Nonlinear Mixing Length Model for Prediction of Secondary Currents in Uniform Channel Flows

A nonlinear turbulence model for numerical solution of uniform channel flow is presented. Turbulent stresses are evaluated from a nonlinear mixing length model that relates turbulent stresses to quadratic products of the mean rate of strain and the mean vorticity. The definition of the mixing length, based on a three-dimensional integral measure of boundary proximity, eliminates the need for solution of additional transport equations for the turbulence quantities. Experimental data from the literature for closed and open-channel flows are utilized to validate the model. The model produced the secondary flow vortices successfully. Velocity field and wall shear stresses affected by secondary flow vortices are accurately computed. Bulging of velocity contour lines toward the corners and dipping phenomena of maximum velocity are successfully simulated.     

Three-Dimensional Numerical Simulation of Compound Channel Flows

A three-dimensional numerical study is presented for the calculation of turbulent flow in compound channels. The flow simulations are performed by solving the three-dimensional Reynolds-averaged continuity and Navier–Stokes equations with the k?ε turbulence model for steady-state flow. The flow equations are solved numerically with a general-purpose finite-volume code. The results are compared with the experimental data obtained from the UK Flood Channel Facility. The simulated distributions of primary velocity, bed shear stress, turbulent kinetic energy, and Reynolds stresses are used to investigate the accuracy of the model prediction. The results show that, using an estimated roughness height, the primary velocity distributions and the bed shear stress are predicted reasonably well for inbank flows in channels of high aspect ratio (width/depth ≥ 10) and for high overbank flows with values of the relative flow depth greater than 0.25.     

Application of Several Depth-Averaged Turbulence Models to Simulate Flow in Vertical Slot Fishways

Vertical slot fishways are hydraulic structures which allow the upstream migration of fish through obstructions in rivers. The velocity, water depth, and turbulence fields are of great importance in order to allow the fish swimming through the fishway, and therefore must be considered for design purposes. The aim of this paper is to assess the possibility of using a two-dimensional shallow water model coupled with a suitable turbulence model to compute the flow pattern and turbulence field in vertical slot fishways. Three depth-averaged turbulence models of different complexity are used in the numerical simulations: a mixing length model, a k?ε model, and an algebraic stress model. The numerical results for the velocity, water depth, turbulent kinetic energy, and Reynolds stresses are compared with comprehensive experimental data for three different discharges covering the usual working conditions of vertical slot fishways. The agreement between experimental and numerical data is very satisfactory. The results show the importance of the turbulence model in the numerical simulations, and can be considered as a useful complementary tool for practical design purposes.     

Modeling Study of the Flow past Irregularities in a Pressure Conduit

Results are presented to investigate the characteristics of turbulent flow in a pressure conduit, such as water supply pipes and flood discharging tunnels. The turbulent flow governing equations, the Reynolds-averaged Navier–Stokes equations, in conjunction with a k–ε turbulent model are numerically solved using SIMPLEC. The study focuses on the modeling and calculation of the flow velocity field, pressure distribution, and the incipient cavitation number of the surface irregularities in the conduit. Different types and sizes of irregularities are simulated for various incoming flow velocities. The computed results are in good agreement with laboratory experimental data.     

Two-Dimensional Simulation Model of Sediment Removal and Flow in Rectangular Sedimentation Basin

A steady, two-dimensional numerical model was created to study the hydrodynamics of a rectangular sedimentation basin under turbulent conditions. The strip integral method was used to formulate the flow equations, using a forward marching scheme for solving the governing partial differential equations of continuity, momentum, advection–diffusion, turbulent kinetic energy, and its dissipation. In this way the flow equations were converted to a set of ordinary differential equations (ODEs) in terms of the key physical parameters. These parameters, along with a set of shape functions, describe flow variables including the velocity, the concentration of suspended sediments, and both the kinetic energy and its dissipation rate. Four Gaussian distributions were investigated, one corresponding to each flow parameter. In order to calculate the turbulent shear stresses, a two-equation turbulence model (i.e., k-ε model) was used. A fourth order Runge–Kutta method numerically integrates the set of ODEs. Simulation results were compared with experimental data, and close agreement (generally within 5–10%) was observed.     

Two-Dimensional Numerical Simulation of Primary Settling Tanks by Hybrid Finite Analytic Method

In order to investigate the turbulent flow and mass transfer in primary settling tanks, numerical simulations are conducted by using a modified k?ε two-layer model based Boussinesq’s approximation to model the Reynolds stress in primary settling tanks, and solving the governing equations using a hybrid finite analytic method (HFAM). The simulation results obtained using the mathematical model are compared with the experimental data and simulation results available in the literature, and the results of comparison indicate that the profiles of the primary velocity field are in line with the experimental results and the flow-through curve obtained using the mathematical model are in good agreement with the curves based on experimental data. It is therefore concluded that the HFAM approach can be used to simulate the turbulent flow and mass transfer in a primary settling tank, and the modified k?ε two-layer model can be used to establish the velocity field distribution at the bottom of a primary settling tank.     

