Three-Dimensional Numerical Modeling of Initial Mixing of Thermal Discharges at Real-Life Configurations

A three-dimensional Reynolds-averaged Navier–Stokes computational fluid dynamics (CFD) model is developed for simulating initial mixing in the near field of thermal discharges at real-life geometrical configurations. The domain decomposition method with multilevel embedded overset grids is employed to handle the complexity of real-life diffusers as well as to efficiently account for the large disparity in length scales arising from the relative size of the ambient river reach and the typical diffuser diameter. An algebraic mixing length model with a Richardson-number correction for buoyancy effects is used for the turbulence closure. The governing equations are solved with a second-order-accurate, finite-volume, artificial compressibility method. The model is validated by applying it to simulate thermally stratified shear flows and negatively buoyant wall jet flows and the computed results are shown to be in good overall agreement with the experimental measurements. To demonstrate the potential of the numerical model as a powerful engineering simulation tool we apply it to simulate turbulent initial mixing of thermal discharges loaded from both single-port and multiport diffusers in a prismatic channel and a natural river. Comparisons of the CFD model results with those obtained by applying two widely used empirical mixing zone models show that the results are very similar in terms of both the rate of dilution and overall shape of the plumes. The CFD model further resolves the complex three-dimensional features of such flows, including the complex interplay of the ambient flow and thermal discharges as well as the interaction between each of discharges loaded from multiple ports, which are obviously not accessible by the simpler empirical models.     

Vertical Penetration of Inclined Heated Water Jets Discharged Downward

In most experimental studies concerning negatively buoyant water jets the buoyancy was produced by density differences due to salt while the temperature of the jet and the ambient fluid was identical. Another method to produce a negatively buoyant water jet is to use different temperatures between the jet and the ambient fluid. However, there are essential differences between thermal and saltwater buoyant jets. In this technical note a modified version of the integral Fan–Brooks model has been used to calculate the vertical penetration of inclined heated water jets discharged downward. The classical initial densimetric Froude number is replaced by an initial effective Froude number based on the thermal expansion coefficient of water. Using the above model, a new equation is derived that predicts the vertical penetration of the thermal jet at a given effective Froude number and discharge angle. This formula reduces to Turner's equation for vertical jets if the densimetric Froude number is substituted by the effective Froude number.     

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.     

Mixing in Water Storage Tanks. II: With Buoyancy Effects

Experiments on jet-induced mixing in water storage tanks with various single- and multiple-nozzle inlet configurations with positive and negative density differences between the inflow and stored water were conducted. Mixing was observed and quantified by a three-dimensional laser-induced fluorescence system. Small density differences can prevent mixing, and criteria to predict whether mixing occurs were presented. It depends primarily on the total inflow momentum flux, density difference, water depth, and nozzle locations and orientations. When the tanks did mix, their mixing times were generally within 20% of the corresponding times with no density differences. Some flows with negative buoyancies mixed significantly more quickly, possibly due to the destruction of the organized gyres that occurred with no buoyancy. Good mixing can be achieved by injecting positively buoyant inflows horizontally at the bottom, or negatively buoyant inflows horizontally near the water surface, resulting in long jet entrainment path lengths. Mixing of vertical negatively buoyant inflows in standpipes can be improved by the use of a draft tube. Mixing can usually be accomplished by relatively simple nozzle configurations, provided they are suitably configured, and overly elaborate mixing devices are probably unnecessary. An example is given that shows that the hydraulic head, and therefore power cost, required for jet mixing is generally quite low.     

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.     

Energy Dissipative Plunging Flows

The analysis of plunging flows using energy dissipation hypothesis is presented in this paper. The classic two-control-volume theory has recently been found questionable and needs to be corrected. In this study, we avoid the questionable part of that framework and use a single control volume for the analysis of plunging flows. Furthermore, we hypothesize that the increase in kinetic energy in the underflow and entrained flow should be no greater than the loss in potential energy as the inflow plunges. In the current framework, the entrained flow rate does not exceed approximately 40% of the total inflow rate. The densimetric Froude number at the plunge point, Fdp = q/, where q = inflow rate per unit width; g′ = reduced gravity of inflow; and Hp = flow depth at the plunge point, is typically in the range of 0.3相似文献   

