|
|
| (11 dazwischenliegende Versionen von 2 Benutzern werden nicht angezeigt) |
| Zeile 4: |
Zeile 4: |
| </P> | | </P> |
|
| |
|
| # [[FAQ_General:SourcesofMaterialData | <B>Sources of Material Data</B>]] | | # [[FAQ:General:SourcesofMaterialData | <B>Sources of Material Data</B>]] |
| # [[FAQ_General:SourcesofClimateData | <B>Sources of Climate Data</B>]] | | # [[FAQ:General:SourcesofClimateData | <B>Sources of Climate Data</B>]] |
| # [[FAQ_General:VolumePercent,MassPercent | <B>Volume Percent, Mass Percent</B>]] | | # [[FAQ:General:VolumePercent,MassPercent | <B>Volume Percent, Mass Percent</B>]] |
| # [[FAQ_General:RelativeHumidityinaBuildingComponent | <B>Relative Humidity in a Building Component</B>]] | | # [[FAQ:General:RelativeHumidityinaBuildingComponent | <B>Relative Humidity in a Building Component</B>]] |
| <TR><TD align="right"><B> 5:</B></TD><TD><B><A HREF="#05">Default Moisture Storage Function</A></B></TD></TR>
| | # [[FAQ:General:DefaultMoistureStorageFunction | <B>Default Moisture Storage Function</B>]] |
| <TR><TD align="right"><B> 6:</B></TD><TD><B><A HREF="#06">Water Content of an Air Layer</A></B></TD></TR> | | # [[FAQ:General:WaterContentofanAirLayer | <B>Water Content of an Air Layer</B>]] |
| <TR><TD align="right"><B> 7:</B></TD><TD><B><A HREF="#07">Convergence Failure Caused by Vapor-Permeable Layer</A></B></TD></TR>
| | # [[FAQ:General:ConvergenceFailureCausedbyVapor-PermeableLayer | <B>Convergence Failure Caused by Vapor-Permeable Layer</B>]] |
| <TR><TD align="right"><B> 8:</B></TD><TD><B><A HREF="#08">Moisture Content at a Monitoring Position</A></B></TD></TR>
| | # [[FAQ:General:MoistureContentataMonitoringPosition | <B>Moisture Content at a Monitoring Position</B>]] |
| <TR><TD align="right"><B> 9:</B></TD><TD><B><A HREF="#09">Liquid Transport Coefficient of a Paint Layer</A></B></TD></TR>
| | # [[FAQ:General:LiquidTransportCoefficentofaPaintLayer | '''Liquid Transport Coefficient of a Paint Layer''']] |
| <TR><TD align="right"><B>10:</B></TD><TD><B><A HREF="#10">Rain Absorption Factor of an Unrendered Sandstone Wall</A></B></TD></TR>
| | # [[FAQ:General:RainAbsorptionFactorofanUnrenderedSandstoneWall | '''Rain Absorption Factor of an Unrendered Sandstone Wall''']] |
| <TR><TD align="right"><B>11:</B></TD><TD><B><A HREF="#11">Hygric Parameters of Ecological Insulation Materials</A></B></TD></TR>
| | # [[FAQ:General:HygricParametersofEcologicalInsulationMaterials | <B>Hygric Parameters of Ecological Insulation Materials</B>]] |
| <TR><TD align="right"><B>12:</B></TD><TD><B><A HREF="#12">Typical Initial Moisture Content</A></B></TD></TR>
| | # [[FAQ:General:TypicalInitialMoistureContent | <B>Typical Initial Moisture Content</B>]] |
| <TR><TD align="right"><B>13:</B></TD><TD><B><A HREF="#13">Water-Repellent Facade</A></B></TD></TR>
| | # [[FAQ:General:WaterRepellentFacade | <B>Water-Repellent Facade</B>]] |
| <TR><TD align="right"><B>14:</B></TD><TD><B><A HREF="#14">Simulation of Absorption Experiment</A></B></TD></TR>
| | # [[FAQ:General:SimulationofAbsorptionExperiment | <B>Simulation of Absorption Experiment</B>]] |
| <TR><TD align="right"><B>15:</B></TD><TD><B><A HREF="#15">Absorption Experiment with Limited Water Supply</A></B></TD></TR>
| | # [[FAQ:General:AbsorptionExperimentwithLimitedWaterSupply | '''Absorption Experiment with Limited Water Supply''']] |
| <TR><TD align="right"><B>16:</B></TD><TD><B><A HREF="#16">Why Never 100% RH in the Component?</A></B></TD></TR>
| | # [[FAQ:General:WhyNever100RHintheComponent | '''Why Never 100% RH in the Component?''']] |
| <TR><TD align="right"><B>17:</B></TD><TD><B><A HREF="#17">100% RH at the Facade</A></B></TD></TR>
| | # [[FAQ:General:100RHattheFacade | '''100% RH at the Facade''']] |
| <TR><TD align="right"><B>18:</B></TD><TD><B><A HREF="#18">Criteria for Evaluating Hygrothermal Performance</A></B></TD></TR>
| | # [[FAQ:General:CriteriaforEvaluatingHygrothermalPerformance | '''Criteria for Evaluating Hygrothermal Performance''']] |
| <TR><TD align="right"><B>19:</B></TD><TD><B><A HREF="#19">Ventilated Curtain Walls</A></B></TD></TR>
| | # [[FAQ:General:VentilatedCurtainWalls | '''Ventilated Curtain Walls''']] |
| <TR><TD align="right"><B>20:</B></TD><TD><B><A HREF="#20">Heat Flow Through Exterior Surface Is Not Realistic?</A></B></TD></TR>
| | # [[FAQ:General:HeatFlowThroughExteriorSurfaceIsNotRealistic | '''Heat Flow Through Exterior Surface Is Not Realistic?''']] |
| <TR><TD align="right"><B>21:</B></TD><TD><B><A HREF="#21">More Recent Weather Data?</A></B></TD></TR>
| | # [[FAQ:General:MoreRecentWeatherData | '''More Recent Weather Data?''']] |
| <TR><TD align="right"><B>22:</B></TD><TD><B><A HREF="#22">Averaging of Conductivities at Element Boundaries</A></B></TD></TR>
| | # [[FAQ:General:AveragingofConductivitiesatElementBoundaries | '''Averaging of Conductivities at Element Boundaries''']] |
| <TR><TD align="right"><B>23:</B></TD><TD><B><A HREF="#23">Conversion of Radiation Data for Other Directions</A></B></TD></TR>
| | # [[FAQ:General:ConversationofRadiationDataforOtherDirections | '''Conversion of Radiation Data for Other Directions''']] |
| </TABLE>
| |
| | |
| <P>
| |
| <B><A NAME="01">(1):</A></B><BR>
| |
| <B>Where can I find material data for materials which are not included in the
| |
| database?</B>
| |
| </P>
| |
| <P>
| |
| 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.
| |
| </P>
| |
| <P>
| |
| A collection of design values for <A HREF="BasicMaterialData.htm">heat conductivity</A>
| |
| (including the effect of practical moisture content) and
| |
| <A HREF="BasicMaterialData.htm">diffusion resistance factors</A>
| |
| 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.
| |
| </P>
| |
| <P>
| |
| An extensive list of "NIST Heat Transmission Properties of Insulating and Building
| |
| Materials" is available on-line at <A HREF="http://srdata.nist.gov/insulation/">http://srdata.nist.gov/insulation/</A>.
| |
| </P>
| |
| <P>
| |
| <A HREF="MoistureStorageFunction.htm">Moisture storage functions</A> and
| |
| <A HREF="LiquidTransportCoefficients.htm">liquid transport coefficients</A> may
| |
| be estimated from the
| |
| standard parameters
| |
| <A HREF="MoistureStorageFunction.htm">w<small>f</small>, w<small>80</small></A> and the
| |
| <A HREF="LiquidTransportCoefficients.htm">A-value</A> which may
| |
| also be found in some textbooks (at least for selected materials) and data sheets or
| |
| can be measured relatively easily.
