Turbulence Structures in Flow over Two-Dimensional Dunes

This paper presents a large eddy simulation (LES) of turbulent open channel flow over two-dimensional periodic dunes. The Reynolds number R based on the bulk velocity U(bulk) and the maximum flow depth h, is approximately 25,000. The instantaneous flow field is investigated with special emphasis on the occurrence of coherent structures. Instantaneous vortices were visualized and it is shown that separated vortices are formed downstream of the dune crest due to Kelvin–Helmholtz instabilities. Near the point of reattachment the so-called kolk-boil vortex evolves in form of a hairpin vortex. Also present are previously separated vortices, which are convected along the stoss side of the downstream dune and elevated toward the water surface. The existence of near wall streaks which reform shortly after reattachment is also shown. The spacing between two low-speed streaks is very similar to that observed previously over smooth and rough walls. For validation, profiles of the time-averaged velocities, streamwise, and wall-normal turbulent intensities and the Reynolds shear stress calculated by the LES are presented and compared with available laser Doppler velocimetry measurements and overall good agreement is found.     

LES and RANS Studies of Oscillating Flows over Flat Plate

Oscillatory flows over a flat plate are studied by using Large Eddy Simulation (LES) and Reynolds-Average Navier-Stokes (RANS) methods. A dynamic subgrid scale (SGS) model is employed in LES, while the Saffman's turbulence model in RANS. The mean velocity profile, the turbulence intensity, and the wall shear stress are computed and compared with earlier experimental and numerical works. The results indicate that the flow behaviors are quite different during the accelerating and decelerating phases of the oscillating cycle. The transition from laminar to turbulent is also investigated as a function of the Reynolds number, R, which represents the square of the ratio of the oscillation amplitude at free stream to the thickness of the Stokes layer at the plate. The present results both from LES and RANS show that the transition occurs in the range of 5 × 104 < R < 5 × 105. The evolution of the flow structure in the Stokes layer during the transition from laminar to turbulent is clearly demonstrated from the numerical results. The friction coefficient of the amplitude of oscillatory surface shear stress varies as R?0.5 with a phase angle of 45° in laminar regime and transition to R?0.23 with a phase angle of about 10° in turbulence regime. These variations in the surface shear stress with the Reynolds number are in excellent agreement with the earlier experimental results of Kamphuis and the numerical results of Blondeaux. The excellent agreement between the LES and RANS demonstrated that Saffman's turbulence model, as originally intended by Saffman, is applicable for unsteady flows.     

Coupling of U-Tube and Shear Layer Oscillations in an Interconnected Flow Compartment

Results of experiments conducted in a 2?m high flume at large Reynolds numbers are reported in this paper. The flume was partitioned into two compartments. Flow entered the bottom of the upstream test compartment as a wall jet, at jet Reynolds number ranging from 11,000 to 170,000. Periodic oscillations of the free surface in the two compartments resembling the oscillatory flow in a liquid-filled U-tube, and large coherent structures formed above the potential core of the wall jet were observed. Coupling of the U-tube oscillations and vortex shedding is attributed to fluid-dynamic and fluid-resonant feedback processes. For test compartment length, Lc = 0.8?m, fluid-resonant feedback was found to be dominant, and the shear layer was observed to oscillate at the natural frequency of the two-compartment, U-tube system. The observed U-tube oscillations are initiated by the oscillations of the shear layer at a frequency equal to the subharmonic component for the U-tube. The flow oscillations were generally weaker for Lc = 1.2 and 2.0?m with oscillation frequencies governed by fluid-dynamic feedback, verified from a comparison with the results from a previously reported study.     

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.     

