Air Humidity Tutorial (English)

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Thomas
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Air Humidity Tutorial (English)

Post by Thomas » Fri Nov 09, 2018 4:00 am -1100

Air Humidity Tutorial

The humidity data for the exterior or the interior air describe the moisture content of the air. In a hygrothermal simulation, the humidity of the ambient air is needed to determine
  • the strength of the vapor diffusion exchange between the building component surface and the ambient air,
  • the hygroscopic moisture content of a material exposed to the air.

There exists a variety of quantities describing the humidity of the air. Most of these humidity measures are in fact different physical quantities, not only different scales describing the same quantity (for example, degrees Fahrenheit and degrees Celsius are only two different scales describing the physical quantity "temperature"). While this variety may seem confusing, each of these quantities has its own advantages for certain applications. The user does not need to be familiar with these details to use the program, but the descriptions provided below may be helpful for a deeper understanding of hygric processes or for creating a user-defined weather file.

Humidity in WUFI

Different humidity measures are needed to describe different hygrothermal processes:

• In a hygrothermal simulation, vapor pressure differences are the driving force for vapor diffusion transport, both across the surfaces of a component and within the component. Diffusion processes are trying to equalize vapor pressure differences.

WUFI uses the humidity of the ambient air and the moisture content of the component surface to compute the vapor pressures on both sides of the surface - in the air and in the material. Their difference then determines the vapor diffusion flow across the surface. This vapor diffusion flow has to cross the boundary air layer which sticks to the surface and acts as a diffusion resistance. The diffusion flow across the surface is proportional to the driving vapor pressure difference and to the water vapor transfer coefficient which describes the properties of the boundary air layer.

Within the component, vapor pressure differences in the pore air also give rise to vapor diffusion transport, redistributing the moisture within the component. The diffusion resistance of the pore air is described by the μ-value of the material.

• If the surface temperature of the component falls below the dew point temperature of the ambient air, dew deposition occurs.

• The equilibrium water content in a porous material exposed to ambient air is determined by the relative humidity of the air.

Moreover, differences of relative humidity within a porous material are the driving force for capillary transport of liquid water within the material. Capillary transport processes are trying to equalize differences in relative humidity. The intensity of the liquid flow is determined by the liquid transport coefficients.

If there is a temperature gradient across the building component, vapor pressure gradients and relative humidity gradients may point in opposite directions, giving simultaneously rise to vapor diffusion flows and liquid capillary flows which go in opposite directions . This is an example for a case where different humidity parameters are instrumental in determining the strengths and directions of different moisture transport mechanisms, possibly even acting simultaneously in opposite directions.

For a building component, this situation often occurs in winter when due to the low outdoor temperatures the indoor vapor pressure is higher than the outdoor vapor pressure while at the same time the outdoor relative humidity is higher than the indoor relative humidity.

Image


Humidity Parameters

The climate file formats WUFI can read use the relative humidity as a measure of the moisture content of the air. However, if you are using weather data from other sources, you may encounter other humidity parameters. The following sections provide discussions of various popular humidity parameters for reference. Beyond the mere definitions, some background information about the parameters is presented which is not required to perform hygrothermal simulations but which may be helpful in understanding hygric processes.

Some of the humidity parameters depend on temperature and pressure as well as on the amount of moisture in the air. That is, they change not only when water molecules are added to or removed from the air, but also when temperature or pressure changes occur. This is not a shortcoming of these parameters, it is appropriate for describing the respective properties of the moist air.
(In hygrothermal building simulations where the pressure is usually the atmospheric pressure, the effect of pressure changes is usually negligible. It may be important in compressed air systems, for example.)



• Water vapor partial pressure

The water vapor partial pressure (or water vapor pressure for short) is the pressure which the water vapor in the air contributes to the total pressure of the air (Dalton's law).

The water vapor pressure increases if water molecules are added to the air because the pressure of a gas is proportional to the number of molecules (Avogadro's law).