| |
| </P>
| |
| <P>
| |
| Occasionally, some data may be found scattered through the specialised literature,
| |
| but there is no systematic way to retrieve them.
| |
| </P>
| |
| <P>
| |
| Sometimes the manufacturer may be able to provide material data. Some laboratories
| |
| (including IBP) can measure the required data if samples are provided.
| |
| </P>
| |
| | |
| <P>
| |
| <B><A NAME="02">(2):</A></B><BR>
| |
| <B>Where can I find climate data?</B>
| |
| </P>
| |
| <P>
| |
| Hourly climate data which include rain are even harder to find than material data.
| |
| </P>
| |
| <P>
| |
| 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.<BR>
| |
| In addition, weather data for 93 locations in Europe, America and Japan are provided
| |
| with the professional WUFI version.
| |
| </P>
| |
| <P>
| |
| Another source of hourly weather data for Germany are the Test Reference Years of the German Meteorological Service DWD which represent typical as well as extreme weather situations.
| |
| Since they are primarily intended for heating and energy consumption investigations, they
| |
| have no rain data, however, and thus are of only limited usefulness for hygrothermal
| |
| investigations.
| |
| </P>
| |
| <P>
| |
| For other possible climate data sources see <A HREF="SourcesForClimateData.htm">Sources
| |
| for Climate Data</A>.
| |
| </P>
| |
| <P>
| |
| If the situation of a specific object is to be investigated, it may be necessary to measure
| |
| the weather in-situ anyway.
| |
| </P>
| |
| | |
| | |
| <P>
| |
| <B><A NAME="03">(3):</A></B>
| |
| <B>WUFI gives me the water content of the simulated wall in units of kg/m³ or in
| |
| volume percent. However, I need the result in mass percent. How do I convert the
| |
| results?</B><BR>
| |
| </P>
| |
| | |
| <P>
| |
| WUFI usually gives the water content as "water density", i.e. how many kg of water are
| |
| in one m³ of building material.<BR>
| |
| A result given in volume percent tells you how many m³ of water are in one m³ of
| |
| building material (expressed as percentage).<BR>
| |
| 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.
| |
| </P>
| |
| | |
| <P>
| |
| With
| |
| </P>
| |
| <TABLE>
| |
| <TR><TD><TT>m_W</TT> :</TD><TD>mass of the water in the component</TD></TR>
| |
| <TR><TD><TT>r_W</TT> :</TD><TD>density of water (= 1000 kg/m³)</TD></TR>
| |
| <TR><TD><TT>V_W</TT> :</TD><TD>volume of the water in the component</TD></TR>
| |
| <TR><TD><TT>m_C</TT> :</TD><TD>mass of the component</TD></TR>
| |
| <TR><TD><TT>r_C</TT> :</TD><TD>density of the (dry) component</TD></TR>
| |
| <TR><TD><TT>V_C</TT> :</TD><TD>volume of the component</TD></TR>
| |
| </TABLE>
| |
| <P>
| |
| we have
| |
| </P>
| |
| <TABLE>
| |
| <TR><TD COLSPAN="3">water content as expressed by WUFI:</TD></TR>
| |
| | |
| <TR><TD COLSPAN="3"> </TD></TR>
| |
| | |
| <TR><TD> </TD><TD><TT>u</TT></TD><TD><TT>= m_W / V_C [kg/m³]</TT></TD></TR>
| |
| | |
| <TR><TD COLSPAN="3"> </TD></TR>
| |
| | |
| <TR><TD COLSPAN="3">water content expressed in volume percent:</TD></TR>
| |
| | |
| <TR><TD COLSPAN="3"> </TD></TR>
| |
| | |
| <TR><TD> </TD><TD><TT>u_v</TT></TD><TD><TT>= V_W / V_C * 100</TT></TD></TR>
| |
| | |
| <TR><TD> </TD><TD> </TD><TD><TT>= (m_W / r_W) / V_C * 100</TT></TD></TR>
| |
| | |
| <TR><TD> </TD><TD> </TD><TD><TT>= (m_W / V_C) / r_W * 100</TT></TD></TR>
| |
| | |
| <TR><TD> </TD><TD> </TD><TD><TT>= u * 100 / r_W</TT></TD></TR>
| |
| | |
| <TR><TD> </TD><TD> </TD><TD><TT>= u * 100 / 1000</TT></TD></TR>
| |
| | |
| <TR><TD> </TD><TD> </TD><TD><TT>= u / 10</TT></TD></TR>
| |
| | |
| <TR><TD COLSPAN="3"> </TD></TR>
| |
| | |
| <TR><TD COLSPAN="3">water content expressed in mass percent:</TD></TR>
| |
| | |
| <TR><TD> </TD><TD><TT>u_m</TT></TD><TD><TT>= m_W / m_C * 100</TT></TD></TR>
| |
| | |
| <TR><TD> </TD><TD> </TD><TD><TT>= m_W / (r_C * V_C ) * 100</TT></TD></TR>
| |
| | |
| <TR><TD> </TD><TD> </TD><TD><TT>= (m_W / V_C) * (100 / r_C)</TT></TD></TR>
| |
| | |
| <TR><TD> </TD><TD> </TD><TD><TT>= u * (100 / r_C)</TT></TD></TR>
| |
| | |
| <TR><TD> </TD><TD> </TD><TD><TT>= u / (r_C / 100)</TT></TD></TR>
| |
| </TABLE>
| |
| <P>
| |
| So you get the water content in volume percent if you divide the
| |
| WUFI result [kg/m³] by <TT>10</TT>.<BR>
| |
| You get the water content in mass percent if you divide the WUFI
| |
| result by <TT>(density of the building component / 100)</TT>.
| |
| </P>
| |
| | |
| <P>
| |
| <B><A NAME="04">(4):</A></B><BR>
| |
| <B>I'm trying to make sense of the WUFI results, but I'm confused. What exactly is
| |
| 'relative humidity' and what is the relative humidity in a building component
| |
| referred to?</B><BR>
| |
| </P>
| |
| <P>
| |
| In air the relative humidity is the ratio of the actual water vapor partial pressure
| |
| p and the water vapor saturation pressure p<small>s</small>. Example: If the air
| |
| temperature is 20°C (and therefore p<small>s</small> = 2340 Pa) and the actual
| |
| vapor pressure is 1872 Pa, then the relative humidity is 1872 Pa / 2340 Pa = 0.8 = 80%.
| |
| </P>
| |
| <P>
| |
| 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.<BR>
| |
| 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.
| |
| </P>
| |
| <P>
| |
| 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.
| |
| </P>
| |
| <P>
| |
| 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.
| |
| </P>
| |
| <P>
| |
| 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.
| |
| </P>
| |
| <P>
| |
| The <A HREF="MoistureStorageFunction.htm">moisture storage function</A> 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.
| |
| </P>
| |
| | |
| <P>
| |
| <B><A NAME="05">(5):</A></B><BR>
| |
| <B>When I do not define a moisture storage function for a material, WUFI uses
| |
| a default moisture storage function instead. What does this function look like?</B>
| |
| </P>
| |
| <P>
| |
| 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.).