Numerical Investigation of Plunging Density Current

When a buoyant inflow of higher density enters a reservoir, it sinks below the ambient water and forms an underflow. Downstream of the plunge point, the flow becomes progressively diluted due to the fluid entrainment. The entrainment rate is strongly dependent on the Richardson number and reaches a constant value well downstream of the plunge point. This study is concerned with the analysis of the plunging phenomenon and the determination of the entrainment. A k-ε model including buoyancy effects, both in a sloping and a diverging channel, is used to reproduce the main flow characteristics. A relation between the depth at the plunge point in a channel of constant width and in a diverging channel is established, and theoretical results for the calculation of the dense layer thickness are provided. The latter indicates that the spreading rate of the dense layer in a diverging channel is a function of both the entrainment rate and the channel width. The predictions of the plunge line location are in agreement with most semiempirical equations.     

Vertical Penetration of Double-Diffusive Water Plumes Discharged Vertically Downward

Previously, it was shown that, in Turner’s formula which predicts the penetration depth of negatively buoyant jets, the classical initial densimetric Froude number should be replaced by an initial effective Froude number if the formula is applied to a heated water jet discharged downward. In the present paper, this conclusion is extended to double-diffusive plumes with two buoyancy components (heat and salt) which both oppose the downward flow. A new effective Froude number is introduced for double-diffusive plumes. For the calculation of the penetration depth a modified version of the integral Fan–Brooks model has been used. The same model is used to calculate the vertical penetration in the strongly nonlinear regions around the density maxima that appear in water at some special values of temperature and salinity. It is found that the penetration depth becomes very large if the existing ambient temperature and salinity are close to density extremum values and becomes infinite if the existing ambient temperature and salinity coincide with the maximum density values.     

Time-Varying Underflow into a Continuous Stratification with Bottom Slope

Results are presented from a laboratory investigation of a continuous discharge gravity current moving down an inclined plane into a linearly stratified fluid; the density of the inflow decreasing linearly with time, initially larger and finally smaller than the bottom ambient density. The inflowing water was observed to follow both underflowing and intrusive flow regimes. Hence, during the time in which the inflow was denser than the water in the stratified reservoir, an underflow was observed to descend down the sloping bottom with a speed that was consistent with that given by the theory for a buoyancy-conserving gravity current on gentle slopes. However, the continuous decrease of the density at the source shortly lead to an unstable density distribution within the initial underflow, which then collapsed into an intrusion that traveled as a horizontal gravity intrusion. Scaling arguments were used to identify both the position and time to the breakup of the underflow. To the end of the experiment, multiple intrusions were established successively at different depths in between the initial underflow and the surface buoyant plume.     

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.     

Modeling a Plunging Underflow

A coupled three-dimensional hydrodynamics and two-dimensional underflow model is adapted to provide simulation of plunging inflows in reservoirs. The new approach accounts for the effect of the barotropic term prior to the plunge point of the inflow. Simulations of plunging flows in constant width and constant slope channels are conducted and the resulting plunge depths are in agreement with prior empirical models. Simulation of a previously measured underflow in Wellington Reservoir (Australia) demonstrates the model application to a plunging inflow in a natural water body and good agreement between field and model results.     

Near-Field Mixing Downstream of a Multiport Diffuser in a Shallow River

Near-field mixing downstream of a multiport diffuser in a wide shallow river was studied with a field dye test. Dye concentrations at different depths and lateral locations were measured. The near-field mixing was analyzed in four zones: the free jet zone, the jet surface-impingement zone, the merging zone, and the vertical mixing zone. Analytical models were proposed to derive the three-dimensional concentration field after the jets impinged the water surface. After the impingement, the dye concentration can be predicted well by treating the multiple jets as a simple mathematical summation of individual jets. The vertical mixing zone was dominated by the riverbed friction-induced turbulence, with little effect from the effluent momentum and buoyancy. The results of the field data were also used to validate the applicability of some existing models for multiport diffusers.     

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.     

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.     

