CFD Online Discussion Forums - solarLoad - results not coherent with analytical

The case I use to test solarLoad is an aluminium cube with size 1 m within a cubic dummy fluid region with size 1.5 m (used to introduce solarLoad) representing deep space (i.e. T = 0K and vacuum).

The solarLoad is set to be fixed in direction (x axis) and fixed with a value of 1400 W/m2 with no reflected rays and only one band in the spectrum (i.e. nBands 1) If the value of absorptivity and emissivity are equal the analytical solution is 253 K. The results given by the simulation are between 242 K and 245 K, quite far from the analytical solution. Furthermore, if the values of absorptivity and emissivity are changed but kept equal the solution changes. This should not be happening, if the ratio absorptivity/emissivity is one the solution should be still 253 K.

The analytical solution is verified by using a workaround that does not use solarLoad: the dummy fluid region is split so that there is a region in front of the cube thus it is possible to simply set qro to 1400 in 0//qr file. In this case, changing the values of absorptivity and emissivity but keeping the ratio equal to 1 the solution does not change, that is coherent with analytical results.

The values of the view factors for the geometry in exam are checked and coherent with analytical.
The workaround of course cannot be applied to curved surfaces as the input flux has to be scaled according to the angle between the sun direction and the cell face normal. That is the reason why I want to use solarLoad

Analytical solution: T = (q_sun/sigma * abosrptivity/emisivity * A_in_sun/A_tot) ^ (1/4) for a cube with equal values of absorptivity and emissivity the solution is T = (q_sun/sigma * 1/6) ^ (1/4)

Can anyone explain this behaviour? I leave attached the files "boundaryRadiationProperties" and "radiationProperties" for the dummy fluid region called "space"

"boundaryRadiationProperties"

Code:

/*--------------------------------*- C++ -*----------------------------------*\

| =========                 |                                                 |

| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |

|  \\    /   O peration     | Version:  v2106                                 |

|   \\  /    A nd           | Website:  www.openfoam.com                      |

|    \\/     M anipulation  |                                                 |

\*---------------------------------------------------------------------------*/

FoamFile

{

    version     2.0;

    format      ascii;

    class       dictionary;

    object      boundaryRadiationProperties;

}

// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //



".*"

{

    type            transparent;

    wallAbsorptionEmissionModel

    {

        type            multiBandAbsorption;

        emissivity      (1);

        absorptivity    (0);

    };

}



space_to_cube

{

    type    opaqueDiffusive;

    wallAbsorptionEmissionModel

    {

        type            multiBandAbsorption;

        emissivity      (0.86);

        absorptivity    (0.86);

    };

}



// ************************************************************************* //

"radiationProperties"

Code:

/*--------------------------------*- C++ -*----------------------------------*\

| =========                 |                                                 |

| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |

|  \\    /   O peration     | Version:  v2106                                 |

|   \\  /    A nd           | Website:  www.openfoam.com                      |

|    \\/     M anipulation  |                                                 |

\*---------------------------------------------------------------------------*/

FoamFile

{

    version     2.0;

    format      ascii;

    class       dictionary;

    object      radiationProperties;

}

// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //



radiation       on;



radiationModel  viewFactor;



solarLoadCoeffs

{

    sunDirectionModel       constant;

    sunDirection            (1 0 0);



    sunLoadModel            constant;

    directSolarRad          1400;

    diffuseSolarRad         0;



    // see solarCalculator.H for other model examples and details



    // Energy spectrum

    spectralDistribution    (1);



    // Radiative flux coupling flags

    solidCoupled    true; // Couple through Qr the solid regions (default true)

    wallCoupled     true;  // Couple through Qr wall patches (default false)



    // Reflecting rays

    useReflectedRays false;



    absorptionEmissionModel none;

    scatterModel            none;

    sootModel               none;

}





viewFactorCoeffs

{

    smoothing true; //Smooth view factor matrix (use when in a close surface

                    //to force Sum(Fij = 1)

    constantEmissivity true; //constant emissivity on surfaces.



    nBands    1;



    useSolarLoad       true;

}



// Number of flow iterations per radiation iteration

solverFreq 1;



absorptionEmissionModel none;



scatterModel    none;



sootModel       none;





// ************************************************************************* //