Particle Image Velocimetry Measurements and Numerical Modeling of a Saline Density Current

Particle image velocimetry scalar measurements were carried out on the body of a stably stratified density current with an inlet Reynolds number of 2,300 and bulk Richardson number of 0.1. These measurements allowed the mass and momentum transport between the current and the less dense ambient fluid to be investigated. Reynolds stress, Reynolds flux, and shear production of turbulent kinetic-energy profiles revealed local maxima at the bed, as well as at the interface with the ambient fluid. Profiles of excess density variance and buoyancy production of turbulent kinetic energy revealed only local maxima at the interface with the ambient. These maxima decreased downstream as the stable density gradient reduced the turbulent intensities, until turbulence collapsed. A two-dimensional, unsteady, Reynolds-averaged Navier-Stokes (2DV-URANS) simulation was also performed on this density current. Good agreement was found between the modeled and measured normalized mean flow profiles. A comparison was also made between the measured and modeled outer flow scales of the density current.     

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.     

Characteristics of Skimming Flow over Stepped Spillways

This paper presents the results of a laboratory study on the characteristics of fully developed skimming flow in a large model of a stepped spillway for two slopes, for a range of discharges with yc∕h in the range of 0.7–4.4. Fully developed aerated flow on a stepped spillway can be divided into lower and upper regions, similar to those for self-aerated flow in steep chutes. The air concentration distributions in these two regions agree with the equations developed by Straub and Anderson for flow in steep chutes. It was found that the depth at which the air concentration is equal to 90% can be considered as the depth of aerated flow on stepped spillways. In the lower region, the velocity profiles were described by the Karman-Prandtl equation for rough turbulent flow when an equivalent bed roughness was used. A correlation was developed for the skin friction coefficient to predict the Reynolds shear stress at the virtual bed of the stepped spillway. It was found that the relative energy loss in the stepped spillway is in the range of 48–63%. It was also found that the mean air concentration on a stepped spillway is larger than that in a corresponding chute.     

Turbulence Structure of Hydraulic Jumps of Low Froude Numbers

Turbulence characteristics of hydraulic jumps with Froude numbers of 2.0, 2.5, and 3.32 are presented. A Micro Acoustic Doppler velocimeter was used to obtain measurements of the velocities, turbulence intensities, Reynolds stresses, and power spectra. The maximum turbulence intensities and Reynolds stress at any section were found to decrease rapidly from the toe of the jump towards downstream within the jump and then gradually level off in the transition region from the end of the jump to the friction dominated open channel flow downstream. The maximum turbulence kinetic energy at each section decreases linearly with the longitudinal distance within the jump and gradually levels off in the transition region. The Reynolds stress and turbulence intensities within the jump show some degree of similarity. The dissipative eddy size was estimated to vary from 0.04 mm within the jump to 0.15 mm at the end of the transition region. The dominant frequency is in the range from 0 to 4 Hz for both horizontal and vertical velocity components.     

Measurements of Turbulence Generated by Oscillating Grid

Turbulence generated by a vertically oscillating grid in a water tank was investigated using the digital particle image velocimetry technique. The statistical turbulence characteristics computed based on the experimental data agree well with the two main findings reported in the literature: (1) The turbulence decays following the power law; and (2) the integral length scale increases linearly with the distance from the grid. In addition, the flow structure near the grid was observed in detail with the advantage of the planar measurements. It was found that the velocity fluctuations in the region near the grid vary depending on the grid geometry. The fluctuations immediately over the bar position are significantly different from those over the grid openings. Turbulence with the highest intensity occurs above the intersection of the square bars that constitute the grid. The results imply that shear flow clearly exists near the grid and homogeneity of the turbulence can only be achieved at a distance from the grid greater than about three mesh sizes. In addition, it was found that at least 400 vector maps should be taken to ensure the accuracy of the measured velocity fluctuations.     

