Simultaneous Fog Formation and Thermophoretic Droplet Deposition in a Turbulent Pipe Flow

Simultaneous aerosol formation by equilibrium condensation and the migration of the resulting droplets to the cold surface by thermophoresis is studied theoretically for a turbulent pipe flow. The problem is one in which a mixture of a vapor and noncondensable gas flows into a section of pipe where the pipe wall is cooled far below the dew point of the vapor. Because the temperature gradient at the pipe wall decays to zero once the gas travels far enough into the pipe, only some fraction of the droplets formed will deposit on the pipe wall. The equations of energy and diffusion suggest that turbulence leads to a discontinuity in the aerosol (fog) concentration at the boundary between the fog and clear regions. Numerical solutions are obtained for CsOH fog formation and deposition in steam flow—a particular case of current practical interest in water reactor safety. The axial and radial variations of the aerosol and vapor concentrations are displayed graphically, as are the location of the fog boundary as a function of axial distance and the efficiency of deposition as a function of the pipe wall temperature.