Software / WUFI / Application / Q&A
Unfortunately, finding material data for hygric simulations can prove difficult since there are no standard collections of such data as yet. While thermal data can be found in many books, hygric data are sparse and hard to come by.
A collection of design values for heat conductivity (including the effect of practical moisture content) and diffusion resistance factors is listed in German standard DIN 4108-4 and numerous textbooks on building physics. The new DIN EN 12524 lists thermal as well as basic hygric design values for building materials.
An extensive list of "NIST Heat Transmission Properties of Insulating and Building Materials" is available on-line at http://srdata.nist.gov/insulation/.
Moisture storage functions and liquid transport coefficients may be estimated from the standard parameters wf, w80 and the A-value which may also be found in some textbooks (at least for selected materials) and data sheets or can be measured relatively easily.
Occasionally, some data may be found scattered through the specialised literature, but there is no systematic way to retrieve them.
Sometimes the manufacturer may be able to provide material data. Some laboratories (including IBP) can measure the required data if samples are provided.
Hourly climate data which include rain are even harder to find than material data.
IBP offers one year of hourly weather data with WUFI (the file can also be
downloaded from
the IBP website). These data from 1991 are considered fairly representative for the climate
of the Holzkirchen region.
IBP will also provide data for one 'cold' and one 'warm' year from the Holzkirchen region
which can be used with WUFI.
In addition, weather data for three Swiss cities (Zurich, Davos, Locarno; one warm and one
cold year each) and, in the English version, for 53 North American cities are provided with
the professional versions of WUFI.
Another source of hourly weather data are the Test Reference Years of the Deutscher
Wetterdienst DWD. They even cover all 12 climate regions of the former West Germany. They
are not cheap, however, and since they were primarily intended for heating and energy
consumption investigations, the simulated rain in these files is not as realistic as would
be desirable for hygric simulations involving driving rain.
The newly developed TRYs from the DWD do cover all of Germany but don't contain any rain
data.
If the situation of a specific object is to be investigated, it may be necessary to measure the weather in-situ anyway.
No. In order to correctly evaluate the amount of radiation incident on a surface with
specific orientation and inclination, WUFI must reconstruct the altitude and azimuth of
the sun at the moment of the measurement, so it needs the coordinates of the place where
the measurement was performed. If other coordinates are entered, the computed solar
positions in the sky will not be consistent with the measured data and the conversion
will simply give erroneos results.
See question 24 for details.
WUFI usually gives the water content as "water density", i.e. how many kg of water are in
one m³ of building material.
A result given in volume percent tells you how many m³ of water are in one m³ of building
material (expressed as percentage).
A result given in mass percent tells you how many kg of water are in one kg of dry building
material (expressed as percentage). Please note that the water content in mass percent may
easily exceed 100% if the dry material has low density.
| With | |||
| m_W | : | mass of the water in the component | |
| r_W | : | density of water (= 1000 kg/m³) | |
| V_W | : | volume of the water in the component | |
| m_C | : | mass of the component | |
| r_C | : | density of the (dry) component | |
| V_C | : | volume of the component | |
| we have | |||
| water content as expressed by WUFI: | |||
| u | = | m_W / V_C [kg/m³] | |
| water content expressed in volume percent: | |||
| u_v | = | V_W / V_C * 100 | |
| = | (m_W / r_W) / V_C * 100 | ||
| = | (m_W / V_C) / r_W * 100 | ||
| = | u * 100 / r_W | ||
| = | u * 100 / 1000 | ||
| = | u / 10 | ||
| water content expressed in mass percent: | |||
| u_m | = | m_W / m_C * 100 | |
| = | m_W / (r_C * V_C ) * 100 | ||
| = | (m_W / V_C) * (100 / r_C) | ||
| = | u * (100 / r_C) | ||
| = | u / (r_C / 100) | ||
So you get the water content in volume percent if you divide the WUFI result [kg/m³] by 10.
You get the water content in mass percent if you divide the WUFI result by (density of the
building component / 100).
In air the relative humidity is the ratio of the actual water vapor partial pressure p and the water vapor saturation pressure ps. Example: If the air temperature is 20°C (and therefore ps = 2340 Pa) and the actual vapor pressure is 1872 Pa, then the relative humidity is 1872 Pa / 2340 Pa = 0.8 = 80%.
The condition in a porous building material corresponds to a RH of x % if it has been
exposed to air with a RH of x % until equilibrium was reached and no moisture was taken
up or given off any more.
The moisture in the material is then in equilibrium with the RH of the air in the pore
spaces.
At RHs less than ca. 50% this means that a molecular layer with a thickness of one or a
few molecules has been adsorbed at the surfaces of the pores; at higher RHs capillary
condensation occurs.
Here is what happens in detail: the usual formulas for the saturation vapor pressure (such as in German standard DIN 4108) are only valid for plane water surfaces. At concavely curved surfaces, where the water molecules are bound stronger, the saturation vapor pressure is reduced; the more so the stronger the curvature of the surface is.
In a partly filled capillary the interface surface between air and water forms a curved meniscus whose curvature is determined by the surface energies involved and in particular by the radius of the capillary. If the air space in such a capillary is filled with air whose partial water vapor pressure is greater than the saturation vapor pressure at the meniscus (whereas the RH in the air is still less than 100%), then the air in the immediate neighborhood of the meniscus is supersaturated and water condenses from the air onto the meniscus, i.e. the capillary fills up.
