Technical Papers
Apr 30, 2020

Three-Dimensional Numerical Study of Multiple Vertical Buoyant Jets in Stationary Ambient Water

Publication: Journal of Hydraulic Engineering
Volume 146, Issue 7

Abstract

In this paper, the mixing and dilution characteristics of vertical buoyant jets discharged from multiport diffusers are studied numerically. The performances of four different turbulence closures are investigated, including the standard k-ε, renormalization group (RNG) k-ε, standard k-ω, and k-ω shear stress transport (SST) models, and the simulated results are compared to available experimental measurements. The comparisons demonstrate that a fully three-dimensional (3D) numerical model can be a reliable tool for the study of multiple vertical buoyant jets. Different fit measurement methods are employed to evaluate the turbulence models, and the results show that the predictions by the RNG k-ε model are the most accurate. The validated model is utilized to carry out additional computations with different port spacings and densimetric Froude numbers (Fr), and the simulated centerline and transverse concentrations at various cross sections are extracted and analyzed. The study reveals how varying port spacing and Fr affect multiple vertical buoyant jets. A new empirical formula that considers the port-spacing effect is proposed to describe the concentration decay along the jet centerline. The study also provides clues about merging points, well-mixed locations, and jet spread under the influences of port spacing.

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Data Availability Statement

Some or all data, models, or code generated or used during the study are available from the corresponding author by request. (The experimental data, the numerical results, and the OpenFOAM files).

Acknowledgments

This work was funded by the Natural Sciences and Engineering Council of Canada (NSERC Discovery Grants). Xiaohui Yan was a recipient of a scholarship from the China Scholarship Council (CSC). We would like to thank the Editor in Chief, the anonymous Associate Editor, and the four reviewers for their careful reading of our manuscript and their insightful comments and suggestions.

