Surface relative humidity

[thiago.afonso]

Hello,

I have a conceptual doubt.

When we click, in the 1D animation film, exactly on the inner surface of a wall, exporting the "surface" RH and temperature of this wall (to the WUFI-Bio, for example), what does it really means?

I understand that the temperature exported is the temperature of the surface of the wall.

But when it comes to the RH i'm a bit confused.

My understanding is that this RH value refers to the RH of the air, right in contact with the wall, in the micro climate of the interface air-subtrate, which will be maily influencied by the interior air RH and the surface temperature (saturation pressure), but will also be affect by the diffusion of water vapour through the wall, and the storage of humidity by the wall (sorption or desorption). Is this right?

Thanks a lot!

[thiago.afonso]

Or....

The surface RH is obtained from the Water storage function of the material , in acordance with the water content of the material right at the surface....

In this case, the surface RH is a concept related to the moisture of the material, and not to the air.

Can someone please help me?

Thanks!

[Thomas]

Hi thiago.afonso,

yes, the surface relative humidity is the relative humidity of the pore air in the material, right at the surface (but conceptually as a property of the material). It is determined by the water content of the material at this spot. The relationship between the relative humidity and the water content is given by the moisture storage function of the material.

The stagnant boundary air layer at the surface is not explicitly modelled by WUFI. It acts as a resistance to heat and vapor flows, and WUFI describes its effects by assigning a heat transfer resistance and a vapor transfer resistance to the surface.

Because of this resistance, the heat flow through the surface causes a "temperature drop", and the vapor flow causes a "vapor pressure drop" across the boundary air layer, just like an electrical current causes a "voltage drop" across an electrical resistor. For this reason, temperature, vapor pressure and relative humidity at the surface are usually different from temperature, vapor pressure and relative humidity in the ambient air.

Regards,
Thomas

[thiago.afonso]

Thank you, Thomas.

[thiago.afonso]

Thomas,

Can you suggest any literature that treats about this (surface RH)?

Thank you again.

[thiago.afonso]

Hi thiago.afonso,

yes, the surface relative humidity is the relative humidity of the pore air in the material, right at the surface (but conceptually as a property of the material). It is determined by the water content of the material at this spot. The relationship between the relative humidity and the water content is given by the moisture storage function of the material.

But Thomas,

If the surface RH is determined by the water content of the material (right at the surface) and its moisture storage function, and this function is temperature-independent, how can we explain why colder surfaces (for example in thermal bridges, in cold days at unsteady state) have higher surface RH?

[Manfred Kehrer]

Because the air in/at the pores of material at the surface has a limited capacity to contain water vapor depending on the temperature according to psychometric charts.
Relationship RH <-> Water Content in Material = defined by moisture storage function
Relationship RH <-> Water Content in the Air = defined by psychometric charts

[thiago.afonso]

Thank you for the fast reply.

I understand your comentaries, but see how Thomas explained before..... when we export the surface temperature and the surface RH from WUFI (to use in the Wufi-Bio, for exemple), the surface RH is obtained from the water content of the material (at the surface), and it's moisture storage function. Not from the air.....

Thinking of a explanation....

I understand that the driving potential of moisture transport and storage in porous material is the Relative Umidity of the air.

But in transient conditions (unsteady state), this relative humidity of the air, considered in the calculation, is the RH of the room air (at the room temperature), or is the RH of the air in contact with the wall surface (at the surface temperature), wich in case of a colder surface, would result in higher RH?

[Manfred Kehrer]

The results of the temperature and vapor pressure on the surface are in such way to satisfy the governing equations. so both of your mentioned parts (and the mentioned relationships I stated before) do contribute to the result.

[Thomas]

If the surface RH is determined by the water content of the material (right at the surface) and its moisture storage function, and this function is temperature-independent, how can we explain why colder surfaces (for example in thermal bridges, in cold days at unsteady state) have higher surface RH?

Hi Thiago,
let me rephrase your question:

Suppose we have some porous hygroscopic material, exposed to the ambient air and in equilibrium with the air (same temperature; same relative humidity in the pore air as in the ambient air).

Now wrap the material with some vapor-tight material (to prevent moisture loss or gain) and cool it down. If we cool a parcel of air without changing the number of water molecules it contains, we know that its relative humidity will increase. The behavior or our material is different, however, because we assume that its moisture storage function is temperature-independent. Since the moisture content stays the same (we prevented loss or gain) and the moisture storage function also stays the same (being temperature-independent), the relative humidity corresponding to the moisture content via the moisture storage function stays the same, too. Cooling the wrapped material does not change the relative humidity of the pore air (as long as no water molecules are removed or added).

The question arises: If cooling the material does not change the relativ humidity of its pore air, why have cooler parts of a wall (e.g. in cooler corners) higher relative humidity than the rest of the wall?

This is not a direct result of the cooling itself; it is a secondary effect. Let us consider the same material once more, initially in equilibrium with the ambient air, and cool it down but now without wrapping. During the first moments, nothing special happens, only the temperature falls and the relative humidity in the pore air stays the same.

However, the relative humidity is the ratio beween the vapor pressure in the air and the saturation vapor pressure corresponding to the current temperature. Because the temperature drops, the saturation vapor pressure drops, too, and because we know that the ratio between vapor pressure and saturation vapor pressure remains constant (relative humidity being constant) the vapor pressure in the pore air obviously drops because of the cooling.