In a porous material there exists a wide range of pore sizes. In the smallest pores, any menisci may be curved so strongly that in these pores moisture condenses onto the menisci from 50% RH in the pore air upwards. The smallest pores get filled with water, and subsequently larger and larger pores (with smaller curvatures of the menisci) get filled until a pore size is reached where – because of the larger pore size and the smaller curvature of the meniscus – the saturation vapor pressure at the meniscus is equal to the vapor pressure in the pore air. In this way capillary condensation results in an equilibrium between the moisture content and the relative humidity in the pore air, even if this RH is less than 100%. The amount of water needed to fill the pores up to this point depends on the pore structure and the pore size distribution.
The moisture storage function describes the amount of moisture taken up in this manner by the building material if it is exposed to air with a specific RH. Since this relationship between RH and moisture content is largely temperature-independent, the RH is an important and unique parameter describing the moisture content of a material.
WUFI needs a well-defined moisture field for each time step, so it must assign a moisture content even to materials which nominally don't have any appreciable moisture content (e.g. water-repellent mineral wool, air layers etc.).
| The default moisture storage function used by WUFI is described by the function | |||
| w | = | a / (b – phi) + c | |
| w | : | water content [kg/m³] | |
| phi | : | relative humidity [-] | |
| Since phi must be 0 for w = 0, it follows immediately that | |||
| c | = | -a/b | |
| The constants a and b are determined as follows: | |||
| b is set to 1.0105. | |||
| The moisture content at free saturation, wf, corresponds to a relative humidity of 1 (=100%). Since WUFI also needs a unique relationship between moisture content and RH for moisture contents above free saturation, this oversaturation region is assigned RHs greater than 1, up to phimax = 1.01. This value phimax is reached when the moisture content reaches maximum saturation wmax which is determined by the porosity: | |||
| wmax | = | porosity * 1000 kg/m³ | |
| Therefore we have | |||
| wmax | = | a / (b-phimax) – a/b. | |
| Solving for a yields: | |||
| a | = | wmax * b * (b – phimax) / phimax, | |
| and thus: | |||
| w / wmax | = | phi / (b – phi) * (b – phimax) / phimax. | |
| In particular, for phi = 1 we have | |||
| wf / wmax | = | 1 / (b – 1) * (b – phimax) / phimax = 0.047. | |
| So this pseudo material has a free saturation of wf = 0.047 wmax. | |||
WUFI was developed to simulate the hygrothermal processes in porous building materials. The detailed simulation of heat and moisture transport in air layers (including convection, turbulence etc.) is much more complicated and is outside WUFI's scope. Furthermore, it does not make much sense to try and implement these inherently two- or three-dimensional processes in a one-dimensional simulation program.
Air layers can therefore only approximately be simulated by treating them as a 'porous' material. It is possible to allow for the amplifying effect of convection on heat and moisture transport by employing appropriate effective heat conductivities and vapor diffusion resistance factors.
However, the moisture storage function of an air layer can only very crudely be
approximated by the moisture storage function of a porous material. The latter is largely
temperature-independent (and implemented as such in WUFI), so that the functional
dependence of the moisture content in air on the relative humidity and temperature
cannot be reproduced.
Furthermore, the default moisture storage function used by WUFI for materials for which
the user has not defined one assumes that capillary condensation will occur in the material
already at relative humidities less than 100%, which is not true for an air layer (it has
been modeled after the moisture contents of dense mineral wool).
As a result you will get unrealistically large moisture contents for air layers. Note,
however, that WUFI uses the relative humidity as the driving potential for moisture
transport and computes the water content as a secondary quantity from the resulting
relative humidity (using the moisture storage function of the respective material).
So the resulting distribution of relative humidity should in general be quite realistic,
its temporal behavior will just be damped much more than in reality (the moisture content
acts as a 'capacity term' for moisture transport in the same way the heat capacity acts
as a capacity term for heat transport). If short-term fluctuations don't play a major role,
the general trend in the behavior of the relative humidity should be tolerably realistic.
This also means that quantities that depend on the relative humidity in or near the air
layer (e.g. mould growth rates) can be evaluated more realistically than quantities that
primarily depend on the moisture content (e.g. heat conductivity, heat capacity).
Please note that the unrealistically large moisture capacity of an air layer may also affect other layers. If you are interested in the moisture distribution in an assembly that contains an air layer, the air may (or may not) take up more moisture than realistic, so that less moisture remains for distribution among the other layers.
You may mitigate these problems by explicitly defining a slightly more realistic moisture storage function for the air layer. To this end, use a linear function like
| phi: | w: | |
| 0 | 0 | |
| 1 | wf |
with a low value for wf (the numerics may not be able to cope with very low values, you'll need to experiment a bit) (*). This avoids the spurious capillary condensation.
Also see the next question for a related problem.
(*) Note, however, that the porosity and thus wmax should remain high. If the water content exceeds wf, WUFI reduces the vapor permeability, in proportion to the excess, to reflect the fact that the pore volume gets increasingly filled with water and thus vapor transport decreases. At w=wmax the permeability reaches zero (all pores are filled). For vapor-permeable materials like air layers or mineral wool where moisture transport occurs mainly via vapor transport, wmax should therefore remain at a realistic value.
One situation where serious convergence failures tend to occur is a component with a vapor-permeable layer (e.g. air or mineral wool) which has accumulated a lot of moisture (RH ~ 100%) and which is now exposed to a high temperature gradient (e.g. caused by intense solar radiation). WUFI originally wasn't developed to treat these cases which sometimes prove too demanding for the numerics that are mainly tuned to massive porous materials.
