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    Validation Case: Solar Load on an Airbox

    This solar load validation case belongs to fluid dynamics and heat transfer including solar radiation. This test case aims to validate the solar load model on a small airbox. The results obtained from the simulation were compared to the analytical solution. The parameter that was compared is:

    • Surface temperature of the plate

    The geometry of the airbox has the following dimensions:

    • Height: 0.005 m
    • Width: 0.15 m
    • Length: 0.15 m

    The top surface has a fixed temperature and the side walls are set adiabatically. The bottom surface is the wall for which the temperature is to be calculated and compared. The solar load is applied in the normal direction of the wall.

    Solar Radiation Validation Geometry
    Figure1: Airbox geometry with schematic boundary conditions

    Tool type: OpenFOAM

    Analysis type: Incompressible Conjugate Heat Transfer with radiation

    Turbulence model: kω SST turbulence model

    Time dependency: Steady-state

    Mesh and element types: The mesh was created using SimScale’s standard mesher. The box has 13,000 cells and a boundary layer mesh on the wall surface.

    Solar Radiation Validation Mesh
    Figure 2: Mesh of the Airbox with boundary layer mesh at the wall

    Material:

    • Air
      • Kinematic viscosity ν = 1.529e-5 m2s

    Boundary conditions:

    Top and side surfaces:

    • Top surface: Constant Temperature 300 K
    • Side walls: Adiabatic

    Wall without thermal wall modeling:

    • Wall Model: External Wall Heat Flux Heat transfer coefficient: 10 WKm2
      • Ambient Temperature: 330 K
      • Wall thermal: No Wall Thermal
      • Outer surface emissivity: 0.9
      • Solar radiative behavior: Opaque
      • Emissivity: 0.9

    Wall with thermal wall modeling:

    • Wall Model: External Wall Heat Flux
      • Heat transfer coefficient: 10 WKm2
      • Ambient Temperature: 330 K
      • Wall thermal: Layer Wall thermal
      • Thermal conductivity: 0.3 WmK
      • Layer thickness: 1 m
      • Outer surface emissivity: 0.9
      • Solar radiative behavior: Opaque
      • Emissivity: 0.9

    Side Walls: Adiabatic

    For the validation of the solar load, the analytical solution for the wall temperature was calculated using the following equations1:

    Equations for heat flux from ambient to wall and heat flux from wall to top:

    (1)qAmbientToWall=(TWallTA)h qSolarDiffϵ

    (2)qWallToTop=(TTTWall)κfhf+qSolarDirϵ

    Continuity of heat flux:

    (3)qAmbientToWall=qWallToTop

    Put equation 1 and 2 into equation 3 and solve for TWall

    (4)TWall=1h+κfhf(TTκfhf+TAh+(qSolarDiff+qSolarDir)ϵ)

    Where,

    • TWall : Wall Temperature K
    • TA: Ambient Temperature K
    • TT: Top Temperature K
    • h: Heat transfer coefficient wall WKm2
    • qSolarDiff: Diffuse solar load Wm2
    • qSolarDir: Direct solar load Wm2
    • ϵ: Emissivity
    • κf: Thermal conductivity of the fluid WKm
    • hf: Height of fluid m

    For the validation of the solar load, the analytical solution for the wall temperature was calculated using the following equations:

    (5)qAmbientToWall=(TThTA)hqSolarDiffϵ

    (6)qWallToTop=(TTTWall)κfhf+qSolarDirϵ

    Calculation of the thermal wall temperature:

    (7)TTh=TWall(1λ)+λTA+qSolarDiffϵh+κtwhtw

    Calculation of λ from the setup of the thermal wall:

    (8)λ=hh+κtwhtw

    Continuity of heat flux:

    (9)qAmbientToWall=qWallToTop

    Equation 5, 6, 7, 8 into Equation 9 and solving for TWall

    (10)TWall=1(1λ)h+κfhf(h((λ1)TA+qSolarDiffϵh+κtwhtw)+TTκfhf+ϵ(qSolarDiff+qSolarDir))

    Where,

    • TTh : Temperature of thermal wall K
    • κtw: Thermal conductivity of the thermal wall WKm
    • htw: Height of thermal wall m

    Comparison of the analytical results to the results obtained from SimScale simulation for the surface temperature:

    CaseAnalytical Result [K]Simulation Result [K]Deviation
    [%]
    No thermal Wall Modeling343.3 343.55 0.072
    Thermal Wall Modeling351.67 351.660.002
    Table 1: Deviation of SimScale Solar Load simulation results from analytical results.

    Convergence of the wall temperature without thermal wall modeling:

    Solar Radiation Validation Convergency no thermal Wall Modeling
    Figure 3: Convergence of the surface temperature without thermal wall modeling

    Convergence of the wall temperature with thermal wall modeling:

    Solar Radiation Validation Convergency thermal Wall Modeling
    Figure 4: Convergence of the wall temperature with thermal wall modeling

    Next, we take a look at the temperature distribution on the walls of the airbox:

    Temperature without thermal Wall Modeling
    Figure 5: Temperature gradient from the wall face to the top surface
    Temperature thermal Wall Modeling
    Figure 6: Higher temperature gradient from the wall surface to the top surface than without thermal wall modeling.

    Overall the results obtained from the SimScale platform are in good agreement with the analytical solutions, and hence this serves as a good solar load validation for this feature.

    Last updated: June 9th, 2022