Inclined Negatively Buoyant Discharges

Analytical solutions are developed to predict the behavior of inclined negatively buoyant discharges and these solutions are compared with data from previous studies and from experiments described here, where light attenuation and laser-induced fluorescence techniques are employed to study these flows. Comparisons show that the analytical solutions provide reasonable predictions of the flow’s path for initial discharge angles ranging from 0 to 75° and initial Froude numbers ranging from 14 to 99. The solutions also predict the maximum height of the outer edge of the jet with reasonable accuracy, and thus the outer spread of the jet is well predicted. However, the inner spread is underestimated and minimum dilution predictions are shown to be conservative by approximately 18% at the centerline maximum height and 34% at the return or impact point. Predictions from the CorJet and VisJet numerical models are also shown to be conservative.     

Experimental Investigation of Three-Dimensional Nonbuoyant Rectangular Jets

The behavior of a nonbuoyant three-dimensional rectangular water jet with aspect ratios of 5, 10, and 20 were investigated based on experimental results of the mean velocity field obtained by particle image velocimetry. The theoretical centerline velocity equation derived from the point source concept using the spreading rate for the axisymmetric jet gave velocity results that agreed well with the measured centerline velocity, and provided the potential core region, two-dimensional region, and axisymmetric region. The similarities of the measured cross-sectional velocity profiles along both major and minor axes were verified. In the two-dimensional region, the Gaussian constant and Strouhal number tended to be preserved, and the spreading rate decreased at the end of the two-dimensional region. In the transition zone between the two-dimensional and the axisymmetric regions, the centerline velocity decay rate and the spreading rate were observed to drop, whereas the Gaussian constant and Strouhal number were found to increase with axial distance. The range of the two-dimensional region demarcated by the criterion of the theoretical centerline velocity decay was very similar to those based on the conservations of the Gaussian constant and Strouhal number, and that based on the change in the spreading rate along the minor axis.     

Improved Discharge Configurations for Brine Effluents from Desalination Plants

Sea water desalination plants discharge a concentrated brine effluent into coastal waters. Modern, large capacity plants require submerged discharges, in the form of a negatively buoyant jet, that ensure a high dilution in order to minimize harmful impacts on the marine environment. Existing design practice favors a steep discharge angle of 60° above horizontal, a practice based on limited and outdated laboratory data for dilutions at the level of maximum rise. Examination of more recent laboratory data and the parametric application of a jet integral model suggest that flatter discharge angles of about 30–45° above horizontal may have considerable design advantages. These relate to better dilution levels at the impingement location, especially if bottom slope and port height are taken into account, there is better offshore transport of the mixed effluent during weak ambient current conditions, and there is the ability to locate in more shallow water near shore.     

Buoyant Surface Discharges into Water Bodies. I: Flow Classification and Prediction Methodology

Buoyant surface discharges into ambient water bodies can exhibit multiple complex flow processes, which cover the spatial range from the near field with initial jet mixing to the far field with passive ambient diffusion. Multiple flow phenomena can occur, such as buoyant collapse motions, bottom attachment, deflection by the ambient current, and dynamic shoreline interaction, in the near field, and lateral and/or upstream spreading motions and turbulent diffusion processes, in the far field. Efficient and reliable predictive techniques covering the whole range of these processes are needed for the design and prediction of wastewater effluents that are subject to water quality regulations that can apply in either near and/or far field. A new comprehensive classification framework distinguishes among ten hydrodynamically distinct flow classes within four major flow categories: free jets, shoreline-attached jets, wall jets, and upstream intruding plumes. A prediction methodology for these discharges has been presented that covers the entire spatial domain from the near to the far field. It is based on the linkage of separate predictive modules in form of the expert system CORMIX3. These hydrodynamic modules are implemented by specific flow protocols and transition criteria determine their spatial extent. The methodology, corroborated by numerous detailed laboratory and some field data sources, constitutes a simple and efficient, yet accurate and robust, tool with few data requirements for surface discharge design and mixing analysis.     