射流细分氧煤燃烧器气固两相流动数值模拟

由气固两相流的多流体模型、气相湍流Ｋ－ε模型和颗粒湍流代数模型出发，对射流细分氧煤燃烧器在高炉直吹管中的气固两相流进行了数值模拟，得到了其中不同截面上气相速度场，颗粒速度场及浓度场。与实验结果比较，数值模拟结果较为合理。     

Characteristics of Horseshoe Vortex in Developing Scour Holes at Piers

The outcome of an experimental study on the turbulent horseshoe vortex flow within the developing (intermediate stages and equilibrium) scour holes at cylindrical piers measured by an acoustic Doppler velocimeter (ADV) are presented. Since the primary objective was to analyze the evolution of the turbulent flow characteristics of a horseshoe vortex within a developing scour hole, the flow zone downstream of the pier was beyond the scope of the investigation. Experiments were conducted for the approaching flow having undisturbed flow depth ( = 0.25?m) greater than twice the pier diameter and the depth-averaged approaching flow velocity ( = 0.357?m/s) about 95% of the critical velocity of the uniform bed sand that had a median diameter of 0.81?mm. The flow measurements by the ADV were taken within the intermediate (having depths of 0.25, 0.5, and 0.75 times the equilibrium scour depth) and equilibrium scour holes (frozen by spraying glue) at a circular pier of diameter 0.12?m. In order to have a comparative study, the ADV measurements within an equilibrium scour hole at a square pier (side facing the approaching flow) of sides equaling the diameter of the circular pier were also taken. The contours of the time-averaged velocities, turbulence intensities, and Reynolds stresses at different azimuthal planes (0, 45, and 90°) are presented. Vector plots of the flow field at azimuthal planes reveal the evolution of the characteristics of the horseshoe vortex flow associated with a downflow from intermediate stages to equilibrium condition of scour holes. The bed-shear stresses are determined from the Reynolds stress distributions. The flow characteristics of the horseshoe vortex are discussed from the point of view of the similarity with the velocity and turbulence characteristic scales. The imperative observation is that the flow and turbulence intensities in the horseshoe vortex flow in a developing scour hole are reasonably similar.     

3D Numerical Simulation for Water Flows and Sediment Deposition in Dam Areas of the Three Gorges Project

This paper presents a three-dimensional (3D) mathematical model for suspended load transport in turbulent flows. Based on the stochastic theory of turbulent flow proposed by Dou, numerical schemes of Reynolds stresses for anisotropic turbulent flows are obtained. Instead of a logarithmic law, a specific wall function is used to describe the velocity profile close to wall boundaries. The equations for two-dimensional suspended load motion and sorting of bed material have been improved for a 3D case. Numerical results are in good agreement with the measured data of the Gezhouba Project. The present method has been employed to simulate sediment erosion and deposition in the vicinity of the Three Gorges Dam. The size distribution of the deposits and bed material, and flow and sediment concentration at different times and elevations, are predicted. The results agree well with the observations in physical experiments. Thus, a new method is established for 3D simulation of sediment motion in the vicinity of dams.     

Large-Eddy Simulation of Turbulent Flow over a Fixed Two-Dimensional Dune

Turbulent open-channel flow over a two-dimensional dune is studied using an established large-eddy simulation code. The free surface is approximated as a shear free boundary. Turbulence statistics and instantaneous flow structures are examined. Numerical results from two computational grids agree with each other, and are also in good agreement with recently obtained experimental data. The mean velocity profiles show significant changes along the dune and there is no region that conforms to the standard law-of-the-wall. Profiles of the Reynolds stresses show distinct peaks marking the shear layer that originates from flow separation at the dune crest. Secondary peaks found further from the dune are ascribed to the shear layer over the upstream dune. Details of the separated flow and development of the flow after reattachment are well predicted. Quadrant analysis of the Reynolds shear stress shows that turbulent ejections dominate the near-wall motions. Complex water surface flow structures are visualized.     

Unsteady Friction in Rough Pipes

An energy dissipation model is presented for the computation of unsteady friction losses adapted to smooth-to-rough transition and fully rough pipes. The eddy viscosity model used to compute the Reynolds stresses in turbulent flow is modified to include the effect of roughness, which is considered in the computation of the velocity profiles. The model is tested by comparing the computed transient pressures with measured data from a laboratory test facility and a prototype test. Details of the experimental setup, pressure-head measurements, and valve characteristics during transient flow conditions are presented. The quasi-steady approximation gives an inaccurate prediction of the pressure head history; however, significantly better results are obtained if the unsteady friction effects are included.     