| |
| </P>
| |
| <P>
| |
| The default <A HREF="MoistureStorageFunction.htm">moisture storage function</A> used
| |
| by WUFI is described by the function<BR>
| |
| | |
| <TABLE>
| |
| <TR><TD COLSPAN="3"><TT>w = a / (b - phi) + c</TT></TD></TR>
| |
| <TR><TD><TT>w</TT></TD><TD ALIGN="RIGHT">[kg/m³]:</TD><TD>water content </TD></TR>
| |
| <TR><TD><TT>phi</TT></TD><TD ALIGN="RIGHT">[-]:</TD><TD>relative humidity</TD></TR>
| |
| </TABLE>
| |
| </P>
| |
| <P>
| |
| Since <TT>phi</TT> must be 0 for <TT>w=0</TT>, it follows immediately that<BR>
| |
| <TT>c = -a/b</TT><BR>
| |
| <BR>
| |
| The constants <TT>a</TT> and <TT>b</TT> are determined as follows:<BR>
| |
| <BR>
| |
| <TT>b</TT> is set to 1.0105.<BR>
| |
| <BR>
| |
| The moisture content at free saturation, w<small>f</small>, 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
| |
| <TT>phi<small>max</small> = 1.01</TT>. This value
| |
| <TT>phi<small>max</small></TT> is
| |
| reached when the moisture content reaches maximum saturation
| |
| <TT>w<small>max</small></TT> which is
| |
| determined by the <A HREF="BasicMaterialData.htm">porosity</A>:<BR>
| |
| <BR>
| |
| <TT>w<small>max</small> = porosity * 1000 kg/m³</TT><BR>
| |
| <BR>
| |
| Therefore we have<BR>
| |
| <BR>
| |
| <TT>w<small>max</small> = a / (b-phi<small>max</small>) - a/b.</TT><BR>
| |
| <BR>
| |
| Solving for <TT>a</TT> yields:<BR>
| |
| <BR>
| |
| <TT>a = w<small>max</small> * b * (b - phi<small>max</small>) /
| |
| phi<small>max</small></TT>,<BR>
| |
| <BR>
| |
| and thus:<BR>
| |
| <BR>
| |
| <TT>w / w<small>max</small> = phi / (b - phi) * (b - phi<small>max</small>)
| |
| / phi<small>max</small></TT>.<BR>
| |
| <BR>
| |
| <BR>
| |
| In particular, for <TT>phi=1</TT> we have<BR>
| |
| <BR>
| |
| <TT>w<small>f</small> / w<small>max</small> = 1 / (b - 1) *
| |
| (b - phi<small>max</small>) / phi<small>max</small> = 0.047</TT>.<BR>
| |
| <BR>
| |
| So this pseudo material has a free saturation of <TT>w<small>f</small> = 0.047 w<small>max</small></TT>.
| |
| </P>
| |
| <P>
| |
| <IMG SRC="pix/e_defaultfspfkt.gif" WIDTH="500" HEIGHT="246" VSPACE="0" HSPACE="0" ALT="">
| |
| </P>
| |
| | |
| <P>
| |
| <B><A NAME="06">(6):</A></B><BR>
| |
| <B>I did a WUFI calculation with an assembly that includes an air layer. However, I get
| |
| completely unrealistic water contents for the air layer. What went wrong?</B>
| |
| </P>
| |
| <P>
| |
| 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.
| |
| </P>
| |
| <P>
| |
| <A HREF="AirLayers.htm">Air layers</A> 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
| |
| <A HREF="BasicMaterialData.htm">heat conductivities</A> and
| |
| <A HREF="BasicMaterialData.htm">vapor diffusion resistance factors</A>.
| |
| </P>
| |
| <P>
| |
| However, the <A HREF="MoistureStorageFunction.htm">moisture storage function</A> 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 <I>and temperature</I> cannot be
| |
| reproduced.<BR>
| |
| 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).
| |
| </P>
| |
| <P>
| |
| As a result you will get unrealistically large moisture contents for air layers.
| |
| Note, however, that WUFI uses the <I>relative humidity</I> as the driving potential
| |
| for moisture transport and computes the <I>water content</I> as a <I>secondary</I>
| |
| quantity from the resulting relative humidity (using the moisture storage function
| |
| of the respective material).<BR>
| |
| So the resulting distribution of <I>relative humidity</I> 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.<BR>
| |
| 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).
| |
| </P>
| |
| <P>
| |
| 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.
| |
| </P>
| |
| <P>
| |
| 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
| |
| </P>
| |
| <TABLE>
| |
| <TR><TD><TT>phi: </TT></TD><TD><TT>w: </TT></TD></TR>
| |
| <TR><TD><TT>0 </TT></TD><TD><TT>0 </TT></TD></TR>
| |
| <TR><TD><TT>1 </TT></TD><TD><TT>w<small>f</small></TT></TD></TR>
| |
| </TABLE>
| |
| <P>
| |
| with a low value for w<small>f</small> (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.
| |
| </P>
| |
| <P>
| |
| Also see the next question for a related problem.
| |
| </P>
| |
| <P>
| |
| (*) Note, however, that the porosity and thus w<small>max</small> should
| |
| remain high. If the water content exceeds w<small>f</small>, 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=w<small>max</small> 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, w<small>max</small>
| |
| should therefore remain at a realistic value.
| |
| </P>
| |
| | |
| <P>
| |
| <B><A NAME="07">(7):</A></B><BR>
| |
| <B>I tried to perform a WUFI simulation, but the water balance never adds up,
| |
| regardless whether I make the grid as fine as possible or whether I choose
| |
| stricter numerical parameters, as suggested in the on-line help. What can I do?</B>
| |
| </P>
| |
| <P>
| |
| 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.
| |
| </P>
| |
| <P>
| |
| <IMG SRC="pix/e_konvf_hivlt.gif" WIDTH="300" HEIGHT="300" VSPACE="0" HSPACE="0" ALT="">
| |
| </P>
| |
| <P>
| |
| If everything else fails, you may try an alternative
| |
| <A HREF="MoistureStorageFunction.htm">moisture storage function</A>.
| |
| 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).
| |
| </P>
| |
| <P>
| |
| 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).<BR>
| |
| 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.<BR>
| |
| Please note that the <I>relative humidity</I> in the material will remain largely
| |
| unaffected by the specific choice of the moisture storage function, 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 moisture storage function to be sure), and if you are
| |
| interested in the moisture content, you should not rely on the default moisture
| |
| storage function anyway, but use measured data instead which represent your
| |
| particular material.
| |
| </P>
| |
| <P>
| |
| A possible choice for the moisture storage function in these cases is a
| |
| table like this:
| |
| </P>
| |
| <TABLE>
| |
| <TR><TD><TT>phi: </TT></TD><TD><TT>w: </TT></TD><TR>
| |
| <TR><TD><TT>0 </TT></TD><TD><TT>0 </TT></TD></TR>
| |
| <TR><TD><TT>1 </TT></TD><TD><TT>w<small>f</small></TT></TD></TR>
| |
| </TABLE>
| |
| <P>
| |
| Use a low value for w<small>f</small> (the numerics may not be able to cope
| |
| with very low values, you'll need to experiment a bit.) (*).<BR>
| |
| 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 w<small>f</small> and up to w<small>max</small>.
| |
| </P>
| |
| <P>
| |
| In particular if you are interested in moisture accumulation by condensation in
| |
| these materials, use such a linear moisture storage function with low
| |
| w<small>f</small>. Then you know that any moisture content exceeding
| |
| w<small>f</small> must have been caused by condensation. You can then analyse
| |
| this excess over w<small>f</small> (test calculations show that this excess is
| |
| only slightly dependent on the specific choice of w<small>f</small>).
| |
| </P>
| |
| <P>
| |
| (*) Note, however, that the porosity and thus wmax should remain high. If the
| |
| water content exceeds w<small>f</small>, 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=w<small>max</small> 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.