If everything else fails, you may try an alternative moisture storage function. In the material database, the moisture storage functions for materials like air or mineral wool are left undefined, so that WUFI uses an internally defined default moisture storage function (see the preceding two questions).
This moisture storage function assumes that for RHs above ca. 50% capillary condensation
occurs which leads to increasingly higher moisture contents until free saturation is
reached at 100% RH. This is not really realistic for air layers or hydrophobic mineral
wool (it may be more appropriate for non-hydrophobic mineral wool).
Since it seems that the problem is mainly caused by the high water content, reduction
of the water content by choosing a different moisture storage function often remedies
the problem.
Please note that the relative humidity in the material will remain largely unaffected
by the specific choice of the m.st.f., as explained above. So if you are interested in
the relative humidity in the layer, your results will be affected only slightly (but
please perform a few test calculations with different choices of the m.st.f. to be sure),
and if you are interested in the moisture content, you should not rely on the default
m.st.f. anyway, but use measured data instead which represent your particular material.
A possible choice for the moisture storage function in these cases is a table like this:
| phi: | w: | |
| 0 | 0 | |
| 1 | wf |
Use a low value for wf (the numerics may not be able to cope with very low values, you'll
need to experiment a bit.) (*).
This linear function is even more realistic than the default function in that it avoids the capillary condensation for RH= 50..100%. The moisture content remains low up to RH=100% (as it should be in air or in hydrophobic insulation materials), and at or above 100% condensation may occur and increase the moisture content beyond wf and up to wmax.
In particular if you are interested in moisture accumulation by condensation in these materials, use such a linear moisture storage function with low wf. Then you know that any moisture content exceeding wf must have been caused by condensation. You can then analyse this excess over wf (test calculations show that this excess is only slightly dependent on the specific choice of wf).
(*) Note, however, that the porosity and thus wmax should remain high. If the water content exceeds wf, WUFI reduces the vapor permeability, in proportion to the excess, to reflect the fact that the pore volume gets increasingly filled with water and thus vapor transport decreases. At w=wmax the permeability reaches zero (all pores are filled). For vapor-permeable materials like air layers or mineral wool where moisture transport occurs mainly via vapor transport, wmax should therefore remain at a realistic value.
WUFI's output includes the temporal behavior of
In order to get the moisture content at a monitoring position, you can either
There are no measurements of transport coefficients or, equivalently, water absorption coefficients for paint layers themselves known to us.
What is measured sometimes is the water uptake for different paint layers by applying the paint on a standard substrate (such as cellular concrete or lime cement mortar) and measuring the water absorption for this composite material.
So the best thing you can do is probably the following:
Don't use a layer of rendering and a layer of paint; instead, use a layer of the 'hybrid'
material for which you already know the combined water uptake from the measurements. Use
the Dws from the hybrid water uptake (let it generate by WUFI from the measured water
absorption coefficient) and use the Dww and other data from the original rendering.
The vapor diffusion resistance of the paint can then be included in the surface transfer coefficients (as long as it is not markedly moisture-dependent).
Please note some possible problems, though:
This should not happen, but the rain absorption factor is very likely not to blame. It does not depend on the material of the wall (it depends a bit on its surface structure and, of course, on its tilt). After all, it simply expresses the fact that some of the rain water splashes off when it hits the wall surface and is no longer available for absorption.
Are you sure that the amount of rain is okay? Maybe you created your own *.KLI file and
used normal rain instead of the correct driving rain?
Several kinds of sandstone have a very high water absorption (e.g. Rüthener) and may
accumulate an inacceptable amount of moisture when exposed to a wet climate such as the
Holzkirchen weather. Maybe you used one of those?
The difference between fibres and porous mineral materials is in general not really crucial for the transport equations. The fibre materials may tend to have preferred transport directions, but these cannot be modeled in a one-dimensional calculation anyway.
Determining the liquid transport coefficients, however, may be difficult or even impossible if they change their consistency upon wetting (e.g. by caking).
On the other hand:
As long as your insulation materials don't become so wet that capillary conduction becomes predominant, you can ignore capillary transport and only consider diffusion transport. That is, you leave the liquid transport coefficients undefined and only enter a µ-value. Surface diffusion phenomena may be allowed for by using a moisture-dependent µ-value.
Since you probably only want to assess whether or not the insulation becomes wet by
rain or condensation, you will mainly be concerned with water contents in the sorption
moisture region of the moisture storage function, for which these simplifications should
be adequate.
As these materials must be prevented from becoming wetted through anyway, there will be
no need to investigate in detail the behavior of an insulation soaked full of water.
That depends on a number of individual circumstances such as the amount of production moisture (e.g. in cellular concrete or lime silica bricks), the amount of mixing water (in concrete or mortar), the amount of rain hitting the wall while it was unrendered, the season when construction took place (warm / cold) etc., so no general answer is possible here. The table gives examples for typical initial moisture contents:
| |||||||||||||||||||||||||||||||||||||||||||||||||||||||||
The rain water absorption factor must be set to zero if the water absorption is indeed completely stopped by the treatment. If water absorption is only reduced, you must determine the water absorption coefficient for the treated material and replace the part of the wall which corresponds to the penetration depth of the treatment with a layer of the treated material.
If the treatment does not change the diffusion permeability of the material, no sd-value
needs to be specified for the exterior surface.