Free-Surface–Vorticity Interactions in an Open Channel Flow

The interactions between vortical structures, free surface, and background shear in an open channel flow is experimentally investigated. Deterministic structures are generated by a vertical injection from the channel bottom and a number of disturbances characterized by different jet amplitudes and Reynolds number are considered. Three cases are selected as representatives of the whole phenomenology and their evolution is discussed in detail. The streamwise perturbation is visualized by fluorescein while the streamwise component of velocity is measured by a laser Doppler anemometer. The perturbation in the cross stream plane is analyzed quantitatively and the velocity field is reconstructed on the symmetry plane, to extract the traces of the individual vortical structures. Depending on the intensity of the external perturbation, the structures either evolve as in the absence of the interface (small intensity) or they approach the free surface to undergo a topological change due to their reconnection with the free surface. The process originating in the so-called blockage and viscous layers is analyzed in detail. As a major conclusion, the interaction with the free surface is found to deplete the velocity gradients generated by the liftup of the quasi-streamwise vortices. This effect is suggested to be a major cause of stabilization of the open channel flow, with respect to a closed channel at the same Reynolds number.     

Rough Wall Boundary Layer on Plates in Open Channels

Experiments were performed to measure the characteristics of a turbulent boundary layer developing on a rough surface placed in an open channel flow at close proximity to the free surface. Streamwise velocity measurements were made with a one-component laser Doppler velocimeter system at the top of the spherical roughness elements. Measurements at three stations downstream of the plate leading edge show the growth of the boundary layer on the rough wall and its interaction with the exterior open-channel flow and the free surface. Resorting to the turbulence profile provides an alternative definition of the boundary layer thickness. The near-wall flow follows the well-known logarithmic law with a shift due to roughness. In the outer layer, there are two opposing effects: the free surface tends to decrease the wake component while the roughness tends to increase it. The streamwise turbulence intensity is affected by the shear and turbulence in the exterior flow, the effect of the free surface being greater than that of wall roughness.     

Characteristics of Shear Layer Structure in Skimming Flow over a Vertical Drop Pool

The characteristics of shear layer structure between the sliding jet and the pool for skimming flows over a vertical drop pool were investigated experimentally, using flow visualization technique and high speed particle image velocimetry. Four series of experiments having different end sill ratios (h/H = 0.12, 0.43, 0.71 and 1.0, where h=end sill height and H=drop height) with various approaching flow discharges were performed to measure the detailed quantitative velocity fields of the shear layer. The mean velocities and turbulence properties were obtained by ensemble averaging the repeated measurements. From the velocity profiles, it is found that the growth of the shear layer in the downward direction as the jet slides down the pool represents the momentum exchange. Analyzing the distribution of measured velocity, the similarity profile of the mean velocity at different cross sections along the shear layer was obtained. The proposed characteristic scales provided unique similarity profiles having promising regression coefficient. The selection of these characteristic scales is also discussed. Further, the spatial variations of mean velocity profiles, turbulence intensities, in-plane turbulent kinetic energy, and Reynolds shear stress were also elucidated in detail. The imperative observation is that the Reynolds shear stress dominates the major part along the shear layer as compared to the viscous shear stress. The study also provides an insight into the flow phenomena through the velocity and turbulent characteristics.     

Experiments on Vertical Turbulent Plane Jets in Water of Finite Depth

Detailed experiments on vertical turbulent plane jets in water of finite depth were carried out in a two-dimensional water tank. The jet velocities were measured with a laser Doppler velocimeter (LDV). The LDV measurement covers the entire flow regime: the zone of flow establishment (ZFE), the zone of established flow (ZEF), the zone of surface impingement (ZSI), and the zone of horizontal jets (ZHJ). From the experimental results, the following conclusions are reached. First, the jet flow is independent of the Reynolds number if the Reynolds number is sufficiently large to produce a turbulent jet. Second, in the initial ZFE, the jet flow is nonsimilar and is characterized by the two free shear layers along the two edges of the jet orifice. Third, the jet flow in ZEF is self-similar. Both mean and fluctuation velocities are scaled with the mean jet centerline velocity. The turbulent shear stress is predictable by Prandtl's third eddy viscosity model. The spreading of the confined vertical jets is larger than that of a free jet, so is the faster decay of jet centerline velocity. Fourth, in ZSI the jet flow is nonsimilar and high turbulent intensities were found. The vertical turbulent jet transforms into two opposite horizontal surface jets after the impingement. And finally, the maximum velocity of the horizontal surface jet in ZHJ decays according to a power law.     