| |
| </P>
| |
| | |
| <P>
| |
| <B><A NAME="08">(8):</A></B><BR>
| |
| <B>How can I get the moisture content at a monitoring position?</B>
| |
| </P>
| |
| <P>
| |
| WUFI's output includes the temporal behavior of
| |
| </P>
| |
| <UL>
| |
| <LI>temperature and relative humidity at the monitoring positions, and of</LI>
| |
| <LI>the mean moisture content of each layer.</LI>
| |
| </UL>
| |
| <P>
| |
| In order to get the <I>moisture content</I> at a <I>monitoring position</I>, you
| |
| can either
| |
| </P>
| |
| <UL>
| |
| <LI>calculate it from the relative humidity prevalent at that monitoring
| |
| position by means of the
| |
| <A HREF="MoistureStorageFunction.htm">moisture storage function</A>, or</LI>
| |
| <LI>insert a thin 'diagnostic' layer at the position in question which has
| |
| the same material properties as the surrounding material. WUFI will
| |
| output curves for the water contents of each layer, including a separate
| |
| curve for the diagnostic layer. This is also a useful way to get the water
| |
| content of, say, the outermost 5 cm of a layer.</LI>
| |
| </UL>
| |
| | |
| <P>
| |
| <B><A NAME="09">(9):</A></B><BR>
| |
| <B>I want to examine the effect of driving rain on a painted wall. What liquid
| |
| transport coefficients D<small>ws</small> do I enter for the paint?</B>
| |
| </P>
| |
| <P>
| |
| There are no measurements of <A HREF="LiquidTransportCoefficients.htm">transport
| |
| coefficients</A> or, equivalently, water absorption coefficients for paint layers
| |
| themselves known to us.
| |
| </P>
| |
| <P>
| |
| 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.
| |
| </P>
| |
| <P>
| |
| So the best thing you can do is probably the following:<BR>
| |
| 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 D<small>ws</small> from the hybrid water uptake (let it generate by WUFI from the
| |
| measured water absorption coefficient) and use the D<small>ww</small> and other data from
| |
| the original rendering.
| |
| </P>
| |
| <P>
| |
| The <A HREF="WaterVaporDiffusion.htm">vapor diffusion resistance</A> of the paint
| |
| can then be included in the <A HREF="DialogEditSurfaceCoefficients.htm">surface
| |
| transfer coefficients</A> (as long as it is not markedly moisture-dependent).
| |
| </P>
| |
| <P>
| |
| Please note some possible problems, though:
| |
| </P>
| |
| <UL>
| |
| <LI>The result of the measurement may (or may not) depend on the substrate material,
| |
| the details of the application etc. So you should make sure that you are using
| |
| a water absorption value that has been measured under the same circumstances
| |
| as the case you consider in your calculations.<LI>
| |
| <LI>The paint may slowly change its properties when it gets wet (e.g. by swelling).
| |
| The mean properties over a rain period of two or three hours may be different
| |
| than the mean properties during a measurement that takes many hours. Again,
| |
| the measurement should be done close to natural conditions.</LI>
| |
| </UL>
| |
| | |
| <P>
| |
| <B><A NAME="10">(10):</A></B><BR>
| |
| <B>What is the right choice for the rain absorption factor for an unrendered natural
| |
| sandstone wall? When I use the value of 0.7 suggested by WUFI, then the entire wall gets
| |
| wet like a sponge. When I reduce the absorption factor to 0.5, the same happens, it just
| |
| takes longer. What's wrong?</B>
| |
| </P>
| |
| <P>
| |
| This should not happen, but the
| |
| <A HREF="RainWaterAbsorptionFactor.htm">rain absorption factor</A> 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.
| |
| </P>
| |
| <P>
| |
| 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?<BR>
| |
| 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?
| |
| </P>
| |
| | |
| <P>
| |
| <B><A NAME="11">(11):</A></B><BR>
| |
| <B>I want to investigate the hygric behavior of ecological insulation materials,
| |
| such as flax, hemp or reed. However, these materials consist of fibres, whereas WUFI
| |
| is mainly designed for capillary-active porous materials. What is the best approach?</B>
| |
| </P>
| |
| <P>
| |
| 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, which would have to be allowed for by using appropriate material
| |
| data for the x and y directions in a two-dimensional calculation.
| |
| </P>
| |
| <P>
| |
| Determining the
| |
| <A HREF="LiquidTransportCoefficients.htm">liquid transport coefficients</A>, however,
| |
| may be difficult or even impossible if they change their consistency upon wetting
| |
| (e.g. by caking).
| |
| </P>
| |
| <P>
| |
| On the other hand:<BR>
| |
| 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
| |
| <A HREF="BasicMaterialData.htm">µ-value</A>. Surface diffusion phenomena
| |
| may be allowed for by using a
| |
| <A HREF="DiffusionResistanceFactorMoistureDependent.htm">moisture-dependent
| |
| µ-value</A>.
| |
| </P>
| |
| <P>
| |
| Since you probably only want to assess <I>whether or not</I> the insulation becomes
| |
| wet by rain or condensation, you will mainly be concerned with water contents in the
| |
| sorption moisture region of the
| |
| <A HREF="MoistureStoragefunction.htm">moisture storage function</A>, for which these
| |
| simplifications should be adequate.<BR>
| |
| 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.
| |
| </P>
| |
| | |
| | |
| <P>
| |
| <B><A NAME="12">(12):</A></B><BR>
| |
| <B>I want to find out how long it takes a wall with construction moisture to dry
| |
| out. Which initial moisture content should I use?</B>
| |
| </P>
| |
| <P>
| |
| 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:
| |
| </P>
| |
| | |
| <TABLE>
| |
| <TR><TD COLSPAN="2" ALIGN="CENTER"><B>Material</B></TD><TD ALIGN="CENTER"><B>Water content [kg/m³]</B></TD></TR>
| |
| <TR><TD COLSPAN="3"><B>Fresh concrete:</B></TD></TR>
| |
| <TR><TD> </TD><TD>free water</TD><TD ALIGN="CENTER">175</TD></TR>
| |
| <TR><TD COLSPAN="3"> </TD></TR>
| |
| <TR><TD COLSPAN="3"><B>Concrete, 28 days old (at 70% hydratation):</B></TD></TR>
| |
| <TR><TD> </TD><TD>bound water</TD><TD ALIGN="CENTER">85</TD></TR>
| |
| <TR><TD> </TD><TD>dried water</TD><TD ALIGN="CENTER">25 ... 45</TD></TR>
| |
| <TR><TD> </TD><TD>free water</TD><TD ALIGN="CENTER">65 ... 45</TD></TR>
| |
| <TR><TD> </TD><TD> </TD><TD ALIGN="CENTER">(sum = 175)</TD></TR>
| |
| <TR><TD COLSPAN="3"><B>Concrete, 3 to 6 months old (at 90% hydratation):</B></TD></TR>
| |
| <TR><TD> </TD><TD>bound water</TD><TD ALIGN="CENTER">105</TD></TR>
| |
| <TR><TD> </TD><TD>dried water</TD><TD ALIGN="CENTER">35 ... 50</TD></TR>
| |
| <TR><TD> </TD><TD>free water</TD><TD ALIGN="CENTER">35 ... 20</TD></TR>
| |
| <TR><TD> </TD><TD> </TD><TD ALIGN="CENTER">(sum = 175)</TD></TR>
| |
| <TR><TD COLSPAN="3">DIN 4108 "thermal protection"</TD></TR>
| |
| <TR><TD> </TD><TD><B>practical moisture content of concrete</B></TD><TD ALIGN="CENTER">50</TD></TR>
| |
| <TR><TD COLSPAN="3"> </TD></TR>
| |
| <TR><TD COLSPAN="2"><B>Cellular concrete</B></TD><TD ALIGN="CENTER">180 ... 220</TD></TR>
| |
| <TR><TD COLSPAN="2"><B>Clay brick masonry</B></TD><TD ALIGN="CENTER">100 ... 150</TD></TR>
| |
| <TR><TD COLSPAN="2"><B>Calcium silica brick masonry</B></TD><TD ALIGN="CENTER">100 ... 120</TD></TR>
| |
| <TABLE>
| |
| | |
| <P>
| |
|
| |
| </P>
| |
| | |
| <P>
| |
| <B><A NAME="13">(13):</A></B><BR>
| |
| <B>How can I simulate a wall whose exterior surface has been treated with a
| |
| water-repellent agent? Is it correct to set the rain water absorption factor to zero?
