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is the ratio of the mass m of the sample and the total volume | is the ratio of the mass m of the sample and the total volume | ||
V<small>tot</small> of the sample: | V<small>tot</small> of the sample: | ||
<math>\rho_{bulk} = m / V_{tot}</math>.<BR> | |||
The true density ρ<small> | The true density ρ<small>true</small>, by | ||
contrast, is the ratio of the mass of the sample and the volume taken | contrast, is the ratio of the mass of the sample and the volume taken | ||
up by the material matrix only: | up by the material matrix only: | ||
ρ<small> | ρ<small>true</small> = m / | ||
(V<small>tot</small> - V<small>pores</small>) = m / V<small>true</small>.<BR> | (V<small>tot</small> - V<small>pores</small>) = m / V<small>true</small>.<BR> | ||
<BR> | <BR> | ||
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[[Details:MoistureStorageFunction | maximum water content]] | [[Details:MoistureStorageFunction | maximum water content]] | ||
w<small>max</small> (by | w<small>max</small> (by | ||
multiplication by < | multiplication by ρ<small>water</small> = 1000 kg/m³).<BR> | ||
<BR> | <BR> | ||
Since most calculations are not sensitive to the exact value of the | Since most calculations are not sensitive to the exact value of the | ||
Zeile 44: | Zeile 44: | ||
<BR> | <BR> | ||
The porosity can be estimated from the true density | The porosity can be estimated from the true density | ||
ρ<small>true</small> and the bulk | |||
density | density ρ<small>bulk</small>:<BR> | ||
ρ<small>bulk</small> = m / V<small>tot</small> = m / (V<small>true</small> + V<small>pores</small>) = ρ<small>true</small> / (1 + V<small>pores</small>/V<small>true</small>) = ρ<small>true</small> * V<small>true</small>/V<small>tot</small> = ρ<small>true</small> * (1 - V<small>pores</small>/V<small>tot</small>) = ρ<small>true</small> * (1 - porosity), therefore<BR> | |||
<BR> | <BR> | ||
<CENTER>porosity = 1 - | <CENTER>porosity = 1 - ρ<small>bulk</small> / ρ<small>true</small>.</CENTER> | ||
<BR> | <BR> | ||
ρ<small>true</small> can in turn be | |||
estimated from other materials which have the same composition but | estimated from other materials which have the same composition but | ||
different bulk density, if their bulk density and porosity are known. | different bulk density, if their bulk density and porosity are known. | ||
Example: a cellular concrete brick with | Example: a cellular concrete brick with ρ<small>bulk</small> = 600 kg/m³ and porosity = 0.72 has | ||
ρ<small>true</small> = | |||
600 / (1 - 0.72) kg/m³ = 2140 kg/m³. The porosity of a | 600 / (1 - 0.72) kg/m³ = 2140 kg/m³. The porosity of a | ||
cellular concrete brick with | cellular concrete brick with ρ<small>bulk</small> = 400 kg/m³ can then be estimated as | ||
porosity = 1 - 400 / 2140 = 0.81.<BR> | porosity = 1 - 400 / 2140 = 0.81.<BR> | ||
<BR> | <BR> | ||
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the specific heat capacity by mass of the dry material.<BR> | the specific heat capacity by mass of the dry material.<BR> | ||
<BR> | <BR> | ||
Using the specific heat capacity by mass has the advantage that this | Using the specific heat capacity <I>by mass</I> has the advantage that this | ||
value only depends on the chemical composition of the material, but | value only depends on the chemical composition of the material, but | ||
not on its porosity. For example, cellular concrete bricks with | not on its porosity. For example, cellular concrete bricks with | ||
Zeile 79: | Zeile 79: | ||
organic materials. In most cases, these estimates will be sufficient | organic materials. In most cases, these estimates will be sufficient | ||
since hygrothermal simulations usually don't depend very sensitively on | since hygrothermal simulations usually don't depend very sensitively on | ||
this value. | this value. | ||
| | ||
WUFI automatically allows for the additional heat capacity of the | WUFI automatically allows for the additional heat capacity of the | ||
water content, if any.<BR> | water content, if any.<BR> | ||
Zeile 97: | Zeile 98: | ||
side of the specimen and condensing at the other side, thus | side of the specimen and condensing at the other side, thus | ||
in effect transporting latent heat without a corresponding | in effect transporting latent heat without a corresponding | ||
heat flow being conducted across the specimen). Since WUFI | heat flow being <I>conducted</I> across the specimen). Since WUFI | ||
explicitly computes this thermal effect of vapor flow, it | explicitly computes this thermal effect of vapor flow, it | ||
should not be included in the heat conductivity, if possible. | should not be included in the heat conductivity, if possible. | ||
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<BR> | <BR> | ||
On the other hand, hygrothermal simulations (in particular the | On the other hand, hygrothermal simulations (in particular the | ||
resulting moisture contents and distributions) usually don't depend | resulting <I>moisture</I> contents and distributions) usually don't depend | ||
very sensitively on the precise values of the heat conductivities, | very sensitively on the precise values of the heat conductivities, | ||
so the difference may be generally negligible unless you are | so the difference may be generally negligible unless you are | ||
specifically interested in heat flows.<BR> | specifically interested in <I>heat</I> flows.<BR> | ||
<BR> | <BR> | ||
Aktuelle Version vom 3. Juli 2009, 09:10 Uhr
Basic Material Data
These material data constitute an indispensable minimum without which a calculation is not possible:
- • Bulk density [kg/m³],
-
serves to convert the specific heat by mass to the specific heat
by volume.
