Liquid Volume Fluxes in Stratified Multiphase Plumes

This paper presents an optimization scheme to estimate the internal entrained fluid fluxes for multiphase plumes in stratification from indirect experimental measurements and applies the results to field-scale plumes. Experiments were conducted in linear stratification using dispersed phases of air bubbles and glass beads (the latter creating an inverted plume). Comparison of pre- and postexperiment salinity profiles provided direct measurements of the net liquid fluxes in the plume; fluorescence profiles provided direct measurements of the fluxes of passive tracer. To separate the net flux measurements into upward and downward flows this paper applies a constrained Bayesian estimation technique based on a conceptual model of the plume. This method provides estimates of the ambient and counterflowing entrained fluid fluxes, the peeling efficiency (percent of entrained fluid that detrains) and the buoyancy flux continuing above the first peel. These quantities correlate with the non-dimensional slip velocity UN, defined as the ratio of the bubble slip velocity us to a characteristic plume fluid rise velocity (BN)1/4; B is the total kinematic buoyancy flux, and N is the buoyancy frequency. The results show that the peeling efficiency is the dominant quantity that controls the plume behavior, and that it is dependent on several processes occurring within the plume. Applications of the results are presented for accidental oil-well blowouts in the deep ocean.     

BIEM Modeling of 3D Circulation and Transport in Stratified Estuaries

Here the boundary integral equation method (BIEM) is used for 3D modeling of hydrodynamics and pollutant transport in stratified estuaries. The flow computations are made using a newly developed BIEM solution. The transport modeling has been done using an Eulerian-Lagrangian BIEM (ELBIEM) model. In ELBIEM, the advection part in the transport equation is treated by the concept of the Eulerian-Lagrangian scheme, which overcomes the limitation of traditional BIEM to deal with an arbitrary velocity field. The coupling of the 3D shallow water BIEM model and advection-diffusion ELBIEM model enables one to effectively deal with fluctuation of free surface and density stratification in an estuary. The main advantages of the BIEM model include reduction in computational dimensions, ease in discretization and data preparation, accurate free surface simulation, less numerical diffusion and dispersion problems, and direct flux solution at boundaries. The numerical simulation results are compared with other model results and found to be satisfactory. The illustrated case study shows the effectiveness of the model in the simulation of mass, momentum, and heat transfer due to air-water interaction in stratified estuary problems.     

Hydrodynamic Forces Generated on a Spherical Sediment Particle during Entrainment

The objective of this research is to study the relationship between the coherent flow structures and the hydrodynamic forces leading to entrainment of a spherical bed sediment particle for a rough bed uniform turbulent flow. Two types of experiments, namely, movable and fixed balls, were conducted using spherical roughness-element beds with particle image velocimetry to measure the instantaneous flow-velocity field. Miniature piezoelectric pressure sensors were used to capture the instantaneous pressure on the surface of the sphere. Movable ball experiments reveal the predominance of large sweep structures at the instant of entrainment. Fixed ball experiments carried out at entrainment conditions show the importance of both vertical and horizontal pressure gradients on the ball leading to entrainment. Probability distribution function plots of pressures based on quadrant analysis of velocities also reveal the higher probability of occurrence of high magnitude force induced by sweep (Q4) events.     

Discrete Particle Modeling of Entrainment from Flat Uniformly Sized Sediment Beds

The stability of randomly deposited sediment beds is examined using a discrete particle model in which individual grains are represented by spheres. The results indicate that the threshold shear stress for flat beds consisting of cohesionless uniformly sized grains cannot be adequately described by a single-valued parameter; rather, it is best represented by a distribution of values. Physically, this result stems from the localized heterogeneity in the arrangement of surface grains. For uniformly sized beds, geometric similarity exists such that the critical entrainment shear stress distributions scale directly with grain size. A Shields parameter of 0.06 is commonly used to define “threshold conditions,” and it was found that this corresponds to a point on the distributions where approximately 1.4% by weight of the surface is mobile. Furthermore the analysis includes a comparison of the contributions of sheltering to variation in critical entrainment shear stress. It was found that remote sheltering, induced by prominent upstream grains, has a significant effect in increasing the apparent critical entrainment shear stress of exposed surface grains.     

Particle Network Model for Simulating the Filtration of a Microfine Cement Grout in Sand

This paper describes the application of a quasi-one-demensional (1D) network, bubble model to simulate the filtration of a microfine cement suspension injected through a column of sand. The bubble model represents the soil column as a series of homogeneous sites linked through bundles of cylindrical bonds that characterize the distribution of pores. The model captures mechanisms of particle sieving at the inlet sites and infiltration within each of the bonds under the action of hydrodynamic and gravitational forces. The behavior of each bond is based on numerical simulations of particle transport, collection, mounding, and clogging within a cylindrical model pore. Two empirical parameters are introduced to account for uncertainties in particle attachment at the pore wall and observed mechanisms of resuspension of hindered particles. In principal, these parameters can be calibrated from measurements of effluent concentrations. The bubble model provides useful physical insights to explain the transient dynamics of filtration processes. The model is able to provide consistent predictions of pore pressures measured in 1D column injection tests reported in the literature.     