Dissipation of Turbulent Kinetic Energy in a Tundish by Inhibitors with Different Designs

Turbulent flow of liquid steel and its control is studied using different geometries of turbulence inhibitors. Four designs of turbulence inhibitors were characterized through experiments of tracer injection in a water model and mathematical simulations using the Reynolds Stress Model (RSM) of turbulence. Inhibitor geometries included octagonal‐regular, octagonal‐irregular, pentagonal and squared. A layer of silicon oil was used to model the behaviour of tundish flux during steel flow. Fluid flows in a tundish using these geometries were compared with that in a bare tundish. Experimental and simulation results indicate that the flow in a bare tundish and a tundish using turbulence inhibitors open large areas of oil close to the ladle shroud due to strong shear stresses at the water‐oil interface with the exception of the squared inhibitor. Oil layer opening phenomena are explained by the high gradient of the dissipation rate of turbulent kinetic energy. Using the squared inhibitor the kinetic energy reports a high gradient from the tundish floor to the free bath surface as compared with other geometries.     

Investigation of Twin Vortices near the Interface in Turbulent Compound Open-Channel Flows Using DNS Data

The direct numerical simulation of turbulent flows in a compound open channel is described. Mean flows and turbulence structures are provided, and are compared with numerical and measured data available in the literature. The simulated results show that twin vortices are generated near the interface of the main channel and the floodplain and that their maximum magnitude is about 5% of the bulk streamwise velocity. Near the interface, the simulated wall shear stress reaches a maximum, contrary to experimental data. A quadrant analysis shows that both sweeps and ejections become the main contributor to the production of Reynolds shear stresses near the interface. Through the conditional quadrant analysis, it is demonstrated how the directional tendency of dominant coherent structures determines the production of Reynolds shear stress and the pattern of twin vortices near the interface. In addition, the time-dependent characteristics of three-dimensional vortical structures in a compound open-channel flow were investigated using direct numerical simulation (DNS) data.     

Confinement Effects in Shallow-Water Jets

This paper documents measurements of the mean velocity field and turbulence statistics of an isothermal, round jet entering a shallow layer of water. The lower boundary of the jet was a solid wall and the upper boundary a free surface. The jet axis was midway between the solid wall and the free surface in all cases. Experiments were performed at a Reynolds number of 22,500 for water layer depths 15, 10, and 5?times the jet exit diameter (9?mm). Particle image velocimetry measurements were made on vertical and horizontal planes—both containing the axis of the jet. The measurements were taken from 10 to 80 jet diameters downstream. Results showed that, for the highly confined cases at downstream locations, the axial velocity was quite uniform over the depth, with a mild peak below the jet axis. In the horizontal plane, the velocity profiles were slightly narrower than the free jet profile, but in the vertical plane, they were wider. The mean vertical velocity profiles showed that entrainment was suppressed in the vertical direction. At the same time, the lateral velocity profiles indicate that fluid flows from the sides toward the jet centerline. For the shallow cases, the mean vertical velocity becomes negative over most of the depth at downstream locations, indicating that this inflow from the sides is directed downward toward the solid wall. The relative turbulence intensity results were suppressed in the axial and vertical directions and mildly enhanced in the lateral direction. As well, the Reynolds shear stress in the vertical plane was significantly reduced by the vertical confinement, while in the horizontal plane it was only slightly affected by the confinement.     

Response of Velocity and Turbulence to Sudden Change of Bed Roughness in Open-Channel Flow

The experimental study shows how an open-channel flow would respond to a sudden change (from smooth to rough) in bed roughness. Using a two-dimensional acoustic Doppler velocimeter and a laser Doppler velocimeter, the velocity, turbulent intensities, and Reynolds stress profiles at different locations along a laboratory flume were measured. Additionally, the water surface profile was also measured using a capacitance-type wave height meter. The experimental data show the formation of an internal boundary layer as a result of the step change in bed roughness. The data show that this boundary layer grows much more rapidly than that formed in close-conduit flows. The results also show that the equivalent bed roughness, bed-shear stress, turbulent intensities, and Reynolds stress change gradually over a transitional region, although the bed roughness changes abruptly. The behavior is different from that observed in close-conduit flows, where an overshooting property—which describes the ability of the bed-shear stress to attain a high-peak value over the section with the larger roughness, was reported. A possible reason for the difference is the variation of the water surface profile when an open-channel flow is subjected to a sudden change in bed roughness.     

