Condensation Risk in a Wood-Frame Wall

This tutorial shows how to model heat and moisture transport in a wood-frame wall to evaluate the risk of condensation inside the wall. Different design and modeling approaches are compared under stationary outdoor conditions. In addition, the effect of the diurnal variation of outdoor humidity on the humidity distribution in the wall is computed.

Model Definition

The model is the 2D representation of a portion of a wood-frame wall placed between different outdoor and indoor conditions. The risk of condensation in the wall is evaluated through the coupled computation of heat and moisture transport. Values of relative humidity close to unity indicate a risk of condensation.

The geometry is shown on the figure below:

Figure 1: Geometry of the model

The wall is made of the following components:

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Two wood studs made in pine

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Three isolation boards made in cellulose

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A bracing made of a wooden panel

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An interior siding made of a gypsum

In addition, a vapor barrier made of plastic coated paper may be placed between the gypsum interior siding and the isolation boards.

Convective heat and moisture flux conditions are applied on the top and bottom boundaries to model the outdoor and indoor air flows surrounding the wall. The outdoor and indoor heat transfer coefficients are set as hext=25 W/(m·K) and hint=8 W/(m·K). The outdoor and indoor moisture transfer coefficients are set to βext=25·10-8 s/m and βint=8·10-8 s/m, according to the heat and mass transfer boundary layers analogy.

The side boundaries are supposed to be totally isolated regarding heat and moisture.

Dynamic modeling of Heat and Moisture Transport

In this approach, both the transport of liquid moisture by capillary forces and the transport of vapor by diffusion are computed, and the latent heat effect due to vapor diffusion is modeled. In addition, heat and moisture storage is considered, and moisture-dependent thermal properties are used. The corresponding equations, defined in the Norm EN 15026, are solved by default by the Moisture Transport in Building Materials and Heat Transfer in Building Materials interfaces:

where:

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(ρCp)eff (SI unit: J/(m3·K)) is the effective volumetric heat capacity at constant pressure

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T (SI unit: K) is the temperature

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keff (SI unit: W/(m·K)) is the effective thermal conductivity

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Lv (SI unit: J/kg) is the latent heat of evaporation

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δp (SI unit: s) is the vapor permeability

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φ (dimensionless) is the relative humidity

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psat (SI unit: Pa) is the vapor saturation pressure

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Q (SI unit: W/m3·s) is the heat source

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ξ (SI unit: kg/m3) is the moisture storage capacity

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Dw (SI unit: m2/s) is the moisture diffusivity

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G (SI unit: kg/m3·s) is the moisture source

See Ref. 1 for details about the norm EN 15026.

Static modeling of Heat and Moisture Transport

By ignoring heat and moisture storage, latent heat effect, and capillary transport of liquid moisture, the following equations are obtained for heat and moisture transport:

These equations are known as the Glaser Method. They can be solved in the Moisture Transport in Building Materials interface by setting the moisture diffusivity to 0, and in the Heat Transfer in Building Materials interface by setting the vapor permeability to 0.

The advantage of this second approach is that you need to provide less hygroscopic material properties. In particular, the moisture diffusivity used for the expression of the liquid transport flux is not required. However, for high values of relative humidity, the simplifications mentioned above may result in an over-estimation of the condensation.

Modeling of the Vapor Barrier

Upside and downside moisture fluxes defined by β(φd − φu) and β(φu − φd) are applied at the interface between the interior siding and the isolation to model the vapor barrier. The moisture transfer coefficient β is defined as

where δ is the vapor permeability of still air (SI unit: s), psat is the saturation pressure of water vapor (SI unit: Pa), μ is the vapor resistance factor (dimensionless), and ds is the vapor barrier thickness (SI unit: m).

Diurnal Variations of Outdoor Conditions

The effect of time-dependent outdoor conditions on condensation risk is studied by using typical weather data from ASHRAE 2013 database. Average temperature and relative humidity ambient conditions in Dublin from the 1st to the 3rd of June are used for the definition of the convective flux conditions on the exterior side of the wall. The simulation is run over two days with the temperature and relative humidity conditions shown on the graph of Figure 2.

