Integrated modeling of single port brine discharges into unstratified stagnant ambient

An integrated model is presented for the calculation of the characteristics in the intermediate field region of brine discharges from reverse osmosis desalination plants into unstratified stagnant coastal waters. The model consists of the near field model Modified CorJet Model and the far field model, which are interconnected via a coupling algorithm. This algorithm has been developed to simulate the flow and concentration characteristics of negatively buoyant jets (NBJ) after their impingement on the bottom. The coupling method was developed to be active according to literature, however further work and investigation is needed to be applicable for NBJ discharged into other ambient environments and especially in cases where the background values of ambient flow and concentrations affect the NF values and vice versa. The integrated model was validated with data from the literature as well as with data from experiments conducted in this study showing a good agreement. The coupling algorithm was also compared to other coupling techniques used in the literature for NBJ discharges showing better estimations of the experimental data.     

Stability and Mixing of a Vertical Axisymmetric Buoyant Jet in Shallow Water

The stability, mixing and effect of downstream control on axisymmetric turbulent buoyant jets discharging vertically into shallow stagnant water is studied using 3D Reynolds-averaged Navier–Stokes equations (RANS) combined with a buoyancy-extended k –ε model. The steady axisymmetric turbulent flow, temperature (or tracer concentration) and turbulence fields are computed using the finite volume method on a high resolution grid. The numerical predictions demonstrate two generic flow patterns for different turbulent heated jet discharges and environmental parameters (i) a stable buoyant discharge with the mixed fluid leaving the vertical jet region in a surface warm water layer; and (ii) an unstable buoyant discharge with flow recirculation and re-entrainment of heated water. A stratified counterflow region always appears in the far-field for both stable and unstable buoyant discharges. Provided that the domain radius L exceeds about 6H, the near field interaction and hence discharge stability is governed chiefly by the jet momentum length scale to depth ratio l_M/H, regardless of downstream control. The near field jet stability criterion is determined to be l_M/H = 3.5. A radial internal hydraulic jump always exists beyond the surface impingement region, with a 3- to 6-fold increase in dilution across the jump compared with vertical buoyant jet mixing. The predicted stability category, velocity and temperature/concentration fields are well-supported by experiments of all previous investigators.     

Integral Model for Turbulent Buoyant Jets in Unbounded Stratified Flows Part 2: Plane Jet Dynamics Resulting from Multiport Diffuser Jets

An integral model for the plane buoyant jet dynamics resulting from the interaction of multiple buoyant jet effluxes spaced along a diffuser line is considered as an extension of the round jet formulation that was proposed in Part I. The receiving fluid is given by an unbounded ambient environment with uniform density or stable density stratification and under stagnant or steady sheared current conditions. Applications for this situation are primarily for submerged multiport diffusers for discharges of liquid effluents into ambient water bodies, but also for multiple cooling tower plumes and building air-conditioning. The CorJet model formulation describes the conservation of mass, momentum, buoyancy and scalar quantities in the turbulent jet flow in the plane jet geometry. It employs an entrainment closure approach that distinguishes between the separate contributions of transverse shear and of internal instability mechanisms, and contains a quadratic law turbulent pressure force mechanism. But the model formulation also includes several significant three-dimensional effects that distinguish actual diffuser installations in the water environment. These relate to local merging processes from the individual multiple jets, to overall finite length effects affecting the plume geometry, and to bottom proximity effects given by a “leakage factor” that measures the combined affect of port height and spacing in allowing the ambient flow to pass through the diffuser line in order to provide sufficient entrainment flow for the mixing downstream from the diffuser. The model is validated in several stages: First, comparison with experimental data for the asymptotic, self-similar stages of plane buoyant jet flows, i.e. the plane pure jet, the pure plume, the pure wake, the advected line puff, and the advected line thermal, support the choice of the turbulent closure coefficients contained in the entrainment formulation. Second, comparison with data for many types of non-equilibrium flows with a plane geometry support the proposed functional form of the entrainment relationship, and also the role of the pressure force in the jet deflection dynamics. Third, the observed behavior of the merging process from different types of multiport diffuser discharges in both stagnant and flowing ambient conditions and with stratification appears well predicted with the CorJet formulation. Fourth, a number of spatial limits of applicability, relating to terminal layer formation in stratification or transition to passive diffusion in a turbulent ambient shear flow, have been proposed. In sum, the CorJet integral model appears to provide a mechanistically sound, accurate and reliable representation of complex buoyant jet mixing processes, provided the condition of an unbounded receiving fluid is satisfied.     