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.     

Characteristics of a Three-Dimensional Square Jet in the Vicinity of a Free Surface

The characteristics of a turbulent jet issuing from a square cross section nozzle in the vicinity of a free surface are presented. Two-component laser Doppler measurements were obtained at eight stations downstream of the nozzle exit, up to a distance of 27 nozzle widths. The Reynolds number based on the exit condition was 40,000. The proximity of the free surface influence the turbulence levels in the jet. Both confinement effects and axis switching influence the evolution of the velocity profiles downstream of the nozzle. The shear stress profiles indicate the formation of a wider mixing zone in the bottom portion of the jet in regions closer to the nozzle exit. Through quadrant decomposition, ejection, and entraining type events were identified. The magnitudes of the peak shear stress in the various quadrants indicate differences in the turbulence characteristics on the top and bottom portions of the jet. As distinguished in the extreme event plots, there are differences in the magnitudes of the peaks and also in their locations.     

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.     

Effect of Upward Seepage on Scour and Flow Downstream of an Apron due to Submerged Jets

The upward seepage through the bed sediment downstream of an apron of a sluice gate structure is a common occurrence due to afflux of the flow level between the upstream and downstream reaches of a sluice gate. The result of an experimental investigation on the characteristics of the scour hole and the flow-field downstream of an apron due to submerged jets under the influence of upward seepage through the bed sediment is presented. Experiments were run for the conditions of submerged jets, having submergence factors from 0.99 to 1.72 and jet Froude numbers from 3.15 to 4.87, over beds of sediments (median sizes = 0.8, 1.86, and 3?mm) downstream of an apron under upward seepage velocities. The characteristic lengths of the scour hole determined from the scour profiles are: the maximum equilibrium scour depth, the horizontal distance of the location of maximum scour depth from the edge of the apron, the horizontal extent of the scour hole from the edge of the apron, the dune height, and the horizontal distance of the dune crest from the edge of the apron, all of which were found to increase with an increase in the seepage velocity. Using experimental results, the time variation of the scour depth is scaled by an exponential law, where the nondimensional time scale decreases linearly with an increase in the ratio of the seepage velocity to the issuing jet velocity. The flow field in the submerged jets over both the apron and within the scour hole was detected using an acoustic Doppler velocimeter. The vertical distributions of time-averaged velocities, turbulence intensities and Reynolds stress at different streamwise distances, and the horizontal distribution of bed-shear stress are plotted for the conditions of scour holes with and without upward seepage. Vector plots of the flow field show that the rate of decay of the submerged jet decreases with an increase in the seepage velocity. The flow characteristics in the scour holes are analyzed in the context of the influence of upward seepage velocity on the decay of the velocity and turbulence intensities and the growth of the boundary layer.     

Fine-Scale Characterization of the Turbulent Shear Layer of an Instream Pebble Cluster

This study characterizes the shear layer and associated vortex shedding around an isolated submerged pebble cluster in a gravel-bed river. The approach combines flow visualization and high frequency three-dimensional velocity (acoustic Doppler velocimeter) measurements. Two vortex shedding modes in the wake of the cluster were identified: A small scale high frequency initial instability mode and a lower frequency mode that scales with cluster height. The lower frequency mode arose from the intermittent interaction and amalgamation of the small-scale instability vortices. Reynolds shear stresses, velocity spectra, and coherence functions indicated a dominance of longitudinal-vertical shedding vortices in the wake of the cluster. Simultaneous flow visualization was required to determine the nature and behavior of the shedding modes. Quadrant analysis revealed that Q2 and Q4 events contributed 80% of the local longitudinal-vertical component Reynolds shear stress, and demonstrated a dominance of ejection events in the wake of the cluster. Through flow visualization, the behavior of the shear layer was seen to vertically expand and contract with the passage of Q2 and Q4 events, respectively.     

