In this paper, a three-dimensional numerical model for a round jet discharged at right angles into a cross flow in shallow water body is developed based on the two-equation k −ε nonlinear model and VOF method. The study focuses on the dilution produced in the mixing region by the jet. Based on a lot of simulating with jet velocities varied from 1 to 12 times the mean velocity of the cross flow, the bed effect and the free surface effect on the concentration distribution are revealed. The model is validated by comparing numerical results with other scholars' numerical results and experimental fitted equations. The concentration trajectory, the jet structure including the horseshoe vortex, the counter-rotating vortex pair(CVP) and the decay of the concentration are discussed here.


The study of a round vertical jet in cross flow is related to the design of coastal outfalls for the disposal of domestic and industrial effluents. Effluents discharged into rivers or oceans generally require significant dilution in the initial dilution region. The vertical non-buoyant and buoyant jet in a cross flow has been extensively studied and summarized(Battistin and Iafrati,2004, Fischer, List, Koh, Imberger and Brooks,1979). It is believed that a submerged vertical jet discharge into cross flow gives good mixing. Recently several laboratory experiments' results show that the proximity of bed and the free surface influences the co-flow pattern, the dilutions of both non-buoyant and buoyant jets are significantly reduced when receiving water is shallow(Lee and Lee,1998, Rajaratnam and Langat,1995). The integral models based on an appropriate entrainment hypothesis are classical for jet discharging into an unconfined environment. However, it is difficult to get an appropriate entrainment hypothesis for a problem with complex boundaries. For free surface should be considered for verticaljet in shallow water, the integral models is not appropriate.

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