An improved integral model for a round turbulent buoyant jet based on the turbulent measurements

Abstract

The development of an improved integral model for a round turbulent buoyant jet discharged into a stagnant fluid is reported here, based on the published laboratory measurements of the turbulent quantities in recent years. In order to include turbulent terms into the integral model, instead of using the control volume method, the differential method that necessitates tedious mathematical procedures is used to derive the equations. The approach is as follows: The three-dimensional governing equations of fluid mechanics are firstly transformed to the partial differential forms in a natural coordinate system; Secondly, the solution variables in the instantaneous equations are decomposed into the mean and fluctuating components, and the Reynolds averaging operations are then performed; Finally, the Reynolds-averaged governing equations are integrated over the jet cross-section, based on the axisymmetrical assumption and the best-fit curves obtained from the experimental data. Since the fluxes of a passive tracer or momentum due to the turbulent transport were measured to be about 8-15% of the advective mean fluxes, incorporating the turbulent quantities into the integral model should improve the accuracy of the prediction.