Deposition from Particle-Laden, Round, Turbulent, Horizontal, Buoyant Jets in Stationary and Coflowing Receiving Fluids

Results are presented from a series of laboratory experiments investigating the characteristic features of particle-laden, round, turbulent, buoyant jets discharged horizontally into stationary and coflowing receiving fluids. For the volumetric source concentrations of particles tested ( ～ 0.1%), the presence of the particle load was found to have no significant influence on mean buoyant jet trajectories. Deposition patterns on the bed of the receiving water container indicated the existence of two separate sedimentation processes for discharges into stationary or coflowing ambients, namely (1) a relatively concentrated, narrow band of particle accumulation associated with near-source fallout from the buoyant jet margins; and (2) a broader and more disperse downstream depositional fan associated with particle fallout from the radially-expanding surface gravity current formed by the impingement of the buoyant jet with the free surface of the receiving fluid. Scaling arguments have been developed and applied successfully to deposition length scales associated with these sedimentation patterns, allowing the quantitative characteristics and parametric dependences of the deposition distributions to be established.     

Deposition from Particle-Laden, Plane, Turbulent, Buoyant Jets

Laboratory and computational fluid dynamics (CFD) model studies with turbulent, plane, particle-laden buoyant jets discharged horizontally into a quiescent ambient fluid have demonstrated that the presence of particles has no significant influence upon the buoyant jet trajectories over a wide range of forcing conditions and source concentrations of 0.1% or less. Bed deposition distributions show a large initial maximum close to the source, indicative of a dominant, localized particle fall-out from the buoyant jet margins. Beyond this near-source region, the distributions show a gradual decrease in particle deposition with increasing distance from the source, as a result of particle fall-out from the spreading surface layer generated by the buoyant jet impinging on the free surface of the receiving waters. In both cases, the deposition distributions scale well with the nondimensional settling parameter ws/b01/3 and the source Froude number F0. CFD simulations show good agreement with the laboratory data, particularly for deposition distributions downstream of the source. Additionally, the simulations indicate clearly that the receiving water boundaries can produce significant secondary return flows through fluid displacement by the spreading surface gravity current and its subsequent reflection.     

Buoyant Jets of Elliptic Shape: Approximation for Duckbill Valves

The intrusion of seawater into a pipeline servicing an ocean outfall can significantly reduce its operational efficiency. Duckbill valves are sometimes installed on sewage outlet ports to help prevent such intrusions. While there is growing literature associated with the hydraulics of duckbill valves, there appears to be little published information on the trajectory and dilution achieved by the buoyant jets when the outlet ports are fitted with duckbill valves. Further, no models presently exist that incorporate the effects on the rise and dilution of buoyant jets discharged through orifices fitted with duckbill valves for which the size and shape of the opening varies with the effluent flow. Solutions to the asymptotic equations for jets and plumes are generated for ports fitted with duckbill valves by assuming that the shape of the duckbill is elliptical. This allows asymptotic expressions to be generated for the trajectory and dilution of the jet/plume. In the limiting case when the ellipse becomes circular, these expressions reduce to those for discharges from round outlets and are consistent with expressions for round ports found in literature.     

Influence of Cohesion on Scour under Submerged Circular Vertical Jets

The results of an experimental study on scour under submerged circular vertical jets of water in cohesionless and cohesive sediments are presented. The difference between scour patterns in cohesionless and cohesive sediments is identified. In cohesive sediments, the variations of maximum depth and volume of scour have been studied with respect to the percentage of clay content, dry density, antecedent moisture content, etc. Empirical relationships have been proposed for the maximum depth and volume of scour for both nonplastic and plastic cohesive sediments. The range of data for the applicability of the proposed relationships is specified.     