Many treatments do, however, increase the diffusion resistance factor (µ-value) of the
material. In these cases, this additional resistance should be allowed for by an
appropriate sd-value. Alternatively, and even better, you can replace the part of the wall
which corresponds to the penetration depth of the treatment with a new layer that has the
same material properties but an appropriately increased µ-value.
Even if the water absorption is negligible (so that adjusting the rain absorption factor
instead of the liquid transport coefficients would be sufficient) and vapor diffusion is
not hindered by the treatment (so that no µ-value needs to be adjusted), it might
nevertheless be preferable to model the treated part of the wall by defining a separate
layer whose liquid transport coefficients have been reduced or even set to zero.
This is because the capillary conduction in this layer does not only determine the amount
of absorbed rain water; it also influences the wall's drying behavior.
Drying-out proceeds faster if water from the interior of the wall can be conducted to the
surface by capillary transport and can evaporate from there. Drying-out is impeded,
however, if capillary transport stops a few centimeters behind the surface and moisture
can only dry out after crossing this treated layer by vapor diffusion. So this is another
mechanism by which water-repellent treatment may reduce the drying potential of a wall,
in addition to a possibly increased µ-value.
You can check the estimated Dws or determine an unknown water absorption coefficient from known Dws by simulating a water absorption experiment.
Define an initially dry layer consisting of the material in question, let it rain on the surface (with a higher rain load than the layer can absorb to be sure that no insufficient rain load is limiting the water uptake) and look at the amount of water absorbed after e.g. 100 or 200 hours.
This may be done with a one-line *.KLI-file such as:
| [h: | rain: | rad: | t_ext: | RH_ext: | t_int: | RH_int:] |
| 500 | 1000 | 0 | 20 | 1 | 20 | 0 |
The number of hours entered for the duration of this one-line climate file does not matter since WUFI re-starts reading from the beginning of the climate file if the simulation period extends beyond the end of the climate file.
Set the vapor diffusion thickness of the interior surface to a very high value to prevent vapor transport through that surface.
You should perform a few test calculations in order to find a suitable thickness of the test specimen which assures that the moisture front traverses most of the specimen (in order to make the most efficient use of the numerical grid) but not all of it.
The reason why WUFI does not accept your spreadsheet file is probably that you did not write it in ASCII format and/or did not write the header lines in the correct format. Please consult the on-line help for details on creating *.KLI files with your own programs.
Also note that if you want to simulate a simple absorption experiment with a specified constant water supply and constant climate conditions it is sufficient to create a *.KLI file which consists of only one single line, for example the line:
| [h: | rain: | rad: | t_ext: | RH_ext: | t_int: | RH_int:] |
| 1000 | 5 | 0 | 20 | 1 | 20 | 0.8 |
means that for 1000 hours after the starting time of the climate file there is a constant rain load of 5 Ltr/m²h.
An alternative would be a single line like
| [h: | rain: | rad: | t_ext: | RH_ext: | t_int: | RH_int:] |
| 1 | 5 | 0 | 20 | 1 | 20 | 0.8 |
which states that for 1 hour after the starting time of the climate file there is a
constant rain load of 5 Ltr/m²h. When WUFI reaches the end of a climate file, it starts
reading the file anew from the beginning, so you can simulate an experiment which is
running for 100 hours (or whatever) and the climate file will automatically be read 100
times over.
The only difference between these two files is that in the latter case WUFI does not
accept a calculation time step greater than 1 hour, whereas in the former case you may
also choose any convenient time step greater than one hour.
For a simple absorption experiment I usually make sure the climate file contains a rain
load large enough so that it does not limit the absorption of the specimen, for example 100
Ltr/m²h, which would not be plausible for real rain.
If you want to have a specified limited supply please don't forget that WUFI reduces the
amount of rain it reads from the climate file by the rain absorption factor which allows
for the fact that some rain splashes off of the wall on impact and is not available for
absorption. This factor should be set to 1 during your experiments.
Furthermore, please note a small subtlety involved in using limited rain supply. Let's
assume you have a specimen with a water absorption factor of 3 kg/m² h^0.5 and the climate
file specifies a rain load of 3 Ltr/m²h. During each time step, WUFI performs a test step
with an unlimited supply and subsequently evaluates the amount of water taken up. If this
amount of water is less than the amount supplied in the climate file, then the material is
the limiting factor and WUFI accepts the result of this time step and proceeds with the
calculation.
However, if the amount taken up is more than the amount supplied, WUFI performs additional
iteration steps in which a fictitious 'flow resistance' at the specimen surface is
adjusted until the amount taken up matches the amount supplied.
If you are using 1-hour steps in your calculation, and the dry specimen absorbs 3 kg/m² of
water in the first step and the climate file supplies 3 kg/m²h, then WUFI accepts the trial
step done with unhindered absorption and proceeds with the calculation.
But if you are repeating the same calculation with a time step of half an hour, things are
different! Since the water uptake is not linear in time, the specimen will absorb more than
1.5 kg/m² in the first half hour, while WUFI compares this with 1.5 kg/m² of rain in the
first half hour (assuming the rain is evenly distributed over the hour) and now limits the
amount absorbed to 1.5 kg/m².
This is usually of no concern with real rain data and real building materials, but it may
be beneficial to be aware of these subtleties if performing test calculations with limited
rain supply.