| |
| Do I need to change the s<small>d</small>-value of the exterior surface, even though
| |
| I use a diffusion-permeable treatment?</B>
| |
| </P>
| |
| <P>
| |
| The
| |
| <A HREF="RainWaterAbsorptionFactor.htm">rain water absorption factor</A> 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
| |
| <A HREF="LiquidTransportCoefficients.htm">water absorption coefficient</A> for
| |
| the treated material and replace the part of the wall which corresponds to the
| |
| penetration depth of the treatment with da layer of the treated material.
| |
| </P>
| |
| <P>
| |
| If the treatment does not change the
| |
| <A HREF="WaterVaporDiffusion.htm">diffusion permeability</A> of the material, no
| |
| <A HREF="DialogEditSurfaceCoefficients.htm">s<small>d</small>-value</A> needs to
| |
| be specified for the exterior surface.<BR>
| |
| 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 s<small>d</small>-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.
| |
| </P>
| |
| <P>
| |
| 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.</BR>
| |
| 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.<BR>
| |
| 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.
| |
| </P>
| |
| | |
| <P>
| |
| <B><A NAME="14">(14):</A></B><BR>
| |
| <B>WUFI gives me the option to estimate the liquid transport coefficients
| |
| D<small>ws</small> from the water absorption coefficient. How can I check how
| |
| good this estimate is?</B>
| |
| </P>
| |
| <P>
| |
| You can check the <A HREF="LiquidTransportCoefficients.htm">estimated</A> Dws or
| |
| determine an unknown water absorption
| |
| coefficient from known Dws by simulating a water absorption experiment.
| |
| </P>
| |
| <P>
| |
| 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.
| |
| </P>
| |
| <P>
| |
| This may be done with a one-line *.KLI-file such as:
| |
| <TABLE>
| |
| <TR><TD WIDTH="14%">[h:</TD><TD WIDTH="14%">rain:</TD><TD WIDTH="14%">rad:</TD><TD WIDTH="14%">t_ext:</TD><TD WIDTH="14%">RH_ext: </TD><TD WIDTH="14%">t_int:</TD><TD>RH_int:]</TD></TR>
| |
| <TR><TD WIDTH="14%">500</TD><TD WIDTH="14%">1000</TD><TD WIDTH="14%">0</TD><TD WIDTH="14%">20</TD><TD WIDTH="14%">1</TD><TD WIDTH="14%">20</TD><TD>0</TD></TR>
| |
| </TABLE>
| |
| </P>
| |
| <P>
| |
| 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.
| |
| </P>
| |
| <P>
| |
| Set the vapor diffusion thickness of the interior surface to a very high value
| |
| to prevent vapor transport through that surface.
| |
| </P>
| |
| <P>
| |
| 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.
| |
| <P>
| |
| <P>
| |
| <IMG SRC="pix/e_BaumbergerSaug.gif" WIDTH="300" HEIGHT="225" VSPACE="0" HSPACE="0" ALT="">
| |
| </P>
| |
| | |
| <P>
| |
| <B><A NAME="15">(15):</A></B><BR>
| |
| <B>I want to evaluate the effect of different material parameters on water absorption by
| |
| simulating a laboratory experiment in which different specimens are exposed to a limited
| |
| water supply. I created the corresponding KLI file with a spreadsheet program to avoid
| |
| typing in all those numbers by hand, but WUFI can't read this KLI file.</B>
| |
| </P>
| |
| <P>
| |
| 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.
| |
| </P>
| |
| <P>
| |
| 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:
| |
| <TABLE>
| |
| <TR><TD WIDTH="14%">[h:</TD><TD WIDTH="14%">rain:</TD><TD WIDTH="14%">rad:</TD><TD WIDTH="14%">t_ext:</TD><TD WIDTH="14%">RH_ext: </TD><TD WIDTH="14%">t_int:</TD><TD>RH_int:]</TD></TR>
| |
| <TR><TD WIDTH="14%">1000</TD><TD WIDTH="14%">5</TD><TD WIDTH="14%">0</TD><TD WIDTH="14%">20</TD><TD WIDTH="14%">1</TD><TD WIDTH="14%">20</TD><TD>0.8</TD></TR>
| |
| </TABLE>
| |
| means that for 1000 hours after the starting time of the climate file there is a constant
| |
| rain load of 5 Ltr/m²h.
| |
| </P>
| |
| <P>
| |
| An alternative would be a single line like
| |
| <TABLE>
| |
| <TR><TD WIDTH="14%">[h:</TD><TD WIDTH="14%">rain:</TD><TD WIDTH="14%">rad:</TD><TD WIDTH="14%">t_ext:</TD><TD WIDTH="14%">RH_ext: </TD><TD WIDTH="14%">t_int:</TD><TD>RH_int:]</TD></TR>
| |
| <TR><TD WIDTH="14%">1 5</TD><TD WIDTH="14%">0</TD><TD WIDTH="14%">20</TD><TD WIDTH="14%">1</TD><TD WIDTH="14%">20</TD><TD>0.8</TD></TR>
| |
| </TABLE>
| |
| 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.
| |
| </P>
| |
| <P>
| |
| 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.
| |
| </P>
| |
| <P>
| |
| 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 ould not be plausible for real rain.
| |
| </P>
| |
| <P>
| |
| 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
| |
| <A HREF="RainWaterAbsorptionFactor.htm">rain absorption factor</A> 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.
| |
| </P>
| |
| <P>
| |
| 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/m²h<sup>1/2</sup> and the climate file specifies a rain load of
| |
| 3 Ltr/m²h. During each time step,
| |
| WUFI performs a <I>test</I> step with an <I>unlimited</I> 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.<BR>
| |
| 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.
| |
| </P>
| |
| <P>
| |
| 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.<BR>
| |
| 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 <I>more</I> than 1.5 kg/m⊃ in the first half hour, while WUFI compares
| |
| this with 1.5 kg/m⊃ of rain in the first half hour (assuming the rain is
| |
| evenly distributed over the hour) and now <I>limits</I> the amount absorbed to
| |
| 1.5 kg/m².<BR>
| |
| 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.
| |
| </P>
| |
| | |
| <P>
| |
| <B><A NAME="16">(16):</A></B><BR>
| |
| <B>I'm familiar with steady-state water vapor diffusion calculations (in particular,
| |
| the Glaser method described in German standard DIN 4108). So I knew I had to expect
| |
| more or less frequent dew conditions in the wall I was simulating. However, when I
| |
| watched the WUFI film, I could never see the relative humidity reach 100%.</B>
| |
| </P>
| |
| <P>
| |
| 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).
| |
| </P>
| |
| <P>
| |
| That's because a relative humidity of 100% would correspond to a
| |
| <A HREF="MoistureStorageFunction.htm">moisture content</A>
| |
| 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.
| |
| </P>
| |
| <P>
| |
| 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.
| |
| </P>
| |
| <P>
| |
| Furthermore, real materials (as opposed to Glaser) usually have some
| |
| <A HREF="LiquidTransportCoefficients.htm">capillary conductivity</A> 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.
| |
| </P>
| |
| <P>
| |
| Of course, you <I>may</I> 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...
| |
| </P>
| |
| | |
| <P>
| |
| <B><A NAME="17">(17):</A></B><BR>
| |
| <B>OK, this explains why I didn't see dew conditions in the wall. But shouldn't
| |
| condensation at least happen at the facade on days with high humidity and little
| |
| sunshine?</B>
| |
| </P>
| |
| <P>
| |
| 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).<BR>
| |
| 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.
| |
| </P>
| |
| <P>
| |
| You'll have
| |
| <A HREF="MoistureStorageFunction.htm">free saturation</A> (i.e. 100% RH) at the
| |
| surface when enough rain is absorbed, but this is not due to dew conditions.
| |
| </P>
| |
| <P>
| |
| The surface temperature will fall below air temperature when the wall
| |
| <A HREF="LongWaveRadiationEmissivity.htm">emits</A> 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.<BR>
| |
| 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.
