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    SimScale DocumentationValidation CasesValidation Case: Thermal Bridge Case 2 – Insulated Wall

    Validation Case: Thermal Bridge Case 2 – Insulated Wall

    This thermal bridge validation case belongs to heat transfer. In this project, a simplified wall geometry is validated against analytical data for temperature and heat flux, provided by the EN ISO 10211 Standard, case 2.

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    Geometry

    The geometry for this project is an insulated wall, as seen in Figure 1:

    thermal bridge geometry iso 10211 case 2 validation
    Figure 1: Side view of the thermal bridge geometry from EN ISO 10211 case 2

    This problem involves a 2D simulation of the insulated door from Figure 1. Since SimScale requires a 3D model to run, the model was extruded by 0.002 meters in the y-direction. An isometric view from the model is shown in Figure 2:

    isometric view iso 10211 case 2 validation
    Figure 2: Isometric view, showing the 2 \(mm\) depth in the y-direction

    Taking Figure 1 as a reference, the x- and z-coordinates of the points are given below:

    CoordinatesABCDEFGHIJKLM
    x \([mm]\)050001550001505001.5151.5500
    z \([mm]\)47.547.541.541.541.536.536.50035351.51.5
    Table 1: Coordinate of the points in the thermal bridge geometry

    Analysis Type and Mesh

    Tool Type: Code_Aster

    Analysis Type: Steady-state heat transfer

    Mesh and Element Types: The mesh used in this simulation was created in SimScale, using the standard mesher. The table below contains an overview of the resulting mesh.

    CaseMesh TypeNodesElement Type
    EN ISO 10211 Case 2Second-order standard2011690Standard
    Table 2: Mesh details for this validation case

    In the image below, it’s possible to see the standard mesh in detail:

    standard meshing tool second-order mesh
    Figure 3: Second-order tetrahedral mesh, created with the Standard meshing tool

    Simulation Setup

    Material: For this validation case, the model consists of 4 materials:

    materials thermal bridge door
    Figure 4: Materials identification for this validation case
    Material IdentificationThermal Conductivity \([\frac{W}{m.K}]\)Density \([\frac{kg}{m^3}]\)Specific Heat \([\frac{J}{kg.K}]\)
    1 – Concrete1.15, isotropic2240750
    2 – Wood0.12, isotropic5001260
    3 – Insulation (Cork)0.029, isotropic200350
    4 – Aluminum230, isotropic2700897
    Table 3: Overview of the material properties

    Boundary Conditions:

    Still using Figure 1 as a reference, the following boundary conditions are defined:

    • Convective heat flux boundary condition on the top face AB:
      • 0 \(ºC\) Reference temperature
      • Heat transfer coefficient of 16.667 \(\frac{W}{m^2.K}\), which is equivalent to a thermal resistance of 0.06 \(\frac{m^2.K}{W}\)
    • Convective heat flux boundary condition on the bottom face HI
      • 20 \(ºC\) Reference temperature
      • Heat transfer coefficient of 9.0909 \(\frac{W}{m^2.K}\), which is equivalent to a thermal resistance of 0.11 \(\frac{m^2.K}{W}\)

    Result Comparison

    The results obtained with SimScale were compared to those presented in the EN ISO 10211 Standard. According to the aforementioned standard, to satisfy the precision requirements, the temperature differences between the simulation results and the reference values must not exceed 0.1 \(ºC\). Furthermore, the heat flow rate should be within 0.1 \(\frac {W}{m}\) of the analytical solution.

    The EN ISO 10211 Standard provides the temperature results on points A, B, C, D, E, F, G, H, I, and also the total flow rate through the wall. The table below provides an overview of the temperature results:

    PointAnalytical \([º C]\)SimScale \([º C]\)Difference \([º C]\)Meets Criteria? (<0.1 \(ºC\))
    A7.17.06-0.04Yes
    B0.80.76-0.04Yes
    C7.97.900.00Yes
    D6.36.27-0.03Yes
    E0.80.83+0.03Yes
    F16.416.41+0.01Yes
    G16.316.34+0.04Yes
    H16.816.77-0.03Yes
    I18.318.33+0.03Yes
    Table 4: Overview of the temperature results, based on the points from Figure 1

    The temperatures found with SimScale for all nine points are well within the acceptance criteria defined by the standard. Furthermore, the ISO standard also provides the analytical solution for the integral heat flux in the z-direction through the wall.

    For the Heat Flow rate results, the Heat Flow result control item was used. The average value between the interior and exterior faces is used to account for any numerical deviations. Also, the computed Heat Flow \([W]\) is normalized to the thickness of the model so it is in line with the standard’s results \([W/m]\). The table below shows the results:

    Analytical \([\frac {W}{m}]\)SimScale Average Heat Flow \([W]\)SimScale Heat Flow per Unit Thickness \([\frac {W}{m}]\)Difference \([\frac {W}{m}]\)Meets Criteria? (<0.1 \([\frac {W}{m}]\))
    9.50.01897649.48820.0118Yes
    Table 5: Result comparison for the heat flux through the wall, showing great agreement between the simulation and analytical data

    Again, the result obtained with SimScale satisfies the accuracy requirements from the reference standard. Find below the temperature profile observed in the SimScale results:

    simscale iso 10211 case 2 results
    Figure 5: Side view, showing the temperature profile along with the wall thickness.

    Since all results obtained with SimScale satisfy the EN ISO 10211 precision requirements, we conclude that SimScale fulfills the accuracy standards for EN ISO 10211 Validation Case 2.

    References

    Last updated: August 3rd, 2022

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