Semi-permeable flow surface

The flow solver models semi-permeable flow surfaces for humid air using two methods.

  • Humidity based permeability permits the diffusion of only water vapor.
  • Mixture based permeability permits the diffusion of humid air mixtures, including air, water vapor, and other gas components.

Humidity based permeability

In this method, the flux of the water vapor, m", across the boundary is given by the following equation:

where

  • ρav is the specified ambient water vapor density. If it is not defined, its value is set to zero.
  • ρev is the water vapor density at the flow surface location in the computational domain.
  • R is the specified humidity diffusion resistance. This value can be a constant or time-varying.

The flux crossing the semi-permeable surface depends solely on the difference between the water vapor densities across the interface. An outflow is predicted from a humid enclosure to a dry ambient even when the ambient pressure is much higher than the enclosure pressure. This method does not allow the pressure to be equalized across the boundary in a steady state simulation.

Mixture based permeability

This method is derived from the concept of head loss in the opening boundary condition. The relationship between the specified ambient pressure, Pa, the pressure at the opening, Pe, and the specified head loss, h, is given by the following equations:

  • For inflows:

  • For outflows:

Assuming that the velocities, U, in these equations are normal to the surface, the mass flux at the semi-permeable surface is calculated as:

The plus and minus sign corresponds to the sign of the pressure difference, Pa - Pe. For an inlet, the following further assumption is made: h ≅ h + 1. This assumption is valid for very large values of h.

The density ρ is either equal to the mixture density at semi-permeable flow surface or to the ambient density:

To suppress the occurrence of alternating inflow and outflow conditions in individual semi-permeable cells at each iteration, the flow solver uses a minimum mass flux criterion. With this criterion, when the mass flux is smaller than the specified minimum mass flux, the mass flux is set to zero. You specify the minimum mass flux using the MINIMUM SEMI PERMEABLE MEMBRANE FLUX advanced parameter. By default, the specified minimum mass flux is set to zero.

By default, the mass flux magnitude of each cell is compared to the specified minimum mass flux. If the cell mass flux magnitude is smaller that the specified minimum mass flux, it is set to zero. You can also apply this criterion on the complete semi-permeable flow surface. It this case, the average mass flux magnitude of all flow surface cells is compared to the specified minimum mass flux. If the average value is smaller than the specified minimum mass flux, the mass fluxes of all flow surface cells are set to zero. You specify the global criterion using the PERFORM MINIMUM FLUX CHECK GLOBALLY advanced parameter.

The minimum mass flux can be computed from the values specified by the manufacturers of semi-permeable membranes, as follows:

where:

  • ρ is the density of air that can be approximated to 1.0 kg/m3.
  • is the minimum volume flow rate given in manufacturer specifications.
  • Av is the vent area that can be computed from the design and dimensions given in manufacturer specifications.

You can specify a constant humidity flux m" instead of the loss coefficient. To do this add the line EXPLICIT_HUMIDITY_FLUX=TRUE to the user.prm file.

The flow solver applies the specified loss coefficient value as the value of the constant humidity flux in SI unit crossing the specified wall face.

For more information on user.prm file, see Flow solver files.