Numerical Simulation of Dense Discharges from 30o Submerged Inclined Jet in Free and Bed-Affected Conditions

Document Type : Research Article


1 Babol Noshirvani University of Technology

2 assistant professor, Babol Noshirvani University of Technology


Introduction: Human population growth and industrialization have led to an increase in freshwater demand all around the world, specifically in coastal areas. The conventional resources of freshwater (e.g., rain, rivers, lakes, etc.) do not meet this demand; hence finding new resources of freshwater besides preserving and the optimal use of the available freshwater resources is strictly considered recently. During the last decades, the desalination of seawater by removing salt from the roughly unlimited supply of seawater has emerged as a new source of freshwater in coastal zones. One of the major by-products of desalination plants is the effluent with higher salt concentration than the feeding water, called brines. Disposal of the produced brine into coastal bodies has raised serious concerns due to its potential to cause negative impacts on the marine environment, especially on the benthic communities. The disposal of brines is typically done through a single inclined nozzle or multiport diffuser that laid on the seafloor far enough from the coastline. So far, many different studies have been performed on dense jets to find the optimal angle of the inclination. The generally accepted design practice recommends a 60° angle as the optimal angle. However, the terminal rise height associated with this angle is relatively high. Consequently, smaller angles are more appropriate for shallow coastal waters. This paper investigates geometrical and mixing characteristics of 30° inclined dense jets in free and proximate to bed conditions through simulating two numerical series. In the first series, nozzles are placed well above the bed in terms of y_0⁄d to act like free jets. In the second series, the distance of nozzles to the lower boundary has reduced to observe the possible effect of proximity to bed on dense jets behavior.

Methodology: The governing equations of the present problem are continuity, conservation of momentum, and tracer advection-diffusion equations. These governing equations are solved using an open-source finite volume model named OpenFOAM. The buoyantBoussinesqPimpleFoam solver, which is a transient solver for buoyant, turbulent flow of incompressible fluids, is modified within the OpenFOAM to solve the governing equations of the present problem. Moreover, the realizable k-ε model and the Boussinesq approximation are employed for turbulent closure and buoyancy effects, respectively.

Results and discussion: The major geometrical characteristics of dense jets, including the centerline trajectory, the location of centerline peak, the terminal rise height, etc., are presented. The centerline trajectories are in acceptable agreement with previous analytical and experimental studies. They are generally symmetrical; however, a slight asymmetry was observed in the boundary-affected cases. The other geometrical characteristics in all cases are in good agreement with previous data. The mixing and dilution characteristics were also studied through cross-sectional concentration profiles. It is observed that the present simulations predict the dilution at the return point significantly conservative. The buoyant instabilities on the inner edge of flow are also evident in the mean concentration profiles.

Conclusions: Ocean outfalls are the most widely used method for brines disposal. Therefore, predicting the flow behavior along the near field region (a short distance from the nozzle tip) is vital. The review of the previous studies showed that the literature is rich in this field. Several investigations, experimentally and theoretically, have been reported for predicting the brine flow through surface and submerged discharges into both stagnant and flowing waters. There are also commercial models developed for this purpose, which work based on simplifying assumptions for the governing equations. Recently, thanks to progress in computer performance, the use of numerical methods to solve physical problems has become possible for engineering purposes. The discharge of brines, as with many other engineering flows, are physically complicated and fully turbulent, so requiring robust and accurate modeling.
In the present paper, a numerical study was reported for inclined dense jets at the angle of 30o. Two series of simulations were performed. In the first series, the nozzles were placed far from the bed. While in the second series, the nozzles were placed in a close distance to the bed. The aim was to investigate the possible effects of proximity to bed on dense jets behavior. The locations of the terminal rise height and impact point, as well as the dilution at the return point, were determined. The simulations predict trajectory data in free jets with reasonable accuracy, but dilution predictions are conservative in comparison to previous analytical and experimental studies. Comparisons between two numerical series showed discharging 30° inclined dense jets in a close distance to the bed in the cases that in this study were examined had no appreciable effects on neither the geometrical characteristics nor mixing and dilution characteristics.