| |
| </P>
| |
| <P>
| |
| 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.<BR>
| |
| 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.
| |
| </P>
| |
| | |
| <P>
| |
| <B><A NAME="18">(18):</A></B><BR>
| |
| <B>I used WUFI to compute the water content in a variety of wall assemblies. In
| |
| order to evaluate their hygrothermal performance, I now need appropriate criteria,
| |
| e.g. standards that should not be exceeded.</B>
| |
| </P>
| |
| | |
| <P>
| |
| There are no general criteria which are applicable for every case. Different
| |
| materials and different applications require different criteria. Here are some
| |
| general hints:
| |
| </P>
| |
| | |
| <UL>
| |
| <LI>The most important criterion: the moisture must not accumulate over time. Water
| |
| condensing in the building component must be able to dry out again. If the
| |
| moisture content in your component keeps increasing - even slowly - you'll run
| |
| into problems sooner or later.</LI>
| |
| | |
| <LI>The building materials which come into contact with moisture must not be damaged
| |
| (e.g. by corrosion or mould growth).<BR>
| |
| Mineral building materials are usually not at risk; some of them may be susceptible
| |
| to frost damage if they contain a lot of moisture.<BR>
| |
| Wood should not exceed 20 mass-% of moisture during a prolonged period; otherwise
| |
| mould growth may result (possible exception: increased moisture while temperatures
| |
| are low).<LI>
| |
| </UL>
| |
| <P>
| |
| German standard DIN 4108-3 adds the following criteria:
| |
| </P>
| |
| <UL>
| |
| <LI>The amount of condensing moisture in roof or wall assemblies must not exceed
| |
| a total of 1.0 kg/m².<BR>
| |
| This is a more or less arbitrary criterion. In order to test it with WUFI, start
| |
| the calculation with the normal equilibrium moisture (corresponding to 80% RH) and
| |
| see if the total water content exceeds the starting value by more than 1 kg/m².</LI>
| |
| | |
| <LI>At interfaces between materials that are not capillary-active, no moisture
| |
| increase exceeding 0.5 kg/m² is permissible.<BR>
| |
| This is meant to avoid moisture running or dripping off, which could accumulate
| |
| elsewhere and cause damage.</LI>
| |
| | |
| <LI>The moisture increase in wood must not exceed 5 mass-%, the moisture increase
| |
| in materials made of processed wood must not exceed 3 mass-%.<BR>
| |
| These are more or less arbitrary numbers.</LI>
| |
| </UL>
| |
| <P>
| |
| In addition, special criteria may be applicable in specific cases, for example:
| |
| </P>
| |
| <UL>
| |
| <LI>Are there any materials which are particularly sensitive to moisture damage?</LI>
| |
| <LI>Does increased heat loss by moist insulation exceed any energy conservation
| |
| requirements?</LI>
| |
| <LI>Is the building material at this moisture level sensitive to frost damage?</LI>
| |
| <LI>Is there salt in the wall which must be kept from crystallizing or from moving
| |
| around?</LI>
| |
| <LI>Etc.</LI>
| |
| </UL>
| |
| <P>
| |
| Even if you don't have clear criteria which fit your case, you may still perform a
| |
| <I>ranking</I> of your assemblies by comparing them with each other or with a
| |
| standard case.
| |
| </P>
| |
| | |
| <P>
| |
| <B><A NAME="19">(19):</A></B><BR>
| |
| <B>I want to simulate a ventilated curtain wall; how can I do this? I can model
| |
| the air gap as an air layer in WUFI but it seems these air layers are assumed
| |
| to be stagnant, which is certainly not the case in my ventilation gap.</B>
| |
| </P>
| |
| | |
| <P>
| |
| If you model the ventilation gap as an
| |
| <A HREF="AirLayers.htm">air layer</A> 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
| |
| <A HREF="AirLayers.htm">effective</A>
| |
| <A HREF="MaterialData.htm">heat conductivities</A> and
| |
| <A HREF="MaterialData.htm">vapor diffusion resistance factors</A>.
| |
| </P>
| |
| <P>
| |
| The air flow and air exchange phenomena in a ventilated air layer cannot be
| |
| simulated with a one-dimensional program like WUFI-1D; WUFI-2D currently does not
| |
| take air flows into account.<BR>
| |
| 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
| |
| <A HREF="RainWaterAbsorptionFactor.htm">rain absorption factor</A> = 0).<BR>
| |
| It will be advisable to choose appropriate effective values for the exterior
| |
| heat transfer coefficient and the short-wave solar absorptivity, but this
| |
| requires calibration by experimental data.
| |
| </P>
| |
| <P>
| |
| 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.
| |
| </P>
| |
| <P>
| |
| The investigations described in [1] used a simplified treatment of a roof. WUFI-1D
| |
| 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.<BR>
| |
| 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<small>s</small>=0.6 and an
| |
| effective heat transfer coefficient of <FONT FACE="SYMBOL">a</FONT>=19 W/m²K.
| |
| The effective absorptivity is roughly identical with the real absorptivity
| |
| (for red roof tiles), while the effective <FONT FACE="SYMBOL">a</FONT> 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.<BR>
| |
| The question to which extent this isolated result can be generalised could only
| |
| be answered by more extensive comparisons with measurements.
| |
| </P>
| |
| <P>
| |
| [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.
| |
| </P>
| |
| | |
| <P>
| |
| <B><A NAME="20">(20):</A></B><BR>
| |
| <B>I calculated the sum of the heat flows through the exterior and the interior
| |
| surfaces during one year and I noted that the heat flow out of the building
| |
| component through the exterior surface is much larger than the heat flow into
| |
| the component through the interior surface. But shouldn't they be nearly equal?
| |
| How can more heat flow out of the component than into it? No heat can be created
| |
| in the wall.</B>
| |
| </P>
| |
| | |
| <P>
| |
| 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.<BR>
| |
| 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).
| |
| </P>
| |
| <P>
| |
| 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.
| |
| </P>
| |
| <P>
| |
| 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).
| |
| </P>
| |
| | |
| <P>
| |
| <B><A NAME="21">(21):</A></B><BR>
| |
| <B>Are there more recent weather data available? The copy of WUFI I downloaded still
| |
| has those of 1991.</B>
| |
| </P>
| |
| | |
| <P>
| |
| '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 may be made available as two 'Hygrothermal Reference Years'.
| |
| </P>
| |
| | |
| <P>
| |
| <B><A NAME="22">(22):</A></B>
| |
| <B>For the numerical solution of the transport equations the component must be divided
| |
| into a series of grid elements for whose midpoints the resulting temperatures and water
| |
| contents are computed at each time step, and across whose element boundaries the heat
| |
| and moisture fluxes required by the equations are flowing. In order to arrive at correct
| |
| fluxes across the boundaries, effective conductivities have to be assigned to the
| |
| boundaries which represent the integral effect of the conductivities between the
| |
| midpoints of the two elements. The investigations reported in [1] show that the results
| |
| do in fact depend on the way these effective heat and moisture conductivities are
| |
| determined from the real conductivities of the two elements: obviously linear
| |
| interpolation between the neighboring conductivities is preferable within a material
| |
| layer, and a resistance formulation is more appropriate for boundaries between layers
| |
| with different materials. How does WUFI treat these element boundary
| |
| conductivities?</B><BR>
| |
| </P>
| |
| | |
| <P>
| |
| 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.<BR>
| |
| 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.