2D brine sewage after impinging on a shallow sea free surface

We consider the problem of the vertically upwards disposal of heavy brine sewage from a two-dimensional diffuser in a lighter, homogeneous, motionless and shallow ambient sea. The rejected high salinity water of seawater desalination plants for urban and agricultural uses is such a case of a two dimensional fountain. The disposal of brine sewage produces a negative buoyant jet due to its initial momentum, which impinges on the free surface, spreads laterally on it and then sinks downwards, because of the negative buoyancy. Laboratory experiments and dimensional considerations are used in this paper in order to investigate the spreading behavior (width) of the vertical fountain which impinges on the free surface of the shallow ambient fluid. The experimental results have been used to derive an equation relating the width at the free surface with the initial parameters of the flow. In addition, the experimentally measured dilution of the heavier brine sewage on the recipient’s surface is compared with the dilution which was calculated by a numerical simulation of a well-known commercial software package, CORJET (a CORMIX sub model).     

A review of gravity currents formed by submerged single-port discharges in inland and coastal waters

In this paper, the authors review the current state of the science on the dynamics of gravity currents generated by positively and negatively buoyant jet discharges from submerged round outfalls (i.e., a point source) in inland and coastal waters. Specifically, this article focuses on describing gravity currents occurring at both the bottom boundary and the free surface of the receiving fluid. The manmade discharge operations generating both types of gravity currents and their significance to sustainability of the surrounding hydro-environment are first described. The authors then summarize the flow regimes characteristics of these discharges before becoming gravity currents and how those flow regimes influence the dynamics of the gravity currents. The gravity current dynamics in the calm receiving waters are then analyzed. This analysis is followed by an analysis of the influence of the hydrodynamic forces (e.g., currents, turbulence, waves) on the dynamics of gravity currents. Finally, the authors review quantitative modeling approaches for different forms of gravity current, and identify the current knowledge gaps and research needs.     

Influence of Downstream Control and Limited Depth on Flow Hydrodynamics of Impinging Buoyant Jets

Much study has been performed on the mixing properties of submerged, turbulent buoyant jets. It is safe to say that the problem of estimating dilution rates in vertical buoyant jets spreading in an `infinitely deep' ambient water has been more than adequately resolved by previous researchers. However, the majority of environmental applications involve discharges into ambient waters of finite depths in which a bounding surface serves to re-direct the impinging buoyant jet horizontally into a radial spreading layer. Previous research indicates that this impinging jet undergoes additional mixing before buoyancy stabilizes vertical mixing and confines the spreading layer to the vicinity of the bounding surface. Unfortunately, the conceptualization and subsequent mathematical modeling of this additional mixing phenomenon is surrounded by considerable amount of disagreement between researchers. The purpose of this study is to provide, by means of velocity and concentration profile measurements, independent experimental evidence for the existence of a critical flow state immediately downstream of the active mixing zone in the horizontally flowing, radial flow that forms after impingement. It is further shown that this critical flow state must be expressed in terms of a composite Froude Number that takes into account the possibility of a non-zero exchange layer flow. Finally, the influence of the presence of a sill-like topographic downstream control on the criticality of the radial flow immediately downstream of the active mixing zone is also investigated.     

