Wet plume rise from cooling towers in strong winds

A mathematical model is presented that predicts, as a function of distance downwind, the height of the center line of a single visible plume from a wet natural-draft cooling tower in moderate to strong winds. The analytic method is quasi-Lagrangian; that is, the behavior of a small section or parcel of the plume is analyzed as a function of time. Eight first-order differential equations describe the parcel in terms of change in mass, vertical velocity, vertical displacement, length of side, temperature, mass of liquid water, horizontal velocity, and horizontal displacement. The equations are tractable for solution by well-known computer integration techniques. The model was tested on plumes from four cooling towers at an electric generating plant, and its predicted plume path was compared with data interpreted from time-lapse photographs of the plumes. Best results were obtained by applying dry plume entrainment rates in the early stages and cloud entrainment rates in the later stages. The computed prediction, employing reasonable estimates where necessary, closely approximated the photographic data for a distance of 1500 m downwind on a day with high relative humidity. The model can also be used to analyze the nature of wet plume behavior.