References

Abessi, O., and P. J. Roberts. 2014. “Multiport diffusers for dense discharges.” J. Hydraul. Eng. 140 (8): 04014032. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000882.
Abessi, O., and P. J. Roberts. 2017. “Multiport diffusers for dense discharge in flowing ambient water.” J. Hydraul. Eng. 143 (6): 04017003. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001279.
Abessi, O., M. Saeedi, M. Davidson, and N. H. Zaker. 2012. “Flow classification of negatively buoyant surface discharge in an ambient current.” J. Coastal Res. 28 (1A): 148–155. https://doi.org/10.2112/JCOASTRES-D-10-00131.1.
Angioletti, M., E. Nino, and G. Ruocco. 2005. “CFD turbulent modelling of jet impingement and its validation by particle image velocimetry and mass transfer measurements.” Int. J. Therm. Sci. 44 (4): 349–356. https://doi.org/10.1016/j.ijthermalsci.2004.11.010.
Behrens, T. 2009. OpenFOAM’s basic solvers for linear systems of equations. Gothenburg, Sweden: Dept. of Applied Mechanics, Chalmers Univ. of Technology.
Bleninger, T., and G. H. Jirka. 2008. “Modelling and environmentally sound management of brine discharges from desalination plants.” Desalination 221 (1–3): 585–597. https://doi.org/10.1016/j.desal.2007.02.059.
Bogey, C., and C. Bailly. 2006. “Large eddy simulations of transitional round jets: Influence of the Reynolds number on flow development and energy dissipation.” Phys. Fluids 18 (6): 065101. https://doi.org/10.1063/1.2204060.
Botelho, D. A., M. E. Barry, G. C. Collecutt, J. Brook, and D. Wiltshire. 2013. “Linking near-and far-field hydrodynamic models for simulation of desalination plant brine discharges.” Water Sci. Technol. 67 (6): 1194–1207. https://doi.org/10.2166/wst.2013.673.
Chen, C. J., and W. Rodi. 1980. Vertical turbulent buoyant jets: A review of experimental data.. New York: Pergamon Press.
Davidson, M. J., and K. L. Pun. 2000. “Locating discharge trajectories in still and moving ambient fluids.” J. Hydraul. Eng. 126 (7): 513–524. https://doi.org/10.1061/(ASCE)0733-9429(2000)126:7(513).
Drami, D., Y. Z. Yacobi, N. Stambler, and N. Kress. 2011. “Seawater quality and microbial communities at a desalination plant marine outfall. A field study at the Israeli Mediterranean coast.” Water Res. 45 (17): 5449–5462.
Fischer, H. B., E. J. List, R. C. H. Koh, J. Imberger, and N. H. Brooks. 1979. Mixing in Inland and coastal waters. New York: Academic Press.
Gruber, M. F., C. J. Johnson, C. Y. Tang, M. H. Jensen, L. Yde, and C. Hélix-Nielsen. 2011. “Computational fluid dynamics simulations of flow and concentration polarization in forward osmosis membrane systems.” J. Membr. Sci. 379 (1–2): 488–495. https://doi.org/10.1016/j.memsci.2011.06.022.
Hodgson, J. E., A. K. Moawad, and N. Rajaratnam. 2010. “Concentration field of multiple circular turbulent jets.” J. Hydraul. Res. 37 (2): 249–256. https://doi.org/10.1080/00221689909498309.
Holzmann, T. 2016. “Mathematics, numerics, derivations and OpenFOAM®.” Accessed November 29, 2017. https://holzmann-cfd.com/en/publications/all-publications/freeDownloads?CFD=17.
Jiang, B., A. W. K. Law, and J. H. W. Lee. 2014. “Mixing of 30° and 45° inclined dense jets in shallow coastal waters.” J. Hydraul. Eng. 140 (3): 241–253. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000819.
Jirka, G. H. 2004. “Integral model for turbulent buoyant jets in unbounded stratified flows. Part I: Single round jet.” Environ. Fluid Mech. 4 (1): 1–56. https://doi.org/10.1023/A:1025583110842.
Jirka, G. H. 2006. “Integral model for turbulent buoyant jets in unbounded stratified flows. Part II: Plane jet dynamics resulting from multiport diffuser jets.” Environ. Fluid Mech. 6 (1): 43–100. https://doi.org/10.1007/s10652-005-4656-0.
Jirka, G. H. 2007. “Buoyant surface discharges into water bodies. II: Jet integral model.” J. Hydraul. Eng. 133 (9): 1021–1036. https://doi.org/10.1061/(ASCE)0733-9429(2007)133:9(1021).
Jones, G. R., J. D. Nash, R. L. Doneker, and G. H. Jirka. 2007. “Buoyant surface discharges into water bodies. I: Flow classification and prediction methodology.” J. Hydraul. Eng. 133 (9): 1010–1020. https://doi.org/10.1061/(ASCE)0733-9429(2007)133:9(1010).
Kheirkhah Gildeh, H., A. Mohammadian, I. Nistor, and H. Qiblawey. 2014. “Numerical modeling of turbulent buoyant wall jets in stationary ambient water.” J. Hydraul. Eng. 140 (6): 04014012. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000871.
Kheirkhah Gildeh, H., A. Mohammadian, I. Nistor, and H. Qiblawey. 2015. “Numerical modeling of 30° and 45° inclined dense turbulent jets in stationary ambient.” Environ. Fluid Mech. 15 (3): 537–562. https://doi.org/10.1007/s10652-014-9372-1.