Double-Averaged Open-Channel Flows with Small Relative Submergence

We investigate the turbulent structure of shallow open channel flows where the flow depth is too small (compared with the roughness height) to form a logarithmic layer but large enough to develop an outer layer where the flow is not directly influenced by the roughness elements. Since the log layer is not present, the displacement height d, which defines the position of the zero plane, and the shear velocity u* cannot be found by fitting the velocity data to the log law. However, these parameters are still very important because they are used for scaling flow statistics for the outer and roughness layers. In this paper we propose an alternative procedure for evaluating d in laboratory conditions, where d is found from additional experiments with the fully developed log layer. We also point out the appropriate procedure for evaluating the shear velocity u* for flows with low submergence. These procedures are applied to our own laboratory flume experiments with uniform sphere roughness, where velocities were measured using Particle Image Velocimetry. Results were interpreted within the framework of the double-averaged Navier–Stokes equations and include mean velocities, turbulence intensities, Reynolds stresses, and form-induced normal and shear stresses. The data collapse well and show that in flows without a developed log layer the structure of turbulence in the outer layer remains similar to that of flows with a log layer. This means that even though the roughness layer in the experiments reported herein was sufficiently high to prevent the development of the log layer, influence of the bed roughness did not spread further up into the outer layer. Furthermore, the results show that flow statistics do not depend on relative submergence except for the form-induced stresses which increase when relative submergence decreases.     

Turbulence Characteristics of Open-Channel Flow with Bed Suction

The influence of bed suction on the characteristics of turbulent open channel flow is studied in a laboratory flume using a two-component laser Doppler velocimeter. The experimental results show how bed suction significantly affects the mean flow properties, turbulence levels, and Reynolds stress distributions. The data reveal the presence of a more negative vertical (downward) velocity. The results also show how the horizontal and vertical turbulence intensities and Reynolds shear stresses respond to suction. All these properties are found to reduce with increasing relative suctions: decreasing more rapidly around the bed region than that near the free surface. In the downstream direction, the flow structure in the suction zone undergoes a process of rapid readjustment within a transitional region. Beyond this region, the turbulence flow structures asymptotes toward an “equilibrium” region.     

Turbulence Characteristics in Gradual Channel Transition

A field study was conducted to determine the effects of a channel transition on turbulence characteristics. Detailed three-dimensional (3D) flow measurements were collected at a cross section that is located downstream of a gradual channel expansion. These measurements were obtained via an acoustic doppler velocimeter and include the 3D velocity field, the mean local velocities, the turbulent intensities, the frictional characteristics of the flow, the secondary velocity along the transverse plane, and the instantaneous shear stress components in the streamwise and transverse directions. Analysis of the 3D flow data indicates that the turbulent flow on the outer bank of the channel is anisotropic. Such anisotropy of turbulence, which is attributed to the gradual expansion in the channel and bed roughness, yields the development of a secondary flow of Prandtl’s second kind as reported in 1952. In particular, it was found that turbulent intensities in the vertical and transverse directions on the outer bank section are different in magnitude creating turbulence anisotropy in the cross-sectional plane and secondary flows of the second kind. Turbulent intensities increase toward the free surface indicating the transfer of a higher-momentum flux from the channel bed to the free surface, which contradicts common wisdom. Results for the normalized stress components in the streamwise and transverse direction show similar behavior to the intensities. Moreover, the nonlinear distribution of stresses is indicative of the oscillatory nature of the flow induced by the secondary flows of Prandtl’s second kind. A similar behavior was found for flows in straight rectangular channels over different roughness. Finally, a comparison between the secondary current velocity with the mainstream velocity indicates that secondary flow of Prandtl’s second kind is present within the right half of the measured cross section.     

3D Numerical Simulation of Turbulent Buoyant Flow and Heat Transport in a Curved Open Channel

A three-dimensional buoyancy-extended version of k–ε turbulence model was developed for simulating the turbulent flow and heat transport in a curved open channel. The density-induced buoyant force was included in the model, and the influence of temperature stratification on flow field was considered. The flow and temperature fields were simulated simultaneously. The model was validated by comparison with laboratory measurements, and the simulated fields were generally in good agreement with experimental data. A comparison of velocity fields in thermal and isothermal flow in curved open channel is presented and the effects of channel curvature and buoyant force on the velocity fields are also discussed.     

