Thermal Performances of Roller Shutters

During the design of a building, environmental issues have gained considerable influence in the entire project. One of the first concerns is to improve thermal performances. In this process, simulation software provide key tools for modeling thermal losses and performances in the building.

The international standard ISO 10077-2:2012 (Ref. 1) deals with thermal performances of windows, doors, and shutters. It provides computed values of the thermal characteristics of frame profiles in order to validate a simulation software.

COMSOL Multiphysics successfully passes the entire benchmark. This document describes two test cases of ISO 10077-2:2012 related to roller shutters only. Other test cases from this standard are available in the following applications:

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Thermal Performances of Windows

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Glazing Influence on Thermal Performances of a Window

Figure 1: 3D representation of the roller shutter box with shutters inside.

Model Definition

On each test case, a shutter section separates a hot internal side from a cold external side. After solving a model, two quantities are calculated and compared to the normative values:

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the thermal conductance between the internal and external sides;

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the thermal transmittance of the shutter frame.

air cavities

The roller shutter structure contains many cavities. The purpose is to ensure thermal insulation. According to the ISO 10077-2:2012 standard, cavities are modeled in different ways depending on their shapes.

The heat flow rate in cavities is represented by an equivalent thermal conductivity, keq, which includes the heat flow by conduction, convection, and radiation. It also depends on the geometry of the cavity and on the adjacent materials. The definition of keq is detailed in the next paragraphs.

Cavities are divided into three types:

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unventilated cavities, completely closed or connected either to the exterior or to the interior by a slit with a width not exceeding 2 mm;

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slightly ventilated cavities, connected either to the exterior or to the interior by a slit greater than 2 mm but not exceeding 10 mm;

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well-ventilated cavities: corresponding to a configuration not covered by one of the two preceding types, it is assumed that the whole surface is exposed to the environment so that boundary conditions are applied to (see the Boundary conditions section below for more information).

For the main cavity within a roller shutter box, these rules are slightly different (see Figure 2):

Figure 2: Opening of a roller shutter box.

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If e1 + e3 ≤ 2 mm, the cavity is considered as unventilated.

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If etot ≤ 35 mm, the cavity is considered as slightly ventilated.

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If etot > 35 mm, the cavity is considered as well-ventilated.

Unventilated Rectangular Cavity

For an unventilated rectangular cavity, the equivalent thermal conductivity is defined by:

where d is the cavity dimension in the heat flow rate direction, and R is the cavity thermal resistance given by:

Here, ha is the convective heat transfer coefficient, and hr is the radiative heat transfer coefficient. These coefficients are defined by:

where:

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C1 = 0.025 W/(m·K)

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C2 = 0.73 W/(m2·K4/3)

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ΔT is the maximum surface temperature difference in the cavity

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σ = 5.67·10-8 W/(m2·K4) is the Stefan-Boltzmann constant

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Tm is the average temperature on the boundaries of the cavity

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E is the intersurface emittance, defined by:

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ε1 and ε2 are the surface emissivities (both are equal to 0.90 in this model)

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F is the view factor of the rectangular section, defined by:

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d is the cavity dimension in the heat flow rate direction

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b is the cavity dimension perpendicular to the heat flow rate direction

Slightly Ventilated Rectangular Cavities

For a slightly ventilated cavity, the equivalent thermal conductivity is twice that of an unventilated cavity of the same size.

Nonrectangular Cavities

Nonrectangular cavities are transformed into rectangular cavities of same area and aspect ratio according to defined rules in ISO 10077-2:2012 presented below. Then, keq is evaluated following one of the two previous rectangular cases.

Figure 3: Nonrectangular cavity transformation.

Figure 3 shows a nonrectangular cavity of area A′. Then, d′ and b′ are the depth and the width (in accordance with the direction of the heat flow) of the smallest rectangle than can contain of the nonrectangular cavity. The equivalent rectangular cavity, of size b × d and area A must satisfy:

Hence, b and d are given by:

Boundary conditions

The heat flux conditions for internal and external sides are given by the Newton’s law of cooling:

where Text is the exterior temperature (Text = Ti = 20°C for the internal side and Text = Te = 0°C for the external side). The standard defines thermal surface resistance, Rs, which is related to the heat transfer coefficient, h, by:

Internal and external thermal surface resistances are not equal.

Description of the two Applications

Figure 4 and Figure 5 depict the geometry of each model. Unventilated cavities are red-numbered while slightly ventilated cavities are green-numbered. Adiabatic boundaries are represented with striped rectangles.

Application 1: Roller Shutter Box

The first application studies the heat conduction in a roller shutter box. The main structure is made of polyvinyl chloride (PVC) which has a low thermal conductivity k of 0.17 W/(m·K). Inside the box, there is an insulation panel which has a very low thermal conductivity of 0.035 W/(m·K).

In this application, there are thirty-eight cavities. Thirty-seven of them are not connected to the exterior so they are considered as unventilated cavities. The main cavity is considered as slightly ventilated because of the large opening in the box (15 mm).

Figure 4: Geometry of the roller shutter box.

Application 2: PVC Shutter Profile

This application studies the heat conduction in a PVC shutter profile. The shutter is made of two PVC blocks which have a thermal conductivity of 0.17 W/(m·K).

In this application there are five cavities. They are not connected to the exterior so they are considered as unventilated cavities.

Figure 5: Geometry of the PVC shutter profile.

Results and Discussion

Temperature profiles

The temperature profiles for each model are shown in Figure 6 and Figure 7.

Figure 6: Temperature distribution in the roller shutter box.

Figure 7: Temperature distribution in the PVC shutter profile.

Quantities of interest

The quantities of interest are the following:

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The thermal conductance of the entire section, L2D, given by:

where

is the heat flow rate through the shutter (in W/m), Te = 0°C is the external temperature and Ti = 20°C is the internal temperature.

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The thermal transmittance of the frame Uf defined by:

where l is the projected length of the internal section perpendicularly to the heat flow direction (expressed in meters).

Table 1 and Table 2 compare the numerical results of COMSOL Multiphysics with the expected values provided by ISO 10077-2:2012.

Table 1: comparison between expected values and Computed values of Quantities in Application 1.


Quantity	Expected value	Computed value	Relative Error
L2D (W/(m·K))	0.181	0.183	1.10%
Uf (W/(m2·K))	1.05	1.035	1.43%

Table 2: comparison between expected values and Computed values of Quantities in Application 2.


Quantity	Expected value	Computed value	Relative Error
L2D (W/(m·K))	0.207	0.207	0.00%
Uf (W/(m2·K))	3.64	3.63	0.27%

The maximum permissible differences to pass this test case are 3% for the thermal conductance and 5% for the thermal transmittance. The measured values are completely coherent and meet the validation criteria.

Reference

1. European Committee for Standardization, ISO 10077-2:2012, Thermal performance of windows, doors and shutters – Calculation of thermal transmittance – Part 2: Numerical method for frames, 2012.

Heat_Transfer_Module/Buildings_and_Constructions/roller_shutter_thermal_performances

Modeling Instructions

Root

Start by opening the following prepared file. It already contains global definitions, geometries, local variables, selections, operators and material properties.

From the menu, choose .

Browse to the model’s Application Libraries folder and double-click the file roller_shutter_thermal_performances_preset.mph.

Roller Shutter Box

Roller Shutter Box (comp1)

In the window, expand the node.

Definitions (comp1)

Variables 1

Define the thermal conductance of the section for the postprocessing part as follows.