Heat conductivity of moist materials

[josephbeag]

Hi
This is my first post on the forum. I'm trying to wrestle with the issue of moisture and long term thermal performance.

1a) Can you please explain how I can work out the adjusted poorer conductivity of building materials (especially insulants) due to the higher moisture content shown in a WUFI simulation? To link lower thermal performance with moisture would be powerful. I have read the WUFI online file titled 'Heat Conductivity, Moisture-dependent'. It doesn't answer my quesdtions. Is it necesary to carry out this equation every time?:
"Lambda(w) = Lambda(o)·(1 + b · w/Rho(s))"

1b) What does the second "w" mean here?

1c) Is there a longer list of "b" (moisture-induced heat conductivity supplement) for materials than that given?

1d) The online help states that:
"WUFI can generate:
• Liquid transport coefficients (from the A-value and the free saturation)
• Heat conductivity, moisture-dependent (from the heat conductivity dry, the bulk density and the moisture-induced heat conductivity supplement)."
This is exactly what I want but I can't see where it does this.

2) Do you also know if there exists a document that lists at what level of moisture content (MC) do certain materials lose their original characteristics? I say this because I carried out a five-year simulation of a drylined wall after water had ben 'dumped' into the insulation layer in WUFI: while the moisture levels did decrease over time the initial rise in MC of the glasswool insulation close to the masonry was so high that it made me think the insulation must have lost all its shape and insulation ability: therefore the fact that it dried out afterwards is almost irrelevant.

I very much appreciate your help.

[Thomas]

1a) Can you please explain how I can work out the adjusted poorer conductivity of building materials (especially insulants) due to the higher moisture content shown in a WUFI simulation? To link lower thermal performance with moisture would be powerful. I have read the WUFI online file titled 'Heat Conductivity, Moisture-dependent'. It doesn't answer my quesdtions. Is it necesary to carry out this equation every time?:
"Lambda(w) = Lambda(o)·(1 + b · w/Rho(s))"

1b) What does the second "w" mean here?

[...]

1d) The online help states that:
"WUFI can generate:
• Liquid transport coefficients (from the A-value and the free saturation)
• Heat conductivity, moisture-dependent (from the heat conductivity dry, the bulk density and the moisture-induced heat conductivity supplement)."
This is exactly what I want but I can't see where it does this.

Dear josephbeag,

there are three ways to treat the dependence of the thermal conductivity on the water content:

a) Ignore it. The thermal conductivity is then assumed constant, and this constant value is entered in the field "Thermal Conductivity, Dry" in the "Basic Values" section. Instead of using the value for the dry material, one may enter a slightly increased value to account for typical water contents, but whatever value has been entered is used for the calculation in each grid element regardless of the current moisture content computed for the element.

b) Use tabulated values for different water contents. This is the most flexible method. If you have thermal conductivities measured (or computed somehow) for different water contents, enter these values in the table for the "Thermal Conductivity, moisture-dependent" in the "Hygric Extensions" section. For each grid element an individual local thermal conductivity is then computed and used, depending on the water content computed for this element.

c) If the relative increase of the thermal conductivity is reasonably proportional to the water content, expressed in mass-% (as is the case for many hygroscopic porous building materials but usually not for insulation materials), WUFI can generate a table for you. Click on the "Generate" option above the table and enter the "Moisture-dependent Thermal Conductivity Supplement" in the text field which opens in the "Approximation Parameters" section. WUFI then uses the dry thermal conductivity, the bulk density and the supplement value to generate a table with two entries (one for the dry material, one for the material filled to maximum capacity). WUFI automatically uses this table for the simulation run, interpolating linearly for intermediate water contents.

This is equivalent to evaluating the linear formula

"Lambda(w) = Lambda(o)·(1 + b · w/Rho(s))"

(where w is the local water content resulting from the simulation), but all of this is done by WUFI itself; all you need to do is to decide which of the above three options you wish to use and to supply the required material data. The material data may be taken from the relevant literature or from laboratory measurements.

1c) Is there a longer list of "b" (moisture-induced heat conductivity supplement) for materials than that given?

There is a voluminous literature survey published in 1984 on which we usually rely for moisture-dependent thermal conductivities of not-too-modern materials:

J. Cammerer, J. Achtziger:
Einfluss des Feuchtegehaltes auf die Wärmeleitfähigkeit von Bau- und Dämmstoffen
(Influence of moisture content on the thermal conductivity of building and insulation materials)
Gräfelfing, 1984

The b-values for WUFI were taken from a short synopsis:

J. Cammerer, J. Achtziger:
Einfluss des Feuchtegehaltes auf die Wärmeleitfähigkeit von Bau- und Dämmstoffen
Kurzberichte aus der Bauforschung, Sep. 1985, p. 491

An advantage of the b-value is that it is usually the same for materials with the same composition but different bulk densities, as long as the difference in bulk density results from a different content of macropores while the chemical composition and the micropore structure are the same.
This is true, for example, for different bulk density classes of aerated concrete, so that you can easily derive the moisture-dependent thermal conductivity for any aerated concrete with a bulk density which is not in the material database: interpolate the dry conductivity between known bulk densities and let WUFI generate a moisture-dependent table, using the same b-value which also applies to all the other bulk density classes.

