Evaporation and Condensation
Vapor–liquid equilibrium is enforced by prescribing the mass fractions in accordance with Equation 3-195. The resulting vapor pressure drives evaporation or condensation across the vapor–liquid interface. When the vapor pressure at the interface is higher than the ambient vapor pressure, mass evaporates from the liquid into the vapor. If instead the vapor pressure drops below the ambient vapor pressure, for example due to a decrease in temperature, vapor will instead condense into liquid. These processes will proceed until the vapor pressure at the interface and the ambient vapor pressure are in equilibrium.
The total mass flux transported across the interface (kg/(m2·s)) can be computed by summing all fluxes of evaporated species in the manner of
(3-200)
Here jiV denotes the diffusive mass flux resulting from enforcing the equilibrium conditions in Equation 3-195, n is the surface normal, and uV the mass averaged vapor velocity at the interface. Fluxes from species that does not evaporate or condensate should not be included in the sum. Assuming that the interface is stationary the total mass flux is used to define a Stefan velocity to be applied at the interface
(3-201)
For two-phase flow, the relationship governing the velocities of the vapor and the liquid at the surface is
(3-202)
where the mass transfer across the interface corresponds to the total vapor mass flux jV. It can be noted that a nonzero mass flux is necessary for the phase velocities to differ. The difference is prescribed in the normal direction of the surface.
For two-phase flow with evaporation, the position of the vapor–liquid interface needs to also be updated. When using a Moving Mesh to track the interface position, the relationship between the mesh velocity and the liquid velocity is
(3-203)
The mesh velocity is the velocity of the vapor–liquid interface. In a situation without evaporation or condensation, the normal mesh velocity equals the normal liquid velocity. Which in turn is equal to the vapor velocity according to Equation 3-202. For a non-zero mass flux on the other hand, the interface normal mesh velocity differs from that of the liquid phase.
To conserve mass during phase transfer, the normal mass flux on the liquid side should equal that of the vapor side. The normal diffusive mass fluxes on the liquid side are therefore defined as
(3-204)
The heat of evaporation at the vapor–liquid interface (W/m2) is defined as
(3-205)
where ΔHvap,i is the species heat of evaporation (J/kg). When coupled to a thermodynamic system, functions for the heat of evaporation are added automatically.