Unobstructed and Obstructed Turbulent Flow in Gravel Bed Rivers

An acoustic Doppler velocimeter was used to characterize turbulence in two gravel bed rivers. Data were collected in unobstructed flow and compared to recent investigations. Additional data collected in the wake of emergent boulders indicate that mean flow velocity, turbulent kinetic energy, gradients in the streamwise velocity, and Reynolds stress downstream from large rocks deviate from unobstructed flow results, but similar turbulence patterns are found behind each boulder. Results of this study are discussed with regard to natural channel design and fish habitat.     

Evaluation of Mean Velocity and Turbulence Measurements with ADCPs

To test the ability of acoustic Doppler current profilers (ADCPs) to measure turbulence, profiles measured with two pulse-to-pulse coherent ADCPs in a laboratory flume were compared to profiles measured with an acoustic Doppler velocimeter, and time series measured in the acoustic beam of the ADCPs were examined. A four-beam ADCP was used at a downstream station, while a three-beam ADCP was used at a downstream station and an upstream station. At the downstream station, where the turbulence intensity was low, both ADCPs reproduced the mean velocity profile well away from the flume boundaries; errors near the boundaries were due to transducer ringing, flow disturbance, and sidelobe interference. At the upstream station, where the turbulence intensity was higher, errors in the mean velocity were large. The four-beam ADCP measured the Reynolds stress profile accurately away from the bottom boundary, and these measurements can be used to estimate shear velocity. Estimates of Reynolds stress with a three-beam ADCP and turbulent kinetic energy with both ADCPs cannot be computed without further assumptions, and they are affected by flow inhomogeneity. Neither ADCP measured integral time scales to within 60%.     

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.     

Particle Image Velocimetry Study of Flow near Trashrack Models

This paper provides results of an experimental study of turbulent flow near trashrack models that are comprised of an array of three rectangular bars. The bar thickness, bar depth, and center-to-center spacing were maintained constant. The flow characteristics were studied by aligning the bars with the approach flow and conducting measurements at three different approach freestream velocities. Subsequently, the freestream velocity was kept constant and detailed measurements were conducted for four different bar inclinations relative to the approach flow. For each test condition, a high-resolution particle image velocimetry (PIV) technique was used to conduct detailed velocity measurements in streamwise-spanwise planes at middepth of flow. From these measurements, isocontours and profiles of the mean velocities, turbulence intensities, Reynolds shear stress, and production term in the transport equation for the turbulent kinetic energy were obtained to study the flow characteristics around and downstream of the aligned and inclined bars. Flow characteristics near hydroelectric station trashracks are important for efficient turbine operation and reduction of fish entrainment.     

Shallow Turbulent Flow Simulation Using Two-Length-Scale Model

Numerical simulations of the planar starting jets were conducted using a two-length-scale turbulence model and a hydraulic code to study the effect of friction on 2D turbulence in shallow open-channel flow. The simulation results were compared with the data of the starting jets obtained in a recent series of laboratory experiments conducted in a large tank of small thickness. Dividing the turbulence energies into large and small scales, and calculating the energies with separate models, the observed friction effects on the 2D large-scale turbulent motion were correctly simulated by a two-length-scale turbulence model. To maintain the large-scale turbulence in the shallow shear flow, the production of turbulence energy by the transverse shear must be greater than the dissipation of the energy by friction. The critical gradient bed-friction number obtained from the simulations of the starting jets was Sc ? 0.08, which is consistent with the experimental observations in other shallow turbulent flows.     

