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This paper presents the numerical results for inclined dense effluent discharges into a shallow receiving water body. Two jet discharge angles relative to the horizontal (30° and 45°) were investigated based on the experimental results from Jiang et al. (J Hydraul Eng 140:241–253, 2014). Five Reynolds-averaged Navier–Stokes (RANS) turbulence models were examined in this study: realizable k-e and k-ω SST models (known as two-equation turbulence models), v2f (four equations to model anisotropic behavior) and LRR and SSG turbulence models (known as Reynolds stress models—six equations to model anisotropic behavior). Three mixing regimes introduced in Jiang et al. (J Hydraul Eng 140:241–253, 2014) were reproduced numerically for both discharge angles applying various turbulence models: full submergence, plume contact and centerline impingement regimes (i.e., FSR, PCR and CIR). Key geometrical and dilution properties of these jets at surface contact (Xs, Ss) and jet centerline return point (Xr, Sr) were compared to those available from experiments. Normalization parameter that was selected for jets in shallow waters is H/D (water depth above discharge point over nozzle diameter). It was found that surface attachment increases the return point length from the nozzle and that surface dilution decreases from FSR toward CIR. Among turbulence models tested herein, Reynolds stress models (LRR and SSG) predicted the effluent discharge kinematic and dilution properties better compared to two- and four-equations models. This is mainly attributed to the anisotropic nature of the effluent discharge problem studied herein and that these models are better capable to account for anisotropies.

Recent catastrophic failures of tailings storage facilities have highlighted the critical roles that dam engineers can play in ensuring public safety, and have motivated the mine waste industry to assess and improve the practice of tailings dam breach analysis (TDBAs). As industry moves towards a standard of no catastrophic failures, it is critical that practitioners, owners, and operators have a unified understanding when conducting TDBA, in order to provide a high level of confidence within communities and environments surrounding operational or closed facilities. Currently, uncertainties exist surrounding the industry’s standard practice in conducting appropriate TDBA. This paper provides a summary of the currently available approaches and models for TDBA and when it is appropriate to use a particular method. A critical review of key challenges of TDBA (release volume estimate, hydrograph development, and routing the breach hydrograph downstream) is also provided. This paper aims to be a thorough summary of what is known about TDBA and a reference source for engineers and researchers.

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.

Numerical modeling of inclined turbulent dense jets discharging into a calm homogeneous environment has been investigated in this chapter. The jets are discharged at four angles: 60, 75, 80, and 85°. The higher inclinations are more suitable for deep water outfalls where terminal rise height of the jet does not attach to the ambient water surface. Such jets, especially 60° jets, are used frequently to discharge industrial effluents. The numerical model (OpenFOAM) used in this study is based on the Finite-Volume Method applying Launder-Reece-Rodi (LRR) turbulence model closure. Two different densimetric Froude numbers were simulated for each discharge angle, and important geometrical characteristics of the jet trajectory are investigated, that is, the initial terminal rise height reached by the jet at flow initiation, the final terminal rise height at the steady state, and the point where the jet returns to the nozzle height. Concentration properties of these jets are also characterized numerically, that is, the dilution at the main geometrical points of the jet. All the results are presented in the dimensionless forms in order to compare them to the previous experimental studies.

Bends and confluences are often observed in rivers, and one of the phenomena that characterize flows in open channel bends and confluences is secondary current. Instead of moving somewhat parallel to the channel axis, the movement of the fluid particles in curved and confluent channels takes a spiral path. In this paper, a 3D OpenFOAM numerical model is employed to simulate the effect of secondary currents on water velocity in channel bends and confluences. The behavior of these currents is simulated by using the finite volume method (FVM). The experimental data of a sharply curved channel and a confluent channel were used to compare the numerical results and to evaluate the validity of the model. To assess the performance of different models in predicting the behavior of these secondary flows, two turbulence models (i.e., standard k–e and realizable k–e) were applied in the current study, and the accuracy of the standard and realizable k–e turbulence models was evaluated and discussed. The results of this study showed the better performance of the standard k–e model in curved channels and the realizable k–e model in confluent channels.

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.

Dispersion of turbulent jets in shallow coastal waters has numerous engineering applications. The accurate forecasting of the complex interaction of these jets with the ambient fluid presents significant challenge and has yet to be fully elucidated. In this paper, numerical simulation of $$30{^\circ }$$ and $$45{^\circ }$$ inclined dense turbulent jets in stationary water have been conducted. These two angles are examined in this study due to lower terminal rise heights for $$30{^\circ }$$ and $$45{^\circ }$$ , this is critically important for discharges of effluent in shallow waters compared to higher angles. Mixing behavior of dense jets is studied using a finite volume model (OpenFOAM). Five Reynolds-Averaged Navier–Stokes turbulence models are applied to evaluate the accuracy of CFD predictions. These models include two Linear Eddy Viscosity Models: RNG $$ k-\varepsilon $$ , and realizable $$k-\varepsilon $$ ; one Nonlinear Eddy Viscosity Model: nonlinear $$k-\varepsilon $$ ; and two Reynolds Stress Models: LRR and Launder–Gibson. Based on the numerical results, the geometrical characteristics of the dense jets, such as the terminal rise height, the location of centerline peak, and the return point are investigated. The mixing and dilution characteristics have also been studied through the analysis of cross-sectional concentration and velocity profiles. The results of this study are compared to various advanced experimental and analytical investigations, and comparative figures and tables are discussed. It has been observed that the LRR turbulence model as well as the realizable $$k-\varepsilon $$ model predicts the flow more accurately among the various turbulence models studied herein.

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