Condensation in Jets, Industrial Plumes and Cooling Tower Plumes

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Abstract
The one-dimensional theory for the condensation of buoyant plumes is extended to include supersaturation as an extra variable. An additional equation describing the dynamics of droplet growth is used to make the system tractable. Some simple mathematical results are obtained which allow one to relate the theory to, and so extend, a commonly used graphical representation of the condensation process. The theory is then simplified to a single nonlinear first-order differential equation for the condensed water content. This is solved numerically for a typical jet, scrubbed industrial plume and natural-draft cooling tower plume to obtain down-plume profiles of condensed water content, supersaturation and mean droplet size. High supersaturation is predicted in all three cases, corresponding to mean relative humidities of up to 170% (jet), 150% (scrubbed plume) and 105% (cooling tower). These results may be important in predicting the growth of “foreign” carry-over droplets in plumes from industrial sources or cooling towers. Predictions of plume length in these cases is found to be insensitive to supersaturation, but plume length is noticeably affected by supersaturation in the case of a jet. In the examples considered maximum mean droplet radii never exceed 10 μm which supports the belief that rain-out is caused primarily by carry-over from imperfect mist eliminators.

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