Abstract: | In this study, simple flows, such as buoyant jet and line thermal discharged into a still, uniform environment, are modelled mathematically by using integral equations of mass, momentum and thermal energy conversation. The governing equations are solved for entrainment rate by using an assumed growth rate model, the coefficients of which are fixed empirically. Entrainment models obtained by this method predict just as well as do models developed by other researchers who used different approaches. Our entrainment models are then applied to the problem of a turbulent jet discharged into a turbulent cross flow including both the near, intermediate, and far fields in a single model. It is assumed that the entrainment rate for this case can be obtained as a sum of terms representing near field entrainment of a buoyant jet and a line thermal, and far field mixing due to ambient turbulence. The predicted trajectories, velocities, and dilution rates agree satisfactorily with experimental results. In this study, simple flows, such as buoyant jet and line thermal discharged into a still, uniform environment, are modelled mathematically by using integral equations of mass, momentum and thermal energy conservation. The governing equations are solved for entrainment rate by using an assumed growth rate model, the coefficients of which are fixed empirically. Entrainment models obtained by this method predict just as well as do models developed by other researchers who used different approaches. Our entrainment models are then applied to the problem of a turbulent jet discharged into a turbulent cross flow including both the near, intermediate, and far fields in a single model. It is assumed that the entrainment rate for this case can be obtained as a sum of terms representing near field entrainment of a buoyant jet and a line thermal, and far field mixing due to ambient turbulence. The predicted trajectories, velocities, and dilution rates agree satisfactorily with experimental results. |