Details:MoistureStorageFunction - Versionsgeschichte

SebSta am 13. Juni 2013 um 12:45 Uhr

2013-06-13T12:45:28Z

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	The moisture storage function of non-hygroscopic materials		The moisture storage function of non-hygroscopic materials
	(essentially insulating materials, but		(essentially insulating materials, but
	[[AirLayers\|air layers]] as well) is		[[Details:AirLayers\|air layers]] as well) is
	theoretically more or less zero in the region		theoretically more or less zero in the region
	φ = 0..1, whereas for		φ = 0..1, whereas for

Barbara: /* Approximation of the moisture storage function */

2009-03-25T10:19:21Z

Approximation of the moisture storage function

← Nächstältere Version		Version vom 25. März 2009, 12:19 Uhr
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	</P>		</P>
	<TABLE>		<TABLE>
	<TR><TD VALIGN="CENTER">w = w<small>f</small>·</TD><TD><U>(b-1)·~~<FONT FACE="SYMBOL">j</FONT>~~</U><BR>b-~~<FONT FACE="SYMBOL">j</FONT>~~</TD><TD> </TD></TR>		<TR><TD VALIGN="CENTER">w = w<small>f</small>·</TD><TD><U>(b-1)·φ</U><BR>b-φ</TD><TD> </TD></TR>
	<TR><TD COLSPAN="3"> </TD></TR>		<TR><TD COLSPAN="3"> </TD></TR>
	<TR><TD>w</TD><TD>[kg/m³]:</TD><TD>moisture content corresponding to relative humidity ~~<FONT FACE="SYMBOL">j</FONT>~~</TD></TR>		<TR><TD>w</TD><TD>[kg/m³]:</TD><TD>moisture content corresponding to relative humidity φ</TD></TR>
	<TR><TD>w<small>f</small></TD><TD>[kg/m³]:</TD><TD>moisture content at free saturation</TD></TR>		<TR><TD>w<small>f</small></TD><TD>[kg/m³]:</TD><TD>moisture content at free saturation</TD></TR>
	<TR><TD>~~<FONT FACE="SYMBOL">j</FONT>~~</TD><TD>[-]:</TD><TD>relative		<TR><TD>φ</TD><TD>[-]:</TD><TD>relative
	humidity</TD></TR>		humidity</TD></TR>
	<TR><TD>b</TD><TD>[-]:</TD><TD>approximation factor,</TD></TR>		<TR><TD>b</TD><TD>[-]:</TD><TD>approximation factor,</TD></TR>
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	[[AirLayers\|air layers]] as well) is		[[AirLayers\|air layers]] as well) is
	theoretically more or less zero in the region		theoretically more or less zero in the region
	~~<FONT FACE="SYMBOL">j</FONT>~~ = 0..1, whereas for		φ = 0..1, whereas for
	~~<FONT FACE="SYMBOL">j</FONT>~~ = 1 it takes on some indefinite		φ = 1 it takes on some indefinite
	value between zero and w<small>max</small>, so that no		value between zero and w<small>max</small>, so that no
	well-defined functional relationship exists. Because of numerical		well-defined functional relationship exists. Because of numerical

Barbara: /* The moisture storage function in WUFI */

2009-03-25T10:16:33Z

The moisture storage function in WUFI

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	The pressure plate measurements would even allow a still finer		The pressure plate measurements would even allow a still finer
	subdivision of the table in the high-moisture region, but then		subdivision of the table in the high-moisture region, but then
	at ~~<FONT FACE="SYMBOL">j</FONT>~~ ~ 1 the curve would approach		at φ ~ 1 the curve would approach
	the ordinate so closely that its immensely steep slope might cause		the ordinate so closely that its immensely steep slope might cause
	numerical problems. If the moisture transport across the interface		numerical problems. If the moisture transport across the interface
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	<CENTER>		<CENTER>
	<TABLE>		<TABLE>
	<TR><TD ALIGN="CENTER">~~<FONT FACE="SYMBOL">j</FONT>~~[-]<BR> </TD><TD ALIGN="CENTER">w[kg/m³]<BR> </TD></TR>		<TR><TD ALIGN="CENTER">φ[-]<BR> </TD><TD ALIGN="CENTER">w[kg/m³]<BR> </TD></TR>
	<TR><TD ALIGN="CENTER">...</TD><TD ALIGN="CENTER">...</TD></TR>		<TR><TD ALIGN="CENTER">...</TD><TD ALIGN="CENTER">...</TD></TR>
	<TR><TD ALIGN="CENTER">1.01</TD><TD ALIGN="CENTER">w<small>max</small></TD></TR>		<TR><TD ALIGN="CENTER">1.01</TD><TD ALIGN="CENTER">w<small>max</small></TD></TR>

Len am 30. September 2008 um 19:03 Uhr

2008-09-30T19:03:28Z

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	The moisture storage function of non-hygroscopic materials		The moisture storage function of non-hygroscopic materials
	(essentially insulating materials, but		(essentially insulating materials, but
	[[~~Details:~~AirLayers\|air layers]] as well) is		[[AirLayers\|air layers]] as well) is
	theoretically more or less zero in the region		theoretically more or less zero in the region
	<FONT FACE="SYMBOL">j</FONT> = 0..1, whereas for		<FONT FACE="SYMBOL">j</FONT> = 0..1, whereas for