Sedimentation from Buoyant Jets

An integral model is developed to describe sedimentation from a turbulent, buoyant jet injected at an angle into a stationary, uniform ambient fluid. Entrainment is modeled using the standard entrainment assumption and sediment is assumed to fall from the jet where the outward component of the fall velocity normal to the jet boundary exceeds the inward entrainment velocity. When appropriately scaled by source momentum and buoyancy fluxes, turbulent, buoyant jets may be described in terms of a single parameter: the angle θ0 between the flow and the horizontal at the virtual origin (which is close to the actual source for large initial densimetric Froude numbers). Including sedimentation in the model introduces a further parameter ws, which is the ratio of the fall speed of the sedimenting particles to a typical entrainment velocity (and so wS is a nondimensional fall speed). An important result is that this ratio is independent of the source speed, so that the proportion of the sediment load deposited near the source is independent of the flow rate. Sediment remaining in the plume beyond the near-source region is deposited when the plume spreads horizontally once it reaches the free surface. Results for plume shapes, deposition patterns, and the proportion of sediment load deposited in the near-source region (as functions of θ and ws) are given. The results are supported by some preliminary laboratory experiments. The effects of flow in the ambient fluid are discussed briefly and a further parameter uF is introduced, which is the ratio of the ambient flow speed to a typical entrainment velocity (again this ratio is independent of the flow rate).     

Combined Particle Image Velocimetry/Planar Laser Induced Fluorescence for Integral Modeling of Buoyant Jets

Combined particle image velocimetry and planar laser induced fluorescence is an efficient measurement approach for laboratory studies in environmental hydraulics. The coupling of the two well-known techniques enables synchronized planar measurements of flow velocity and concentration in an area yielding both their mean distribution as well as turbulence covariance. In this paper, the merits and limitations of the combination are first discussed. An example of experimental setup is then briefly described. Finally, an application is demonstrated for the integral modeling of an inclined round buoyant jet that takes full advantage of the capability of the combined approach.     

Numerical Simulation of Obstructed Round Buoyant Jets in a Static Uniform Ambient

The k-ε turbulence closure model is used to simulate obstructed round buoyant jets in a static uniform ambient, and the results compare well with available experimental data. On the basis of the axial line velocity distribution, three regions in the flow behind the disk are identified: the wake region, the transitional region, and the self-similarity region. The length of the wake region, which varies with flow and geometrical parameters, and the existence of self-similarity are also addressed.     

Two-Phase Analysis of Vertical Sediment-Laden Jets

In this study, we investigated a vertical dilute sediment-laden jet both experimentally and theoretically. First, an instantaneous whole-field velocimetry tool, particle image velocimetry, was applied to measure the sediment and fluid mean and fluctuating velocities of a downward sediment-laden jet at the same time. Subsequently, an analysis was performed based on two-phase conservation equations for both downward and upward jets. The analysis shows that the mean sediment velocity can be taken as the sum of fluid velocity and the settling velocity in both cases. For the downward jets, the decay rate of the centerline sediment concentration increases with the sediment settling velocity while decreases with the initial discharge velocity. The zone of flow establishment for the sediment velocity is found to be longer than that of the fluid. For the upward jets, the maximum rise of the sediment particles and their deposition distribution on the ground were derived theoretically. The predicted results compare well to the experimental data in the literature.     

Erosion of Finite Thickness Sediment Beds by Single and Multiple Circular Jets

Sediment management in reservoirs with the help of water jets has motivated this work. Erosion caused by single and multiple submerged circular turbulent wall jets on a noncohesive sediment bed of finite thickness lying on a fixed boundary was studied with the help of laboratory experiments. Different combinations of jet diameter, jet separation, and sediment thickness to jet diameter ratio were tested. Results show a relation between dimensionless parameters characterizing the steady state bed profile and the densimetric particle Froude number F0 given by the velocity at the nozzle and the effective diameter and submerged specific density of the sediment. Evolution of scour with time confirms previous studies where the erosion was found to initially grow with the logarithm of time up to a certain reference time t*. This time, made dimensionless with a time scale tc involving the volume of sediment scoured and the rate of erosion, was also related to the densimetric Froude number. A comparison with studies regarding erosion of a semiinfinite layer of sediment is also presented.     

