An Improved Analytical Model for Vapour Plume Visible Outline Predictions

The derivation of one-dimensional conservation equations for a buoyant wet plume in the atmosphere is reviewed, and a small correction to the conservation of energy statement is suggested. Subsequently, an analytical solution for plume trajectory and radius is obtained under the Boussinesq, bent-over plume, and constant windspeed, lapse rate, and humidity gradient restrictions. Unlike previously published solutions, however, latent heat effects are explicitly retained in this solution for all lapse conditions, and the significance of these effects on plume predictions can be examined quantitatively. Consideration is also given to the formulation of source conditions consistent with the approximations introduced into the governing equations. It is shown that a consistent formulation of source fluxes leads to a significant change in plume outline predictions. In particular, when the analytical model presented in this paper is applied to cooling tower data from Paradise steam plant, the predicted visible plume length is increased by up to a factor of three, and brought into reasonable agreement with measurements.