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An Improved Integral Model for a Non-Buoyant Turbulent Jet in Wave Environment

1
State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing 210098, China
2
College of Harbor, Coastal and Offshore Engineering, Hohai University, Nanjing 210098, China
3
Shanghai Academy of Environmental Sciences, Shanghai 200233, China
*
Author to whom correspondence should be addressed.
Water 2019, 11(4), 765; https://doi.org/10.3390/w11040765
Received: 24 February 2019 / Revised: 2 April 2019 / Accepted: 10 April 2019 / Published: 12 April 2019
(This article belongs to the Section Water Quality and Ecosystems)
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Abstract

The integral model developed by Chin (1988) for modelling a non-buoyant turbulent jet in wave environment is improved by introducing two new parameters, i.e., the jet spreading rate c1 and the shortening rate pe. The parameter c1 is used to simplify the model by explicitly describing the radial velocity and scalar profiles under the assumption of “instantaneous” Gaussian distribution. By doing so, the governing equations can be easily solved by simultaneously integrating the conservation laws of momentum and scalars across the jet cross-section. The parameter pe is used to shorten the initial length of zone of flow establishment (ZFE), so as to more accurately account for the wave effect on the jet initial dilution near the jet nozzle. The parameters are calibrated by the particle image velocimetry (PIV)-measured data from three groups of jet experiments, i.e., the group of vertical jet towards the wave direction (vertical jet), the group of horizontal jet along the wave direction (co-wave jet) and the group of horizontal jet opposing to the wave direction (op-wave jet). The results show that both parameters are well related to the ratio of jet and wave characteristic velocities in the same group, but it is not able to be generalized among different groups. Under the same wave condition, the value of c1 in the vertical jet is larger than that of the horizontal jets; while the value of pe in the vertical jet is smaller than that of the horizontal jets, which indicates that the jet has a faster decay rate of centerline velocity and a wider width of jet cross-section profile in the near field when it is vertically discharged into the wave environment. With the well-calibrated parameters, the improved model can achieve a higher accuracy than the original model developed by Chin (1988). View Full-Text
Keywords: turbulent jet; regular waves; integral model; hydrodynamic characteristics; jet dilution turbulent jet; regular waves; integral model; hydrodynamic characteristics; jet dilution
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Fang, S.; Chen, Y.; Xu, Z.; Otoo, E.; Lu, S. An Improved Integral Model for a Non-Buoyant Turbulent Jet in Wave Environment. Water 2019, 11, 765.

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