Modeling the buoyant flow of heated water discharged from surface and submerged side outfalls in shallow and deep water with a cross flow

In this study, a three-dimensional model was used to numerically study the buoyant flow, along with its mixing characteristics, of heated water discharged from the surface and submerged side outfalls in shallow and deep water with a cross flow. Hydraulic experimental data were used to evaluate the applicability of the model. The simulation results agree well with the experimental results, particularly, the jet trajectories, the dimensions of the recirculating zone, and the distribution of the dimensionless excess temperature. The level of accuracy of the simulation results of the present study is nearly identical to that of the results conducted by McGuirk and Rodi (1978). If the heated water is discharged into shallow water where the momentum flux ratio and the discharge densimetric Froude number are high, the submerged discharge method is better than the surface discharge method in terms of the scale of the recirculating zone and the minimum dilution. In deep water, where the momentum flux ratio and discharge densimetric Froude number are low, however, the submerged discharge method had few advantages. In shallow water, the discharge jet is deflected by the ambient cross flow, while forcing the ambient flow to bend towards the far bank for the full depth. For a submerged discharge in shallow water, the recirculating zone is the largest in the lowest layer but becomes smaller in the upper layer. As the water depth increases, the ambient flow goes over the jet and diminishes the blocking effect, thereby decreasing the bending of the jet.     

k-ε Predictions of the initial mixing of desalination discharges

Predictions from a k-ε model are compared with recently acquired experimental data from inclined negatively buoyant discharges. The k-ε model is part of a standard computational fluid dynamics package (CFX). Two approaches are taken when implementing the model. One involves using an essentially standard form of the model to predict flow behaviour. The other approach involves calibrating the model, through adjustment of the turbulent Schmidt number in the tracer transport equation, to achieve reasonable predictions for positively buoyant vertical discharges and then applying it to inclined negatively buoyant discharges. While the calibrated approach improves the predictions of some bulk parameters (notably the tracer spread and dilution) when compared to predictions from the standard model, the overall effect on the quality of the predictions is small. Comparisons with experimental data indicate that predictions from both the standard and calibrated simulations compare favourably with trajectory data, but integrated dilution predictions at the centreline maximum height are conservative (mean-integrated concentrations are over-predicted). The standard and calibrated k-ε predictions confirm the importance of buoyant instabilities on the lower (inner) side of the flow, the effects of which are clearly evident in the mean concentration profiles. However, these simulations have a tendency to overestimate the influence of stabilizing density gradients on the upper (outer) side of the flow and are unable to effectively predict the cross-sectional distribution of a tracer. In contrast to a previous study, the above comparisons indicate that predictions of bulk parameters from such models can be poor and indeed are no better than those obtained from relatively simple analytical solutions.     

Removing the boundary influence on negatively buoyant jets

A comprehensive laboratory study of negatively buoyant discharges is presented. Unlike previous studies, here the focus is on generating data sets where influences of the bottom boundary have been eliminated. There are significant discrepancies in the published dilution data for these flows and a contributing factor is the large variation in the bottom boundary condition. A Laser-induced Fluorescence system is employed to gather flow spread, peak concentration (minimum dilution) and trajectory data for a wide range of densimetric Froude numbers and initial discharge angles. Data from these experiments are compared with previously published data, along with predictions from integral models and a revised form of the previously published semi-analytical solutions. The new data sets are not distorted by mixing processes associated with the bottom boundary and therefore provide the basis for more meaningful assessments of the predictive capabilities of existing models, given that the influences of the bottom boundary on contaminant mixing are not incorporated into these models. In general the models assessed are able to predict key geometric quantities with reasonable accuracy, but their minimum dilution predictions are conservative. Importantly dilution at the return point shows a strong dependence on the initial discharge angle and this could have important implications for the design of discharge systems.     

Warm discharges in cold fresh water: 2. Numerical simulation of laminar line plumes

