The integral momentum and tracer equations for the mean motion with the turbulence contribution in momentum and tracer fluxes are integrated on the centreline of either plane or round buoyant jets, using suitable assumptions for the spreading coefficients and a closing function, and unified first- and second-order solutions are derived in the entire buoyancy range for mean axial velocities and mean concentrations. Comparisons to experimental data in the literature validate the model and show that second-order solutions deviate less than first-order solutions. Both types are used in conjunction with the integral continuity and kinetic energy equations for the mean motion to determine the variation of the local Richardson and Froude numbers, dispersion ratio, bulk dilution, dilution ratio, entrainment coefficient and mean velocity, kinetic energy flux and its gradient for the mean motion; and the variations of these quantities are evaluated using reported experimental or theoretical data. Finally, the variation of the product of kinetic energy flux and the local Richardson number is examined and a universal constant for both plane and round buoyant jets is revealed, leading to a unified definition of the local Richardson number, which is independent of the flow and mixing geometry and could be useful. Simple computational programming and good overall agreement make the proposed model a very promising tool for laboratory and field studies, outfall design and validation of numerical models.
An integral model predicting the mean flow and mixing properties of inclined plane and round turbulent buoyant jets in a motionless environment of uniform density is proposed. The escaping masses from the main buoyant jet flow are simulated, and the model can be successfully applied to initial discharge inclinations θ 0 from 90 to −75 • with respect to the horizontal plane. This complementary approach introduces a concentration coefficient, which is calibrated using experimental evidence. The present model has incorporated the second-order approach and, regarding the jet-core region, a jet-core model based on the advanced integral model for the production of more correct transverse profiles of the mean axial velocities and mean concentrations than the common Gaussian or top-hat profiles. The partial differential equations for momentum and tracer conservation are written in orthogonal and cylindrical curvilinear coordinates for inclined plane and round buoyant jets, respectively, and they are integrated under the closure assumptions of (a) quasi-linear spreading of the mean flow and mixing fields, and (b) known transverse profile distributions. The integral forms are solved by employing the Runge-Kutta algorithm. Since the most important contribution in the present model is the simulation of the escaping masses, the model has been called the escaping mass approach (EMA). Herein EMA is applied to predict the mean flow properties (trajectory characteristics, mean axial velocities and mean concentrations) for inclined plane and round buoyant jets. The results predicted are compared with experimental data available in the literature, and the accuracy obtained is more than satisfactory. The performance of the EMA is up to 56 % better than using classical integral procedures. EMA can be used for design purposes and for environmental impact assessment studies.
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