| |
| </P>
| |
| <P>
| |
| [1] Galbraith, G.H. et al.: Evaluation of Discretized Transport Properties for
| |
| Numerical Modelling of Heat and Moisture Transfer in Building Structures,<BR>
| |
| Journal of Thermal Env. & Bldg. Sci., Vol. 24, Jan. 2001
| |
| </P>
| |
| | |
| <P>
| |
| <B><A NAME="23">(23):</A></B><BR>
| |
| <B>I want to perform a hygrothermal simulation of a wall on which every day a shadow
| |
| is cast for some time by a building on the other side of the street. WUFI does not
| |
| offer an option to allow for such a shadow, but I could simply use a self-created *.KLI
| |
| file by converting the measured radiation myself and allowing for the sadow in this
| |
| process. But, how is the conversion of the radiation data done?</B>
| |
| </P>
| |
| | |
| <P>
| |
| 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.
| |
| </P>
| |
| | |
| <H3>Position of the Sun:</H3>
| |
| | |
| <P>Let <TT>J</TT> be the number of the day in the year (1 .. 365 or 366). Then
| |
| compute the auxiliary quantity <TT>x</TT>:
| |
| </P>
| |
| <P>
| |
| <TT>x = 0.9856° * J - 2.72°</TT>
| |
| </P>
| |
| <P>
| |
| and the equation of time <TT>Z</TT> (in minutes):
| |
| </P>
| |
| <P>
| |
| <TT>Z = -7.66*sin(x) - 9.87*sin( 2*x + 24.99° + 3.83°*sin(x) ).</TT>
| |
| </P>
| |
| <P>
| |
| 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.
| |
| </P>
| |
| <P>
| |
| 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.
| |
| </P>
| |
| <P>
| |
| When the apparent sun (i.e. the actually observed sun) crosses the meridian it
| |
| is 12 noon local apparent solar time (<TT>LAT</TT>); when the mean sun crosses the
| |
| meridian it is 12 noon local mean time (<TT>LMT</TT>). The equation of time is
| |
| therefore the difference between <TT>LAT</TT> and <TT>LMT</TT> (<TT>Z = LAT - LMT</TT>).
| |
| </P>
| |
| <P>
| |
| 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, <TT>CET</TT>), the difference between local mean time and
| |
| zone time must be allowed for, which is 4 minutes for 1° difference in
| |
| geographical longitude <TT>L</TT> and one hour for 15° difference. If the
| |
| measurement was timed in Central European Summer Time <TT>CEST</TT>, convert
| |
| to <TT>CET</TT> first by subtracting one hour (<TT>CET = CEST - 1h</TT>).
| |
| </P>
| |
| <P>
| |
| In this way you can now compute the corresponding local apparent time
| |
| <TT>LAT</TT> from the known measurement time (in <TT>CET</TT>):
| |
| </P>
| |
| <P>
| |
| <TT>LAT = CET - (15°-L)/(15°/h) + Z/(60 min/h) [h]</TT>
| |
| </P>
| |
| <P>
| |
| and thus determine the position of the sun: at 12 noon <TT>LAT</TT> 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.<BR>
| |
| The distance between the sun and the meridian is measured by the hour angle:
| |
| </P>
| |
| <P>
| |
| <TT><FONT FACE="SYMBOL">w</FONT> = (LAT - 12h) * 15°/h.</TT>
| |
| </P>
| |
| <P>
| |
| The hour angle <FONT FACE="SYMBOL">w</FONT> 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.
| |
| </P>
| |
| <P>
| |
| The hour angle gives the distance of the sun from the meridian; the declination
| |
| <FONT FACE="SYMBOL">d</FONT>, 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 <TT>J</TT> under consideration:
| |
| </P>
| |
| <P>
| |
| <TT>
| |
| sin(<FONT FACE="SYMBOL">d</FONT>) = 0.3978 * sin( x - 77.51° + 1.92° * sin(x) ),<BR>
| |
| cos(<FONT FACE="SYMBOL">d</FONT>) = sqrt(1 - sin(<FONT FACE="SYMBOL">d</FONT>)^2)
| |
| </TT>
| |
| </P>
| |
| <P>
| |
| where <TT>x</TT> is the auxiliary quantity introduced above.
| |
| </P>
| |
| <P>
| |
| The last step is the transformation from the coordinate system determined
| |
| by <FONT FACE="SYMBOL">w</FONT> and <FONT FACE="SYMBOL">d</FONT> into the more
| |
| familiar coordinates altitude <FONT FACE="SYMBOL">g</FONT> and azimuth
| |
| <FONT FACE="SYMBOL">y</FONT> (=compass direction). The geographical latitude
| |
| <FONT FACE="SYMBOL">j</FONT> of the measurement location is needed for this.
| |
| </P>
| |
| <P>
| |
| <TT>
| |
| sin(<FONT FACE="SYMBOL">g</FONT>) = cos(<FONT FACE="SYMBOL">d</FONT>)*cos(<FONT FACE="SYMBOL">w</FONT>)*cos(<FONT FACE="SYMBOL">j</FONT>)+sin(<FONT FACE="SYMBOL">d</FONT>)*sin(<FONT FACE="SYMBOL">j</FONT>)<BR>
| |
| cos(<FONT FACE="SYMBOL">g</FONT>) = sqrt(1 - sin(<FONT FACE="SYMBOL">g</FONT>)^2)<BR>
| |
| <BR>
| |
| if cos(<FONT FACE="SYMBOL">g</FONT>)=0 then <FONT FACE="SYMBOL">y</FONT> = 0<BR>
| |
| else begin<BR>
| |
| sin(<FONT FACE="SYMBOL">y</FONT>) = cos(<FONT FACE="SYMBOL">d</FONT>)*sin(<FONT FACE="SYMBOL">w</FONT>)/cos(<FONT FACE="SYMBOL">g</FONT>)<BR>
| |
| cos(<FONT FACE="SYMBOL">y</FONT>) = (cos(<FONT FACE="SYMBOL">d</FONT>)*cos(<FONT FACE="SYMBOL">w</FONT>)*sin(<FONT FACE="SYMBOL">j</FONT>)-sin(<FONT FACE="SYMBOL">d</FONT>)*cos(<FONT FACE="SYMBOL">j</FONT>))/cos(<FONT FACE="SYMBOL">g</FONT>)<BR>
| |
| <FONT FACE="SYMBOL">y</FONT> = atn2(sin(<FONT FACE="SYMBOL">y</FONT>), cos(<FONT FACE="SYMBOL">y</FONT>))<BR>
| |
| end
| |
| </TT>
| |
| </P>
| |
| <P>
| |
| This formula uses <TT>atn2(A,B)</TT>, the arctangent function for two arguments
| |
| <TT>A</TT> and <TT>B</TT>, which is provided by many programming languages, and which
| |
| gives the arctangent of <TT>A/B</TT> 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 <TT>y=atn(A/B)</TT>, and in the case <TT>B<0</TT>
| |
| you add <TT>180°</TT> if <TT>y<=0</TT> or subtract <TT>180°</TT> if <TT>y>0</TT>.
| |
| If <TT>B=0</TT> and <TT>A<0</TT> then <TT>y=-90°</TT>, if <TT>B=0</TT> and
| |
| <TT>A>0</TT>, then <TT>y=+90°</TT>.).<BR>
| |
| The azimuth <FONT FACE="SYMBOL">y</FONT> is counted from south=0°, positive
| |
| towards the west and negative towards the east.
