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Vertical dense effluent discharges are popular in outfall system designs. Vertical jets provide the opportunity to be efficient for a range of ambient currents, where the jet is pushed away so as not to fall on itself. This study focuses on the worst-case scenario of the dilution and mixing of such jets: vertical dense effluent discharges with no ambient current, in shallow water, where the jet impinges the water surface. This scenario provides conservative design criteria for such outfall systems. The numerical modelling of such jets has not been investigated before and this study provides novel insights into simulations of vertical dense effluent discharges in shallow waters. Turbulent vertical discharges with Froude numbers ranging from 9 to 24 were simulated using OpenFOAM. A Reynolds stress model (RSM) was applied to characterize the geometrical (i.e., maximum discharge rise Zm and lateral spread Rsp) and dilution μmin properties of such jets. Three flow regimes were reproduced numerically, based on the experimental data: deep, intermediate, and impinging flow regimes.

Effluent discharge mixing and dispersion have been studied for many decades. Studies began with experimental investigations of geometrical and concentration characteristics of the jets in the near-field zone. More robust experiments were performed using Laser-Induced Fluorescence (LIF) and Particle Image Velocimetry (PIV) systems starting in the 20th century, which led to more accurate measurement and analysis of jet behavior. The advancement of computing systems over the past two decades has led to the development of various numerical methods, which have been implemented in Computational Fluid Dynamics (CFD) codes to predict fluid motion and characteristics. Numerical modeling of mixing and dispersion is increasingly preferred over laboratory experiments of effluent discharges in both academia and industry. More computational resources and efficient numerical schemes have helped increase the popularity of using CFD models in jet and plume modeling. Numerous models have been developed over time, each with different capabilities to facilitate the investigation of all aspects of effluent discharges. Among these, Reynolds-averaged Navier-Stokes (RANS) and Large Eddy Simulations (LES) are at present the most popular CFD models employing effluent discharge modeling. This paper reviews state-of-the-art numerical modeling studies for different types and configurations of discharges, including positively and negatively buoyant discharges, which have mostly been completed over the past two decades. The numerical results of these studies are summarized and critically discussed in this review. Various aspects related to the impact of turbulence models, such as k-ε and Launder-Reece-Rodi (LRR) models, are reviewed herein. RANS and LES models are reviewed, and implications for the simulation of jet and plume mixing are discussed to develop a reference for future researchers performing numerical investigations on jet mixing and dispersion.

A three-dimensional numerical model of inclined turbulent jets with negatively buoyant discharge into stationary ambient water is presented in this paper to study certain jet parameters with turbulence schemes that have not been employed before in this context such as standard Boussinesq gradient diffusion hypothesis and general gradient diffusion hypothesis to account for the buoyancy-induced turbulence generation. Two jet discharge angles have been chosen for this study: 30° and 45° with the horizontal. These two angles are chosen in this study due to lower terminal rise heights for 30° and 45°, a fact which is critically important for discharges of effluent into shallow waters compared to higher angles than these values. The spatio-temporal jet evolutions for these cases have been modeled using OpenFOAM open-source CFD code, which is based on Finite-Volume Method. Results presented in this paper deal with the geometrical and flow properties of the inclined dense jets. The densimetric Froude number of the effluent at the nozzle ranges between 10 and 34. Two Reynolds-Averaged Navier–Stokes turbulence models are applied to evaluate the accuracy of the numerical predictions: the realizable k–ε (a two-equation model) and the Launder Reece Rodi (a Reynolds Stress Model – RSM). This publication was made possible by NPRP grant #4-935-2-354 from the Qatar National Research Fund (a member of Qatar Foundation). Scopus