The behaviour of a discharge of warm water upwards into a homogeneous body of cold fresh water was investigated by means of a numerical model. The discharge has a parabolic velocity profile, with Reynolds number \(Re=50\), Prandtl number \(Pr=7\) and Froude number varied over the range \(0.2 \le {\rm Fr} \le 2.5\). Water density is taken to be a quadratic function of temperature, so that an initially positively buoyant discharge will experience buoyancy reversal as it mixes with an ambient below the temperature of maximum density. The resulting plume has some similarities to a fountain resulting from injection of negatively buoyant fluid upward into a less dense ambient. The plume is initially symmetric, but then its head detaches as it approaches its maximum height. The detached head is denser than the fluid in the plume below it, and the interaction between the sinking head and the rising plume causes a sideways deflection; as this cycle is repeated, the plume displays side-to-side flapping motion and vertical bobbing. As Froude number is increased (i.e. buoyancy reduced) the growth of the plume becomes slower, but the plume eventually reaches a greater height. We obtain empirical power-law scalings for maximum height and time taken to reach that height as functions of Froude number; these scalings are simlar to those for fountains with a linear dependence of density on temperature in the very weak regime.     

Velocity measurements in inclined negatively buoyant jets

Experiments were performed with a particle tracking velocimetry system to investigate the behaviour of inclined negatively buoyant jets with source angles of 15°, 30°, 45°, 60°, 65°, 70°, and 75° in stationary ambient conditions. Velocities were measured in a plane aligned with the central axis of the flow and the experiments were designed such that the flow did not interact with boundaries in the region were the flow behaviour was measured. The results of this study complement previous research, which has largely focused on the mean geometric characteristics and the mean dilution of the discharged fluid. Geometric characteristics, spreading rates, and time-averaged (mean) centreline velocity results are compared with relevant experimental results from previous studies and integral model predictions. Axial and transverse mean velocity profiles at maximum height and the return point provide additional insights into the detrainment of discharged fluid due to the unstable density gradient on the inner side of the flow.     

Dynamics of the buoyant plume off the Pearl River Estuary in summer

Field measurements of salinity, wind and river discharge and numerical simulations of hydrodynamics from 1978 to 1984 are used to investigate the dynamics of the buoyant plume off the Pearl River Estuary (PRE), China during summer. The studies have shown that there are four major horizontal buoyant plume types in summer: Offshore Bulge Spreading (Type I), West Alongshore Spreading (Type II), East Offshore Spreading (Type III), and Symmetrical Alongshore Spreading (Type IV). River mouth conditions, winds and ambient coastal currents have inter-influences to the transport processes of the buoyant plume. It is found that all of the four types are surface-advected plumes by analysing the vertical characteristic of the plumes, and the monthly variations of the river discharge affect the plume size dominantly. The correlation coefficient between the PRE plume size and the river discharge reaches 0.85 during the high river discharge season. A wind strength index has been introduced to examine the wind effect. It is confirmed that winds play a significant role in forming the plume morphology. The alongshore wind stress and the coastal currents determine the alongshore plume spreading. The impact of the ambient currents such as Dongsha Current and South China Sea (SCS) Warm Current on the plume off the shelf has also assessed. The present study has demonstrated that both the river discharge and wind conditions affect the plume evolution.     

Comments on “Simulation of Jeddah multi–port sea outfall” by Abdullah S. Al-Ghamdi [J. Coast. Conserv.] (2010) 14:63–69

In a paper published recently in the Journal of Coastal Conservation, Al-Ghamdi (J Coast Conserv 14:63–69, 2010) analyzes the wastewater multi-pot outfall of Jeddah using CORMIX2 for average ambient conditions. Both the near–field and the far–field mixing are calculated with CORMIX2. It is found in Al-Ghamdi (J Coast Conserv 14:63–69, 2010) that the near-field extends 187.5 m downstream from the diffuser, where the dilution reaches 1,047.8. It is at this same distance, 187.5 m, that the plume touches the water surface. The far-field dilution and plume width is calculated as the plume finally fills the entire water depth at a distance of 18,927 m downstream. From these analyses, it is concluded that local and international standards for treated wastewater are met and that the plume “will not pose any treats to the local venerable environment”. These findings, if correct, will help to protect the surrounding marine environment. However, is argued here that the use of CORMIX2, particularly for the far-field environment is not well justified and that the inherent simplifications in the software and its use, mainly the characterization of the physical environment, undermine the main conclusions.     