Kheirkhah Gildeh, H., A. Mohammadian, I. Nistor, H. Qiblawey, and X. Yan. 2016. “CFD modeling and analysis of the behavior of 30° and 45° inclined dense jet-new numerical insights.” J. Appl. Water Eng. Res. 4 (2): 112–127. https://doi.org/10.1080/23249676.2015.1090351.
Killingstad, P. E. 2018. “A study of dead water resistance Reynolds Averaged Navier Stokes simulations of a barge moving in stratified waters.” Master’s thesis, Dept. of Mathematics, Univ. of Oslo.
Knudsen, M., and I. R. Wood. 2010. “The interaction between a boundary and a horizontal buoyant jet.” J. Hydraul. Res. 28 (3): 375–385. https://doi.org/10.1080/00221689009499076.
Knystautas, R. 1964. “The turbulent jet from a series of holes in line.” Aeronaut. Q. 15 (1): 1–28. https://doi.org/10.1017/S0001925900002985.
Kuang, C. P., and J. H. Lee. 2006. “Stability and mixing of a vertical axisymmetric buoyant jet in shallow water.” Environ. Fluid Mech. 6 (2): 153–180. https://doi.org/10.1007/s10652-006-0001-5.
Lai, A. C., and J. H. Lee. 2012. “Dynamic interaction of multiple buoyant jets.” J. Fluid Mech. 708: 539–575.
Lai, A. C., B. Zhao, A. W. K. Law, and E. E. Adams. 2015. “A numerical and analytical study of the effect of aspect ratio on the behavior of a round thermal.” Environ. Fluid Mech. 15 (1): 85–108. https://doi.org/10.1007/s10652-014-9362-3.
Lai, C. C., and S. A. Socolofsky. 2019. “Budgets of turbulent kinetic energy, Reynolds stresses, and dissipation in a turbulent round jet discharged into a stagnant ambient.” Environ. Fluid Mech. 19: 349–377. https://doi.org/10.1007/s10652-018-9627-3.
Lattemann, S., and T. Höpner. 2008. “Environmental impact and impact assessment of seawater desalination.” Desalination 220 (1–3): 1–15.
Launder, B. E., and D. B. Spalding. 1983. “The numerical computation of turbulent flows.” In In Numerical prediction of flow, heat transfer, turbulence and combustion, 96–116. New York: Pergamon.
Lee, A. W. T., and J. H. W. Lee. 1998. “Effect of lateral confinement on initial dilution of vertical round buoyant jet.” J. Hydraul. Eng. 124 (3): 263–279. https://doi.org/10.1061/(ASCE)0733-9429(1998)124:3(263).
Liseth, P. 1973. “Mixing of merging buoyant jets from a manifold in stagnant receiving water of uniform density.” In Proc., 6th Int. Conf. on Advances in Water Pollution Research, 921–936. New York: Pergamon Press.
Lyu, S., I. W. Seo, and Y. Do Kim. 2013. “Experimental investigation on behavior of multiple vertical buoyant jets discharged into a stagnant ambient.” KSCE J. Civ. Eng. 17 (7): 1820–1829. https://doi.org/10.1007/s12205-013-0525-4.
Menter, F. R. 1992. “Influence of freestream values on k-omega turbulence model predictions.” AIAA J. 30 (6): 1657–1659. https://doi.org/10.2514/3.11115.
Menter, F. R. 1993. “Zonal two equation k-w turbulence models for aerodynamic flows.” In Proc., 23rd Fluid Dynamics, Plasmadynamics, and Lasers Conf., 2906. Reston, VA: AIAA.
Oliver, C. J., M. J. Davidson, and R. I. Nokes. 2013. “Removing the boundary influence on negatively buoyant jets.” Environ. Fluid Mech. 13 (6): 625–648. https://doi.org/10.1007/s10652-013-9278-3.
OpenCFD Limited. 2014. OpenFOAM [user guide]. Version 2.3.1. London: OpenCFD Limited.
Pitts, W. M. 1991. “Reynolds number effects on the mixing behavior of axisymmetric turbulent jets.” Exp. Fluids 11 (2–3): 135–141. https://doi.org/10.1007/BF00190289.
Roberts, P. J., A. Ferrier, and G. Daviero. 1997. “Mixing in inclined dense jets.” J. Hydraul. Eng. 123 (8): 693–699. https://doi.org/10.1061/(ASCE)0733-9429(1997)123:8(693).
Shao, D., D. Huang, B. Jiang, and A. W. K. Law. 2017. “Flow patterns and mixing characteristics of horizontal buoyant jets at low and moderate Reynolds numbers.” Int. J. Heat Mass Transfer 105 (Feb): 831–846. https://doi.org/10.1016/j.ijheatmasstransfer.2016.10.022.
Shao, D., and A. W. K. Law. 2010. “Mixing and boundary interactions of 30 and 45 inclined dense jets.” Environ. Fluid Mech. 10 (5): 521–553. https://doi.org/10.1007/s10652-010-9171-2.
Shinneeb, A. M., R. Balachandar, and J. D. Bugg. 2011. “Confinement effects in shallow-water jets.” J. Hydraul. Eng. 137 (3): 300–314. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000306.
Socolofsky, S. A., T. Bhaumik, and D. G. Seol. 2008. “Double-plume integral models for near-field mixing in multiphase plumes.” J. Hydraul. Eng. 134 (6): 772–783. https://doi.org/10.1061/(ASCE)0733-9429(2008)134:6(772).
