radiationModel: P1CFDEM

The P1CFDEM model introduces a radiation field G into the solver that is solved alonside the fluid flow fields.

Syntax

Configured in radiationProperties dictionary:

radiationModel   P1CFDEM; // select the P1CDFEM radiation model

radiation        <bool>;
solverFreq       <integer>;

  • radiation = switch radiation modeling on/off

  • solverFreq = number of CFD timesteps per radiation solution

Additionally the radiation model requires that models for the absorption-emission, the scattering and the soot be defined:

absorptionEmissionModel <word>;

scatterModel            <word>;

sootModel               <word>;

Note

The abovementioned absorption-emission and scattering models add an additional <modelName>Coeffs sub-dicitonary for configuration.

Additional Settings

In addition to configuring the P1CFDEM model in constant/radiationProperties it is necessary to add an appropriate settings for solving for the radiation field G.

This requires setting the boundary conditions for G. The boundary conditions for G are found in the starting time directory for the CFDEM case. For example in 0/G under boundaryField we set Marshak-radiation boundary conditions for the walls:

wall
{
    type            MarshakRadiation;
    T               T;
    emissivityMode  lookup;
    emissivity      uniform <value>;
    value           uniform 0; // (initial condition for compatibility, overwritten by the BC)
}

This boundary condition calucates the (radiative) heat flux at the wall:

\dot{q}_\mathrm{wall} = \frac{\epsilon}{2} (2 - \epsilon) (4 \sigma T^4 - G)

with \epsilon being the emissivity field at the boundary defined in the boundary condition:

Note

For more details regarding all the available boundary conditions please consult you OpenFOAM distributions documentation.

The the solver for G is configuring in system/fvSolution and system/fvSchemes.

For example in system/fvSolution under solvers:

solvers
{
    "(G|GFinal)"
    {
        solver          PCG;
        preconditioner  DIC;
        tolerance       1e-06;
        relTol          0.1;
    }
}

For example in system/fvSchemes under laplacianSchemes:

laplacianSchemes
{
    laplacian(gammaRad,G) Gauss harmonic corrected;
}

Note

For more details regarding all the available finite-volume solvers and schemes please consult you OpenFOAM distributions documentation.

Examples

radiationModel   P1CFDEM;

radiation        true;
solverFreq       10;   // every 10 CFD timesteps

absorptionEmissionModel absorptionEmissionCFDEM;

scatterModel            constantScatterCFDEM;

sootModel               none;

Note

For details regarding the configuration of the absorption-emission model and the scatter model please refer to their documentation.

Description

In order to activate the radiation model the file constant/radiationProperties must be present in the CFD case directory. Otherwise radiation will not be taken into account. Boundary conditions and initial field values for the radiation intensity G must be defined in 0/G.

The P1 model solves a diffusion equation for incident radiation. The model is limited to applications with optical thickness \tau = a L < 3. The equation being solved is:

\div {\gamma \grad G} = a G - 4(e \sigma_\mathrm{SB} T^4 + E)

with the diffusion coefficient \gamma:

\gamma = \frac{1}{3 a + \sigma_\mathrm{eff}}

The absorptivity a, e and emission contribution E come from the absorption model. The effective scattering coefficient \sigma_\mathrm{eff} comes from the scattering model. The Stefan-Boltzmann constant \sigma_\mathrm{SB} = \SI{5.67e-8}{kg / s^3 / K^4}

The energy source term is calculated as Sh() = (Ru() - Rp() * T^4) with Ru() = a * G - 4E) and Rp() = 4*e*sigmaSB leading to Sh() = a * G - 4*(e*sigmaSB * T^4 + E)

The temperature source term is calculated as: ST() = Sh()/(rho * Cp)

For further discussion of the model, consult [1].

Literature

[1] J. Mačak, C. Goniva, St. Radl (2023). “Predictions of the P1 approximation for radiative heat transfer in heterogeneous granular media” Particuology 82: 25-47

Restrictions