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

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.