Effects of turbulent Schmidt number on CFD simulation of $$45^\circ $$ 45 ∘ inclined negatively buoyant jets

Environmental Fluid Mechanics - Employing inclined negatively buoyant jets is one of the most advantageous means to discharge brine or waste in coastal environments. However, numerical prediction...     

Integral Model for Turbulent Buoyant Jets in Unbounded Stratified Flows. Part I: Single Round Jet

The mechanics of buoyant jet flows issuing with a general three-dimensional geometry into an unbounded ambient environment with uniform density or stable density stratification and under stagnant or steady sheared current conditions is investigated. An integral model is formulated for the conservation of mass, momentum, buoyancy and scalar quantities in the turbulent jet flow. The model employs an entrainment closure approach that distinguishes between the separate contributions of transverse shear (leading to jet, plume, or wake internal flow dynamics) and of azimuthal shear mechanisms (leading to advected momentum puff or thermal flow dynamics), respectively. Furthermore, it contains a quadratic law turbulent drag force mechanism as suggested by a number of recent detailed experimental investigations on the dynamics of transverse jets into crossflow. The model is validated in several stages: First, comparison with basic experimental data for the five asymptotic, self-similar stages of buoyant jet flows, i.e., the pure jet, the pure plume, the pure wake, the advected line puff, and the advected line thermal, support the choice and magnitude of the turbulent closure coefficients contained in the entrainment formulation. Second, comparison with many types of non-equilibrium flows support the proposed transition function within the entrainment relationship, and also the role of the drag force in the jet deflection dynamics. Third, a number of spatial limits of applicability have been proposed beyond which the integral model necessarily becomes invalid due to its parabolic formulation. These conditions, often related to the breakdown of the boundary layer nature of the flow, describe features such as terminal layer formation in stratification, upstream penetration in jets opposing a current, or transition to passive diffusion in a turbulent ambient shear flow. Based on all these comparisons, that include parameters such as trajectories, centerline velocities, concentrations and dilutions, the model appears to provide an accurate and reliable representation of buoyant jet physics under highly general flow conditions.     

Particle laden flows through an inverted chimney with applications to ocean carbon sequestration

Plumes of negatively buoyant hydrate particles, formed by reacting liquid CO₂ with seawater at ocean depths of 1000–1500 m, have been suggested as a way to help sequester CO₂. The vertical flux of CO₂ can be increased by constructing a shroud around the hydrate particle source to shelter the plume from effects of ambient stratification and current. The shroud also serves as an inverted chimney, inducing a down draft that will transport the dissolving particles to a depth of lower ambient disturbance. Laboratory PIV measurements are compared to an analysis of an idealized shroud that is long, frictionless and driven by a single phase source of buoyancy distributed uniformly over the shroud base. Results indicate that induced draft, and hence dilution of dissolved CO₂, increases with plume buoyancy, and shroud length and diameter, but efficiency decreases with increasing ratio of particle slip velocity divided by the characteristic induced draft velocity. While larger particles show reduced plume-like behavior and hence are less efficient in inducing draft, they still generated about half of the theoretically predicted flow.     

Combined integral and particle model for describing the dispersion,dilution, terminal layer formation and influence area from a point source discharge into a water body

Contamination of coastal water is a persistent threat to ecosystems around the world. In this study, a novel model for describing the dispersion, dilution, terminal layer formation and influence area from a point source discharge into a water body is presented and compared with field measured data. The model is a Combined Integral and Particle model (CIPMO). In the initial stage, the motion, dispersion and dilution of a buoyant jet are calculated. The output from the buoyant jet model is then coupled with a Lagrangian Advection and Diffusion model describing the far-field. CIPMO ensures that both the near- and far-field processes are adequately resolved. The model either uses empirical data or collects environmental forcing data from open source hydrodynamic models with high spatial and temporal resolution. The method for coupling the near-field buoyant jet and the particle tracking model is described and the output is discussed. The model shows good results when compared with measurements from a field study.