Abessi, O. (2018). Chapter 7 - Brine Disposal and Management—Planning, Design, and Implementation. V. G. B. T.-S. D. H. Gude, ed., Butterworth-Heinemann, 259–303.
Abessi, O., and Roberts, P. J. W. (2015a). Effect of nozzle orientation on dense jets in stagnant environments. Journal of Hydraulic Engineering, American Society of Civil Engineers, 141(8), 6015009.
Abessi, O. and Roberts, P.J.W. (2015b). Dense jet discharges in shallow water. Journal of Hydraulic Engineering, American Society of Civil Engineers, 142(1), 4015033.
Abessi, O., Roberts, P.J. and Gandhi, V. (2017). Rosette diffusers for dense effluents. Journal of Hydraulic Engineering, 143(4), p.06016029.
Abessi, O. and Roberts, P.J.W. (2018). Rosette diffusers for dense effluents in flowing currents. Journal of Hydraulic Engineering.
Abessi, O., Saeedi, M., Davidson, M. and Zaker, N.H. (2012). Flow Classification of Negatively Buoyant Surface Discharge in an Ambient Current. Journal of Coastal Research.
Ardalan, H. and Vafaei, F. (2019). CFD and Experimental Study of 45° Inclined Thermal-Saline Reversible Buoyant Jets in Stationary Ambient. Environmental Processes, Springer, 1–21.
Cederwall, K. (1968). Hydraulics of marine waste water disposal. Chalmers tekniska högskola.
El-Dessouky, H.T. and Ettouney, H.M. (2002). Fundamentals of salt water desalination. Elsevier.
Ferziger, J.H. and Perić, M. (2002). Computational methods for fluid dynamics. Springer.
Fox, R.O. and Stiles, H.L. (2003). Computational models for turbulent reacting flows. Cambridge university press Cambridge.
Gildeh, H.K., Mohammadian, A., Nistor, I., and Qiblawey, H. (2015). Numerical modeling of 30 and 45 inclined dense turbulent jets in stationary ambient. Environmental Fluid Mechanics, Springer, 15(3), 537–562.
Holzmann, T. (2016). Mathematics, numerics, derivations and OpenFOAM®. Loeben, Germany: Holzmann CFD, URl: https://holzmann-cfd. de (visited on Nov. 29, 2017).
Huai, W., Li, Z., Qian, Z., Zeng, Y., Han, J. and Peng, W. (2010). Numerical simulation of horizontal buoyant wall jet. Journal of Hydrodynamics, Springer, 22(1), 58–65.
Kikkert, G.A. (2006). Buoyant jets with two and three-dimensional trajectories. University of Canterbury. Civil Engineering.
Kikkert, G.A., Davidson, M.J. and Nokes, R.I. (2007). Inclined negatively buoyant discharges. Journal of Hydraulic engineering, American Society of Civil Engineers, 133(5), 545–554.
Lai, C.C.K. and Lee, J.H.W. (2012). Mixing of inclined dense jets in stationary ambient. Journal of hydro-environment research, Elsevier, 6(1), 9–28.
Lai, C.C.K. and Socolofsky, S. A. (2018). Budgets of turbulent kinetic energy, Reynolds stresses, and dissipation in a turbulent round jet discharged into a stagnant ambient. Environmental Fluid Mechanics, Springer, 1–29.
Launder, B.E. and Spalding, D.B. (1983). The numerical computation of turbulent flows. Numerical prediction of flow, heat transfer, turbulence and combustion, Elsevier, 96–116.
Oliver, C.J., Davidson, M.J. and Nokes, R.I. (2008). k-ε predictions of the initial mixing of desalination discharges. Environmental Fluid Mechanics, Springer, 8(5–6), 617.
Pope, S. B. (2001). Turbulent flows. IOP Publishing.
Rard, J.A. and Miller, D.G. (1982). Mutual diffusion coefficients of SrCl 2–H 2 O and CsCl—H 2 O at 25° C from Rayleigh interferometry. Journal of the Chemical Society, Faraday Transactions 1: Physical Chemistry in Condensed Phases, Royal Society of Chemistry, 78(3), 887–896.
Roberts, P.J.W., Ferrier, A., and Daviero, G. (1997). Mixing in inclined dense jets. Journal of Hydraulic Engineering, American Society of Civil Engineers, 123(8), 693–699.
Robinson, D., Wood, M., Piggott, M. and Gorman, G. (2016). CFD modelling of marine discharge mixing and dispersion. Journal of Applied Water Engineering and Research, Taylor & Francis, 4(2), 152–162.
Roberts, P.J. and Abessi, O. (2014). Optimization of desalination diffusers using three-dimensional laser-induced fluorescence. Agreement Number R11 AC81, 535.
Saeedi, M., Farahani, A.A., Abessi, O. and Bleninger, T. (2012). Laboratory studies defining flow regimes for negatively buoyant surface discharges into crossflow. Environmental fluid mechanics, 12(5), 439-449.
Shao, D. and Law, A.W.K. (2010). Mixing and boundary interactions of 30° and 45° inclined dense jets. Environmental Fluid Mechanics, 10(5), 521–553.
Shih, T.-H., Liou, W.W., Shabbir, A., Yang, Z. and Zhu, J. (1995). A new k-ϵ eddy viscosity model for high reynolds number turbulent flows. Computers & Fluids, Elsevier, 24(3), 227–238.
Vafeiadou, P., Papakonstantis, I. and Christodoulou, G. (2005). Numerical simulation of inclined negatively buoyant jets. The 9th international conference on environmental science and technology, September, 1–3.
Zeitoun, M.A., Reid, R., McHilhenny, W.F. and Mitchell, T.M. (1970). Model studies of outfall system for desalination plants. Washington, DC.
Zhang, S., Law, A.W.-K. and Jiang, M. (2017). Large eddy simulations of 45° and 60° inclined dense jets with bottom impact. Journal of Hydro-Environment Research, Elsevier, 15, 54–66.
Volume 15, Issue 3 - Serial Number 153
September 2020
Pages 75-91
  • Receive Date: 17 May 2020
  • Revise Date: 06 September 2020
  • Accept Date: 07 September 2020
  • First Publish Date: 22 September 2020