The bulk density ρbulk is the ratio of the mass m of the sample and the total volume Vtot of the sample: Fehler beim Parsen (SVG (MathML kann über ein Browser-Plugin aktiviert werden): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://wikimedia.org/api/rest_v1/“:): {\displaystyle \rho_{bulk} = m / V_{tot}} .
The true density ρtrue, by contrast, is the ratio of the mass of the sample and the volume taken up by the material matrix only: ρtrue = m / (Vtot - Vpores) = m / Vtrue.
The bulk density should be available for virtually every building material. If not, it can be measured very easily. Since it only affects the specific heat value entering into the calculation, and hygrothermal simulations usually don't depend very sensitively on this value, it need not be known with great precision.
- • Porosity [m³/m³],
-
determines the
maximum water content
wmax (by
multiplication by ρwater = 1000 kg/m³).
Since most calculations are not sensitive to the exact value of the maximum water content (you'll rarely encounter water contents above free saturation, it is usually sufficient to estimate it if no value is available for the material in question.
The porosity can be estimated from the true density ρtrue and the bulk density ρbulk:
ρbulk = m / Vtot = m / (Vtrue + Vpores) = ρtrue / (1 + Vpores/Vtrue) = ρtrue * Vtrue/Vtot = ρtrue * (1 - Vpores/Vtot) = ρtrue * (1 - porosity), therefore
porosity = 1 - ρbulk / ρtrue.
ρtrue can in turn be estimated from other materials which have the same composition but different bulk density, if their bulk density and porosity are known. Example: a cellular concrete brick with ρbulk = 600 kg/m³ and porosity = 0.72 has ρtrue = 600 / (1 - 0.72) kg/m³ = 2140 kg/m³. The porosity of a cellular concrete brick with ρbulk = 400 kg/m³ can then be estimated as porosity = 1 - 400 / 2140 = 0.81.
- • Heat capacity [J/kgK],
-
the specific heat capacity by mass of the dry material.
Using the specific heat capacity by mass has the advantage that this value only depends on the chemical composition of the material, but not on its porosity. For example, cellular concrete bricks with bulk densities of 400 kg/m³ and 600 kg/m³ have the same specific heat capacity by mass.
To convert into heat capacity by volume (which enters into the transport equations), WUFI multiplies the mass-specific heat capacity by the bulk density.
Rough values are 850 J/kgK for mineral materials and 1500 J/kgK for organic materials. In most cases, these estimates will be sufficient since hygrothermal simulations usually don't depend very sensitively on this value. WUFI automatically allows for the additional heat capacity of the water content, if any.
- • Heat conductivity dry [W/mK],
-
the heat conductivity of the material in dry condition. A
moisture-dependent
heat conductivity is optional.
Please note that experimentally measured heat conductivities of vapor-permeable materials may include the effect of vapor transport with phase change (i.e. water evaporating at one side of the specimen and condensing at the other side, thus in effect transporting latent heat without a corresponding heat flow being conducted across the specimen). Since WUFI explicitly computes this thermal effect of vapor flow, it should not be included in the heat conductivity, if possible. However, it is usually difficult or impossible to separate this effect out of the measured data.
Furthermore, design values, such as the data given in German Standard DIN 4108, may already contain the contribution of a typical water content and, if so, are not strictly dry values.
If you want to perform the calculation with a constant (i.e. not moisture-dependent) heat conductivity (for example because you have no detailed data on the moisture-dependence), you may use these design values to allow for moisture content at least in a crude approximation. However, if you explicitly use a table of moisture-dependent heat conductivities, you should make sure that the value for moisture content = 0 is really the dry value.
On the other hand, hygrothermal simulations (in particular the resulting moisture contents and distributions) usually don't depend very sensitively on the precise values of the heat conductivities, so the difference may be generally negligible unless you are specifically interested in heat flows.
- • Diffusion resistance factor dry [-]
- the diffusion resistance factor (µ-value) of the
material in dry condition. The µ-value states by how much
the diffusion resistance of the material in question is higher
than that of stagnant air. A
moisture-dependent µ-value
is optional.
The definition of the µ-value and its relation to permeability are discussed in the topic Water Vapor Diffusion.
Please note that even if you do not explicitly use a moisture-dependent µ-value, WUFI will treat it as moisture-dependent for moisture contents above free saturation wf. WUFI will reduce it in proportion to the moisture excess over wf, until it reaches µ=0 at wmax. This reflects - in a first approximation - the fact that at very high moisture contents even the larger capillaries become clogged with water and can't contribute to vapor transport any more.