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Validation Case: Thermal Bridge Case 3 – 3D Corner in Building Construction

This validation case belongs to heat transfer, with the case of a three-dimensional corner where two walls and one floor element meet. The aim of this project is to demonstrate the validity of SimScale’s Heat Transfer solver by replicating the standard test case and comparing the following parameters:

  • Temperature distribution

The simulation results from SimScale were compared to the reference results presented in the standard EN-ISO 10211, “Thermal Bridges in Building Construction”, validation case 3 (Annex C)\(^1\).

Geometry

The structural corner geometry is shown in figure 1:

three dimensional structure heat transfer simscale thermal bridge case 3
Figure 1: Model geometry showing the two walls and the floor elements that meet in the corner

The model is composed of the following parts:

  1. Floor
  2. Horizontal structure (which acts as the thermal bridge)
  3. Internal wall – upper
  4. Internal wall – lower
  5. External wall
  6. Insulation

For the application of boundary conditions and measurement of result quantities, the surfaces of the structure are classified according to the spaces they belong to:

surfaces heat transfer simscale thermal bridge
Figure 2: Definition of surfaces in the model for boundary condition and result referencing
  • Lower internal (\(\alpha\))
  • Upper internal (\(\beta\))
  • External (\(\gamma\))
  • Structure cuts (\(\delta\))

Analysis Type and Mesh

Tool Type: Code_Aster

Analysis Type: Heat Transfer

Mesh and Element Types:

The mesh was computed using SimScale’s standard meshing algorithm, with the fineness parameter maxed up to 10. Statistics of the resulting mesh are presented in Table 1, and illustration shown in Figure 2:

Mesh #Mesh TypeElement TypeNumber of NodesNumber of Elements
1Standard1st order tetrahedrals741457483998
Table 1: Finite elements mesh details
mesh heat transfer simscale thermal bridge
Figure 3: Finite elements tetrahedral mesh used for the thermal simulation using SimScale’s standard meshing algorithm

Simulation Setup

Materials:

  • Interior Wall
    • \((\rho)\) Density: 1700 \(kg/m^3\)
    • Conductivity: Isotropic
    • \( (\kappa)\) ) Thermal conductivity: 0.7 \( W/(m.K) \)
    • Specific Heat: 800 \( J/(kg.K) \)
  • Isolation
    • \((\rho)\) Density: 200 \(kg/m^3\)
    • Conductivity: Isotropic
    • \( (\kappa)\) ) Thermal conductivity: 0.04 \( W/(m.K) \)
    • Specific Heat: 1000 \( J/(kg.K) \)
  • Exterior Wall
    • \((\rho)\) Density: 2000 \(kg/m^3\)
    • Conductivity: Isotropic
    • \( (\kappa)\) ) Thermal conductivity: 1 \( W/(m.K) \)
    • Specific Heat: 1000 \( J/(kg.K) \)
  • Horizontal Structure
    • \((\rho)\) Density: 5000 \(kg/m^3\)
    • Conductivity: Isotropic
    • \( (\kappa)\) ) Thermal conductivity: 2.5 \( W/(m.K) \)
    • Specific Heat: 600 \( J/(kg.K) \)
  • Floor
    • \((\rho)\) Density: 1000 \(kg/m^3\)
    • Conductivity: Isotropic
    • \( (\kappa)\) ) Thermal conductivity: 1 \( W/(m.K) \)
    • Specific Heat: 800 \( J/(kg.K) \)

Boundary Conditions:

The model considers convective heat transfer from the surfaces of the structure to the corresponding spaces. The interior spaces are at 20\(°C\) and 15\(°C\), and the exterior is at 0\(°C\). Also, the standard specifies the heat transfer properties in terms of the thermal resistance \(R\), which must be converted to the heat transfer coefficient used in SimScale, according to:

$$ h = \frac{1}{R} $$

The following boundary conditions were used in the simulation (see Figure 2 for illustration):

  • Lower internal faces \(\alpha\):
    • Convective heat flux
    • (\(T_0\)) Reference temperature 20\(°C\)
    • Heat transfer coefficient 5 \(W/(K.m^2)\)
  • Upper internal faces \(\beta\):
    • Convective heat flux
    • (\(T_0\)) Reference temperature 15\(°C\)
    • Heat transfer coefficient 5 \(W/(K.m^2)\)
  • External faces \(\gamma\):
    • Convective heat flux
    • (\(T_0\)) Reference temperature 0\(°C\)
    • Heat transfer coefficient 20 \(W/(K.m^2)\)
  • Structure cuts \(\delta\):
    • Adiabatic (applied by default)

Reference Solution

The reference solution\(^1\) for the structure is given in terms of the minimum temperatures and heat fluxes at the control surfaces.

Result Comparison

The computed temperature values from the simulation are presented in Table 2, and compared to the expected values from the standard:

ResultReference ValueSimScale ValueDeviation
Minimum temperature on \(\alpha\)11.32\(°C\)11.29\(°C\)0.03\(°C\)
Minimum temperature on \(\beta\)11.11\(°C\)11.12\(°C\)0.01\(°C\)
Table 2: Results comparison for the quantities of interest

The acceptance criterion states that the difference between the computed temperatures by the method being validated and the listed temperatures shall not exceed 0.1\(°C\). Thus, it is found that the SimScale solver is accepted under the standard’s validation case 3.

temperature plot heat transfer simscale
Figure 5: Temperature contours in the corner structure, showing gradient from hot to cold regions

Note

If you still encounter problems validating you simulation, then please post the issue on our forum or contact us.

Last updated: June 22nd, 2021

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