Numerical Modeling of Three-Dimensional Flow Field Around Circular Piers

A three-dimensional numerical model FLUENT is used to simulate the separated turbulent flow around vertical circular piers in clear water. Computations are performed using different turbulence models and results are compared with several sets of experimental data available in the literature. Despite commonly perceived weakness of the k-ε model in resolving three-dimensional (3D) open channel and geophysical flows, several variants of this turbulence model are found to have performed satisfactorily in reproducing the measured velocity profiles. However, model results obtained using the k-ε models show some discrepancy with the measured bed shear stress. The Reynolds stress model performed quite well in simulating velocity distribution on flat bed and scour hole as well as shear stress distribution on flat bed around circular piers. The study demonstrates that a robust 3D hydrodynamic model can effectively supplement experimental studies in understanding the complex flow field and the scour initiation process around piers of various size, shape, and dimension.     

Modeling Hydrogen Sulfide Emission Rates in Gravity Sewage Collection Systems

The factors affecting sulfide buildup in gravity sewers are complex, consisting of biological and physical processes, both in the aqueous and the gas phases of the sewer. The rate of each of these processes varies (among other parameters) according to flow characteristics, temperature, and pH. Under fast and turbulent flow conditions, the stripping of hydrogen sulfide into the gas phase may become the dominant process. The paper presents a semiempirical approach to the problem of quantifying hydrogen sulfide emission rates in sewers. Kinetics of hydrogen sulfide emission as a function of hydraulic parameters was measured in the laboratory using methods adopted from flocculation theory. A flocculation unit was used to impart a selected velocity gradient (G) into the water, and sulfide concentration was measured with time. The process was repeated for a number of G values. Regression analysis was then used to fit the rate of hydrogen sulfide emission equation against G. An equation was developed linking G to HL (head loss) in sewers assuming plug flow conditions. The hydraulic model and the kinetic model were linked (via G) to give the desired rate equation for hydrogen sulfide emission along a sewer line. The model was used to predict H2S emission from a uniform flow sewer and the effect of parameters such as pH, sewer slope and degree of fullness was studied. As expected, results show that low pH, high slope, and low degree of fullness enhance emission rates. Reasonable agreement was attained when the model output was compared with measured results from a field test sewer in Virginia, South Africa, under conditions where sulfide stripping was the rate-dominant process.     

Semianalytical Model for Solid Concentration in Turbulent Pipe Flows with Dispersed Particles

This paper presents a semianalytical model for the radial distribution of the solid concentration in a fully developed vertical turbulent pipe two-phase flow. A simplified momentum equation in the radial direction for solid phase in a two-phase flow with dilute suspended particles was first obtained. A linear empirical closure relation for the mean gas and solid velocities along the pipe direction was constructed using published experimental data. By incorporating the closure relation, an analytical solution to the simplified solid momentum equation with the appropriate boundary conditions at the pipe center and wall was obtained. The results from this semianalytical model are able to describe the core-annulus phenomenon commonly occurring in two-phase turbulent pipe flows. Very good agreements were found between the model predictions and published experimental data.     

Turbulent flow field over fluvial obstacle marks generated in a laboratory flume

The study is aimed at investigating the mean flow and turbulence characteristics in scour geometry developed near a circular cylinder of length 10cm placed over the sand bed transverse to the flow. The obstacle placed on a sand bed, on the way of a unidirectional flow, develops a crescent-shaped scour mark on the bed. The scour is caused by generation of vortex developed on the upstream side of the obstacle. Sand grains eroded by this vortex, are deposited on the downstream side of the obstacle as wakes. The turbulent flow field within the scour mark was measured in a laboratory flume using an Acoustic Doppler Velocimeter (ADV). The scour marks named as current crescents preserved in geological record are traditionally used as indicators of palaeocurrent direction. The distribution of mean velocity components, turbulent intensities and Reynolds stresses at different positions of the mark are presented. The experimental evidence also shows that the geometric characteristics of the scour mark (width) depend primarily on the cylinder aspect ratio, cylinder Reynolds number and sediment Froude number.     

Characteristics of Flow around Open Channel 90° Bends with Vanes

Sharp open-channel bends are commonly encountered in hydraulic engineering design. Disturbances such as secondary flows and flow separation caused by the bend may persist for considerable distances in the downstream channel. A simple way of reducing these disturbances is through the insertion of vertical vanes in the bend section. A laser Doppler anemometry (LDA) unit was used to measure the three-dimensional mean and turbulent velocity components of flow in an experimental rectangular open-channel bend. Flow characteristics of the bend with no vanes are compared with those of bends having one or three vertical vanes. The size of the flow separation zone at the inner wall of the bend was determined from dye visualization data and confirmed with mean streamwise velocity data. Results show that the vertical vanes are effective in considerably reducing flow separation, intensity of secondary flows, and turbulence energy in the downstream channel. Furthermore, energy loss for bends with vanes is slightly less than for the no-vane case.