Moisture exchange between the material and the ambient air occurs through vapor diffusion, and the driving force for vapor diffusion is a difference in vapor pressures. At the beginning, when the material and the ambient air were in equilibrium, their temperatures and the relative humidities were the same which implies that the vapor pressures were the same, too. No vapor diffusion occurred therefore between the ambient air and the material (which is what we expect since they are assumed to be in equilibrium).

Now, however, because of the cooling the vapor pressure in the pore air is less than before (while the relative humidity remains unchanged). We have a vapor pressure difference between the pore air and the ambient air, and vapor diffusion will now transport moisture from the air into the material. This additional moisture raises the vapor pressure in the pore air and, consequently, the relative humidity. The increased vapor pressure in the surface region of the material drives a vapor diffusion flow into the deeper regions of the material, the intensity of which is determined by the diffusion resistance of the material. The increased relative humidity in the surface region drives a liquid flow into the deeper regions of the material, the intensity of which is determined by the liquid transport coefficients of the material.

During the equilibration phase, the moisture state of the surface is determined by the interplay between the diffusion flow from the ambient air to the surface, the diffusion flow from the surface into the material, and the liquid flow from the surface into the material, each of these flows affecting the vapor pressure and the relative humidity of the pore air in the surface region, and thus in turn affecting the flows themselves. (Have no fear: WUFI does the calculation for you ).

If we have static boundary conditions, a new static state will finally be reached, in which the moisture transported into the material has raised the moisture content of the material and therefore (via the moisture storage function) the relative humidity of the pore air to such a degree that the vapor pressure (which was initially reduced by the cooling) is back at its original value and no diffusion exchange between the ambient air and the material happens any more.

But in transient conditions (unsteady state), this relative humidity of the air, considered in the calculation, is the RH of the room air (at the room temperature), or is the RH of the air in contact with the wall surface (at the surface temperature), wich in case of a colder surface, would result in higher RH?

In transient conditions, things may be quite complicated.

Consider the vapor pressure profile: In the ambient air it is more or less constant (due to the permanent mixing), at the surface it has a value which is determined by the temperature of the surface and the relative humidity of the surface (which in turn depends on the moisture content of the surface material). In the boundary layer between the ambient air and the surface, the vapor pressure goes from the air value to the surface value (maybe in some non-linear profile, but fortunately we do not need to know the details going on within the boundary layer).

Consider the temperature profile: In the ambient air it is more or less constant (due to the permanent mixing), at the surface it is the temperature of the surface material. In the boundary layer between the ambient air and the surface, the temperature goes from the air value to the surface value (maybe in some non-linear profile, but fortunately we do not need to know the details going on within the boundary layer).

If you know these two profiles, you can compute the profile for the relative humidity: at each point of the profile, take the vapor pressure and divide it by the saturation vapor pressure corresponding to the temperature at that point. The result may be quite complicated. If there is a vapor pressure difference but no temperature difference between ambient air and surface, you will have a difference in relative humidity. If there is a temperature difference but no vapor pressure difference between ambient air and surface, you will have difference in relative humidity. You can have a vapor pressure difference and a temperature difference which conspire in such a way that there is no difference in relative humidity.

As you see, it is not very useful to ask whether the relative humidity at the surface is really the relative humidity of the ambient air or of the boundary air layer or whatever... What WUFI does at the surface is this: It knows the initial moisture content at the surface. Using the moisture storage function, it determines the relative humidity of the pore air at the surface. Using the known temperature of the material at the surface, it derives the vapor pressure from the relative humidity. It also knows the vapor pressure and the temperature in the ambient air, and it knows the vapor pressure, the relative humidity and the temperature deeper in the material. Now it can compute the heat, vapor and liquid flows driven by the various driving potentials:

* the heat flow through the surface is driven by the temperature difference between the surface and the ambient air, it also depends on the heat transfer coefficient at the surface.
* the diffusion flow through the surface is driven by the vapor pressure difference between the surface and the ambient air, it also depends on the vapor transfer coefficient at the surface.
* the heat flow from the surface into deeper regions of the material is driven by the temperature difference between the surface and the deeper layer, it also depends on the thermal conductivity of the material.
* the diffusion flow from the surface into the material is driven by the vapor pressure difference between the surface and the deeper layer, it also depends on the vapor resistance (µ-value) of the material.
* the liquid flow from the surface into the material is driven by the difference of relative humidity between the surface and the deeper layer, it also depends on the liquid transport coefficients of the material.

In general, the amount of heat and moisture flowing towards the surface will be different from the amount flowing away. So heat and moisture will either accumulate at the surface (net flow towards the surface) or drain from the surface (net flow away from the surface). WUFI determines the new heat and moisture content at the surface, these are the result of the current time step. Then all this happens for the next time step, and so on.


I recently added some background discussion of various physical aspects of humidity to the help file for WUFI-Pro. I'm attaching a PDF of this topic (the forum limit does not allow to attach the whole help file). It does not specifically discuss humidity at surfaces, but you may find it useful nevertheless. If not, ignore it

Regards,
Thomas

Edit 2019-05-02:
Removed the attached PDF. An updated version can now be found here in the FAQ section:
Air Humidity Tutorial (English)
Luftfeuchte-Tutorial (Deutsch)

[thiago.afonso]

Dear Thomas,

Thank you very much. Actually, I don't have words to thank you enough.

Your knowledge and your will to help others are just inspiring. Congratulations.