AntretterF am 11. März 2008 um 16:55 Uhr

2008-03-11T16:55:45Z

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	the equilibrium moisture.		the equilibrium moisture.
	</P>		</P>
	[[Bild:e_fspfkt_k]]		[[Bild:e_fspfkt_k.gif]]


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	materials (e.g. some kinds of concrete).		materials (e.g. some kinds of concrete).
	</P>		</P>
	[[Bild:E_fspfkt_meas_approx]]		[[Bild:E_fspfkt_meas_approx.gif]]

AntretterF am 11. März 2008 um 16:53 Uhr

2008-03-11T16:53:59Z

← Nächstältere Version		Version vom 11. März 2008, 18:53 Uhr
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	the equilibrium moisture.		the equilibrium moisture.
	</P>		</P>
			[[Bild:e_fspfkt_k]]

	~~<IMG SRC="pix/e_fspfkt_k.gif" WIDTH="300" HEIGHT="242" VSPACE="0" HSPACE="0" ALT="">~~

	<P>		<P>
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	materials (e.g. some kinds of concrete).		materials (e.g. some kinds of concrete).
	</P>		</P>
	~~<IMG SRC="pix/e_fspfkt_meas_approx.gif" WIDTH="472" HEIGHT="177" VSPACE="0" HSPACE="0" ALT="">~~		[[Bild:E_fspfkt_meas_approx]]


	<H3>WUFI's default moisture storage function</H3>		<H3>WUFI's default moisture storage function</H3>

AntretterF: Die Seite wurde neu angelegt: = Moisture Storage Function = === The moisture storage function ===
In a porous hygroscopic material, the surfaces of the pore system accumulate water molecules un...

2008-03-11T16:46:10Z

Die Seite wurde neu angelegt: = Moisture Storage Function = === The moisture storage function === In a porous hygroscopic material, the surfaces of the pore system accumulate water molecules un...

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= Moisture Storage Function =

=== The moisture storage function ===

In a porous hygroscopic material, the surfaces of the pore system
accumulate water molecules until a specific equilibrium moisture
content corresponding to the humidity of the ambient
air is reached.
Due to the reduction of the saturation vapor pressure in the smaller
capillaries, there is also some condensation which - at relative
humidities above ca. 0.6 .. 0.8 - results in a marked increase of
the equilibrium moisture.


<IMG SRC="pix/e_fspfkt_k.gif" WIDTH="300" HEIGHT="242" VSPACE="0" HSPACE="0" ALT="">


A capillary-active material in contact with water will take up this
water until it reaches its free saturation wf.
This water content wf corresponds to the moisture
storage function at a relative humidity of 1 (=100%). Because of
air pockets trapped in the pore structure, however, the free
saturation is less than the maximum water content
wmax which is determined by the
[[Details:BasicMaterialData | porosity]]. Moisture
contents exceeding wf may e.g. result from
condensation in a temperature gradient (especially in insulation
materials; these are often not capillary-active and therefore
have wf ~ 0).


The free saturation wf ranks among the standard
material data and is known for most materials. The 'practical
moisture content' w80 that corresponds to the
equilibrium moisture at a RH of 0.8 is another standard quantity.


The dependence of the moisture storage function on the temperature is marginal and is ignored in WUFI.


=== Measurement of the moisture storage function ===

Because of limitations of the respective measuring procedures,
the moisture storage function has to be composed from sorption
isotherms (up to ~ 0.9 RH) and pressure plate measurements
(above 0.95 RH) [1]. The hysteresis between adsorption and
desorption isotherms is usually not very pronounced, so that it
is sufficient to use the adsorption isotherm. Where necessary, a
mean isotherm may be used. Due to the measuring technique, the
pressure plate measurements are 'desorption' measurements.


=== The moisture storage function in WUFI ===

In WUFI, the moisture storage function is described by means of
a table with relative humidities and the corresponding moisture
contents. The table may contain an arbitrary number of entries
between which WUFI interpolates linearly.


Example: Sander sandstone

<CENTER>
<TABLE>
<TR ALIGN="CENTER"><TD>j [-]</TD><TD>w[kg/m³]</TD></TR>
<TR ALIGN="RIGHT"><TD> </TD><TD> </TD></TR>
<TR ALIGN="RIGHT"><TD>0</TD><TD>0</TD></TR>
<TR ALIGN="RIGHT"><TD>0.1</TD><TD>4.4</TD></TR>
<TR ALIGN="RIGHT"><TD>0.3</TD><TD>10.2</TD></TR>
<TR ALIGN="RIGHT"><TD>0.65</TD><TD>15.2</TD></TR>
<TR ALIGN="RIGHT"><TD>0.8</TD><TD>19.0</TD></TR>
<TR ALIGN="RIGHT"><TD>0.91</TD><TD>30.0</TD></TR>
<TR ALIGN="RIGHT"><TD>0.95</TD><TD>45.9</TD></TR>
<TR ALIGN="RIGHT"><TD>0.99</TD><TD>61.7</TD></TR>
<TR ALIGN="RIGHT"><TD>0.995</TD><TD>75.0</TD></TR>
<TR ALIGN="RIGHT"><TD>1.0</TD><TD>130.0</TD></TR>
</TABLE>
</CENTER>

