Simultaneous trajectory and dilution predictions from a simple integral plume model

Abstract

Studies of plumes from natural draft cooling towers have indicated that there is an underlying shortcoming in many of the integral plume models in the literature, which prevents them from simulta- neously predicting both plume trajectory and dilution rate accurately. Typically, if the entrainment constant(s) is chosen to yield trajectory predictions in good agreement with measurement, the corresponding dilution rate is overestimated and hence the visible length of a cooling tower plume is often greatly underestimated. By following the approaches of Slawson and Csanady (1971, J. Fluid Mech. 47, 33–49) and Briggs (1975, AMS) which lead to analytical expressions for plume variables, it is demonstrated that the inclusion of the resistive force of the atmosphere opposing the motion of the plume has a significant effect on model performance. For buoyancy dominated sources, the inclusion of this resistive or dynamic pressure force in the momentum balance, either through an added mass factor or through a drag term, allows trajectory predictions to be brought into agreement with measurements while the corresponding growth rate prediction is reduced. For momentum dominated sources, a reformulation of the initial condition for momentum flux, consistent with the assumptions of the integral analysis including the dynamic pressure force, is presented, and is also shown to reduce the entrainment rate required to match trajectory predictions to measurements. When this dynamic pressure force and modified initial momentum flux are included, simultaneous predictions of plume trajectory and growth rate obtained from a simple integral analysis are brought more into line with experimental data.