Reynolds Stress Anisotropy in Open-Channel Flow

This paper reports the results of an experimental study characterizing turbulence and turbulence anisotropy in smooth and rough shallow open-channel flows. The rough bed consists of a train of two-dimensional transverse square ribs with a ratio of the roughness height (k) to the total depth of flow (d) equal to 0.10. Three rib separations (p/k) of 4.5, 9, and 18 were examined. Here, p is the pitch between consecutive roughness elements and was varied to reproduce the classical condition of d- and k-type roughness. For each case, two-component velocity measurements were obtained using a laser Doppler velocimetry system at two locations for p/k = 4.5 and 9: on the top of the rib and above the cavity, and an additional location for p/k = 18. The measurements allow examination of the local variations of the higher-order turbulent moments, stress ratios as well as turbulence anisotropy. Large variations of the turbulence intensities, Reynolds shear stress, turbulent kinetic energy and turbulence production are found for y1<3k. In this region, the flow is more directly influenced by the shear layers from the preceding ribs. The higher-order moments appear to be similar for all rough surfaces beyond y1 ≈ 7k. In the outer layer (y1>3k), all higher-order turbulent moments for the k-type roughness show a substantial increase due to the complex interactions between the roughness and the remnants overlying shear layers shed from succeeding ribs. Analysis of the components of the Reynolds stress anisotropy tensor shows that at p/k = 18, the flow at y1<5k tends to be more isotropic which implies that for this particular case, the effect of the roughness density could also be important. On the smooth bed, at the shallower depths, the correlation coefficient near the free surface increases and turbulence tends to become less anisotropic.     

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.     

Steady and Unsteady Simulations of Turbulent Flow and Transport in Ultraviolet Disinfection Channels

The effects of unsteadiness in the turbulent flow through a staggered array of circular cylinders, modeling an ultraviolet disinfection system, are studied by means of solutions of the two-dimensional Reynolds-averaged Navier–Stokes equations incorporating the standard k–? turbulence model. Time averaging is applied to the unsteady solution, and the time-averaged characteristics are compared with a solution where a steady flow is a priori assumed, as well as with time-averaged measurements. Differences between the predictions of time-averaged and the steady-flow models are found to be largest in the entrance region of the array, and to decline in importance in the downstream direction. Comparison with measurements indicate that, while the time-averaged unsteady model predictions exhibited better agreement in some respects, the turbulent kinetic energy remained substantially underpredicted. Predictions of head losses through the array are also discussed.     

Turbulent Fluid Flow Phenomena in a Water Model of an AOD System

Experimental measurements are reported regarding fluid flow and turbulence property measurements in a water model of an AOD vessel. Laser velocimetry was used to determine the time smoothed velocities, the turbulent kinetic energy, and the Reynolds stresses in the system; in addition, the rate of melting of immersed ice rods was also measured to determine the local heat transfer rates. The measurements have shown that for the model AOD studied both the velocity fields and the distribution of the turbulent kinetic energy were quite uniform; the absence of inactive or dead zones would render these systems ideal for mixing and for a range of ladle metallurgical operations. The rate at which immersed ice rods dissolved depended on both the local velocities and on the turbulence levels; a previously developed correlation could be employed to predict the appropriate heat transfer coefficients. Finally, the rate of turbulent energy dissipation per unit volume in real industrial AOD vessels was found to be much higher than in any other ladle metallurgy operations. This could raise interesting possibilities regarding the more widespread use of these systems for molten metals processing.     

URANS Computations of Shallow Grid Turbulence

This paper describes the unsteady Reynolds-averaged Navier–Stokes (URANS) computations of a quasi-two-dimensional (2D) grid turbulence in shallow open-channel flows, generated downstream of multiple piers aligned at regular intervals over the channel width. In shallow open-channel flows, the vertical confinement of the flow generally suppresses the three dimensionality and attains two-dimensional features with up-cascading of turbulent kinetic energy from small-scale toward large-scale structures. In this study, 2D depth averaged and 3D Reynolds-averaged equations with linear and nonlinear URANS turbulence models are applied to a shallow open-channel flow downstream of multiple piers and numerical results are discussed through a comparison with the experimental results performed by Uijttewaal and Jirka in 2003. We employed 0-equation models and k-ε models for the 2D and 3D computations, respectively. In 2D computations, vortices downstream of the grid occurred synchronously in the computation with both the linear and nonlinear 0-equation models. In the 3D computations, vortex merging and up-cascading of the kinetic energy were captured when artificial disturbance is added at the inlet. The measured decay of the turbulent kinetic energy in the streamwise direction, with a slope of ?1.3, was well captured by computation with the 3D models with inlet disturbance. The flow sensitivity on the inlet disturbance was rather small in the wide range of the disturbance ratios.     