A disadvantage is that the b-value only applies if the relative increase of the thermal conductivity is more or less proportional to the moisture content in mass-%, which is usually not true for insulation materials in which you are interested. In these cases, the above authors therefore give b-values restricted to a certain moisture range (within which the assumption of linearity can be justified). However, since WUFI should have thermal conductivities for all water contents up to maximum saturation, we instead took the original measurements reported by the authors, computed a polynomial passing through the measured points at low moisture contents and through 0.6 W/mK (the thermal conductivity of water) at maximum saturation, and then tabulated this curve.

2) Do you also know if there exists a document that lists at what level of moisture content (MC) do certain materials lose their original characteristics? I say this because I carried out a five-year simulation of a drylined wall after water had ben 'dumped' into the insulation layer in WUFI: while the moisture levels did decrease over time the initial rise in MC of the glasswool insulation close to the masonry was so high that it made me think the insulation must have lost all its shape and insulation ability: therefore the fact that it dried out afterwards is almost irrelevant.

Sorry, no such criteria exist as yet (as far as I know). WUFI is a tool which allows you to determine the heat and moisture conditions to be expected in a construction element, but the assessment of these results with respect to thermal and hygric performance, long-term stability, aging, specific damage risks etc. is still outside the scope of simulation programs and must be left to a professional with sufficient background knowledge (in other words: to you).

The problem here is that there are many conceivable aging or damage mechanisms. They are either (yet) too complex for an automated assessment, or too little is (yet) known about the behavior of the materials exposed to hot/cold/dry/wet conditions. This will be an active field of research for the next decades, now that software like WUFI can provide the hygrothermal data on which an assessment must rest.

Our goal is to finally provide a series of post-processors which will read WUFI's output and produce a risk assessment for mold growth, or rot, or corrosion, or frost damage, or strength reduction, or consistency changes etc. WUFI-Bio is such a post-processor for estimating the risk of mold growth; others are expected to follow.

Your concern that even a short-term high-moisture condition may lead to unacceptable degradation of some materials is presumably not unfounded but I'm afraid I cannot give you a definite answer here.

Kind regards,
Th. Schmidt

[josephbeag]

Many thanks Thomas. A very useful detailed answer!

Regards,
Joseph

[Antoine]

Hello,

I would like to use the wufi database to calculate the conductivity for a material considering the water content.
I read your answer. In the WUFI database, I can see the "Hygric Extensions" but I can't add values in the table. I can't check the "generate" button.

And the normalized water content. Is this the water content in M% ?
It is the water content in kg/m3, divided by the max water content in kg/m3 ?
In this case, I can read the value with the graph, and next extrapolate with the data given in the database ?

For example, in a Lime cement plaster (stucco). I can see that the avarage water content in one year is 10kg/m3. What can i do to evaluate the conductivity ?

I'm asking this in a hurry. I will elaborate tomorrow.
Thanks

[Thomas]

In the WUFI database, I can see the "Hygric Extensions" but I can't add values in the table. I can't check the "generate" button.

Hi Antoine,

in the database itself, you cannot change any values. Here you only can select a material for use in the calculation. If you want to change the values of a material, you can either

* assign the material data to an empty layer in the assembly, open the material data editor with a double click on that layer, unlock the read-only data with a click on the "lock" icon in the upper right corner of the dialog and proceed editing the data, or

* open the database editor via the menu "Database | Materials", highlight the material you want to change and click on the "New" menu item.


In the first case, you can immedately use the edited material for a calculation; if you want to save it for later use, you can save it to a user-defined catalog in the database.
In the second case, you can save the material to a user-defined catalog and use it later for a calculation.

And the normalized water content. Is this the water content in M% ?
It is the water content in kg/m3, divided by the max water content in kg/m3 ?

The "normalized water content" used in some of the diagrams is the water content divided by the maximum water content (which in turn is given by the porosity, multiplied by 1000 kg/m³, the density of water).

In this case, I can read the value with the graph, and next extrapolate with the data given in the database ?

For example, in a Lime cement plaster (stucco). I can see that the avarage water content in one year is 10kg/m3. What can i do to evaluate the conductivity ?

You can do that if the water is evenly enough distributed across the lime cement plaster. Then all the parts of the plaster have roughly the same thermal conductivity and you can read it from the table of moisture-dependent thermal conductivities provided in the material data of the plaster.
In this case, the table shows that the thermal conductivity varies between 0.8 W/mK for a water content of 0 kg/m³ and 1.608 W/mK at 240 kg/m³. Linear interpolation yields a thermal conductivity of 0.83 W/mK at 10 kg/m³.

A more elaborate method, also applicable for layers containing a very uneven distribution of moisture is this:

* Add the point in time for which you want to analyse the layer to the time table in the "Calculation Period / Profiles" dialog. This will tell WUFI to save the temperature, humidity and water content profiles occurring at that time.

