Theory for Moisture Transport

In moist air, the transport of moisture is done by convection and binary diffusion of vapor in air.

Two formulations are available, depending on the magnitude of moist air density variations with moisture content.

In both formulations, the moisture is supposed to be constituted only of vapor when considering moist air. In other terms the liquid concentration is null, except on boundaries where condensation may take place.

Diluted Species Formulation

With this formulation, it is supposed that the spatial and temporal variations of the vapor concentration are small enough not to induce significant variations of the moist air density.

The Moisture Transport in Air Interface solves for the following equation, in which the moisture content variation is expressed through the transport of vapor concentration, cv, by convection and binary diffusion in air:

(4-135)

with the following material properties, fields, and source:

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Μv (SI unit: kg/mol) is the molar mass of water vapor.

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ϕw (dimensionless) is the relative humidity.

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csat (SI unit: mol/m3) is the vapor saturation concentration.

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D (SI unit: m2/s) is the vapor diffusion coefficient in air.

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u (SI unit: m/s) is the air velocity field.

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gw (SI unit: kg/(m2⋅s)) is the vapor diffusive flux.

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G (SI unit: kg/(m3⋅s)) is the moisture source (or sink).

Concentrated Species Formulation

When the spatial and temporal variations of the vapor concentration induce significant variations of the moist air density, the moisture content variation is expressed through the transport of vapor mass fraction, ωv, defined as:

where ρg is the moist air density (SI unit: kg/m3).

The Heat Transfer in Moist Air Interface solves for the following equation:

(4-136)

This is equivalent to solve the following equations on the vapor concentration:

By neglecting the spatial and temporal variations of ρg in the equations above, the equation of the diluted species formulation, Equation 4-135, is obtained.