Probability Density Function of Instantaneous Drag Forces and Shear Stresses on a Bed

A probability density function (PDF) of the instantaneous bed shear stress in a turbulent flow is derived in this paper. It is argued that the shape of the PDF is similar to the PDF of the instantaneous drag forces on bed roughness elements. The influence of the near-bed relative turbulence intensity is included in the PDF. The shape of the distribution compares well with our measurements of the instantaneous drag force on a protruding bed element for a range of turbulence intensities. However, deviations are apparent at high turbulence intensities. The PDF also compares well with measurements of shear stresses on a smooth wall.     

Skimming Flow in the Nonaerated Region of Stepped Spillways over Embankment Dams

Traditionally, research on stepped spillway hydraulics has been focused on the air-water flow region but for the hydraulic design of small embankment dams experiencing relatively large overtopping flows, the nonaerated region can be very important. Empirical formulas are presented for predicting skimming flow properties upstream of the point of inception of air entrainment for 1V:2H sloping stepped spillways, and the location and flow depth at the point of inception. Particular emphasis is placed on the clear-water depth, velocity distribution, and the energy dissipation characteristics in the developing nonaerated flow region. The velocity distribution is well described by a power law. The normalized clear-water depth and the normalized specific energy varied with the relative distance along the spillway and the effect of the normalized critical depth was negligible. Finally, the rate of energy dissipation was small, which has direct implications for the design of the downstream energy dissipator.     

Modeling Total Dissolved Gas Concentration Downstream of Spillways

Dams are often operated to facilitate downstream juvenile anadromous fish migration over the spillways, but such operation can cause high dissolved concentrations of oxygen and nitrogen that can be harmful to fish. The concentration of total dissolved gas (TDG) in the flow changes with distance downstream of the spillway crest and depends on the geometric configuration of the spillway and on hydraulic and operating conditions. A model is presented that simulates the physical processes of gas transfer with the goal of having an accurate and more widely applicable TDG model for plunging spillway discharges. Bubble transfer is dominant in the stilling basin, while water surface transfer is dominant downstream. Sensitivity analyses suggest which physical processes are important for accurate total dissolved gas predictions. Instantaneous bubble coalescence and breakup based upon local turbulence conditions is an appropriate assumption. Vertical bubble profiles do not need to be simulated in this type of model. Water surface roughness provides a significant increase to surface transfer. Tailwater depth is important to downstream TDG concentrations. Finally, a 10% difference in air entrained at the plunge point causes relatively minor differences in TDG of 1.4 and 3.1% at low and high discharges, respectively.     

Experimental Validation of Numerical Model of Flow in Pump-Intake Bays

Experiments were conducted in a laboratory model to validate a numerical model developed to simulate the three-dimensional turbulent flow in a water-pump-intake bay. The laboratory model was designed to reproduce the essential flow features of practical installations, including free-surface and wall-attached vortices, but was geometrically simple to enable the numerical model to be applied without undue complications of grid topology. The experiments involved flow visualizations and measurements with particle image velocimetry. The numerical model solves the Reynolds-averaged Navier-Stokes equations with a near-wall turbulence model. In the validation of this numerical model, therefore, emphasis was placed on prediction of the average properties of the various types of vortices that were found in the experiments. The predicted number, location, and general structure of the vortices were found to be in good agreement with those observed in the experiments, but they were generally larger and weaker than the measured ones. These differences are attributed to the unsteadiness of the flow and inadequacy of the turbulence model.