Figure 2: Ambient data for temperature and relative humidity used on the exterior side of the wall.

Results and Discussion

Temperature and Moisture Distributions Without Vapor Barrier

The temperature and moisture distributions due to the different outdoor and indoor conditions are shown on Figure 3 and Figure 4. The highest values of relative humidity are obtained close to the bracing.

Figure 3: Temperature distribution, stationary study without vapor barrier

Figure 4: Relative humidity distribution, stationary study without vapor barrier

Effect of vapor barrier on Heat and Moisture Distribution

The graph of Figure 5 shows that the addition of a vapor barrier between the interior siding and the isolation reduces the risk of condensation at the interface between the wooden frame/isolation and the bracing.

Figure 5: Effect of vapor barrier on relative humidity distribution across the wall, in the wooden frame and in the isolation.

The effect on temperature distribution is shown on Figure 6.

Figure 6: Effect of vapor barrier on temperature distribution across the wall, in the wooden frame and in the isolation.

Comparison of the Modeling Approaches

The Glaser method over-estimates condensation by not taking into account the liquid transport which becomes significant when the relative humidity is high, close to the bracing. The effect on temperature and moisture distribution is shown on Figure 7 and Figure 8.

Figure 7: Comparison of the modeling approaches for the temperature distribution across the wall, in the wooden frame and in the isolation.

Figure 8: Comparison of the modeling approaches for the relative humidity distribution across the wall, in the wooden frame and in the isolation.

Reference

1. EN 15026, Hygrothermal performance of building components and building elements - Assessment of moisture transfer by numerical simulation, CEN, 2007.

Heat_Transfer_Module/Buildings_and_Constructions/wood_frame_wall

Modeling Instructions

From the menu, choose .

New

In the window, click .

Model Wizard

In the window, click .

In the tree, select .

Click .

In the tree, select .

Click .

Root

First define the geometry of the wall, composed of wood studs and isolation boards, completed at the top and bottom by a bracing and an interior siding.

Global Definitions

In the window, under click .

In the window for , locate the section.

Click .

Browse to the model’s Application Libraries folder and double-click the file wood_frame_wall_parameters.txt.

Geometry 1

Rectangle 1 (r1)

In the toolbar, click and choose .

In the window for , locate the section.

In the text field, type L.

In the text field, type t_il + t_i + t_b.

Click .

Click to expand the section. In the table, enter the following settings:


Layer name	Thickness (m)
Layer 1	t_il
Layer 2	t_i

Click .

Rectangle 2 (r2)

In the toolbar, click and choose .

In the window for , locate the section.

In the text field, type d_wf.

In the text field, type t_i.

Locate the section. In the text field, type L/4-d_wf/2.

In the text field, type t_il.

Click .

Rectangle 3 (r3)

Right-click and choose .

In the window for , locate the section.

In the text field, type 3*L/4-d_wf/2.

Click .

In the toolbar, click .

Definitions

Ambient Thermal Properties 1 (amth1)

In the window, under click .

In the window for , locate the section.

In the Tamb text field, type T_ext.

In the φamb text field, type phi_ext.

Now, set the physics interfaces for the modeling of heat and moisture transport with the method described in Dynamic modeling of Heat and Moisture Transport.

Heat Transfer in Building Materials (ht)

Building Material 1

In the window, under click .

In the window for , locate the section.

From the list, choose .

Heat Flux 1

In the toolbar, click and choose .

Select Boundary 7 only.

In the window for , locate the section.

Click the button.

In the h text field, type h_ext.

From the Text list, choose .

Heat Flux 2

In the toolbar, click and choose .

Select Boundary 2 only.

In the window for , locate the section.

Click the button.

In the h text field, type h_int.

In the Text text field, type T_int.