Buoyant Surface Discharges into Water Bodies. II: Jet Integral Model

The near-field region of a buoyant surface discharge into water bodies often displays significant jet-like motions in form of free jets, shoreline-attached jets, and wall jets, respectively, as classified by the CORMIX3 expert system [see Jones et al., (2007, Paper I)]. A new jet integral model CorSurf has been developed that addresses in a single formulation this entire spectrum of jet motions in both deep or shallow environments. The model employs an entrainment closure approach for the separate contributions of entrainment resulting from transverse shear, buoyant damping, advected puff motions, frontal mixing, and interfacial mixing due to lateral spreading. It also contains a quadratic law turbulent drag force mechanism. An alternative model formulation applies to the two-dimensional bottom-attached form of the jet. This formulation contains a deflecting pressure force mechanism as well as the bottom shear force. Specific criteria describe bottom attachment and detachment processes. Finally, a number of confinement effects on the jet dynamics due to shallow water and/or lateral boundaries are included. The model has been validated under a wide range of geometric and dynamic conditions using, in particular, hitherto unavailable high-resolution laboratory data.     

Comparison of Far-Field Turbulent Structure of a Rectangular Surface Jet to Three-Dimensional Free and Wall Jets

The turbulence structure of a rectangular surface jet is compared to that of the three-dimensional free and wall jets. The surface jet turbulence quantities are mapped using laser Doppler velocimetry. In general, the turbulence structure of these three jets is found to be significantly different. For the surface jet, the free surface kinematic condition has a predominant effect on the whole structure, while for the wall jet, the influence of wall kinematic constraint is contained in the wall layer. A surface current with a higher lateral spreading rate than the submerged portion of the jet is developed, which does not exist for the wall jet because of the no-slip boundary condition. Unlike free jets, the submerged portion of the rectangular surface jet is characterized by two length scales. The Prandtl hypothesis with constant eddy viscosity provides a good estimate for the shear stresses in the lateral direction, but fails in the vertical direction, where the velocity profiles are much flatter, due to the free surface condition, than those for the free and wall jets.     

Scour Downstream of an Apron Due to Submerged Horizontal Jets

The results of an experimental investigation on scour of noncohesive sediment beds (uniform and nonuniform sediments) downstream of an apron due to a submerged horizontal jet issuing from a sluice opening are presented. Attempts are made to explain the similarity existing in the scour process and profiles (including dune in the downstream of the scour hole). The scour profiles at different times follow a particular geometrical similarity and can be expressed by the combination of two polynomials. Using experimental scour depth at different times, the time variation of scour depth is scaled by an exponential law, where time scale increases linearly with densimetric Froude number. The equilibrium scour depth, related to the sediment size relative to the sluice opening, decreases with increase in sediment size and sluice opening. On the other hand, the equilibrium scour depth increases with increase in densimetric Froude number. The variation of equilibrium scour depth with tailwater depth indicates a critical tailwater depth corresponding to a minimum equilibrium scour depth. The effect of sediment gradation on scour depth is pronounced for nonuniform sediments, which reduce scour depth significantly due to formation of an armor layer, and therefore prompted study of the reduction of scour depth by a launching apron placed downstream of the rigid apron. The results show that the average reduction of scour depth by placing a launching apron was 39%, having a maximum of 57.3% and a minimum of 16.2%. The characteristic parameters affecting maximum equilibrium scour depth are identified based on the physical reasoning and dimensional analysis. Equation of maximum equilibrium scour depth obtained empirically agrees well with the experimental data.     

