Theory for the Moisture Flow Interface
The following points of the theory of Moisture Flow are discussed in this part:
See Theory for the Single-Phase Flow Interfaces and Theory for the Turbulent Flow Interfaces in the CFD Module User’s Guide for a description of the theory related to laminar and turbulent single-phase flow interfaces.
The Moisture Flow Equations
The density and viscosity of moist air depend on its moisture content. This module includes the Moisture Flow predefined multiphysics coupling to simulate systems in which the airflow depends on moisture content through its density and viscosity.
The density and viscosity of air might also vary due to temperature variations. See Theory for the Nonisothermal Flow and Conjugate Heat Transfer Interfaces for details on this other kind of dependency.
The Moisture Flow interface contains the fully compressible formulation of the continuity and momentum equations. For laminar flow they read:
(4-117)
where
  ρ is the density (SI unit: kg/m3)
  u is the velocity vector (SI unit: m/s)
  p is the pressure (SI unit: Pa)
τ is the viscous stress tensor (SI unit: Pa), equal for a compressible fluid to:
  μ is the dynamic viscosity (SI unit: Pa·s)
  F is the body force vector (SI unit: N/m3)
It also solves the equation for moisture transport in air, given in Equation 4-100 by
where in addition to the quantities above
Mv is the molar mass of water vapor (SI unit: kg/mol)
cv is the vapor concentration (SI unit: mol/m3)
g is the moisture flux by diffusion (SI unit: kg/(m2·s)):
D (SI unit: m2/s) is the vapor diffusion coefficient in air.
G contains moisture sources (SI unit: kg/(m3·s))
Turbulent Moisture Flow Theory
The Favre average of the vapor concentration cv is defined by
where the bar denotes the usual Reynolds average. The full field can be decomposed as the sum of the Favre average and the Favre fluctuation:
By applying this decomposition and averaging the moisture transport equations, unclosed terms are introduced in the equations. Among them, the turbulent moisture transport flux contains the velocity and vapor concentration fluctuations:
This flux is modeled using a gradient based assumption, where the additional transport is related to the turbulent viscosity νT through the turbulent Schmidt number ScT. The turbulent diffusivity DT is defined by
The following moisture transport equation is solved:
(4-118)
Kays-Crawford Model for Turbulent Diffusivity
By analogy with turbulent heat transfer, the turbulent Schmidt number ScT is given by (Ref. 26)
(4-119)
where the Schmidt number at infinity is ScT = 0.85 and the Schmidt number is defined as
where ν is the kinematic viscosity.
Moisture Transport Wall Functions
Analogous to the single-phase flow wall functions (see Wall Functions described for the Wall boundary condition), there is a theoretical gap between the solid wall and the computational domain for the fluid and relative humidity fields. This gap is often ignored when the computational geometry is drawn.
Assuming that the turbulent heat and moisture transfer in the near-wall region are analogous, the same type of wall functions used for the temperature (Ref. 28) is also applicable for the moisture transport. The moisture transfer wall function is formulated as a function of the turbulent Schmidt number, instead of the corresponding Prandtl number.
The moisture flux at the lift-off position between the air with vapor concentration cv,a and a wall with vapor concentration cv,w, is:
where uτ is the friction velocity, csat is the saturation concentration at the lift-off position, and is the dimensionless relative humidity given by (Ref. 28):
where in turn
where κ is the von Karman constant equal to 0.41, Cμ is a turbulence modeling constant, and k is the turbulent kinetic energy.
The distance between the computational fluid domain and the wall, δw, is always hw/2 for automatic wall treatment where hw is the hight of the mesh cell adjacent to the wall. hw/2 is almost always very small compared to any geometrical quantity of interest, at least if a boundary layer mesh is used. For wall function, δw is at least hw/2 and can be bigger if necessary to keep δw+ higher than 11.06. The computational results should be checked so that the distance between the computational fluid domain and the wall, δw, is everywhere small compared to any geometrical quantity of interest. The distance δw is available for evaluation on boundaries.
Theory for the Screen Boundary Condition in Moisture Flow
When the Moisture Flow multiphysics coupling feature is active, the conditions that apply across a screen in moisture flow are complemented by:
(4-120)
to ensure mass conservation.
See Screen for the feature node details.
Also see Screen boundary condition described for the single-phase flow interfaces.
Theory for the Interior Fan Boundary Condition in Moisture Flow
When the Moisture Flow multiphysics coupling feature is active, the conditions that apply across an interior fan are complemented by: