fluid element by diffusion and turbulence plus the heat source term plus the heat source by radiation :
| (4) |
The change rate of the total energy is the sum of the above two equations:
| (5) |
Instead of the internal energy there is also the option to solve the equation for the enthalpy :
| (5) |
The source code can be found in EEqn.H:
{ volScalarField& he = thermo.he(); fvScalarMatrix EEqn ( fvm::ddt(rho, he) + fvm::div(phi, he) + fvc::ddt(rho, K) + fvc::div(phi, K) + ( he.name() == "e" ? fvc::div ( fvc::absolute(phi/fvc::interpolate(rho), U), p, "div(phiv,p)" ) : -dpdt ) - fvm::laplacian(turbulence.alphaEff(), he) == rho*(U&g) + rad.Sh(thermo, he) + Qdot + fvOptions(rho, he) ); EEqn.relax(); fvOptions.constrain(EEqn); EEqn.solve(); fvOptions.correct(he); thermo.correct(); rad.correct(); Info<< "Min/max T:" << min(thermo.T()).value() << ' ' << max(thermo.T()).value() << endl; }