Relative humidity of the airlayer

[WEI LI]

Hi there,

The help document, air layer chapter says:

This moisture level is much more realistic. However, the free saturation is always fixed at the quoted value and does not vary with temperature, as it would do in real air. Furthermore, since WUFI always assumes that the moisture storage functions are temperature-independent (usually a good approximation for porous materials, but not for air), the change in relative humidity which is caused by a change in air temperature (even with the water content remaining fixed) is not modelled in the old as well as in the new air layers.

I did a simple simulation, the geometry is consisted of:
1 mm metal deck (unpreforated)
10 mm airlayer without additional moisture capacity
1 mm metal deck (unpreforated)
In this case, the water content of the airlayer should be fixed. Since water vapour and liquid are not allowed to transported through the outer or inner metal deck. I expected the RH of the airlayer remains a constant. However, it ends up fluctuating.

In the help document, chapter climate data-humidity, we can see RH=p/psat, and both p and psat are related to the temperature. How come "the change in relative humidity which is caused by a change in air temperature is not modelled"?

Could you please help me with it, thanks a lot.

[WEI LI]

Hopefully this post can be noticed.

[Thomas]

Hi WEI LI,

WUFI has been developed to simulate hygroscopic porous materials. The pore space of these materials contains water both in liquid and in vapour form. The two forms of water content are not independent, their relationship is given by the moisture storage function which describes the amount of liquid water which is in equilibrium with a given relative humidity of the pore air. The moisture storage functions of the various materials are slightly temperature-dependent; in WUFI this temperature-dependence is ignored and moisture storage functions are assumed to be temperature-independent.

The water contents reported by WUFI as the simulation results are only the liquid water contents.The water vapour in the unfilled pore space is not part of the output since it is usually of no interest to the user, and given the low porosities of most building materials, the vapour mass is negligible when compared to the mass of the liquid water content.

However, even though the vapour portion of the total water content is usually small, the interaction between liquid and vapor must be taken into account if any change of the water content is to be modelled. If relative humidity and temperature in a numerical grid element change, WUFI takes into account

• the change of liquid water content which corresponds to the change of relative humidity (via the moisture storage function),

• the change of vapour content in the air-filled part of the pore volume which is caused by the change of relative humidity,

• the change of vapour content in the air-filled part of the pore volume which is caused by the change in the air-filled portion of the volume when the liquid-filled portion of the volume changes,

• the change of vapour content in the air-filled part of the pore volume which is caused by the temperature-depencende of the saturation vapour pressure.

So even if the component is in a vapour-tight enclosure, because of the last item a temperature change in the material will cause a change of the vapour content in the pore air, which in turn will cause some evaporation or condensation of liquid water. In other words, although in this situation the total water content in the component must remain constant, the relative amounts of liquid and vapour will change because of the temperature change. In materials with low porosity (= small amount of vapour) the effect will be small, in materials with higher porosity, such as the air layers, the effect will be larger.

Since WUFI's output only reports the liquid water content, you will see a change in the reported water content, caused by temperature changes, even though the total mass of water (liquid and vapour) remains the same.

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Since the moisture storage function describes the amount of liquid water and air layers usually contain no liquid water, their moisture storage function should be zero. However, then WUFI would report zero as the water content and users would be confused because they expect some moisture in the air. Also, since WUFI treats air layers in the same way as porous hygroscopic materials, a (liquid) water content zero would also imply relative humidity zero and WUFI couldn't even compute a non-zero vapour content for the air layers.

As a makeshift solution, we have given the air layers a small moisture storage function which is close to what's expected as a typical vapour content (a few grams per m³) so that the water contents reported by WUFI are not completely unrealistic. However, this means that an air layer now has both a "reservoir" of liquid water (described by the moisture storage function) and the normal vapour content (implicitly taken into account by WUFI during the simulation). If the relative humidity or the temperature changes, part of that change will be compensated by evaporation from or condensation on that fictitious "reservoir" of liquid water, so that you will see some change in the reported amount of (liquid) water, but that change will not really be the change expected in a real air layer (which has no "reservoir"). That's why we warn users not to rely on the water contents reported for the air layers while the reported relative humidities should be more realistic. Future WUFI versions will have a dedicated material type "air" which implements all the relevant moisture transport and storage processes as appropriate for air without needing a fictitious moisture storage function.