However, in technical applications the water vapor pressure may also change without water molecules being added or removed. The water vapor pressure in a given parcel of air increases if the temperature is raised at fixed volume (Charles's law, the molecules move faster), or if the volume is compressed by increased pressure at fixed temperature (Boyle's law, the more concentrated molecules hit the container walls more often). The latter case is relevant for air compressors: If the air is compressed to such a degree that the increased vapor pressure of the contained water vapor exceeds the saturation vapor pressure at the current temperature, condensate is produced.

In hygrothermal simulations, however, these conditions usually do not occur. The air involved in a simulation (outdoor air, indoor air, pore air) is normally open to the ambient atmosphere, and it is therefore the total pressure which remains fixed. Under these conditions, the volume of a given parcel of air is not fixed, it can freely contract and expand if its temperature changes. It is also not compressed or rarefied by pressure changes because its pressure is always the same as the constant ambient barometric pressure (the small meteorological variations in the ambient pressure are negligible in this context). In this situation, the water vapor pressure only changes when water molecules are actually added to or removed from the air. If the temperature increases, the speed of the molecules increases, but because the unrestrained volume increases as well, the density of the molecules decreases in just the right way to keep the water vapor partial pressure constant.

The maximum amount of water the air can hold at a given temperature is usually described in terms of the saturation vapor pressure. For example, at 0° C the saturation vapor pressure is 611 Pa, and at 20° C the saturation vapor pressure is 2339 Pa. A simple formula for calculating the saturation vapor pressure is given below.

Vapor pressure differences are the driving force for vapor diffusion.



• Relative Humidity

Relative humidity is defined as the ratio of the water vapor partial pressure present in the air and the water vapor saturation pressure corresponding to the current air temperature. It is expressed as a percentage (e.g. 78%) or as a fraction (e.g. 0.78).

Image

φ [%] or [-] : relative humidity
p [Pa] : water vapor partial pressure
psat(θ) [Pa] : water vapor saturation pressure at temperature θ

The relative humidity increases if water molecules are added to a given parcel of air because then the vapor pressure p increases (see above).

The relative humidity may also change without water molecules being added or removed. As described above, there are conditions under which the vapor pressure p changes without a change in the number of water molecules in the air, but in hygrothermal simulations where the total pressure remains constant these conditions do not apply. However, if the temperature increases, the temperature-dependent saturation vapor pressure psat increases, and even with the vapor pressure p remaining constant, the relative humidity will decrease. The relative humidity is therefore strongly temperature-dependent.

When the relative humidity of the air reaches 100 %, the air is saturated with humidity. If further moisture is added, the moisture excess will condense out of the air. Note that it is possible for a moist surface to give off moisture into the surrounding air even if that air is already saturated at 100 % relative humidity: If the temperature of the surface is higher than the temperature of the ambient air, the surface can have a higher partial vapor pressure, so that a diffusion flow from the surface into the air is created by the vapor pressure difference (see above). This leads to oversaturation of the air close to the surface and moisture condensation in the air (which may be visible as little vapor plumes emanating from the surface).

The water vapor saturation pressure psat referred to in the above definition assumes chemically pure water and a flat water surface. If solutes (e.g. salts) are present in the water, or if the surface is concavely curved (e.g. in small pores), the actual saturation pressure is reduced and saturation already occurs at less than 100% (since even under these circumstances pure water and a flat surface are used as reference by definition).
In particular, the relative humidity corresponding to saturation over the water meniscus in a partially filled pore is not 100% but somewhat less, depending on the curvature of the meniscus. In small pores, liquid water can therefore begin to condense at relative humidities around 80..90%, leading to a strong increase in absorbed water content for these moisture levels.