Stanley, S. A., S. Sarkar, and J. P. Mellado. 2002. “A study of the flow-field evolution and mixing in a planar turbulent jet using direct numerical simulation.” J. Fluid Mech. 450: 377–407. https://doi.org/10.1017/S0022112001006644.
Tian, X., and P. J. Roberts. 2011. “Experiments on marine wastewater diffusers with multiport rosettes.” J. Hydraul. Eng. 137 (10): 1148–1159. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000409.
Ungate, C. D., D. R. Harleman, and G. H. Jirka. 1975. Stability and mixing of submerged turbulent jets at low Reynolds numbers. Cambridge, MA: MIT Energy Laboratory.
Wang, H. J., and M. J. Davidson. 2003. “Jet interaction in a still ambient fluid.” J. Hydraul. Eng. 129 (5): 349–357. https://doi.org/10.1061/(ASCE)0733-9429(2003)129:5(349).
Wilcox, D. C. 1998. Vol. 2 of Turbulence modeling for CFD, 103–217. La Canada, CA: DCW Industries.
Wood, I. R., R. G. Bell, and D. L. Wilkinson. 1993. Ocean disposal of wastewater. Singapore: World Scientific.
Yakhot, V. S. A. S. T. B. C. G., S. A. Orszag, S. Thangam, T. B. Gatski, and C. G. Speziale. 1992. “Development of turbulence models for shear flows by a double expansion technique.” Phys. Fluids A: Fluid Dyn. 4 (7): 1510–1520. https://doi.org/10.1063/1.858424.
Yan, X., and A. Mohammadian. 2017. “Numerical modeling of vertical buoyant jets subjected to lateral confinement.” J. Hydraul. Eng. 143 (7): 04017016. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001307.
Yan, X., and A. Mohammadian. 2019a. “Multigene genetic-programming-based models for initial dilution of laterally confined vertical buoyant jets.” J. Mar. Sci. Eng. 7 (8): 246. https://doi.org/10.3390/jmse7080246.
Yan, X., and A. Mohammadian. 2019b. “Numerical modeling of multiple inclined dense jets discharged from moderately spaced ports.” Water 11 (10): 1–15. https://doi.org/10.3390/w11102077.
Yan, X., and A. Mohammadian. 2019c. “Three-dimensional numerical simulations of buoyant jets discharged from a rosette-type multiport diffuser.” J. Mar. Sci. Eng. 7 (11): 409. https://doi.org/10.3390/jmse7110409.
Yan, X., and A. Mohammadian. 2020a. “Evolutionary modeling of inclined dense jets discharged from multiport diffusers.” J. Coastal Res. 36 (2): 362–371. https://doi.org/10.2112/JCOASTRES-D-19-00057.1.
Yan, X., and A. Mohammadian. 2020b. “Evolutionary prediction of multiple vertical buoyant jets in stationary ambient water.” Desalin. Water Treat. 178: 41–52. https://doi.org/10.5004/dwt.2020.24938.
Yannopoulos, P. C. 2006. “An improved integral model for plane and round turbulent buoyant jets.” J. Fluid Mech. 547: 267–296. https://doi.org/10.1017/S0022112005007263.
Yannopoulos, P. C., and G. C. Noutsopoulos. 2010a. “Interaction of vertical round turbulent buoyant jets. Part I: Entrainment restriction approach.” J. Hydraul. Res. 44 (2): 218–232. https://doi.org/10.1080/00221686.2006.9521677.
Yannopoulos, P. C., and G. C. Noutsopoulos. 2010b. “Interaction of vertical round turbulent buoyant jets. Part II: Superposition method.” J. Hydraul. Res. 44 (2): 233–248. https://doi.org/10.1080/00221686.2006.9521678.
Yapa, P. D., L. Zheng, and K. Nakata. 1999. “Modeling underwater oil/gas jets and plumes.” J. Hydraul. Eng. 125 (5): 481–491. https://doi.org/10.1061/(ASCE)0733-9429(1999)125:5(481).
Zhang, S., B. Jiang, A. W. K. Law, and B. Zhao. 2016. “Large eddy simulations of 45 inclined dense jets.” Environ. Fluid Mech. 16 (1): 101–121. https://doi.org/10.1007/s10652-015-9415-2.
Zhao, L., Z. Chen, and K. Lee. 2011. “Modelling the dispersion of wastewater discharges from offshore outfalls: A review.” Environ. Rev. 19: 107–120. https://doi.org/10.1139/a10-025.

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Go to Journal of Hydraulic Engineering
Journal of Hydraulic Engineering
Volume 146Issue 7July 2020

History

Received: Nov 20, 2018
Accepted: Jan 13, 2020
Published online: Apr 30, 2020
Published in print: Jul 1, 2020
Discussion open until: Sep 30, 2020

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Ph.D. Candidate, Dept. of Civil Engineering, Univ. of Ottawa, 161 Louis Pasteur, Ottawa, ON, Canada K1N6N5 (corresponding author). ORCID: https://orcid.org/0000-0002-2928-6562. Email: [email protected]
Behnaz Ghodoosipour [email protected]
Ph.D. Candidate, Dept. of Civil Engineering, Univ. of Ottawa, 161 Louis Pasteur, Ottawa, ON, Canada K1N6N5. Email: [email protected]
Abdolmajid Mohammadian, Ph.D. [email protected]
P.Eng.
Professor, Dept. of Civil Engineering, Univ. of Ottawa, 161 Louis Pasteur, Ottawa, ON, Canada K1N6N5. Email: [email protected]

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