Kind regards,
Thomas

[WEI LI]

Thanks a lot, Thomas, for your elaboration.

the change of vapour content in the air-filled part of the pore volume which is caused by the temperature-depencende of the saturation vapour pressure. So even if the component is in a vapour-tight enclosure, because of the last item a temperature change in the material will cause a change of the vapour content in the pore air,

I am still a bit confused about this point. Yes, the saturation vapour pressure raises with the temperature, but how come the temperature (or the saturation vapour pressure) affect the vapour content?

Thank you!

[Thomas]

The vapour pressure in the pore space is the saturation vapour pressure multiplied by the relative humidity. The saturation vapour pressure is temperature-dependent, so it changes when the temperature changes.

\(p_\mathrm{vap} = \varphi \cdot \ p_\mathrm{sat}(\vartheta)\)

This means that when the temperature changes, either the vapour pressure or the relative humidity or both must also change to maintain the equality mentioned above. It depends on the boundary conditions which variable changes how much.

In the current case (a porous material with some liquid moisture content and some vapour content) the relative humidity is more or less fixed because it must correspond to the liquid moisture content (via the moisture storage function), and the liquid moisture content will usually only change slowly (usually by evaporation or condensation which are relatively slow processes). So in this case it is mainly the vapour pressure which must change in response to the temperature change. But a changed vapour pressure corresponds to a changed vapour concentration and thus to a changed vapour mass in the given pore volume.

If you are interested in the details of the behaviour of vapour pressures, humidities etc., you may perhaps find the Humidity Tutorial somewhat useful.

Kind regards,
Thomas

[WEI LI]

Hi Thomas, thanks for your reply.

• In the current case (a porous material with some liquid moisture content and some vapour content) the relative humidity is more or less fixed because it must correspond to the liquid moisture content (via the moisture storage function), and the liquid moisture content will usually only change slowly (usually by evaporation or condensation which are relatively slow processes).

Does "the current case" refer to the case I mention on the original post? The "metal-air-metal' structure?

• ...the relative humidity is more or less fixed because it must correspond to the liquid moisture content (via the moisture storage function)

I remember I have seen it from somewhere in the Wufi help document, says something like: the water content (I assume it means the liquid moisture content) is just a secondary value which is derived from the RH by the moisture storage function. In my opinion, WUFI calculates the RH field, by solving the moisture transport equation, and then calculates the water content (I mean the water content in post process, which is liquid water content) by the moisture storage function. PLEASE CORRECT ME IF I AM WRONG. However, you said the RH is more of less fixed because of the liquid mositure content is changing very slowly. This is quite conflicting with my understanding, or not?

• ...the liquid moisture content will usually only change slowly (usually by evaporation or condensation which are relatively slow processes)

Could you please inform me where I can learn more about how WUFI is taking care of the evaporation and condensation thing? Like which part of the help document I can found them?

Cheers

[Thomas]

Hi Thomas, thanks for your reply.

• In the current case (a porous material with some liquid moisture content and some vapour content) the relative humidity is more or less fixed because it must correspond to the liquid moisture content (via the moisture storage function), and the liquid moisture content will usually only change slowly (usually by evaporation or condensation which are relatively slow processes).

Does "the current case" refer to the case I mention on the original post? The "metal-air-metal' structure?

It refers to the behavior of a porous hygroscopic material between impermeable surfaces which contains some liquid water and some vapour.