The usual building materials always have some moisture sorption capacity. This sorption capacity buffers changes in relative humidity inside the wall. If you define boundary conditions which would provoke instant condensation in a Glaser calculation, you may nevertheless not get condensation in a realistic case (such as simulated by WUFI).
That's because a relative humidity of 100% would correspond to a moisture content equal to free saturation of the material in question, and this amount of water must first be transported into the dew region. The diffusion flows do transport moisture to the location where dew conditions prevail, but the transported amounts of moisture are generally small, and the RH will only slowly rise from the initial value, say 80%, to 81%, 82% etc. It may take days or weeks until sufficient amounts of water have been transported to the dew region so that finally free saturation (i.e. RH=100%) is reached. Meanwhile, boundary conditions may have changed and there are no dew conditions any more.
The Glaser method, on the other hand, simply assumes that 100% RH are reached instantly, it doesn't consider the necessity to actually move water in order to reach the moisture content that corresponds to 100% RH.
Furthermore, real materials (as opposed to Glaser) usually have some capillary conductivity which tries to dispel any moisture accumulations. This effect actively works against local water build-up, so that 100% RH can't be reached easily.
Of course, you may get water accumulation in your building component if conditions are right (or wrong). But this will rarely be accompanied by 100% RH. If you see relative humidity approaching 100% somewhere in your component, it's probably much too late...
The surface of a normal wall in temperate or cool climate regions will always be somewhat
warmer than the surrounding air. By day because of solar radiation (even on foggy or
overcast days), by night because of heat flow from indoors (exceptions: air-conditioned
dwellings or nightly emission, see below).
Since the RH in the air can't be greater than 100% and the RH at the warmer-than-air wall
surface will always be less than the RH of the air, you usually can't reach or surpass
100% there.
You'll have free saturation (i.e. 100% RH) at the surface when enough rain is absorbed, but this is not due to dew conditions.
The surface temperature will fall below air temperature when the wall emits more long-wave radiation than it gets back from surrounding surfaces. If it even falls below the dew-point temperature, you will indeed get dew conditions at the surface. This happens routinely during the night, especially during clear nights, when the long-wave emission of the water vapor in the atmosphere is at a minimum.
In these cases you may get repeated and regular wetting of the surface which may lead to
dust accumulation or algae growth, especially with exterior insulations whose surfaces
cool down particularly strongly.
Currently, WUFI does not routinely allow for this effect, since the necessary data on
atmospheric and terrestrial counterradiation are rarely available. If these data are
provided, WUFI can compute nightly emission cooling in principle, but only approximately.
Future WUFI versions will have a more sophisticated emission model incorporated.
There are no general criteria which are applicable for every case. Different materials and different applications require different criteria. Here are some general hints:
German standard DIN 4108-3 adds the following criteria:
In addition, special criteria may be applicable in specific cases, for example:
Even if you don't have clear criteria which fit your case, you may still perform a ranking of your assemblies by comparing them with each other or with a standard case.
If you model the ventilation gap as an air layer in WUFI, it is indeed treated as a closed air layer without connection to the exterior air. The effect of inner convection on heat and moisture transport across the air layer is allowed for (as a first approximation) by use of effective heat conductivities and vapor diffusion resistance factors.
The air flow and air exchange phenomena in a ventilated air layer cannot be simulated
with a one-dimensional program.
If the air exchange is large enough, it may be justified to assume exterior air conditions
in the air gap. That is, you do not model the curtain facade and the air gap, and you
consider the surface of the insulation or the wall itself (as the case may be) as the
exterior surface in WUFI's component assembly. Rain must be set to zero (simply by setting
the rain absorption factor = 0).
It will be advisable to choose appropriate effective values for the exterior heat transfer
resistance and the short-wave solar absorptivity, but this requires calibration by
experimental data.
The same problem is encountered in simulations of roofs, either because of a ventilation cavity in the roof or because of the question how to model the covering and the batten space.
The investigations described in [1] used a simplified treatment of a roof. WUFI simulations were carried out to examine the moisture balance in a fully insulated west-facing pitched roof (50° inclination). The covering and the batten space could be omitted from the simulated assembly because measured temperatures in a similar roof on IBP's testing area were available and could be used to determine appropriate effective surface transfer coefficients. The measurements were taken on the waterproofing foil (i.e. directly on the insulation layer) and were compared with the computed temperatures at the outer surface of the modeled insulation layer which sufficed to represent the whole roof for the purpose of a thermal adjustment.
The thermal surface transfer coefficients were adjusted in WUFI until good agreement between measurement and calculation was reached. This was the case with an effective short-wave absorptivity of a=0.6 and an effective heat transfer coefficient of alpha=19 W/m²K. The effective absorptivity is roughly identical with the real absorptivity (for red roof tiles), while the effective alpha is slightly higher than the usual standard value of 17 W/m²K. Obviously the covering and the air in the batten space have no major effect on the thermal behavior of the roof, at least in this case. In particular, the amount of heat removed by convection through the ventilated air cavity seems negligible and the entire heat created in the covering by solar radiation is passed on into the underlay.
The question to which extent this isolated result can be generalised could only be answered by more extensive comparisons with measurements.
[1] H.M. Künzel: Außen dampfdicht, vollgedämmt? - Die rechnerische Simulation gibt Hinweise zu dem Feuchteverhalten außen dampfdichter Steildächer. bauen mit holz 8/98, S. 36-41.
The solar radiation incident on the exterior surface is electromagnetic radiation and
not heat flow; it is therefore not included in the heat flow data.
