A Discussion of Schatzmann's Integral Plume Model from a Control Volume Viewpoint

Abstract

Of the numerous integral models that have been developed to describe buoyant plumes in stratified crossflows, Schatzmann's model appears to be the most mathematically rigorous and physically complete. So far, however, a comparative study of the performance of this model with previous simpler integral models has not been reported. To aid such a comparison, a control volume development of Schatzmann's governing equations is presented to parallel his more abstract differential development. Discrepancies between the equation act derived by Schatzmann and that derived from a control volume analysis are reported. The control volume equation act is found to be consistent with the equations published by previous workers, once Schatzmann's suggestion is taken into account that a mean flow convective interaction between the plume and its surroundings be included along with the usual turbulent entrainment interaction. The source of the discrepancies between equation sets is discussed, and a numerical example is presented to illustrate the effect of these differences in the governing equations on plume predictions.