The pressure plate measurements would even allow a still finer
subdivision of the table in the high-moisture region, but then
at j ~ 1 the curve would approach
the ordinate so closely that its immensely steep slope might cause
numerical problems. If the moisture transport across the interface
between two capillary-active materials in capillary contact is to be
calculated, however, the moisture storage function must be as detailed
as possible in this region [2]. (If the capillary contact is non-ideal,
an additional transfer resistance has to be taken into account [2]).


WUFI allows moisture contents in the supersaturated region, since
these may well occur under condensation conditions. However, in
this region there is no unique functional relation between relative
humidity and moisture content. The relative humidity is always 1,
and the moisture content varies between wf and
wmax. 
The moisture content thus doesn't depend on the relative humidity,
it is determined by the boundary conditions: it increases under
condensation conditions and decreases under evaporation conditions.
In order to treat these moisture contents above wf,
WUFI internally extends the table of each material by introducing
an additional entry:

<CENTER>
<TABLE>
<TR><TD ALIGN="CENTER">j[-]  </TD><TD ALIGN="CENTER">w[kg/m³]  </TD></TR>
<TR><TD ALIGN="CENTER">...</TD><TD ALIGN="CENTER">...</TD></TR>
<TR><TD ALIGN="CENTER">1.01</TD><TD ALIGN="CENTER">wmax</TD></TR>
</TABLE>
</CENTER>


Relative humidities between 1 and 1.01 are only fictitious,
of course, but they allow WUFI to assign a unique RH to each
water content, as required by the moisture transport equations.


During the calculation WUFI performs iterations where it samples
small regions of the tabulated curve. Very sharp bends in the
curve may throw the iteration off and thus impede its convergence.
In such a case, the curve should be smoothed by inserting
additional points. A large number of entries may slow the search
in the table, however.


=== Approximation of the moisture storage function ===

If the moisture storage function can be adequately described by
the function

<TABLE>
<TR><TD VALIGN="CENTER">w = wf·</TD><TD>(b-1)·j b-j</TD><TD> </TD></TR>
<TR><TD COLSPAN="3"> </TD></TR>
<TR><TD>w</TD><TD>[kg/m³]:</TD><TD>moisture content corresponding to relative humidity j</TD></TR>
<TR><TD>wf</TD><TD>[kg/m³]:</TD><TD>moisture content at free saturation</TD></TR>
<TR><TD>j</TD><TD>[-]:</TD><TD>relative
humidity</TD></TR>
<TR><TD>b</TD><TD>[-]:</TD><TD>approximation factor,</TD></TR>
</TABLE>


then it is sufficient to specify w80 and
wf, in order to define the moisture storage
function for WUFI (this is called 'approximation of the moisture
storage function'). However, this condition is not met by all
materials (e.g. some kinds of concrete).

<IMG SRC="pix/e_fspfkt_meas_approx.gif" WIDTH="472" HEIGHT="177" VSPACE="0" HSPACE="0" ALT="">

<H3>WUFI's default moisture storage function</H3>

The moisture storage function of non-hygroscopic materials
(essentially insulating materials, but
[[Details:AirLayers|air layers]] as well) is
theoretically more or less zero in the region
j = 0..1, whereas for
j = 1 it takes on some indefinite
value between zero and wmax, so that no
well-defined functional relationship exists. Because of numerical
requirements, however, WUFI assigns a (low) artificial moisture
storage function to all materials for which the user did not
define such a function. 
So the results of a WUFI calculation will indicate some (low)
moisture content even in materials for which you did not define
a moisture storage function. These moisture contents are artificial
and should be regarded with caution. Only when the moisture contents
surpass the fictitious free saturation of ca. 0.05·wmax,
they have resulted from condensation phenomena which are independent
from the choice of the moisture storage function. In that case the
excess of the moisture content over wf can with
appropriate caution be regarded as a realistic measure of the
amount of condensed moisture.


For discussion of some specific questions concerning the moisture storage function, see the
[[FAQ:Main|Questions & Answers]] section.


Literature:

<TABLE>
<TR><TD VALIGN="TOP">[1]</TD><TD>Krus, M.: Moisture Transport and
Storage Coefficients of Porous Mineral Building Materials.
Theoretical Principles and New Test Methods 
Fraunhofer IRB Verlag, 1996</TD></TR>

<TR><TD VALIGN="TOP">[2]</TD><TD>Holm, A., Krus, M., Künzel, H.M.:
Feuchtetransport über Materialgrenzen im Mauerwerk. 
Bauinstandsetzen 2 (1996), H. 5, 375 - 396.
</TABLE>