* Run the calculation. You may abort the calculation once it is beyond the indicated point in time.

* Open the dialog "Outputs | ASCII Export", check the water content profile for the desired point in time, provide a name for the output file and click the button "Export to file(s)". This will write the water content profile you wish to examine to a text file.

* Now go to the "Initial Conditions" dialog, select the option "Read from File" in the "Initial Moisture in Component" section, and use the file browse button to specify the text file you just created.

* In the "Numerics" dialog, uncheck the "Moisture Transport Calculation" option. This switches off the moisture transport and preserves the water content profile. We will do a purely thermal calculation, with the water content profile held fixed.

* In the "Climate" dialog select the sine curves for both indoor and outdoor conditions. Select "User-Defined Sine Curve Parameters" from the drop-down list, set the amplitudes of the sine curves on both sides to zero (resulting in constant temperature conditions) and set the "Mean Values" to values giving a nice temperature gradient across the component (e.g. 40°C on one side and 10°C on the other side).

* Start the calculation. When the temperature profile stops changing you have reached steady-state conditions and you can determine the temperatures and heat flows on both sides of the layer you are interested in. You can read those data from the film by hovering the cursor over the temperature profile and the base of the heat flow arrows. Alternatively, you can export the temperatures and heat flows to an ASCII file, but for this you have to define monitoring positions on both sides of the layer first, so that you can extract the temperatures at these points.

Now you know the temperature drop across the layer and the resulting heat flow. Since we have

heat flow through layer = effective thermal conductivity * temperature drop / layer thickness,

we can easily derive

effective thermal conductivity = heat flow through layer * layer thickness / temperature drop.

Since WUFI computes the temperatures for the centers of the numerical grid elements, you cannot exactly read the temperatures at the layer's boundaries (which always coincide with boundaries between the grid elements). But if you make the grid fine enough, the temperatures in the first and last grid elements in the layer will suffice.

Regards,
Thomas

[Antoine]

Thank you very much for this help.

Another question :
I want to evaluate the Cp (H Cap) of my material considering water. As the Cp of water is different if it is vapor o liquid, I need to know the quantity of liquid water and the quantity of vapor.
Continuing with the same example of the plaster. We have w=10kg/m3. Can we know what is the percentage of vapor or liquid ?

I guess that in the case of hygroscopic materials, there is liquid water even in "classical" conditons (something like RH over 60%), but in the case of other materials, the RH have to be way bigger.

[Thomas]

We have w=10kg/m3. Can we know what is the percentage of vapor or liquid ?

Strictly speaking, in hygroscopic porous materials there is no perfectly clear distinction between vapor and liquid.
The water molecules drifting through the pore air are clearly vapor. The water molecules temporarily adsorbed at the pore walls are not vapor, but not really liquid either. Adsorbed multi-molecular layers are more liquid but not yet really liquid. Condensed water in small pores is basically liquid, but still affected by molecular forces exerted by the pore walls. Water in large pores is clearly liquid.

WUFI, being a simplified simulation tool, ignores this complication. It simply assumes that the "water content" indicated by the moisture storage function is liquid water and has the properties of liquid water as far as capillary transport, heat capacity etc. are concerned. The water contents w given as calculation results are computed using the moisture storage functions of the individual materials and are therefore the amount of "liquid" water (in the above sense) in the material.

Since the moisture storage function is usually determined by weighing a specimen after exposure to a given relative humidity, this means that WUFI treats as "liquid" whatever moisture contributes to the weight of the specimen, including adsorbed layers. This is not strictly correct, but then the contribution of these layers to liquid transport, heat capacity etc. is small anyway, and a not-perfectly-correct treatment of these small contributions is negligible at the level of accuracy attainable in practical building physics.

So if the water content of your material is 10 kg/m3, then WUFI treats all of this as liquid water and evaluates the volumetric heat capacity of the wet material as
(heat capacity) = (bulk density of material)*(specific heat capacity of dry material) + (water content)*(specific heat capacity of water).

WUFI ignores the effect of the water vapor on the heat capacity, as far as I can see from the source code. It should be kept in mind that the presence of additional water vapor molecules in the pore air does not simply add their contribution to the total heat capacity of the material: the vapor molecules displace some of the original dry pore air, so their presence only modifies the heat capacity of the pore air, with the contribution of the dry air already included in the measurement of the heat capacity of the dry material.

If you want to determine the contribution of the water vapor, you can determine the pore volume from the porosity (you may subtract from that the volume taken up by the liquid water w), and you can determine the water vapor concentration in the pore air from the temperature and the relative humidity of the pore air, both of which are provided by WUFI.

I guess that in the case of hygroscopic materials, there is liquid water even in "classical" conditons (something like RH over 60%), but in the case of other materials, the RH have to be way bigger.

Yes, the saturation vapor pressure is lower in the small capillaries, so that liquid water can already condense at relative humidities below 100% ("capillary condensation"). If you look at some moisture storage functions, you will see that they usually start to increase rapidly at some point around 80 .. 95 % RH. At that point capillary condensation begins to occur.

Regards,
Thomas