Moist Air Properties
The thermodynamical properties of moist air can be found with some mixture laws. These are defined in this paragraph.
Preliminary Definitions
Molar Fraction
The molar fraction of dry air, Xa, and the molar fraction of water vapor, Xv, are defined such as:
(4-112)
(4-113)
where:
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na is amount of dry air
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nv is amount of water vapor
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ntot is the total amount of moist air in mol
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pa is the partial pressure of dry air
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pv is the partial pressure of water vapor
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p is the pressure
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φ is the relative humidity, and
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psat is the saturation pressure.
From Equation 4-112 and Equation 4-113, the following relation holds:
Relative Humidity and Moisture Content
Moisture content and relative humidity can be related with the following expression:
(4-114)
Mixture Properties
The thermodynamical properties are built through a mixture formula. The expressions depend on dry air properties and pure steam properties and are balanced by the mass fraction.
Density
According to the ideal gas law, the mixture density ρm expression is defined as follows:
(4-115)
where Ma and Mv are the molar mass of dry air and water vapor, respectively, and Xa and Xv are the molar fraction of dry air and water vapor, respectively.
The ideal gas assumption sets the compressibility factor and the enhancement factor to unity. In fact, the accuracy lost by this assumption is small as the pure steam represents a small fraction.
Heat Capacity at Constant Pressure
According to Ref. 34, the heat capacity at constant pressure of a mixture is:
(4-116)
where Mm represents the mixture molar fraction and is defined by
and where Cp, a and Cp, v are the heat capacity at constant pressure of dry air and steam, respectively.
Dynamic Viscosity
According to Ref. 34 and Ref. 35, the dynamic viscosity is defined as:
(4-117)
where ϕij is given by
Here, μa and μv are the dynamic viscosity of dry air and steam, respectively.
Thermal Conductivity
According to Ref. 35 and Ref. 34, the thermal conductivity of the mixture is defined similarly:
(4-118)
where ka and kv are the thermal conductivity of dry air and steam, respectively.
Pure Component Properties
The dry air and steam properties used to define the mixture properties are temperature-dependent high-order polynomials. The polynomials have been computed according to Ref. 18 for dry air properties and Ref. 36 for pure steam properties. The steam properties are based on the Industrial Formulation IAPWS-IF97.
The valid temperature range is 200 K < T < 1200 K for dry air properties and 273.15 K < T < 873.15 K for steam properties.
Results and Analysis Variables
These variables are provided to display the related quantities:
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Moisture content xvap.
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Vapor mass fraction omega_moist.
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Concentration of water vapor c.
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Relative humidity phi. This variable corresponds to the calculated φ with the system temperature and pressure.
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Condensation indicator condInd; this indicator is set to 1 if condensation has been detected (φ = 1) and 0 if not.
Functions
The following functions are defined and can be used as feature parameters as well as in postprocessing. Here, feature stands for fluid or porous, depending on whether the function is defined in the Fluid or in the Porous Medium feature:
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ht.feature.fc(RH,T, pA), where RH is the relative humidity 0 ≤ φ ≤ 1, T is the temperature (SI unit: K), and pA is the pressure (SI unit: Pa). It returns the corresponding water vapor concentration (SI unit: mol/m3) by deriving the following relation from Equation 4-107, Equation 4-110, and Equation 4-114:
The concentration computation assumes that the ideal gas assumption is valid.
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ht.feature.fxvap(RH, T, pA), where RH is the relative humidity 0 ≤ φ ≤ 1, T is the temperature (SI unit: K) and pA is the pressure (SI unit Pa). It returns the moisture content (SI unit: 1) by using the following relation:
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ht.feature.fpsat(T), where T is the temperature (SI unit: K). It returns the saturation pressure (SI unit: Pa) by using Equation 4-111.
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ht.feature.Lv(T), where T is the temperature (SI unit: K). It returns the latent heat of evaporation (SI unit: J/kg) as a linear interpolation of the data from Ref. 36, which provides steam properties based on the Industrial Formulation IAPWS-IF97. The temperature-dependency is as shown on Figure 4-14.
Figure 4-14: Latent heat of evaporation in function of temperature.