Defogging

The defogging model is based on solving an additional scalar transport equation that represents the mass fraction of water vapor. A source/sink term for the scalar is considered for condensation/evaporation of the fog layer as well as the latent heat required for transition.

When there is a difference between the water vapor content at the fog layer and the cell next to this surface, the model calculates a rate of evaporation or condensation depending on the conditions. The assumptions are:

• The vapor content in the air does not affect the thermal properties of the vapor-air mixture.
• The water vapor mass is neglected with respect to the total mass in a cell.

The rate of mass transfer per unit surface $\left[{\text{kg/s-m}}^2\right]$ is:

where ${\rho }_g$ is density $\left[{\text{kg/m}}^3\right]$ .

where $C_{\text{emp}}$ is the empirical constant useful for calibration (0.05-0.9) for windshield applications, $L$ is a characteristic length (cubic root of cell volume next to fog layer boundary) [m], $D_V$ is diffusion of vapor in air $[{\text{m}}^2/\text{s}]$ , $Re$ is the Reynolds number (which is based on the gas state and the characteristic length $L$ ), and $Sc$ is the Schmidt number, and:

where $C_g$ is the actual concentration of vapor in air and $C_s$ is the saturation concentration of vapor in air.

For a given temperature, the saturation pressure is calculated from the following expression:

The amount of evaporated/condensed vapor in one time-step is:

The thickness of the liquid film is updated as: