Prediction of Near Field Plume Characteristics Using Far Field Circulation Model

3-D numerical models are being used more commonly to predict changes in coastal water quality associated with point discharges such as sewage outfalls. Because these “far field” models use grid sizes which are orders of magnitude larger than the scale of near field entrainment processes, it is of interest to compare their predictive capability with that of initial mixing models and to identify ways in which the two model types can be coupled. Comparisons between the 3-D circulation model ECOMsi and the Environmental Protection Agency's mixing model RSB suggest that the former does a reasonable job predicting plume trap height and volumetric dilution but often overpredicts plume width. Results are sensitive to source representation and parameterization of horizontal and vertical diffusion. The success results from the fact that initial dilution is governed in part by gravitational exchange flow (a large-scale phenomenon that can be resolved in a far field model) in addition to plume entrainment (which is clearly subgrid scale), as well as the self-regulating relationship between plume trap height and initial dilution. Overprediction of plume width is attributed to numerical diffusive effects. Several procedures for improving predictions by coupling near and far field models are explored, ranging from the use of the near field model to dynamically adjust far field mixing parameters, so that the far field model simulates the correct trap height, to simply using the near field model to assign source location and dimension for the far field.     

Physical Model Study of an Alternating Diffuser for Thermal Discharge

Physical model tests were conducted of the mixing of heated water from a proposed thermal diffuser. Dilutions were measured and flows imaged by a three-dimensional laser-induced fluorescence system that provides vastly more data than conventional thermocouple techniques. The flows were quite three-dimensional. For zero current speed, the effluent mixed over the water depth, but only in a limited region, and a two-layer stratified flow developed toward the edges of the effluent field and farther downstream. For zero and slow currents, the lowest surface dilution occurred where the jet centerline intersected the water surface and could be reasonably predicted by simple free-jet calculations. The prediction of an entrainment model, UM3, was close to the observed results because the flow is three-dimensional and the entraining water can be supplied from the ends. CORMIX considerably underestimated the observed dilution because it uses a two-dimensional analysis and neglects the effect of source momentum flux. Two-dimensional analyses and sectional physical models of diffusers with finite lengths should be used with caution until their limitations are better known.     

Experiments on Marine Wastewater Diffusers with Multiport Rosettes

The dispersion capabilities of two types of marine wastewater diffusers, one with risers containing eight radial ports (rosette) and the other with the ports uniformly distributed, were directly compared in laboratory experiments for three scenarios: stationary and flowing unstratified, and flowing stratified. Tracer concentration fields were measured with a three-dimensional laser-induced fluorescence system. The dispersion capabilities, particularly dilution, of the two diffuser types were similar. The primary differences occurred with no current where the rosette diffuser plumes were bent inwards, causing a dynamic interaction. This resulted in a small reduction in near field dilution, an increase in the spreading layer thickness, and a decrease of the near field length. These differences were virtually eliminated by a flowing current when the eight individual plumes from a rosette first merged with themselves and then with those from neighboring risers to become laterally quite uniform at the end of the near field. The major near field characteristics were primarily determined by the buoyancy flux per unit length. Temporal concentration fluctuations were high close to the diffuser and then decreased and leveled off near the end of the near field where the discharge-induced turbulence collapses. The fluctuations do not go to zero, however, owing to remnants of previous fluctuations.     

Marine Wastewater Discharges from Multiport Diffusers. I: Unstratified Stationary Water

Laboratory experiments on the near-field mixing of buoyant plumes discharged from multiport diffusers into unstratified stationary water are reported. Dilution was measured by a newly developed three-dimensional laser-induced fluorescence system and a microconductivity probe. Significant additional mixing (and dilution) occurs beyond the point where the plume impacts the water surface. This mixing ceases when the turbulence generated by the plumes collapses in the surface spreading layer. The port spacing, s, was varied through a range encompassing line to point source conditions. In all cases, the concentration distribution in the surface layer eventually becomes laterally uniform. Measurements of the near-field dilution, length, and layer thickness, and semiempirical equations to predict them are presented. The discharge behaves as a line plume when s/H ? 0.3, and as a point plume when s/H ≥ 1.0. The additional near-field mixing for a point plume is much greater than for a line plume. Basing diffuser design on near-field dilution rather than impact-point dilution allows the use of far fewer ports, or risers, with considerable potential cost savings, particularly for tunneled outfalls.     

Double-Plume Integral Models for Near-Field Mixing in Multiphase Plumes

We present a generalized integral model for multiphase plumes in stratified ambient conditions based on the double-plume approach, where the plume is composed of a rising, multiphase core plume surrounded by a counterflowing outer ring plume of dense fluid. The generalized model captures as limiting cases the current approaches in the literature, including two-fluid and mixed-fluid equations, continuous and discrete detrainment, dispersed-phase mass transfer, and two models for entrainment in the counterflow region. These modeling approaches are compared and validated against both laboratory and field-scale data. In unstratified conditions, all model formulations perform equally well. In stratification, entrainment in the counterflow region is best represented by correlation to the inner plume velocity instead of the difference between the inner and outer plume velocities. The vertical distribution of the exchange between the inner and outer plumes in the models differs from that measured in the prototype due to enhanced entrainment at the detrainment zone and forced entrainment from the collapsing intrusion layer. Nonetheless, the models predict well the length scales and volume fluxes at the detrainment zone and intrusion layer. Applications are demonstrated for reservoir air bubble plumes. The mass transfer and near-field mixing in the double-plume integral model prove sufficiently accurate to predict the depth of maximum plume rise (both the locations of total dissolution of the bubbles and the maximum height of the decelerating plume) and the volume flux, dissolved constituent mass flux, and trap height of the intrusion.     

Distributed Entrainment Sink Approach for Modeling Mixing and Transport in the Intermediate Field

In densely populated coastal cities in Asia, wastewater outfalls are often located not far from sensitive areas such as beaches or shellfisheries. The impact and risk assessment of effluent discharges poses particular technical challenges, as pollutant concentration needs to be accurately predicted both in the near field and intermediate field. The active mixing close to the discharge can be modeled by proven plume models, while the fate and transport far beyond the mixing zone can be well-predicted by three-dimensional (3D) circulation models based on the hydrostatic pressure approximation. These models are usually applied separately with essentially one-way coupling; the action of the plume mixing on the external flow is neglected. Important phenomena such as surface buoyant spread or source-induced changes in ambient stratification cannot be satisfactorily addressed by such an approach. A Distributed Entrainment Sink Approach is proposed to model effluent mixing and transport in the intermediate field by dynamic coupling of a 3D far field shallow water circulation model with a Lagrangian near-field plume model. The action of the plume on the surrounding flow is modeled by a distribution of sinks along the plume trajectory and an equivalent diluted source flow at the predicted terminal height of rise. In this way, a two-way dynamic link can be established at grid cell level between the near and far-field models. The method is demonstrated for a number of complex flows including the interaction of a confined rising plume with ambient stratification, and the mixing of a line plume in cross flow. Numerical predictions are in excellent agreement with basic laboratory data. The general method can be readily incorporated in existing circulation models to yield accurate predictions of mixing and transport in the intermediate/far field.     

Marine Wastewater Discharges from Multiport Diffusers. II: Unstratified Flowing Water

Laboratory experiments on the near-field mixing of buoyant plumes discharged from multiport diffusers into unstratified flowing water are reported. The spatial variation of dilution was measured by a newly developed three-dimensional laser-induced fluorescence system and a microconductivity probe. The near-field hydrodynamics are complex. The plumes discharged upstream dilute and merge more rapidly than those discharged downstream. Even with wide port spacing, the plumes eventually merge to form a laterally uniform surface wastefield. The density profile in this wastefield becomes gravitationally stable and suppresses mixing, marking the end of the near field. The value of the port spacing ratio, s/H, below which the discharge approximates a line plume is greater for discharge into a flowing current than into a stationary environment, so the port spacing plays a lesser role in a flowing current. The mixing and dilution that occurs in the surface layer is less than for a discharge into a stationary environment, and it decreases as the current speed increases. Semiempirical equations to predict the major near field characteristics are presented.     