The amount of equilibrium moisture adsorbed in the pores of a porous hygroscopic material depends on the ratio of the adsorption rate (depending on the water vapor pressure p in the pore air) and the evaporation rate (depending mainly on the saturation vapor pressure psat at the adsorbed water surfaces). It is therefore determined by the relative humidity φ of the pore air and, in consequence, by the relative humidity of the ambient air to which the material is exposed (rather than, say, its absolute humidity). The moisture storage function describes the equilibrium moisture content as a function of relative humidity.
Most instruments for measuring the moisture content of the air use moisture-dependent properties of appropriate materials (e.g. change of length of fibres, change of electrical properties of polymers, etc). Since the moisture content of these materials is determined by the relative humidity of the air, the humidity parameter measured by these instruments is the relative humidity of the air.

As described above, if there is liquid water in the pore system of a porous material, the relative humidity of the pore air in hygric equilibrium with the curved menisci of the water surfaces is less than 100 %, the exact value depending on the curvature of the menisci.
On the other hand, a curved meniscus exerts pulling forces on the water, creating a (negative) capillary pressure in the water, the exact value again depending on the curvature of the meniscus.
In other words: In hygric equilibrium, there exists a mathematical relationship between the relative humidity in the pore air and the capillary pressure in the water. Since capillary pressure differences are driving the capillary liquid transport, it is equivalent to say that differences in relative humidity are driving liquid transport. In fact, WUFI's transport equations are using relative humidity as the driving potential because this has mathematical advantages over using the water content.

The Kelvin equation describes the functional relationship between the relative humidity of the pore air and the capillary pressure in the pore water:

Image

φ [-] : relative humidity of pore air
pc [Pa] : capillary pressure in pore water
ρW [kg/m3] : density of water, 1000 kg m-3
R* [J/(kg K)] : gas constant for water vapor, 461.5 J/(kg K)
T [K] : absolute temperature



• Water vapor concentration, absolute humidity

The water vapor concentration (or absolute humidity) is the ratio of the mass of the water vapor contained in a parcel of moist air to the volume of the parcel:

Image

c [kg/m3] : water vapor concentration, absolute humidity
mw [kg] : mass of water vapor contained in the parcel of air
V [m3] : volume of the parcel of air

The water vapor concentration increases if water molecules are added to a given parcel of air because then the mass of water contained in the volume increases.

But the water vapor concentration may also change without water molecues being added or removed. The water vapor concentration in a given parcel of air decreases if the temperature is raised (at fixed total pressure, as is usually the case in hygrothermal simulations) because then the air expands and the mass of water is spread over a larger volume V.

The water vapor concentration can be measured by using a strong absorbent to absorb all water contained in a known volume of air, and then weighing it to determine the mass of the absorbed water.

Typical values are 4.8 g/m3 at 0° C and saturation, and 17.3 g/m3 at 20°C and saturation.

The relationship between the water vapor concentration and the water vapor partial pressure is given by the ideal gas law:

Image

p [Pa] : water vapor partial pressure
c [kg/m3] : water vapor concentration
R* [J/(kg K)] : gas constant for water vapor, 461.5 J/(kg K)
T [K] : absolute temperature



• Mixing Ratio

The mixing ratio of a given parcel of moist air is the ratio of the mass of the water vapor to the mass of the dry air contained in the parcel:

Image

x [kg/kg] : mixing ratio
mw [kg] : mass of water vapor in the parcel
md [kg] : mass of dry air in the parcel

The mixing ratio only changes when water molecules are added to or removed from the air. If the temperature of the parcel of air increases, its volume expands but the ratio between the number of water molecules and the number of air molecules in the parcel stays the same, and so does the ratio between their masses.
This is useful in technical applications, for example when moist air is pumped through pipes with different temperatures and pressures in different pipe sections: The mixing ratio of the air always stays the same along the way, as long as no evaporation and no condensation takes place.