| |
| </P>
| |
| <P>
| |
| Examples for Munich (<TT>48.13°N</TT>, <TT>11.58°E</TT>):
| |
| </P>
| |
| <TABLE>
| |
| | |
| <TR ALIGN="CENTER"><TD>CET</TD><TD>Altitude</TD><TD>Azimuth</TD><TD>Declination</TD></TR>
| |
| <TR><TD COLSPAN="4"><TT>(J=1)</TT></TD></TR>
| |
| <TR ALIGN="RIGHT"><TD><TT> 1 Jan. 2001 09:00</TD><TD> 6.436°</TD><TD>-44.614°</TD><TD>-22.987°</TD></TR>
| |
| <TR ALIGN="RIGHT"><TD><TT> 1 Jan. 2001 12:00</TD><TD>18.836°</TD><TD> -4.209°</TD><TD>-22.977°</TD></TR>
| |
| <TR ALIGN="RIGHT"><TD><TT> 1 Jan. 2001 16:00</TD><TD> 3.441°</TD><TD> 49.590°</TD><TD>-22.962°</TD></TR>
| |
| <TR ALIGN="RIGHT"><TD><TT> 1 Jan. 2001 16:25</TD><TD> 0.434°</TD><TD> 54.316°</TD><TD>-22.961°</TD></TR>
| |
| <TR><TD COLSPAN="4"> </TD></TR>
| |
| <TR><TD COLSPAN="4"><TT>(J=79)</TT></TD></TR>
| |
| <TR ALIGN="RIGHT"><TD><TT>20 Mar. 2001 07:00</TD><TD> 6.498°</TD><TD>-82.661°</TD><TD> -0.126°</TD></TR>
| |
| <TR ALIGN="RIGHT"><TD><TT>20 Mar. 2001 12:21</TD><TD>41.851°</TD><TD> -0.041°</TD><TD> -0.038°</TD></TR>
| |
| <TR ALIGN="RIGHT"><TD><TT>20 Mar. 2001 16:00</TD><TD>22.726°</TD><TD> 62.242°</TD><TD> +0.022°</TD></TR>
| |
| <TR ALIGN="RIGHT"><TD COLSPAN="4"> </TD></TR>
| |
| <TR><TD COLSPAN="4"><TT>(J=172)</TT></TD></TR>
| |
| <TR ALIGN="RIGHT"><TD><TT>21 Jun. 2001 08:00</TD><TD>34.501°</TD><TD>-87.522°</TD><TD>+23.437°</TD></TR>
| |
| <TR ALIGN="RIGHT"><TD><TT>21 Jun. 2001 12:00</TD><TD>65.126°</TD><TD> -8.437°</TD><TD>+23.437°</TD></TR>
| |
| <TR ALIGN="RIGHT"><TD><TT>21 Jun. 2001 18:00</TD><TD>19.771°</TD><TD>103.475°</TD><TD>+23.436°</TD></TR>
| |
| </TABLE>
| |
| | |
| <P>
| |
| 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 (<TT>1 Jan. 16:25</TT>), 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.
| |
| </P>
| |
| | |
| <P>
| |
|
| |
| </P>
| |
| | |
| <H3>Converting the Radiation Data:</H3>
| |
| <P>
| |
| We assume that your input data are measured hourly values of the global
| |
| (<TT>I_glob</TT>) and the diffuse radiation (<TT>I_diff</TT>) on a horizontal surface.
| |
| </P>
| |
| <P>
| |
| 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 <TT>I_dir_normal</TT>. The direct radiation
| |
| <TT>I_dir</TT> obliquely incident on a horizontal measuring surface depends on
| |
| the solar altitude <FONT FACE="SYMBOL">g</FONT>:
| |
| </P>
| |
| <P>
| |
| <TT>I_dir = I_dir_normal * sin(<FONT FACE="SYMBOL">g</FONT>)</TT>.
| |
| </P>
| |
| <P>
| |
| Since <TT>I_dir</TT> can be computed as the difference between the measured values
| |
| of global and diffuse radiation and <FONT FACE="SYMBOL">g</FONT></TT> can be determined
| |
| from the measurement location and time by the method given above, the corresponding
| |
| direct normal radiation is
| |
| </P>
| |
| <P>
| |
| <TT>I_dir_normal = (I_glob - I_diff) / sin(<FONT FACE="SYMBOL">g</FONT>).</TT>
| |
| </P>
| |
| <P>
| |
| The angle of incidence <FONT FACE="SYMBOL">h</FONT>, i.e. the angle that the direct
| |
| normal radiation makes with the normal to the component surface which is tilted by
| |
| the angle <FONT FACE="SYMBOL">b</FONT> and oriented in the
| |
| direction <FONT FACE="SYMBOL">a</FONT>, is
| |
| </P>
| |
| <TABLE>
| |
| <TR><TD COLSPAN="2">cos(<FONT FACE="SYMBOL">h</FONT>) = sin(<FONT FACE="SYMBOL">g</FONT>)*cos(<FONT FACE="SYMBOL">b</FONT>) + cos(<FONT FACE="SYMBOL">g</FONT>)*sin(<FONT FACE="SYMBOL">b</FONT>)*cos(<FONT FACE="SYMBOL">a</FONT>-<FONT FACE="SYMBOL">y</FONT>)</TD></TR>
| |
| <TR><TD><FONT FACE="SYMBOL">h</FONT>:</TD><TD>Angle of incidence (vertical=0°)</TD></TR>
| |
| <TR><TD><FONT FACE="SYMBOL">g</FONT>:</TD><TD>Altitude of the sun</TD></TR>
| |
| <TR><TD><FONT FACE="SYMBOL">y</FONT>:</TD><TD>Azimuth of the sun (south=0°, positive towards west, negative towards east)</TD></TR>
| |
| <TR><TD><FONT FACE="SYMBOL">b</FONT>:</TD><TD>Tilt of the component surface (vertical wall=90°)</TD></TR>
| |
| <TR><TD><FONT FACE="SYMBOL">a</FONT>:</TD><TD>Azimuth of the normal to the component surface (south=0°, west positive).</TD></TR>
| |
| </TABLE>
| |
| <P>
| |
| The direct radiation incident on the component surface is therefore:
| |
| </P>
| |
| <P>
| |
| <TT>
| |
| I_dir_in = I_dir_normal * cos(<FONT FACE="SYMBOL">h</FONT>)<BR>
| |
| = (I_glob - I_diffus) * cos(<FONT FACE="SYMBOL">h</FONT>) / sin(<FONT FACE="SYMBOL">g</FONT>).
| |
| </TT>
| |
| </P>
| |
| <P>
| |
| 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 <TT>I_diff</TT>,
| |
| 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):
| |
| </P>
| |
| <P>
| |
| <TT>I_diff_in = I_diff * ( cos(<FONT FACE="SYMBOL">b</FONT>/2) )^2</TT>.
| |
| </P>
| |
| <P>
| |
| Additionally, you may add the global radiation reflected from the ground:
| |
| </P>
| |
| <P>
| |
| <TT>I_refl_in = <FONT FACE="SYMBOL">r</FONT> * I_glob * ( sin(<FONT FACE="SYMBOL">b</FONT>/2) )^2</TT>,
| |
| </P>
| |
| <P>
| |
| where <FONT FACE="SYMBOL">r</FONT> 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.
| |
| </P>
| |
| <P>
| |
| The total radiation incident on the surface of the building component is the sum
| |
| of the components:
| |
| </P>
| |
| <P>
| |
| <TT>I_in = I_dir_in + I_diff_in + I_refl_in</TT>.
| |
| </P>
| |
| <P>
| |
| 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.
| |
| </P>
| |
| <P>
| |
| Hint: if the radiation data to be converted have been averaged over some longer
| |
| interval (e.g. one hour), please note the following:
| |
| </P>
| |
| <P>
| |
| It is advisable to compute the solar positions for the middle of the measuring
| |
| interval, i.e. the averaged data measured between <TT>9h</TT> and <TT>10h</TT>
| |
| should be converted using the solar position computed for <TT>9:30h</TT>.<BR>
| |
| 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.
| |
| </P>
| |
| <P>
| |
| 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.
| |
| </P>
| |
| <P>
| |
| Details on these conversion methods can be found in:<BR>
| |
| VDI 3789 Umweltmeteorologie, Blatt 2: Wechselwirkungen zwischen Atmosphäre und Oberflächen; Berechnung der kurz- und der langwelligen Strahlung.
| |
| </P>
| |
| <P>
| |
| In addition to data on global and diffuse radiation, the weather file
| |
| <TT>IBP1991.WET</TT> included with WUFI contains radiation data obtained with
| |
| a west-facing solarimeter which you can use to test your conversion routines.
| |
| </P>
| |