Gravitational and Shear Instabilities in Compound and Composite Channels

Linear analysis of gravitational instabilities in the presence of a shear layer and shear instabilities in the presence of a free surface is performed. This study is relevant to shallow mixing layers, such as flow in compound and composite channels and inflows at channel junctions. The variations of the channel bed, velocity profile, Froude number, and friction coefficients with the transverse (lateral) coordinate are considered. It is found that there is a threshold Froude number above which the flow is unstable with respect to gravity waves and below which the flow is unstable with respect to shear waves for a certain range of the bed friction number. For values of Froude number larger than the threshold value, the influence of the shear layer and channel walls on the characteristics of the gravitational instability is strong when the channel and the shear layer are of comparable width. This influence reduces as the channel becomes wider and disappears in the limit when the channel width becomes infinite. When the Froude number is below the threshold value, free surface deformation in the form of gravitational waves exerts a strong stabilizing influence on the shear instability. In particular, the value of the critical bed friction number decreases when either the Froude number of the fast stream (main channel) or the slow stream (flood plain) increases. That is, shallow mixing layers become more stable as the Froude number increases. Comparisons of the linear stability calculations with experimental data show reasonable agreement.     

Flow Characteristics around a Circular Cylinder Placed Horizontally above a Plane Boundary

Flow characteristics around a circular cylinder positioned near a plane boundary (on which laminar boundary layer flow develops in the absence of circular cylinder), are investigated for Reynolds numbers R ranging from 7.8×102 to 1.15×104. Particle image velocimetry and fiber laser Doppler velocimetry were used to measure the velocity fields and velocity time histories, respectively. Flow structures are particularly revealed using flow visualization technique at R = 7.8×102 for gap ratios G/D (where G is the net gap between the surface of circular cylinder and the plane boundary), varying from 0 to 4. Based on the experimental results, the variation of Strouhal number of shedding vortex (or eddy) with G/D, the mechanism of vortex shedding suppression, and the streamwise velocity profiles of the upper shear layers and gap flows for small G/D are all discussed. Although the regular, alternate vortex shedding is suppressed for G/D<0.5, the periodicity could be detected due to the vortex (or eddy) shedding from the upper shear layer of the circular cylinder. Gap flow switching randomly is found and first put forward to be the main reason of multipeak or broadband spectral characteristics of the shedding event at a certain small gap ratio. It is also found that the streamwise velocity profiles of the upper shear layer, where periodic shedding eddies originate, exhibit well-behaved similarity. In addition, a unique similarity of mean streamwise velocity profiles of the gap flows is demonstrated for G/D ? 0.3. For R<4×103, the S increases as G/D decreases to its maximum around G/D ? 0.5 and then decreases as G/D decreases. For R ≥ 4×103, although most of the previous studies indicate that the S is insensitive to G/D, the present study shows that S still increases as G/D decreases but the variations of S are in a small range (i.e., 0.18 ? S ? 0.22).     

Inhibition of R-[3H]-baclofen binding to rat brain synaptic membranes by a homologous series of phenyl alcohol amides anticonvulsants and their evaluation as GABAB receptor blockers

A mathematical model is developed to investigate blood flow in arterial stenoses up to Reynolds numbers of 1000. The approach is based on Thwaites' method, normally used to treat laminar boundary layer development over a body in a freestream. The model is applicable to any axisymmetric stenosis geometry in all laminar physiological flow regimes, has a minimum of externally input parameters and is implemented as a short program on a personal computer. Maximum bounds on the expected errors are derived by comparison with known results from Poiseuille flow in a pipe. Agreement with shear stresses reported by other researchers using computational fluid dynamics is within 13% rms. The method has been specifically designed to be a useful predictive tool for biomedical investigators.