Mixing in Stratified Jets

Experiments were performed to measure the mixing characteristics of turbulent momentum jets discharged horizontally into a linearly-stratified, stationary environment. These flows can occur when sewage is discharged into water bodies such as lakes. The centerline dilution was found to follow the results for an unstratified jet up to the point where the jet begins to collapse under the influence of the stratification. The distance at which this occurs is slightly longer than that reported previously from visual observations. The dilution then continues to increase with distance, but more slowly. The results are interpreted in terms of stratified turbulence collapse, and a model is proposed for the initial and final collapse of the turbulence in the jet. Implications for mixing zone models are discussed.     

Performance of Tee Diffusers in Shallow Water with Crossflow

The dilution and plume trajectory of the tee diffuser has been investigated via the collection of experimental data for a wide range of ambient current conditions. A new dilution equation in which the stagnation effect between ambient current and diffuser discharge is assumed to be a function of the ratio of the ambient momentum to the discharge momentum, mr, is proposed modifying the conventional theory of Adams that significantly underpredicts mixing for large mr. A simple equation for the plume trajectory including the dependency of the momentum ratio is also derived by dimensional analysis. Experimental results on the near field dilution show that when mr < 1 the dilution decreases with mr, whereas when mr > 1 it increases with increasing mr, and approaches the stagnant water dilution for very large values of mr. The equation is applied to aid the preliminary design of a diffuser discharging heated water from a power station in Korea.     

Mixing of a Rosette Jet Group in a Crossflow

Partially treated wastewater is often discharged into coastal waters through an outfall diffuser fitted with clustered ports on risers. On each riser the effluent is discharged through two to eight ports arranged circumferentially, in the form of a rosette-shaped buoyant jet group. The near field mixing of such a jet group in a tidal flow is determined by the merging and interaction of coflowing, oblique-flowing, cross-flowing, and counterflowing jets. Despite numerous studies, a general predictive method for such complex jet groups has not been reported; ocean outfall design is often based on comprehensive physical model experiments. The mixing of merging nonbuoyant and buoyant jets issuing from a rosette outfall riser into an ambient current is studied experimentally by using the laser-induced fluorescence technique. Detailed cross-sectional measurements of the scalar concentration field downstream of the bent-over jets are made. The trajectories of multiple and individual jets discharging at various angles are measured. For typical outfall designs, the dynamic interaction of adjacent jets is found to be negligible. The average dilution of the jet group can be predicted by accounting for jet merging and plume overlapping. Theoretical predictions using the Lagrangian VISJET model are in excellent agreement with the experimental data and also results of previous studies in a stratified crossflow. The model correctly predicts the changes in near field dilution as a function of the number of nozzles on a riser, or the number of risers on a diffuser, and helps to resolve observed anomalies in previous studies.     

Modeling Mamala Bay Outfall Plumes.?I: Near Field

The near-field behavior of the Sand Island, Hawaii, ocean outfall plume was modeled. The model, a modified version of the Environmental Protection Agency Roberts-Snyder-Baumgartner model, used as input data simultaneous measurements through the water column of currents obtained from Acoustic Doppler Current Profilers and density profiles obtained from thermistor strings. More than 20,000 simulations were run for a modeling period of almost one year, and frequency distributions of plume characteristics were obtained. The currents and density stratification change widely and rapidly, resulting in extreme variability in plume behavior. Rise height was predicted to vary from deeply submerged to surfacing, and near-field dilution was predicted to vary from around 100 to several thousands within a few hours. The length of the near field, or hydrodynamic mixing zone, also varies considerably, so that a fixed regulatory mixing zone may sometimes encompass all of the near field and some of the far field and sometimes only part of the near field. The combination of oceanographic data with suitable mathematical models represents a significant improvement in our ability to predict the statistical variability of ocean outfall plume behavior.     

Particle Image Velocimetry Measurements of the Mean Flow Characteristics in a Bubble Plume

A direct measurement method for the velocity field in multiphase flows using the particle image velocimetry (PIV) and particle tracking velocimetry (PTV) methods is developed to study the flow characteristics of an unbounded bubble plume in quiescent, unstratified ambient conditions. A single camera is used to obtain images containing both bubbles and fluid tracer particles. Using gray-scale thresholding, phase-separated images of the bubbles are produced, and bubble velocities are obtained from these images using the standard PTV method. Regular PIV is applied to the mixed fluid images, and bubble vectors are removed using a velocity threshold and vector median filter that is calibrated to the PTV result. From the separate velocity fields, the time-averaged flow characteristics of a bubble plume are studied. Gaussian velocity profiles match the entrained fluid velocity, and top-hat velocity profiles match the bubble velocity. Time-averaged values are also presented of velocity, plume width, entrained fluid volume flux, and void fraction as a function of height. From these data, the entrainment coefficient for the entrained ambient fluid is calculated and lies between 0.08 near the plume source and 0.05 in the upper reaches. The results for the entrainment coefficient, together with those from the literature, are correlated to a nondimensional velocity, given by the ratio of the bubble slip velocity us to a characteristic velocity in the plume (B/z)1/3, where B = kinematic buoyancy flux and z is the height above the source.     