     

Morphological variation and phenotypic plasticity of buoyancy in the macroalga Turbinaria ornata across a barrier reef

Many aspects of morphology of benthic algae (length, surface area-to-volume ratio, and blade undulation) are plastic traits that vary in response to physical factors (such as light or water flow environment). This study examines whether frond buoyancy is a plastic trait, and whether differences in morphology including buoyancy affect the potential persistence of macroalgae in habitats characterized by different water flow regimes. Fronds of the tropical alga Turbinaria ornata in protected backreef environments in Moorea, French Polynesia possess pneumatocysts (gas-filled floats) and experience positive buoyant forces, whereas fronds in wave-exposed forereef sites either lack pneumatocysts entirely or have very small, rudimentary pneumatocysts and experience negative buoyant forces. Forereef fronds transplanted to the backreef developed pneumatocysts and experienced increased buoyant force indicating that buoyancy is a phenotypically plastic trait in T. ornata. In comparing the potential for dislodgement by drag, drag was greater on forereef fronds at low flow speeds as these fronds were stiffer and did not bend over at low flow speeds and therefore were less streamlined in the flow than backreef algae, which bent easily. The environmental stress factor (ESF) (a measure of the likelihood of detachment for a frond in its habitat) was higher for forereef than backreef fronds at all flow speeds. When examined with respect to the flow velocities likely in their respective habitats however, the chance of detachment for backreef and forereef was similar. Neither backreef nor forereef fronds were predicted to break under normal, non-storm conditions, but both were predicted to break in storms. Strong forereef morphologies are well suited to habitats characterized by rapid flow, whereas the weaker, buoyant, tall backreef fronds are well suited to habitats where crowding and shading is common but hydrodynamic forces are low.     

The effects of Pinus tabuliformis on soil detachment under different influencing factors in the Loess Plateau of China

In situ experiments were undertaken to examine the impacts of Pinus tabuliformis on soil detachment under different influencing factors. Experimental sites with slopes containing vegetation cover, plant roots and bare ground were investigated for slope gradients of 8.7%, 17.6%, 26.8%, 36.4% and 46.6% and flow discharges of 0.25, 0.5, 1.0, 1.5 and 2.0?m³?s^?1. Results from our study provide details on the relationship between soil detachment and both slope gradient and flow discharge. Soil detachment rates increased with an increase in slope and discharge, and discharge was identified to have a stronger influence on soil detachment than slope. In contrast, the combination of litter cover and roots played an important role in reducing soil detachment; detachment rate decreased by about 55% relative to bare slopes; and plant roots had a greater impact on detachment reduction. The presence of vegetation cover can decrease rill erodibility by 83% and increase critical shear stress by 224% compared with bare slopes. These results provide valuable information on the importance of woodland in soil detachment control, and may help to improve vegetation construction in seriously eroded regions of the Loess Plateau.     

Life history theory predicts fish assemblage response to hydrologic regimes

The hydrologic regime is regarded as the primary driver of freshwater ecosystems, structuring the physical habitat template, providing connectivity, framing biotic interactions, and ultimately selecting for specific life histories of aquatic organisms. In the present study, we tested ecological theory predicting directional relationships between major dimensions of the flow regime and life history composition of fish assemblages in perennial free-flowing rivers throughout the continental United States. Using long-term discharge records and fish trait and survey data for 109 stream locations, we found that 11 out of 18 relationships (61%) tested between the three life history strategies (opportunistic, periodic, and equilibrium) and six hydrologic metrics (two each describing flow variability, predictability, and seasonality) were statistically significant (P < or = 0.05) according to quantile regression. Our results largely support a priori hypotheses of relationships between specific flow indices and relative prevalence of fish life history strategies, with 82% of all significant relationships observed supporting predictions from life history theory. Specifically, we found that (1) opportunistic strategists were positively related to measures of flow variability and negatively related to predictability and seasonality, (2) periodic strategists were positively related to high flow seasonality and negatively related to variability, and (3) the equilibrium strategists were negatively related to flow variability and positively related to predictability. Our study provides important empirical evidence illustrating the value of using life history theory to understand both the patterns and processes by which fish assemblage structure is shaped by adaptation to natural regimes of variability, predictability, and seasonality of critical flow events over broad biogeographic scales.