I remember I have seen it from somewhere in the Wufi help document, says something like: the water content (I assume it means the liquid moisture content) is just a secondary value which is derived from the RH by the moisture storage function. In my opinion, WUFI calculates the RH field, by solving the moisture transport equation, and then calculates the water content (I mean the water content in post process, which is liquid water content) by the moisture storage function. PLEASE CORRECT ME IF I AM WRONG.

Yes, we are using relative humidity and temperature as the primary variables describing the hygric and thermal states of the materials. The transport equations (which include processes such as liquid transport, vapour diffusion, moisture storage capacity, evaporation and condensation, moisture sources and sinks, heat flow, heat storage capacity, release and consumption of latent heat, heat sources and sinks, etc.) then determine the values for the relative humidity and the temperature at the end of the next time step. Then the secondary variables, such as liquid water content, are computed from relative humidity and temperature. This is possible because there are unique mathematical relationships between all these quantities.

However, you said the RH is more of less fixed because of the liquid mositure content is changing very slowly. This is quite conflicting with my understanding, or not?

There is no contradiction. There are always situations where the water content or the temperature remains more or less constant for a while (for example, if the component surfaces are impermeable or only poorly permeable to moisture or heat transport, or if the boundary conditions are such that they do not give rise to moisture or temperature changes of the construction). The fact that a variable remains constant under certain conditions does not invalidate its usability as a variable in general.

...the liquid moisture content will usually only change slowly (usually by evaporation or condensation which are relatively slow processes)

In the particular case I considered, a case where the construction surfaces are impermeable to liquid or vapour transport (the case you considered initially), the total amount of moisture (liquid + vapour) is fixed because of the impermeability of the surfaces. However, the relative amounts of liquid versus vapour may still change when the temperature changes. The liquid amount cannot change much because it has only the limited pore space into which it can evaporate. Because relative humidity is connected with the liquid amount through the moisture storage function, it cannot change much either under these circumstances. But some of the liquid water does evaporate, in order to create a new equilibrium with the vapor pressure in the pore air. This explains why you saw a change in the liquid water content with changing temperature even though your construction was tight on all surfaces. The small change in liquid water content also causes (via the moisture storage function) a small change in relative humidity, but unless the porosity is not very large, only a small change in relative humidity is required to reach the new equilibrium.

All of this refers to the behaviour of porous materials. Air layers are not porous materials (they don't have liquid water content, so they don't really have a moisture storage function). But until a new material type "air layer" with specifically tailored mathematical properties will be introduced in a future WUFI version, we have to use porous materials which behave as close to real air layers as possible. It works reasonably well for most cases, in particular if the function of the air layer is just to serve as some moisture or heat flow resistance in the component. But don't expect completely realistic behaviour under all circumstances.

Could you please inform me where I can learn more about how WUFI is taking care of the evaporation and condensation thing? Like which part of the help document I can found them?

There are no specific routines in WUFI whose task it is to treat evaporation and condensation. These phenomena are automatically taken into account by the transport equations: the solution for the new time step is a new moisture field in the construction, and the changes of liquid moisture content which are not caused by liquid transport may be said to be due to evaporation or condensation.

Maybe we are talking about two different things. From your original question it seems that you are interested in condensation which occurs in an air layer bounded by an impermeable surface (e.g. a metal sheet). That problem is conceptually relatively simple: when the vapour pressure in the air is greater than the saturation vapour pressure at the surface (i.e. when relative humidity at the surface reaches or surpasses 100 %), condensation occurs. The condensation rate is determined by the difference of the two vapour pressures and the vapor diffusion surface transfer coefficient. There is either a layer of liquid water or there isn't.

On the other hand, in porous materials there is always some liquid water content present in larger or smaller quantities, and it increases whenever relative humidity increases, even at relative humidities far below 100 %. So in general, condensation in porous materials behaves quite differently from condensation in an air layer and you cannot learn much about condensation in air layers by investigating condensation in porous materials.

Kind regards,
Thomas

[WEI LI]

Thanks Thomas, it has been very helpful.
I would like to read your comments and learn from them time to time.