Locating Discharge Trajectories in Still and Moving Ambient Fluids

The angular momentum principle is employed to locate the trajectories of wastewater plumes. This momentum-based method differs from the traditional approach where a perturbation analysis, based on the centerline velocities, is employed for locating discharges. Evidence of the latter can be found in existing Eulerian-integral and length-scale models. The momentum-based method is incorporated into the hybrid model SD3D, where the regional flow solutions are modified to incorporate the influences of relatively small components of momentum on the discharge trajectory. This method provides a clear understanding of the factors that influence the location of the discharge. The momentum-based approach yields analytical trajectory solutions in many cases, and it eliminates the need to arbitrarily select the appropriate characteristic velocity for locating the flow. Comparisons are made with available experimental data, and they show that the momentum-based method provides accurate predictions of the flow trajectories under a variety of discharge conditions. Comparisons are also made with predictions from the CORMIX1 and JETLAG models. In general the predictions are consistent, but some important discrepancies are highlighted. The use of the momentum-based method for locating discharges is discussed in light of recent experimental studies.     

Marine Wastewater Discharges from Multiport Diffusers. IV: Stratified Flowing Water

Experiments on the near-field mixing of wastewater discharged from multiport diffusers into stratified flowing waters are reported for conditions typical of actual ocean sewage outfalls. Dilutions were measured by a newly developed three-dimensional laser-induced fluorescence system combined with refractive-index matching and by a microconductivity probe. The plume dynamics are complex. Depending on port spacing, plumes discharged from the upstream diffuser side may merge first with themselves, and then with the plumes discharged from the downstream side. Or the plumes that are horizontally opposed may first merge, followed by lateral merging. In all cases, however, the wastefield eventually becomes laterally homogeneous. The results are analyzed in terms of line or point-source parameters and it is found that they can be predicted by assuming the discharge to be a line plume when s/lb<1.0 and as point plumes for s/lb ≥ 6.0. Semiempirical equations to predict the near-field dilution, near-field length, and plume rise height are presented.     

Graphical Sizing and Analysis of Ocean Outfalls with Buoyant Plumes

A graphical model is developed that offers a convenient solution to wastewater disposal problems through submarine outfalls. The model is intended to perform preliminary analysis under worst-case dilution conditions for outfalls with line diffusers, currents from any direction, stratified or unstratified ambient, and submerged or surfacing plumes, and it is also valid for outfalls with single horizontal or vertical ports. The model is thus applicable for most outfall configurations and ambient conditions of practical interest. The model simultaneously considers three dilution mechanisms: initial dilution, dilution through dispersion, and effective dilution due to decay of nonconservative substances. This enables analysis of functional dependencies and grouping of model variables in a way that permits a generalized graphical solution. It also allows one to study the sensitivity of the overall dilution to current speeds and compare the relative performance of perpendicular and parallel line diffusers. The results showed that, contrary to what is widely believed, in most situations of practical interest, high rather than low current speeds are critical in outfall design and parallel rather than perpendicular line diffusers often deliver the best overall performance.     

Modeling Underwater Oil∕Gas Jets and Plumes

A model is developed for simulating oil spills that initially behave as jets or plumes. The model is based on the Lagrangian integral method. The model can simulate a liquid (oil) in an ambient (seawater), or an oil∕gas mixture in seawater. The model considers both shear and forced entrainment. The jet∕plume model is combined with two additional models for oil transport in the intermediate field and the far-field to provide complete simulations of the oil transport and fate. The model can take into account the stratified ambient conditions. 3D unsteady ambient current conditions can be used in the simulations. The model is used to simulate the field experiments conducted by the Institut for Kontinentalsxkkel Undersokelser in the North Sea in 1996 and 1997 and compare with the field data. A scenario simulation using the model is presented to demonstrate the model capability.     

