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.

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

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:

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

Coordinates

A

B

C

D

E

F

G

H

I

J

K

L

M

x \([mm]\)

0

500

0

15

500

0

15

0

500

1.5

15

1.5

500

z \([mm]\)

47.5

47.5

41.5

41.5

41.5

36.5

36.5

0

0

35

35

1.5

1.5

Table 1: Coordinate of the points in the thermal bridge geometry

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.

Case

Mesh Type

Nodes

Element Type

EN ISO 10211 Case 2

Second-order standard

2011690

Standard

Table 2: Mesh details for this validation case

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

Simulation Setup

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

Material Identification

Thermal Conductivity \([\frac{W}{m.K}]\)

Density \([\frac{kg}{m^3}]\)

Specific Heat\([\frac{J}{kg.K}]\)

1 – Concrete

1.15, isotropic

2240

750

2 – Wood

0.12, isotropic

500

1260

3 – Insulation (Cork)

0.029, isotropic

200

350

4 – Aluminum

230, isotropic

2700

897

Table 3: Overview of the material properties

Boundary Conditions:

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

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:

Point

Analytical\([º C]\)

SimScale\([º C]\)

Difference\([º C]\)

Meets Criteria? (<0.1 \(ºC\))

A

7.1

7.06

-0.04

Yes

B

0.8

0.76

-0.04

Yes

C

7.9

7.90

0.00

Yes

D

6.3

6.27

-0.03

Yes

E

0.8

0.83

+0.03

Yes

F

16.4

16.41

+0.01

Yes

G

16.3

16.34

+0.04

Yes

H

16.8

16.77

-0.03

Yes

I

18.3

18.33

+0.03

Yes

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.

The results from SimScale were downloaded and opened in ParaView. By using a Plot over line filter, connecting points A and B, and integrating the values over the line with an Integrate variables filter, we obtain the heat flux in the Z-direction. The table below shows the results:

Analytical \([\frac {W}{m}]\)

SimScale \([\frac {W}{m}]\)

Difference \([\frac {W}{m}]\)

Meets Criteria? (<0.1 \([\frac {W}{m}]\))

9.5

9.49064

-0.00936

Yes

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:

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.

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