However, after absorption it is converted to heat so that there exists indeed a heat
source in the wall. Since the heat source is close to the exterior surface, most of the
generated heat flows outward through the exterior surface, only a small amount flows
inward through the interior surface. This asymmetric heat flow is superimposed on the
usual transmission heat flow (which in colder climates alway goes from the indoor side
to the outdoor side of the building element).
Please note that in the film display the heat flow arrow at the exterior surface does include the solar radiation. Otherwise it would look very strange to see the sun shining on the wall surface but a lot of heat flowing out of the wall. This is a concession to the intuitive expectations of the audience.
Also note that there can be a heat source or sink in the wall when water condenses or evaporates. In some cases these latent heat effects can be non-negligible (e.g. drying of a wall wetted by driving rain).
'Recent' weather data would probably not be very useful to you. It is more important to have weather data which are either known to be typical for a specific location or which repesent defined critical conditions (e.g. for design purposes). We consider 1991 to be a fairly typical year for Holzkirchen. 'Critical' weather data, i.e. one particularly cold year and one particularly warm year, are in preparation and will be made available as two 'Hygrothermal Reference Years'.
It is obvious that at element boundaries where materials with possibly very different conductivities are in contact with each other a simple average of the conductivities (or resistances) cannot result in a realistic effective conductivity to describe the fluxes between the elements. Take as an example a material with very low resistance which borders on a material with very high resistance. The flux flowing between the midpoints of the two elements is determined by the sum of the two successively encountered resistances, not by the arithmetical average of the conductivities.
One might suppose now that this physically motivated reasoning also applies to smaller differences between the neighboring elements and that therefore the resistance formulation (i.e. the harmonic mean of the conductivities) should always be used within the entire component. However, test calculations during the development of WUFI's numerics showed that this is not the case. Within a material the arithmetical mean of the conductivities yielded better results (compared with experimental data), so that WUFI uses harmonic averages at material boundaries and arithmetical averages within a material, in agreement with the cited investigation. The derivation of the resistance formulation assumes equal fluxes in the two element halves, but this need not be the case if transient processes in materials with heat or moisture storage capacities are considered.
[1] Galbraith, G.H. et al.: Evaluation of Discretized Transport Properties for Numerical Modelling of Heat and Moisture Transfer in Building Structures, Journal of Thermal Env. & Bldg. Sci., Vol. 24, Jan. 2001
First you need to determine the radiation incident on the surface of your building element from the measured data describing the radiation on a horizontal surface. For this purpose it is necessary to determine the position of the sun in the sky at the time of the measurement.
Position of the Sun:
Let J be the number of the day in the year (1 .. 365 or 366). Then compute the auxiliary quantity x:
x = 0.9856° * J - 2.72°
and the equation of time Z (in minutes):
Z = -7.66*sin(x) - 9.87*sin( 2*x + 24.99° + 3.83°*sin(x) ) [min].
The equation of time describes the variable difference in time between the actual culmination of the sun and noon. Because of the ellipticity of the Earth's orbit and the obliquity of the Earth's axis the sun wanders with slightly irregular speed across the sky. During the course of the year there are thus times where it reaches culmination earlier than a fictitious sun with constant speed (the so-called 'mean' sun) and times where it reaches culmination later.
The local meridian is the great circle that rises from the horizon due north, passes through the point directly above the observer and crosses the horizon again due south. The instant at which the sun crosses the local meridian on its daily path from east to west is also the instant where its position is due south and where it reaches its daily greatest height.
When the apparent sun (i.e. the actually observed sun) crosses the meridian it is 12 noon local apparent solar time (LAT); when the mean sun crosses the meridian it is 12 noon local mean time (LMT). The equation of time is therefore the difference between LAT and LMT (Z = LAT - LMT).
Furthermore, since the place where the measurements were taken is usually not located on the reference meridian of the time zone (15° East for the Central European Time Zone, CET), the difference between local mean time and zone time must be allowed for, which is 4 minutes for 1° difference in geographical longitude L and one hour for 15° difference. If the measurement was timed in Central European Summer Time CEST, convert to CET first by subtracting one hour (CET = CEST - 1h).
In this way you can now compute the corresponding local apparent time LAT from the known measurement time (in CET):
LAT = CET - (15°-L)/(15°/h) + Z/(60 min/h) [h]
and thus determine the position of the sun: at 12 noon LAT the sun is exactly on the meridian, before noon it stands at an appropriate distance to the east of the meridian, after noon, an appropriate distance to the west.
The distance between the sun and the meridian is measured by the hour angle omega:
omega = (LAT - 12h) * 15°/h.
The hour angle omega is reckoned perpendicular to the meridian; it is negative before noon, zero at noon and positive after noon; it increases steadily by 15° per hour.
The hour angle gives the distance of the sun from the meridian; the declination delta, i.e. the distance of the sun from the celestial equator, then fixes the position of the sun completely. The declination varies between -23°26' at winter solstice, 0° at the equinoxes, and 23°26' at the summer solstice. Since its change during one day is very small, it suffices to compute it once for the day J under consideration:
sin(delta) = 0.3978 * sin( x - 77.51° + 1.92° * sin(x) ),
cos(delta) = sqrt(1 - sin(delta)^2)
where x is the auxiliary quantity introduced above.