Mass Balance in Eulerian-Lagrangian Transport Simulations in Estuaries

This paper investigates the generation of flow mass errors in finite-element shallow water models and the effect of these errors in the mass conservation of Eulerian-Lagrangian transport simulations. Flow mass errors are shown to be similar for several primitive and wave equation formulations. These errors occur primarily in areas of steep bathymetric gradients and near complex boundaries. Forcing Eulerian-Lagrangian transport simulations with nonconservative flow fields generates important mass imbalances, which can be mitigated by refining the flow grid. Comparatively, refining the transport grid only reduces marginally the mass errors.     

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.     

Entrainment and Turbulence in Saline Underflow in Lake Ogawara

Under certain tidal conditions, a saline underflow originating in the Pacific Ocean moves into Lake Ogawara, Japan. The underflow consists of a uniform saline bottom layer that is slightly warmer than the ambient and an interfacial shear layer in which the velocity and density are decreased. Within the experimental area the underflow is confined to a channel approximately 1 km wide and is essentially two-dimensional. The underflow had a bulk Richardson number, defined in terms of the mean properties, between 1 and 2. The rate of entrainment into the bottom layer was calculated using two distinct methods. The first method used the change in the maximum salinity of the underflow measured at two stations along the path of the underflow to infer the amount of ambient water entrained. The second method made direct measurements of vertical mass fluxes with a profiler. The agreement between the two methods was excellent. The measured entrainment coefficients were consistent with the derived entrainment law. The turbulent structure of the flow was mapped for a 3 h quasisteady period of the flow. Turbulence is predominantly generated on the bottom boundary and is transported vertically to the density interface, where it leads to mixing.     

Method for Quantifying Freshwater Input and Flushing Time in Estuaries

A method is developed to quantify total freshwater input and flushing time in estuaries using measured flow and salinity data at the estuary-ocean boundary. A formula is derived to calculate the volume of mixed estuarine water that leaves the estuary on the ebb tide. The calculated volume of mixed estuarine water, along with the volume of new ocean water that enters the estuary on the flood tide, is used to quantify the total volume of freshwater input. The calculated volume of mixed estuarine water is also used to quantify the flushing time. The developed method is applied to Barnegat Bay, N.J. The volume of freshwater input calculated from the new method compares well with that estimated using watershed, aquifer, and meteorological data. The flushing time calculated from the new method is between that calculated from the classical tidal prism method and that from the fraction of freshwater method. An assessment is made on the sensitivity of calculated values to the quality of measured data at the estuary-ocean boundary. The volume of freshwater input and the flushing time calculated from the developed method are highly reliable when there is a significant salinity difference between flood and ebb tides.     

Shields’ Entrainment Criterion in Bridge Hydraulics

Two related problems of sediment hydraulics are addressed: (1) Inception of sediment transport for nearly uniform flow of both uniform and nonuniform sediment beds for two different sediment densities and grain sizes ranging from sand to gravel, and (2) generalized inception conditions if elements are inserted in a plane sediment bed. The Shields’ criterion is formulated with basic quantities involving gravity, viscosity, and densities of the two-phase flow. The results of the analysis relate to the viscous, the transition, and the fully turbulent regimes. The transition regime is verified with extended laboratory experiments. Then, these conditions are used as a basis for formulating a general stability criterion for loose bed hydraulics, and compared to detailed experiments involving pier and square elements located either at the channel side or at its axis. In addition, a generalized densimetric particle Froude number is introduced that accounts for both uniform sediments and mixtures. The engineering application of the present results is straightforward, given that basic parameters of hydraulics, sediment, and fluid are involved.     

Rolling and Lifting Probabilities for Sediment Entrainment

This study addresses the rolling and lifting probabilities for sediment entrainment by incorporating the probabilistic features of the turbulent fluctuation and bed grain geometry. The lognormally distributed instantaneous velocity and uniformly distributed initial grain position, along with a relation between lift coefficient and particle Reynolds number, are used to extend the theoretical formulation of the entrainment probabilities in smooth-bed flows. The two threshold conditions identified herein enable us to precisely define the probabilities of entrainment in the rolling and lifting modes. The results obtained in this study coincide well with the published data. The lifting probability increases monotonously with the dimensionless shear stress θ, which is consistent with the earlier results yet displays improved agreement with the experimental data. The maximum value of rolling probability, with a magnitude of 0.25, occurs at θ ≈ 0.15. For θ<0.05 (or θ>0.6), the rolling (or lifting) probability makes up more than 90% of the total entrainment probability and thus can be used as an approximation to the total probability of entrainment. The proposed rolling and lifting probabilities are further linked to the two separate criteria for incipient motion to explore the critical entrainment probabilities. The results reveal that a consistent probability corresponding to the critical state of sediment entrainment cannot be found.     

