Vapor Transport

Three boundary features are available for vapor transport; the Vapor Inflow, the Vapor–Liquid Interface, and the Vapor–Liquid-Mixture Interface feature. All three features prescribe the equilibrium vapor pressure for one or several vapor species, either at an inlet connected to an upstream system involving liquids, or at a vapor–liquid interface. Evaporation or condensation occurs when the partial pressure in the adjacent gas domain differs from the vapor pressure at the interface. Below the conditions prescribed at the interface and the resulting heat of evaporation is defined.

The saturated water pressure psat,w (Pa) at a liquid water surface is defined as a function of temperature T using the correlation:

The resulting vapor molar concentration (mol/m3) at the interface is

and the corresponding mass fraction

where R is the universal gas constant, Mw is the molar mass of water, and ρ the vapor density.

This option can be used when coupled to a Thermodynamic System through a Chemistry interface. In this case the Thermodynamics node can provide not only the thermodynamic functions for physicochemical properties in vapor phase, but also the fugacity and density for the liquid phase. The thermodynamic functions are affected by the thermodynamics models selected in the system. Most prominently, the fugacity is dependent on the liquid phase model in the Thermodynamics System.

For a multicomponent vapor–liquid interface at equilibrium, the fugacity (Pa) of all components should be the same in both the vapor and the liquid phase

Here fiL is the fugacity in the liquid phase, and fiV the fugacity in the vapor phase for component i. The fugacity in each phase depends on the temperature and pressure, as well as on its mass fraction in the liquid (ωl,i) and vapor phase (ωv,i), respectively. Using the Thermochemistry coupling, functions for the fugacity fi = fiL = fiV at the interface are created automatically.

Using the fugacity instead of the pressure, the vapor molar concentration and the vapor mass fraction an the at the vapor–liquid interface are defined as

The heat flux due to vaporization or condensation of water is

where ΔHvap, w denotes the heat of vaporization of water, jw is the water mass flux at the interface, us is the Stefan velocity, and n a normal unit vector.

The heat flux due to vaporization or condensation of a multicomponent solution is

where ΔHvap,i is heat of vaporization of species i. The evaporative heat flux is defined and announced by the vapor–liquid interface feature for use when modeling heat transfer. It can for example be applied using a Boundary Heat Source feature in Heat Transfer in Fluids Interface.