The relationship between the mixing ratio and the water vapor partial pressure is given by the following formula:

Image

x [kg/kg] : mixing ratio
Ro [J/(kg K)] : gas constant for dry air, 287.1 J/(kg K)
R* [J/(kg K)] : gas constant for water vapor, 461.5 J/(kg K)
p [Pa] : water vapor partial pressure
P [Pa] : barometric pressure



• Specific Humidity

The specific humidity of a given parcel of moist air is the ratio of the mass of the water vapor to the mass of the moist air (i.e. to the sum of the masses of the dry air and the water vapor) contained in the parcel:

Image

s [kg/kg] : specific humidity
mw [kg] : mass of water vapor in the parcel
md [kg] : mass of dry air in the parcel

Just as with the mixing ratio, the specific humidity only changes when water molecules are added to or removed from the air. If the moist air consists almost entirely of water vapor and little air, the specific humidity approaches 1, while the mixing ratio approaches infinity.

The relationship between the specific humidity and the water vapor partial pressure is given by the following formula:

Image

s [kg/kg] : specific humidity
Ro [J/(kg K)] : gas constant for dry air, 287.1 J/(kg K)
R* [J/(kg K)] : gas constant for water vapor, 461.5 J/(kg K)
p [Pa] : water vapor partial pressure
P [Pa] : barometric pressure



• Dew Point Temperature

The dew point temperature of moist air is the temperature to which the air would have to be cooled to begin condensation of the contained water vapor.

A parcel of air can only hold a certain amount of water vapor, the exact maximum amount depending on its temperature: the higher the temperature of the air, the more water vapor it can hold. The maximum water vapor pressure possible at a given temperature θ is the saturation vapor pressure psat(θ).

The dew point temperature θdew of air containing water vapor with the vapor pressure p is the fictitious temperature for which one would have

Image

psat [Pa] : saturation vapor pressure
θdew [°C] : dew point temperature
p [Pa] : current water vapor partial pressure


The dew point temperature therefore measures the water vapor pressure. It expresses the water vapor pressure in terms of the temperature which must be entered in a saturation vapor formula so that the formula returns the vapor pressure in question. Therefore, the remarks made above about the temperature and pressure dependence of the vapor pressure also apply to the dew point temperature.

The dewpoint temperature of air with a water vapor partial pressure of 611 Pa is 0 °C, the dewpoint temperature of air with a water vapor partial pressure of 2339 Pa is 20 °C.

The dew point temperature is a convenient humidity parameter to assess when condensation will occur.

The dew point temperature of the air can directly be measured with chilled-mirror hygrometers.



• Wet Bulb Temperature

The wet bulb temperature is the temperature indicated by a thermometer whose bulb is covered by a wet cloth sleeve. Due to evaporation cooling, this temperature is less than the air temperature indicated by a dry thermometer. The amount of cooling depends on the evaporation rate which is higher in dry air than in moist air. The conversion to other humidity parameters is done with psychrometer tables or empirical psychrometer formulas.

The wet bulb temperature of the air can directly be measured with suitably constructed thermometers.


Saturation Vapor Pressure

The saturation vapor pressure is the equilibrium water vapor partial pressure prevailing over a flat water surface at a given temperature. There exists a large number of empirical saturation vapor pressure formulas, with different levels of complexity and accuracy. 'Magnus'-type formulas are popular because they are relatively simple and can explicitly be solved for the dew point temperature which corresponds to a given vapor pressure. An example for a Magnus-type formula and its inverse is

Image

Image

psat [Pa] : saturation vapor pressure
θ [°C] : temperature
θdew [°C] : dew point temperature

with the following set of coefficients [1]:

Image

Over a concavely curved water surface (e.g. a meniscus in a partially filled material pore), the saturation vapor pressure is less than over a flat surface. The very slight dependence of the saturation vapor pressure on the barometric pressure is usually ignored.


Literature:
[1] Deutscher Wetterdienst: Aspirations-Psychrometer-Tafeln.
5. Auflage, Vieweg