Modeling humidity

The flow solver uses the gas mixture scalar equation to model humidity that is defined as a mixture of water vapor in air.

For more information, see Modeling a gas mixtures.

Rather than specifying the boundary and initial conditions in terms of mass ratio, in this case, they are specified either in terms of relative humidity or specific humidity. The flow solver supports the specification of relative humidity and specific humidity as function of time.

The preprocessor converts the humidity values to mass ratio values. After the solution of the conservation equations is obtained, the postprocessor coverts the mass ratio values back to relative and specific humidity values.

You do not need to specify the water vapor properties, as they are available in the flow solver.

Conversion from relative humidity to mass ratio

The flow solver sets to zero the gradient normal to the wall of the mass ratio, when it solves the humidity equation or the other general scalar equation.

By definition, the relative humidity, φr, is the ratio of the partial pressure of the water vapor, pv, to the saturation pressure of the water vapor at a given temperature pv.sat(T):

A value of φr equal to 100% indicates the onset of condensation. The air/vapor mixture gets closer to the condensation state if:

  • Water vapor is added to the fluid, the partial pressure of water vapor then increases.
  • The temperature goes down.

The flow solver uses analytical formulas, proposed in [13], to calculate the water vapor saturation pressure for -100°C < T < 0°C given by:

with the following coefficients:

  • C1 = 5.6473590 ∙ 103
  • C2 = 6.3925247
  • C3 = 9.6778430 ∙ 10-3
  • C4 = 6.2215701 ∙ 10-7
  • C5 = 2.0747825 ∙ 10-9
  • C6 = -9.4840240 ∙ 10-13
  • C7 = 4.1635019

The water vapor saturation pressure for 0°C < T < 200°C given by:

with the following coefficients:

  • C8 = 5.8002206 ∙ 103
  • C9 = 1.3914993
  • C10 = -4.8640239 ∙ 10-2
  • C11 = 4.1764768 ∙ 10-5
  • C12 = -1.4452093 ∙ 10-8
  • C13 = 6.5459673

In these equations, the temperature T is in Kelvin and pv.sat is in Pascal.

The mass ratio is then obtained as:

  • p is the pressure of the water vapor/air mixture.
  • Rv is the water vapor gas constant.
  • Ra is the air's gas constant.

Conversion from specific humidity to mass ratio

By definition, the specific humidity φs is the ratio of the water vapor density to the dry air density, defined as:

The conversion from specific humidity to mass ratio is given by: