Hybrid models for jets and plumes in a flowing ambient fluid
by Pun Kwok Leung
Ph.D. Civil Engineering
xxiv, 227,  leaves : ill. ; 30 cm
A hybrid of the length-scale and Eulerian integral approaches is applied to develop mathematical models for the prediction of flow behaviour from single buoyant discharges in a crossflow (SD3D) and multiple non-buoyant discharges in a coflow (MCJM)....[ Read more ]
A hybrid of the length-scale and Eulerian integral approaches is applied to develop mathematical models for the prediction of flow behaviour from single buoyant discharges in a crossflow (SD3D) and multiple non-buoyant discharges in a coflow (MCJM).
The SD3D model can predict the behaviour of discharges with three-dimensional trajectories. The traditional centreline velocity ratio approach and the momentum ratio approach are considered for locating the centreline flow trajectory. The predictions of the SD3D model are compared with a range of experimental data as well as the predictions from two existing models - the Expert System CORMIXl and the Lagrangian integral model JETLAG. It is shown through these comparisons that the SD3D model predicts the behaviour of effluent discharged at a variety of angles to the ambient current with reasonable accuracy. Based on the available data, the momentum ratio approach is apparently more accurate in locating flow trajectories than the traditional centreline ratio approach. It is noted that the momentum ratio approach is equivalent to using of the cross-sectional average velocity to locate the flow trajectory. The SD3D model retains the flexibility of a length-scale model enabling it to be more readily developed to deal with merging discharges. In addition, because the model utilises integral solutions it requires less empirical information to develop than an equivalent length-scale model which relies solely on dimensional analysis. Several areas of single discharge behaviour which are not well understood are identified through this study. Of these two important areas are weakly-advected jets and plumes.
The MCJM model also combines the modular structure of a length-scale model with the reduced empiricism of an Eulerian integral model. The model allows the transition between flow regions to occur in stages and this leads to the use of a multiple-point approach. Predictions from the multiple-point hybrid model are compared with an equivalent single-point hybrid model and an Eulerian integral solution for the same problem. The multiple-point approach significantly reduces transition errors when compared to the single-point model. These transition errors can result in inaccurate predictions of merging behaviour. Predictions from the multiple-point hybrid model are in good agreement with the integral solution.
Following on from the development of the SD3D model, experimental investigations into the behaviour of weakly-advected jets and plumes are included in this study. These flows are of considerable practical interest because they commonly occur when wastewater is released into a marine environment. A unique experimental facility, combined with laser-induced fluorescence and image processing techniques, is employed to investigate the weakly-advected flow behaviour. These investigations include the study of the bulk properties and fluctuation statistics of weakly-advected flows. The obtained experimental data show that weakly-advected flows can be modelled effectively assuming the flow profiles are Gaussian and self-similar. Simple advection models for weakly-advected jets and plumes are established based on the assumption that weakly-advected jets and plumes behave in essentially the same way as jets and plumes in a still ambient fluid, but which are in addition advected by the ambient current. Mean concentration profiles of still and weakly-advected flows are shown to be similar. However, in the weakly-advected flow cases there are concentration profile distortions near the edges of the flows and some detachment of tracer from the main body of the flows. Comparisons of spread, dilution and trajectory data with predictions from the simple advection models show that the behaviour of weakly-advected jets and plumes resembles that of still jets and plumes.
The experimental results also show that the appropriate characteristic velocity for predicting the centreline location of a strong jet and an advected plume is the cross-sectional average velocity and not the centreline velocity (which has been utilised for this purpose in the past). This indicates that large scale turbulent structures play a significant role in determining the mean flow behaviour of weakly-advected flows. The importance of these large scale turbulent structures also justifies the use of momentum ratios, which are based on the total local momentum, for predicting flow trajectories. Notable differences can be found in the fluctuation statistics of still and weakly-advected flows. However, the root-mean-square and intermittency of the concentration fluctuations in the central regions of these flows are similar.
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