The last step is the transformation from the coordinate system determined by omega and delta into the more familiar coordinates altitude gamma and azimuth psi (=compass direction). The geographical latitude phi of the measurement location is needed for this.
sin(gamma) = cos(delta)*cos(omega)*cos(phi)+sin(delta)*sin(phi)
cos(gamma) = sqrt(1 - sin(gamma)^2)
if cos(gamma)=0 then psi = 0
else begin
sin(psi) = cos(delta)*sin(omega)/cos(gamma)
cos(psi) = (cos(delta)*cos(omega)*sin(phi)-sin(delta)*cos(phi))/cos(gamma)
psi = atn2(sin(psi), cos(psi))
end
This formula uses atn2(A,B), the arctangent function for two arguments A and B, which is provided by many programming languages, and which gives the arctangent of A/B in the correct quadrant. If this function is not available to you, you can use the ordinary arctangent and then explicitly determine the correct quadrant (i.e. you compute psi=atn(A/B), and in the case B<0 you add 180° if psi<0 or subtract 180° if psi>0. If B=0 and A<0 then psi=-90°, if B=0 and A>0 then psi=+90°).
The azimuth psi is counted from south=0°, positive towards the west and negative towards the east.
Examples for Munich (48.13°N, 11.58°E):
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These values were computed with an astronomical ephemeris program. Of course, the simplified method described above cannot reproduce these data exactly, in particular for low altitudes of the sun (1 Jan. 16:25), since it does not allow for atmospheric refraction. On the other hand, the comparison allows you to assess the overall accuracy of this simple method. Your results should agree with these exact positions within a few tenths of a degree. The declinations have been included as well for testing purposes.
Converting the Radiation Data:
We assume that your input data are measured hourly values of the global (I_glob) and the diffuse radiation (I_diff) on a horizontal surface.
The radiation incident on the measuring or the component surface is split up into a direct and a diffuse component. The direct component is received directly from the sun and is therefore a directed quantity that depends on the position of the sun. The direct radiation vertically incident on a surface which is facing the sun is the direct normal radiation I_dir_normal. The direct radiation I_dir obliquely incident on a horizontal measuring surface depends on the solar altitude gamma:
I_dir = I_dir_normal * sin(gamma).
Since I_dir can be computed as the difference between the measured values of global and diffuse radiation and gamma can be determined from the measurement location and time by the method given above, the corresponding direct normal radiation is
I_dir_normal = (I_glob - I_diff) / sin(gamma).
The angle of incidence eta, i.e. the angle that the direct normal radiation makes with the normal to the component surface which is tilted by the angle beta and oriented in the direction alpha, is
cos(eta) = sin(gamma)*cos(beta) + cos(gamma)*sin(beta)*cos(alpha-psi)
| eta: | Angle of incidence (vertical=0°) |
| gamma: | Altitude of the sun |
| psi: | Azimuth of the sun (south=0°, positive towards west, negative towards east) |
| beta: | Tilt of the component surface (vertical wall=90°) |
| alpha: | Azimuth of the normal to the component surface (south=0°, west positive). |
The direct radiation incident on the component surface is therefore:
I_dir_in = I_dir_normal * cos(eta) = (I_glob - I_diffus) * cos(eta) / sin(gmma).
The diffuse component consists of the radiation scattered by the air ("blue sky") and the clouds which comes from all directions and can approximately be treated as isotropic. Diffuse radiation is measured by blocking the direct radiation with a shadow ring around the solarimeter. The measurement gives I_diff, the diffuse radiation incident on the horizontal measuring surface from the entire sky hemisphere. A component surface with arbitrary tilt and orientation receives the same diffuse radiation (since it is isotropic), but for non-horizontal surfaces the fact has to be allowed for that the sky covers a smaller part of its field of view and the total amount of incident diffuse radiation is reduced proportionately (a vertical wall sees sky only in the upper half of its field of view):
I_diff_in = I_diff * ( cos(beta/2) )^2.
Additionally, you may add the global radiation reflected from the ground:
I_refl_in = rho * I_glob * ( sin(beta/2) )^2,
where rho is the short-wave albedo of the ground and the reflection is assumed to be isotropic. In the current version, WUFI ignores the reflected component of the radiation.
The total radiation incident on the surface of the building component is the sum of the components:
I_in = I_dir_in + I_diff_in + I_refl_in.
You may now modify or supplement this conversion method according to your needs. For example, you can allow for shadows by setting the direct radiation to zero at times where the sun is behind the obstacle, and by reducing at all times the diffuse radiation in proportion to the reduction of the field of view caused by the obstacle. On the other hand, at times where the sun illuminates the facing side of the obstacle, it may be necessary to add some reflected radiation.
Hint: if the radiation data to be converted have been averaged over some longer interval (e.g. one hour), please note the following:
It is advisable to compute the solar positions for the middle of the measuring interval, i.e. the averaged data measured between 9h and 10h should be converted using the solar position computed for 9:30h.
If the sun has risen or set during such a measuring intervall (which is easy to check for, using the solar altitude), the solar position must be computed for the middle of the visibility interval, not for the middle of the measuring interval.
Independent of the duration of the measuring interval, radiation data obtained at very low solar altitudes should not be used, since under these circumstances the direct normal radiation must be calculated from very small and unreliable values obtained for the direct radiation at grazing angles of incidence.
Details on these conversion methods can be found in:
VDI 3789 Umweltmeteorologie, Blatt 2: Wechselwirkungen zwischen Atmosphäre und Oberflächen;
Berechnung der kurz- und der langwelligen Strahlung.
