Boundary conditions - enthalpy balance

[Kevin Taurines]

Dear WUFI users,

I have a little doubt about the modelling of the boundary conditions. The WUFI help specifies that following heat flows

Phi_h_conv_lw = (h_c+h_r)*(T_amb-T_surf)
Phi_ h_conv_sw = alpha*G

and moisture flows

Phi_m_vap = Beta*(Pv_amb-Pv_surf)
Phi_m_liq = R_a*(R1+R2*WS)*Prec

are taken into account.

I cannot find information about the latent heat flow induced by the moisture vapor flow Phi_m_vap given by Phi_h_vap = (Cv*T_surf+Lv)* Phi_m_vap although this heat flow is significant or even dominant, and not considering it leads to overestimate surface temperature.

This is exactly what I observed on several models with both WUFI 5 and 2D: surface temperatures reach ~60-70°C while outdoor air temperature is around 10°C and short wave radiation is around some hundreds of W.m-2 (France winter conditions). I of course checked my model and my weather file and everything looks fine.

My opinion is : this latent heat flow is neglected and, as long as the solar heat gains prevail on the other terms of the boundary heat balance equation, the temperature is overestimated. Does someone confirm this ? Did I missed something ?

Many thanks in advance for your help.

Regards,

Kevin

[Thomas]

Dear Kevin,

latent heat effects are taken into account. Not only at the surfaces but in the whole volume of the component. Wherever vapour condenses, an appropriate amount of latent heat is released, and wherever water evaporates, an appropriate amount of latent heat is consumed. This behaviour is an integral part of the thermal transport equation:

\(\frac{dH}{d\vartheta}\frac{\partial \vartheta}{\partial t} = \nabla \cdot (\lambda \ \nabla\vartheta) + h_v \ \nabla \cdot (\delta_p \ \nabla (\varphi \ p_{sat})) + s\)

\(\frac{dH}{d\vartheta}\): heat storage capacity of the building material
\(\vartheta\): temperature
\(\lambda\): thermal conductivity
\(h_v\): latent heat of evaporation for water
\(\delta_p\): water vapour permeability of the building material
\(\varphi\): relative humidity
\(p_{sat}\): saturation vapour pressure of water
\(s\): heat sources other than latent heat

The second term on the right-hand side

\( h_v \ \nabla \cdot (\delta_p \ \nabla (\varphi \ p_{sat}))\)

describes the effect of the latent heat on the temperature field, acting as a heat source or sink. The expression in parentheses is the vapour flow, and the consumed latent heat is proportional to the divergence of the vapour flow.

This is also taken into account in the region of the component just below and at the surface, so no extra accounting of the latent heat flow across the surface is necessary. Vapour that has been created in the component (using up some latent heat) and which leaves the component takes with it that latent heat which is then lost for the component.

If the surface temperatures computed by WUFI were always grossly wrong, this would certainly have been noticed long ago. Most likely, there will be some problem with the input data. Maybe the entered solar absorptivity is too high? Maybe the heat transfer coefficient is too low, leading to an accumulation of heat? Maybe the text field for the heat transfer coefficient is set to "resistance" instead of "coefficient"? Maybe the inclination of the component is wrong, so that the calculation is done for a flat roof instead of a wall?

With kind regards,
Thomas

[Kevin Taurines]

Dear Thomas,

Many thanks for your quick reply.

We checked again our model, and everything looks right. Just to be sure the problem does not come from our own weather file, we used instead one available from the map (We chose Bordeaux, France). And we still obtain temperature above 50°C in winter (less in summer since our wall is vertical and oriented south), which seems quite unrealistic.
We also tried to run one of the example files (C:\Program Files (x86)\WUFI\WUFI5\Projects\ Example_Japan.w5p) modifying only the orientation of the wall (we set south instead of north). This model also yields surface temperature around 50°C as can be seen below.

img.jpg (95.6 KiB) Viewed 5166 times

I would like to understand whether the term (Cv*T_surf+Lv)* Phi_m_vap is neglected or simply not written in the boundary equations in the WUFI help ? Indeed, as far as I can see, nothing in the WUFI help neither in the related technical document https://wufi.de/de/wp-content/uploads/s ... sport1.pdf clearly indicate it. However, the models developed in the following papers or thesis considered it (both within the material and at the boundary) :

• Conservative modelling of the moisture and heat transfer in building components under atmospheric excitation (Janssen et al, 2007)
• A new mathematical method to solve highly coupled equations of heat and mass transfer in porous media (Mendes et al, 2002)
• Simon Rouchier. Hygorthermal performance assessment of damaged building materials. Architecture, space management. Université Claude Bernard - Lyon I, 2012
• Prediction of moisture transfer in building constructions (Carsten Rode Pedersen, 1992)

Best regards,

Kevin

[Thomas]

Dear Kevin,

to convince yourself that WUFI does take evaporative cooling into account, please have a look at the attached WUFI project "Evaporative_Cooling.w6p" (needs to be unzipped first).

It contains a specimen of Baumberger sandstone (chosen arbitrarily); the heat transfer coefficients on both sides are set to 0 W/(m²K). This suppresses all heat flows across the surfaces, but still allows vapour flows across the surfaces. At the beginning of the calculation the specimen has a temperature of 30 °C and a water content of 20 kg/m³. The ambient relative humidity is 0 % on both sides, so the initial moisture is slowly drying out. The drying occurs everywhere in the specimen, therefore evaporative cooling occurs everywhere. The temperature in the specimen starts to drop while the ambient temperature stays constant, but since inflow of ambient heat is suppressed the temperature in the specimen continues to drop.

If you run the "calculation with film" you can watch the temperature dropping continuously. If you look at the surface temperatures (via the Quick Graphs) you see the surface temperatures dropping, too. So evaporative cooling is taken into account, and it also occurs at the surfaces.

I would like to understand whether the term (Cv*T_surf+Lv)* Phi_m_vap is neglected or simply not written in the boundary equations in the WUFI help ?

The specific term in the form you quote is not included in WUFI. It does not need to be included because WUFI takes evaporative cooling into account wherever water evaporates in the component, not only at the surface. That term describes the latent heat transported across the surface, but in WUFI the latent heat balance is taken into account in every numerical grid cell and including that term would count the latent heat twice.

We also tried to run one of the example files (C:\Program Files (x86)\WUFI\WUFI5\Projects\ Example_Japan.w5p) modifying only the orientation of the wall (we set south instead of north). This model also yields surface temperature around 50°C as can be seen below.

Yes, but the surface of the Japanese component has a solar absorptivity of 0.8 - almost black. With the solar radiation often reaching substantial intensities between 500 and 750 W/m², relatively high short-lived peak temperatures don't necessarily seem implausible to me. If you reduce the absorptivity to 0.4 (a "broken white", more representative for typical facade absorptivities), the temperatures only occasionally exceed 40 °C.

Kind regards,
Thomas