Initial Values 1

In the window, under click .

In the window for , type T_int in the T text field.

Moisture Transport in Building Materials (mt)

In the toolbar, click and choose .

Building Material 1

In the window, under click .

In the window for , locate the section.

From the list, choose .

In the window, click .

Moisture Flux 1

In the toolbar, click and choose .

Select Boundary 7 only.

In the window for , locate the section.

Click the button.

In the βp text field, type beta_ext.

From the Text list, choose .

From the φext list, choose .

Moisture Flux 2

In the toolbar, click and choose .

Select Boundary 2 only.

In the window for , locate the section.

Click the button.

In the βp text field, type beta_int.

In the Text text field, type T_int.

In the φext text field, type phi_int.

Initial Values 1

In the window, under click .

In the window for , locate the section.

In the φ0 text field, type phi_int.

Thin Moisture Barrier 1

In the toolbar, click and choose .

Select Boundaries 4, 9, 12, 15, and 18 only.

Pick materials from the library for the wood studs (pine), the isolation (cellulose), the interior siding (gypsum), and the vapor barrier (plastic coated paper). In addition, define a new material for the bracing.

Add Material

In the toolbar, click to open the window.

Go to the window.

In the tree, select .

Click in the window toolbar.

In the tree, select .

Click in the window toolbar.

In the tree, select .

Click in the window toolbar.

In the tree, select .

Click in the window toolbar.

In the toolbar, click to close the window.

Materials

Wood (pine) (mat1)

Select Domains 4 and 6 only.

Cellulose board (mat2)

In the window, under click .

Select Domains 2, 5, and 7 only.

Gypsum board (mat3)

In the window, under click .

Select Domain 1 only.

Plastic coated paper (mat4)

In the window, under click .

In the window for , locate the section.

From the list, choose .

Select Boundaries 4, 9, 12, 15, and 18 only.

Material 5 (mat5)

In the window, under right-click and choose .

In the window for , type Wooden panel (OSB) in the text field.

Select Domain 3 only.

Wooden panel (OSB) (mat5)

In the toolbar, click and choose .

Interpolation 1 (int1)

In the window, expand the node, then click .

In the window for , type k_eff in the text field.

Locate the section. In the text field, type k_eff.

In the table, enter the following settings:


t	f(t)
0	0.11
0.97	0.14
1	0.6

Locate the section. From the list, choose .

From the list, choose .

Locate the section. In the text field, type 1.

In the text field, type W/(m*K).

Wooden panel (OSB) (mat5)

In the toolbar, click and choose .

Interpolation 2 (int2)

In the window, under click .

In the window for , type Interpolation: Dw in the text field.

Locate the section. In the text field, type Dw.

In the table, enter the following settings:


t	f(t)
0	2.93e-12
0.97	2.93e-12
1	6.52e-10

Locate the section. From the list, choose .

From the list, choose .

Locate the section. In the text field, type 1.

In the text field, type m^2/s.

Wooden panel (OSB) (mat5)

In the toolbar, click and choose .

Analytic 1 (an1)

In the window, under click .

In the window for , type Analytic: wc in the text field.

In the text field, type wc.

Locate the section. In the text field, type 202.68*x^2 - 24.813*x + 6.1962.

Locate the section. In the text field, type 1.

In the text field, type kg/m^3.

Wooden panel (OSB) (mat5)

In the window, under click .

In the window for , locate the section.

In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Thermal conductivity	k_iso ; kii = k_iso, kij = 0	k_eff(mt.phi)	W/(m·K)	Basic
Density	rho	646	kg/m³	Basic
Heat capacity at constant pressure	Cp	1500	J/(kg·K)	Basic
Diffusion coefficient	D_iso ; Dii = D_iso, Dij = 0	Dw(mt.phi)	m²/s	Basic
Water content	w_c	wc(mt.phi)	kg/m³	Basic
Vapor resistance factor	mu_vrf	162	1	Basic