In addition to data on global and diffuse radiation, the weather file IBP1991.WET included with WUFI contains radiation data obtained with a west-facing solarimeter which you can use to test your conversion routines.
(25): For my investigations I need a material which is not in the material database. I can measure the material data myself. Which material properties do I need, and which measurement procedures must I use to ensure that the data are compatible with WUFI?
If a material needed for a hygrothermal simulation is not in WUFI's material database, the material properties must be taken from other sources, such as literature data, estimates, or measurements performed on a representative sample of the material. The following overview of required accuracies and possible measurement methods shall assist the user in selecting appropriate measurement procedures.
In general, any measurement method is permissible for a certain material property as long as it determines the property in the sense defined by the transport equations (refer to Dr. Kuenzel's dissertation for the transport equations and involved material properties). The standardized methods listed in the following table have the advantage that the respective standard documents contain detailed descriptions of the methods, and the required laboratory equipment may already be at hand. In addition, using properties determined according to established standards may be preferable when simulations are needed for expert assessments in legal disputes.
If the material properties are determined for general purposes (e.g. for inclusion in the material database), all the properties required for this kind of material should be determined, if possible, and the highest accuracy achievable with acceptable cost should be aimed at.
On the other hand, if a material is only needed for investigations involving a limited variety of climatic conditions and is kept at a fixed location within the wall assembly, then some material properties may only have a negligible influence on the simulation results. In such a case it may be sufficient to merely estimate the value of this property instead of measuring it. Whether this applies to a given property can be established by WUFI calculations: if varying the property (within plausible limits) leads to negligible variation of the results, a (plausible) estimate will be sufficient. For example, a gypsum board on the indoor side of a wall will usually not be exposed to liquid water, so that a rough estimate of the liquid transport coefficients should be adequate. Of course, if different climatic conditions are used which cause the same gypsum board to be exposed to condensate (for example), it may become important to allow for liquid transport in detail.
The basic material properties bulk density, porosity, dry thermal capacity, dry thermal conductivity and water vapor diffusion resistance factor must always be provided, since otherwise some part of the heat and moisture transport equations remains mathematically undefined.
The additional hygrothermal functions for a material must be defined to the extent that the respective property is present in that material (for example, liquid transport coefficients are only needed for capillary active materials) and that the property influences the result of the investigation (see the example above).
Some hygrothermal functions only provide refinements of the hygrothermal model, for example the moisture-dependence or the temperature-dependence of thermal conductivity. It must be decided by the user whether these refinements are necessary and useful for the investigations at hand.
| Material Property | Needed | Procedure |
| Bulk Density | Always | Insulation Materials: EN 1602, edition January 1997. Mortar and Plaster: EN 1015-10; edition 1999. Bricks: EN 772-4, edition 1998. And others, depending on type of building material. |
| Porosity | Always | Determination of the true density with the helium pyknometer. Bulk density see above. Porosity is then calculated from these two. |
| Specific Heat Capacity, dry | Always | Determination of specific heat capacity according to ISO 11357-4,
edition September 2005. But literature values are usually sufficient. |
| Thermal Conductivity, Dry, 10°C | Always | Thermal performance of building materials and products - Determination of thermal
resistance by means of guarded hot plate and heat flow meter methods: Dry and moist products with medium and low thermal resistance; German version EN 12664:2001 Products of high and medium thermal resistance; German version EN 12667:2001 |
| Water Vapor Diffusion Resistance Factor | Always | Determination of water vapour transmission properties according to EN ISO 12572,
edition September 2001, dry cup. |
| Moisture Storage Function | Only for hygroscopic building materials. (For non-hygroscopic building materials WUFI automatically uses an internal moisture storage function, similar to the properties of mineral fibre and depending only on the porosity.) |
Determination of hygroscopic sorption properties according to DIN EN ISO 12571,
edition April 2000, absorption test. Determination of superhygroscopic sorption properties with the pressure plate or alternatively with approximation methods from IBP. Determination of water absorption and saturation coefficient according to DIN 52103, edition April 1988. |
| Liquid Transport Coefficient, Suction | Only for capillary active building materials. | Determination of the water absorption coefficient according to EN ISO 15148,
edition March 2003. Using this value, estimation of the liquid transport coefficient for water uptake: M. Krus, A. Holm, T. Schmidt, Bauinstandsetzen 3 (1997), H.1, S. 219-234. |
| Liquid Transport Coefficient, Redistribution | Only for capillary active building materials. | Fitting WUFI calculations to measured drying curves:
Bestimmung der Transportkoeffizienten für die Weiterverteilung aus einfachen
Trocknungsversuchen und rechnerischer Anpassung: A. Holm, M. Krus, Bauinstandsetzen
4 (1998), H.1, S. 33-52. |
| Water Vapor Diffusion Resistance Factor, moisture-dependent | Only for polymers with solution diffusion. Sometimes an alternative to liquid
transport coefficients. |
Determination of water vapour transmission properties according to EN ISO 12572,
edition September 2001, dry and wet cup. |
| Thermal Conductivity, moisture-dependent | Always, except for membranes and other thin layers. | EN 12664, but supplements from DIN 4108-4 are generally sufficient. |
| Thermal Conductivity, temperature-dependent | Generally for insulating materials. Otherwise rough typical values are sufficient. |
EN 12664, 12667. |
| Enthalpy, temperature-dependent | Only for phase change materials. | Determination of temperature and enthalpy of melting and crystallization
according to ISO 11357-3, edition July 2005. |