Circulation in Stratified Lakes due to Flood-Induced Turbidity Currents

The river inflow in a natural lake with important suspended sediment load during floods, can impact water quality by mobilizing dissolved matters like phosphorous from deep to surface waters. Generally due to thermal stratification in prealpine lakes, the water column is stable. It does not mix vertically unless acted on by outside forces, for example, currents or winds. Since Lake Lugano has a strong thermal stratification, river inflow exhibits different modes of density currents, from surface flows and thermocline intrusion to bottom currents. Turbidity currents are the direct cause of the downward water flow, and at the same time at the origin of upward directed flow. In this study, the impact of river born turbidity currents in Lake Lugano under varying ambient conditions was investigated using field measurements at the inflow river and inside the lake, together with a full three-dimensional numerical model of the entire lake. The paper characterizes the induced circulation of the turbidity plume and gives some indications on the relevance of turbidity currents on the lake.     

Sensitivity Analysis and Comparative Performance of Outfalls with Single Buoyant Plumes

This paper presents a new approach to analyze the performance of outfalls with single buoyant plumes in flowing ambient sea water, taking into account all three dilution mechanisms: the initial, the dispersion, and the effective dilution due to the decay of nonconservative substances. Simultaneous consideration of all dilution mechanisms, study of their functional relationships, sensitivity analysis of outfall behavior, and graphical presentation of the results, allows recognition of patterns of practical importance that remain otherwise obscure. The generated graphs afford an overview of the relative performance of outfalls with a single port and perpendicular line diffusers over a broad range of operating conditions, and portray the sensitivity of the single-port outfall behavior. The results show that, contrary to common belief, outfalls with a single port outperform those with perpendicular line diffusers over a broad range of operating conditions. They also show that higher rather than lower current speed is the critical factor in the design of single-port outfalls. These findings affect the construction cost of outfall systems and bear a significant impact on the sizing of new outfalls as well as on the performance evaluation of existing ones.     

炼钢温度下复吹转炉流场的数值模拟研究

以某钢厂的110 t复吹转炉为原型, 建立三维全尺寸几何模型, 通过数值模拟的方法研究了环境温度对多流股超音速氧气射流特性的影响, 并对比分析了常温和炼钢温度下氧气射流对转炉熔池的冲击搅拌效果.研究结果表明:随着环境温度的升高, 氧气射流的速度衰减减慢, 射流流股半径增大, 与此同时, 射流本身的温度升高、密度降低, 导致射流动压的增加幅度低于射流速度的增加幅度;而且, 高温环境中射流的聚合现象被抑制.在多相流研究中发现, 当环境温度由300 K提高至1723K时, 氧气射流的冲击深度由0.11035 m升高至0.14807 m, 冲击深度增大了34.18%, 熔池平均速度有一定提高, 说明在多相流研究中环境温度的影响不容忽略.     

Oscillating Jet Flows in a Thin Slab Mold and their Influence on Meniscus Stability

Sustainability of oscillating liquid steel jets discharging from a submerged, two‐port entry nozzle in thin slab molds has been studied through a water model and mathematically simulated using the Reynolds Stress Model of turbulence combined with the Volume of Fluid model to capture dynamics of the water‐air interface. At casting speeds of 5 and 7 m/min, both jets yield long range time‐dependent Reynolds stresses with high gradients which induce oscillating upper roll flows in the mold providing permanent flow asymmetry. Intermittent vortexes at the water‐air interface are generated by the interaction between the flow arising from the upper roll toward the SEN and a high velocity flow which goes through the gap between the SEN shaft and mold wall oriented toward the narrow wall. These flows gather at expansion of the mold funnel generating intermittent vortexes. Meniscus oscillation decreases in narrower molds even at high casting speeds. At lower casting speed like 5 m/min meniscus oscillation decreases considerably in wide and narrow molds. Turbulence understanding in thin slab molds would help to design submerged entry nozzles for higher steel casting speeds through wide molds with better meniscus stability.     

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.     

Initiation of Stagnation in Drinking Water Storage Tanks

Using temperature as a conservative tracer, the initiation of stagnation by buoyant jets was investigated in two drinking water storage tanks operated in fill-and-draw mode. The problem concerns the risk of water quality degradation caused by excessive ageing in stagnant zones. By measuring flow rates into the tanks and temperatures at several points, the initiation of stagnation could be related to the source parameters: the momentum flux M0 and the buoyancy flux B0. In agreement with previous studies, the results indicated that the jet/plume transition length scale, Lm = M03/4/∣B0∣1/2, had to exceed a certain fraction of the depth in order to avoid stagnation resulting from stratification of the water mass. The study provides insights into the parameters governing initiation of stagnation and illustrates how stratifications generated by positive and negative inflow buoyancy can affect the water exchange.