True Flotation and Entrainment of Kaolinitic Ore in Batch Tests

A new method for true flotation and entrainment evaluation is proposed and compared with three renowned methods. Therefore, reverse froth flotation tests were conducted in a laboratory Denver cell with a kaolinitic ore. The evaluation of entrainment and true flotation was based on the recoveries of iron, titanium, and manganese oxides (FeO, TiO₂, and MnO), and the contributions of each oxide on kaolin minerals determined by electronic microprobe. The effect of particle size in the flotation process was analyzed by particle size distributions of four fractions (<25 µm; +25–45 µm, +45–63 µm; and >63 µm). The contribution of entrainment is similar for the three oxides and the degree of entrainment decreases with increasing particle size; however, the recovery by true flotation is different because of its discriminatory effect on minerals. MnO has the greatest recovery, as a consequence of the major contribution of its hydrophobic minerals, while FeO has the lowest recovery values. The results of the proposed method, developed for fully liberated feeds, are coherent with those obtained by the other three methods, despite the slightly overestimated contribution of entrainment in the case of fraction greater than 63 µm.     

Entrainment Properties of Plane Surface-Jets in Shallow Current

The entrainment properties of plane surface-jets in shallow moving water were studied. The jet entrainment characteristics were determined from laser doppler velocimetry measurements of longitudinal velocity. The entrainment constant β was found to be 0.064 within the range of ambient cocurrent studied (0.12相似文献   

Axisymmetric Submerged Intrusion in Stratified Fluid

This paper presents the results of laboratory experiments conducted to study the spreading rates of axisymmetric intrusive gravity currents produced by a constant inflow into a stratified body of water. The experiments were conducted over a wide range of initial parameters. A balance of the forces that drive and retard the flow indicate that the intrusion is characterized by four spreading regimes: (1) the radial jet; (2) the radial momentum flux balanced by the inertia force; (3) the pressure (buoyancy) force balanced by the inertia force; and (4) the pressure force balanced by the interfacial drag (“viscous force”). The experimental results seem to confirm the derived spreading relations. The paper makes three significant contributions. It resolves theoretically and experimentally the existing conflict regarding the proper radial growth of the intrusion in the inertia-buoyancy regime. In addition, it relates the observed transition from the inertia-buoyancy regime to viscous buoyancy regime. It does so using scaling arguments to find the length and time scales for this transition. The paper also gives extensive experimental evidence for the spreading relationships in the inertia-buoyancy and viscous-buoyancy regimes, and it facilitates the determination of the corresponding experimental coefficients.     

Formula for Sediment Transport in Rivers, Estuaries, and Coastal Waters

The aim of the present study is to develop a formula for the relationship between flow strength and sediment discharge. The appropriate definition of energy dissipation rate E in the theorem of Bagnold in 1966 is discussed and it is found that the sediment transport rate gt in unidirectional flows can be well predicted when E is defined as the product of bed shear stress τ0 and near bed velocity u*′. Then the linear relationship between u*′E and the sediment transport rate is examined using measured data. The good agreement between measured and predicted values indicates that the phenomena of sediment transport can be reasonably described by the near bed flow characteristics. As the hydrodynamic modelers are able to calculate the bed shear stress and near bed velocity in various cases now, thus the new relationship may provide numerical modelers a tool to calculate the sediment transport in rivers, estuaries and coastal waters. To prove this, the simplified analytical expressions of E and u*′ in wave-current flows and coastal waters are derived, the results are checked with the available data over a wide range of flow conditions; and good agreements are achieved, indicating that the presumption is valid in the cases investigated.     

Entrainment behavior of copper and copper matte in copper smelting operations

In copper smelting, the loss of copper to the slag due to entrainment is largely influenced by the flotation of copper metal and/or matte in the slag phase. To evaluate this behavior, the surface tension of copper as a function of temperature and oxygen pressure and the interfacial tension of the copper-iron matte-slag system as a function of matte grade were measured. From the surface and interfacial tension values, the spreading and flotation coefficients of the copper, matte, and slag system were calculated. Ternary interfacial energy diagrams were also con-structed using these data. It is shown that matte droplets containing higher than 32 mass pct Cu will not form a film on rising gas bubbles when they collide in the slag phase. However, matte droplets will attach to gas bubbles upon collision and thus can be floated over the entire range of matte composition. Spreading of copper on bubbles is not possible at oxygen pressures between 10⁻¹² and 10⁻⁸ atm. Flotation of copper by gas bubble in slag is possible at oxygen pressure higher than 10⁻⁹ atm. However, it is feasible for rising matte droplets (attached to rising bubble) to trap and float copper irrespective of the matte grade.