Simulations of Dye Releases off the Coast of New Jersey: Development and Validation of an Ocean Outfall Mixing Model

A kinematic mixing model has been developed to predict far field effluent distributions for ocean discharges. The model allows for complex outfall configurations and time varying discharge rates to be simulated. The model can use field observations or the output from a proven near field mixing model as input to this far field mixing model. The model uses observed or simulated horizontal currents at one location to advect the effluent plume and a scale-dependent “diffusion velocity” submodel to account for horizontal diffusive processes. To collect data to calibrate and verify the model, long-term continuous dye release experiments were conducted at two New Jersey ocean outfalls. Based upon the results of the dye release experiments, appropriate values for the diffusion velocity were determined for each outfall. Simulations using these diffusion velocities provided reasonable predictions of plume width and of average dye concentration at each transect for each outfall. This work demonstrates that an Eulerian velocity observed at one location in the coastal ocean off New Jersey may be used to predict Lagrangian transport over a distance of several kilometers.     

Performance of a Three-Dimensional Hvorslev–Modified Cam Clay Model for Overconsolidated Clay

It is well established that critical state soil mechanics provides a useful theoretical framework for constitutive modeling of soil. Most of the critical state models, including the popular modified Cam clay (MCC) model, predict soil behavior in the subcritical region fairly well. However, the predictions for heavily overconsolidated soils, in the supercritical region, are not so satisfactory. Furthermore, the critical state models were developed from triaxial test data and extension of these models into three-dimensional (3D) stress space has not been investigated thoroughly. In the present work, experiments were carried out to obtain stress–strain behavior of overconsolidated soil in triaxial compression, extension, and plane strain conditions. A novel biaxial device has been developed to conduct the plane strain tests. The experimental results were used to formulate Hvorslev–MCC model which has MCC features in the subcritical region and Hvorslev surface in the supercritical region. The model was generalized to 3D stress space using the Mohr–Coulomb failure criterion. A comparison of the model predictions with test results has indicated that the Hvorslev–MCC model performs fairly well up to the peak supercritical point, during which deformations are fairly uniform and the specimens remain reasonably intact. Limitations of this simple model in predicting postpeak localization are also discussed. The model’s predictions for volumetric response in different shear modes seem to agree reasonably well with test results.     

Managing Nitrate Problems for Domestic Wells in Irrigated Alluvial Aquifers

Many irrigated areas in the United States and abroad overlie unconfined aquifers. The soils are coarse textured with low water-holding capacity, and irrigation water is frequently necessary for crop growth. Many of these areas experience elevated nitrate levels in water from shallow domestic wells. It is often observed that the nitrate plumes are stratified with depth with the highest concentration just near the surface. The irrigation wells are generally screened toward the bottom part of the aquifer where the material is coarse and the available drawdown is greater. Pumpage is typically cyclic but can be somewhat continuous during drought conditions. It is often believed that the floating nitrate plume is recycled by the irrigation wells. Simulations were carried out to show that slight deepening of domestic wells in both stratified and more homogeneous aquifers could eliminate nitrate problems for many domestic wells even in close proximity of irrigation wells.     

Measurement of Behavioral Properties of Entrained Ambient Water in a Stratified Bubble Plume

Flow properties of a bubble plume in density-stratified conditions are studied using planar laser-induced fluorescence (PLIF) flow visualization. Entrained ambient fluid is identified by applying an image intensity threshold to the PLIF images of passive dye tracer injected at the bubble diffuser. The density stratification gradually arrests the entrained ambient fluid, causing detrainment, or peeling, of the continuous phase fluid from the bubble plume core and intrusion of the detrained fluid at a level of neutral buoyancy; bubbles continue to rise above each detrainment zone. The peel and intrusion heights for the first detrainment event above the diffuser are measured from the thresholded PLIF images. The nondimensional frequency of fluctuations in the detrainment and intrusion heights fz/us is measured as 0.35 (where f=frequency; z=height above the diffuser; and us=terminal rise velocity of the bubbles in a quiescent fluid), and this value compares well to the plume wandering frequency for similar experiments in unstratified reservoirs.