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    SimScale DocumentationValidation CasesValidation Case: Heat Transfer in a Perforated Plate

    Validation Case: Heat Transfer in a Perforated Plate

    This project belongs to the heat transfer analysis type. The aim of this test case is to validate the following parameter using a transient thermal solver, with a surface and a convective heat flux boundary condition on a perforated plate:

    • Temperature \([K]\) on a single node for 12 consecutive timesteps.

    The simulation results of SimScale were compared to the results presented in case B of [TTLP301]\(^1\).

    View Project

    Geometry

    The geometry used for the analysis with the highlighted node N1 can be seen below. It is a random thick plate with straight and curved edges.

    perforated plate geometry points
    Figure 1: Geometry of a perforated plate with highlighted node N1 (red)

    The coordinates for each vertex of the plate are displayed in the following table:

     ABCDEFGHIJ
    x \([m]\)0.6350.93950.93950.54270.31750.6350.93950.93950.54280.3175
    y \([m]\)000.83380.94010.5499000.83380.94010.5499
    z \([m]\)000000.20.20.20.20.2
    Table 1: The coordinates of the main geometry points

    Analysis Type and Domain

    Tool type : Code_Aster

    Analysis type : Heat transfer, linear

    Time dependency: Transient

    Mesh and element types: Two mesh cases were considered for the analysis of the perforated plate, with 1st order and 2nd order tetrahedral elements:

    CaseMesh typeNumber of nodesNumber of 3D elementsElement type
    (A)Standard5340256761st order tetrahedral
    (B)Standard16807109762nd order tetrahedral
    Table 2: The mesh characteristics for all the cases

    Below, the 1st order tetrahedral mesh for case A is visualized:

    mesh standard first order tetrahedral elements
    Figure 2: The mesh used for case A, created with SimScale’s standard meshing algorithm

    Simulation Setup

    Material/Solid

    • Isotropic:
      • Density \(ρ\) = 1 \( kg \over \ m³ \),
      • Thermal conductivity \(\kappa\) = 0.1 \( W \over \ m \ K\),
      • Specific heat = 1 \( J \over \ kg \ K\)  

    Initial conditions

    • Initial Temperature = 273.15 \(K\)  

    Boundary conditions

    • Surface heat flux on face AFJE:
      • Heat flux value = 1 \(W \over \ m²\)  
    • Convective heat flux on face CHID
      • Reference temperature \(T_{0}\) = 273.15 \(K\)
      • Heat transfer coefficient = 1 \(W \over \ m² \ K\)  

    Results Comparison

    The temperature values at node N1 for 12 time steps obtained with SimScale are compared against the results presented in case B of [TTLP301]\(^1\).

    Timesteps \([s]\)[TTLP301]
    \([K]\)    		Case A \([K]\)Error [%]Case B \([K]\)Error [%]
    0.1274.195274.2012.19E-03274.2032.92E-03
    0.2274.597274.6011.46E-03274.6042.55E-03
    0.3274.892274.8951.09E-03274.8982.18E-03
    0.4275.132275.1351.09E-03275.1382.18E-03
    0.5275.339275.3421.09E-03275.3452.18E-03
    0.6275.523275.5261.09E-03275.5292.18E-03
    0.7275.691275.6951.45E-03275.6972.18E-03
    0.8275.848275.8521.45E-03275.8542.18E-03
    0.9276.996275.9991.09E-03276.0011.81E-03
    1.0276.136276.141.45E-03276.1422.17E-03
    1.1276.27276.2741.45E-03276.2762.17E-03
    1.2276.398276.4031.81E-03276.4042.17E-03
    Table 3: Temperature results for all cases at different time steps

    All of the cases are in good agreement with the reference results.

    You can see the temperature distribution on the plate for the last time step for Case A below:

    temperature distribution perforated plate
    Figure 3: Temperature distribution on the plate for Case A at time 1.2s

    References

    Last updated: July 22nd, 2021

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