New method for developing entrainment rate models for turbulent flows and its application

A general method for deriving expressions for the entrainment rate of jets, plumes, and line thermals is developed. This method is based on the integral equations of mass, momentum, and thermal energy conservation. Since the growth rate of a simple flow can be measured easily in laboratory, the governing equations are solved for entrainment rate by using an assumed growth rate model and similarity hypotheses of velocity, density, and concentration. The resulting entrainment models are as good as the models developed by other researchers using different approaches. These models are then applied to the problem of a buoyant jet discharged into a turbulent cross flow with arbitrary wind and temperature distributions. The cross section of the plume is assumed to be an ellipse with changing aspect ratio as it travels in the cross flow. A far field entrainment model is developed by using the empirical formulas suggested by Briggs. The trajectories, velocity, and dilution rate for buoyant and nonbuoyant jets discharged into a cross flow are obtained. The predictions for various ambient turbulence, thermal stratification, and stack exit conditions are satisfactory when compared with the experiment results