Plane Turbulent Wall Jets on Rough Boundaries with Limited Tailwater

Combining the results of a laboratory study of plane turbulent wall jets on rough boundaries with shallow tailwater, with the results of an earlier work of Rajaratnam on wall jets on rough boundaries with deep tailwater, this paper attempts to describe the effects of boundary roughness and tailwater depth on the characteristics of plane turbulent wall jets on rough beds, which are important in the field of hydraulic engineering. The time-averaged axial velocity profiles at different sections in the wall jet were found to be similar, with some difference from the profile of the classical plane wall jet. The normalized boundary layer thickness δ/b, where b is the length scale of the velocity profile, was equal to 0.35 for wall jets on rough boundaries compared to 0.16 for the classic wall jet. Two stages were seen to exist in the decay of the maximum velocity um as well as in the growth of the length scale, with the first stage corresponding to that of deep tailwater and the second stage to shallow tailwater. In the first stage, the decay of the maximum velocity um at any section in terms of the velocity u0 at the slot, with the longitudinal distance x in terms of L which is the distance where um = 0.5U0, was described by one general function, for smooth as well as rough boundaries. The length scale L in terms of slot width decreases as the relative roughness of the boundary increases. The onset of the second stage was not affected significantly by the bed roughness. The growth rate of the length scale b of the wall jet increased from 0.076 for a smooth boundary to about 0.125 for a relative roughness ks/b0 in the range of 0.25 to 0.50, where ks is the equivalent sand roughness and b0 is the thickness of the jet at the slot.     

Characteristics of Submerged Jets in Evolving Scour Hole Downstream of an Apron

This paper reports an experimental investigation on the velocity and turbulence characteristics in an evolving scour hole downstream of an apron due to submerged jets issuing from a sluice opening detected by an acoustic Doppler velocimeter. Experiments were carried out for the conditions of submerged jets, having submergence factors from 0.96 to 1.85 and jet Froude numbers from 2.58 to 4.87, over sediment beds downstream of a rigid apron. The distributions of time-averaged velocity vectors, turbulence intensities, and Reynolds stress at different streamwise distances are plotted for the conditions of initial flat bed, intermediate scour holes, and equilibrium scour hole downstream of an apron. Vector plots of the flow field show that the rate of decay of the submerged jet velocity increases with an increase in scour hole dimension. The bed-shear stresses are determined from the Reynolds stress distributions. The flow characteristics in evolving scour holes are analyzed in the context of self-preservation, growth of the length scale, and decay of the velocity and turbulence characteristics scales. The most significant observation is that the flow in the scour holes (intermediate and equilibrium) is found to be plausibly self-preserving.     

Impact of Vertical, Turbulent, Planar, Negatively Buoyant Jet With Rigid Horizontal Bottom Boundary

The results of a series of laboratory modeling experiments are presented for the case of a vertical, turbulent, plane, negatively buoyant jet impinging on a horizontal solid surface placed a distance H below the jet source. The results show that the impingement results in the generation of a complex two-dimensional disturbance field at the site of the impact and the generation of a buoyancy-driven boundary current carrying away fluid from the impingement zone. The disturbance field is seen to extend vertically along the time-averaged axis of the incident buoyant jet, thereby distorting the vertical velocity and concentration fields over a vertical distance that depends upon the value of the parameter Fd0?4/3, where Fd0 is the source Froude number of the buoyant jet. Transverse velocity and concentration profiles taken at different axial distances from the source reveal systematic departures from the far-field Gaussian similarity profiles as the solid boundary is approached. Such departures are utilized to quantify and parameterize the vertical distance z??? from the boundary at z = 0 beyond which the impingement of the buoyant jet does not affect significantly the incident flow. Measurements indicate that z???/b ～ 0.4Fd04/3. For distances z相似文献   

Jet Integral–Particle Tracking Hybrid Model for Single Buoyant Jets

The mixing processes of a buoyant jet discharged from a submerged single port were analyzed using a three-dimensional hybrid model. In the proposed hybrid model, the initial mixing was simulated by a jet integral method, and the advection-diffusion process was simulated using a particle tracking method. Laboratory experiments were conducted for various flow conditions in order to verify the proposed model. The simulated horizontal concentration distributions and minimum dilutions at the water surface were generally in agreement with the observations. The vertical concentration distributions for coflowing jets were well simulated by both the jet integral and the particle tracking methods of the hybrid model. Trajectories simulated by the jet integral module of the hybrid model were in agreement with the measured trajectories when the velocity ratio was low. For cases where the velocity ratio was high, the hybrid model in which the vortex-pair distribution was used gave better results than the hybrid model with only Gaussian velocity distribution.