Flow Turbulence over Fixed and Weakly Mobile Gravel Beds

Characteristics of turbulence structure in quasi-2D flows with static and weakly mobile gravel beds are presented. Three sets of measurements with acoustic Doppler velocimeters in an irrigation canal were used: two with subcritical bed shear stress (static beds) and one with the bed shear stress τo close to critical τoc (weakly mobile bed). The analyses included vertical distributions of local mean velocities, turbulence intensities, turbulent shear stresses, velocity auto- and cross-spectra, the quadrant method, and high-order velocity moments. A number of properties of turbulence intensities, high-order moments, streamwise bursting parameters, and velocity spectra appeared to be similar for all three flows, but some properties were different. The most important one was an observed reduction in the von Kármán constant for the flow with weakly mobile bed. Comparison of these results with other studies and analogies with drag-reducing flows suggest that at τo∕τoc ≈ 1 the drag on the bed for a given granular material should be minimized.     

Characteristics of Turbulent Flow in Submerged Jumps on Rough Beds

The results of an experimental investigation on the flow field in submerged jumps on horizontal rough beds, detected by an acoustic Doppler velocimeter, are presented. Experiments were conducted for the conditions of submerged jumps, having submergence factors from 0.96 to 1.85 and jet Froude numbers from 2.58 to 4.87, over rough beds of Nikuradse’s equivalent sand roughness equaling 0.49, 0.8, 1.86, and 3?mm. The vertical distributions of time-averaged velocity components, turbulence intensity components, and Reynolds stress at different streamwise distances from the sluice opening and the horizontal distribution of bed-shear stress are plotted. Vector plots of the flow field show that the rate of decay of jet velocity in a submerged jump increases with increase in bed roughness. The flow characteristics on rough beds, being different from those on smooth bed, are discussed from the point of view of similarity, growth of the length scale, and decay of the velocity and turbulence characteristics scales. The most important observation is that the flow in the fully developed zone is found to be self-preserving.     

Distribution of Bed Shear Stress in Rotating Circular Flume

Distributions of bed shear stress across the width of a rotating circular flume with smooth and rough bed surfaces were obtained by measurement and model prediction. Results with flows over smooth beds showed that the flow in the central part may be considered to be two-dimensional and that effects of flow depth over the operating range of the flume are minor for flow depths not exceeding 0.14 m. For rough beds, the bed shear stress distributions were found to be skewed toward the inner wall. This can be corrected if a compensating roughness is added to the bottom of the ring. Such measures are also effective for flumes with smooth beds. Measured bed shear stress distributions agreed well with the predicted distributions for smooth beds and reasonably well for rough beds. The modified Preston tube, for measurement of bed shear stress in flows over rough beds, was found to give promising results. Further tests are required to completely define the uncertainty in bed shear stress measurements made with this instrument.     

Laboratory Measurements on Turbulent Pressure Fluctuations in and above Gravel Beds

The statistics of pressure fluctuations above and within three types of porous granular beds such as in gravel bed streams, rivers, and man-made canals are investigated by data gained via laboratory flume experiments. The flow conditions examined include a diversity of hydrodynamic loads that increase up to the point where single grains are moving from time to time, without causing severe modification to the bed texture and the related positions of the pressure sensors. Analysis is performed by means of histograms and spectral techniques and vertical intensity profiles. Two simplified equations are found that describe the vertical decrease for the standard deviation of the measured fluctuations indicating drag and lift, respectively, nondimensionalized by the mean bed shear stress. The former fluctuation is described by a crude linear fit, whereas the latter clearly shows that the lift intensity decreases exponentially in the porous bed with a decay distance of one to two times the equivalent grain roughness. Within the subsurface layer the standard deviation reaches a nonzero constant, mainly dominated by long-wave pressure fields that are convected in the outer flow. These findings can be used in future sediment transport models that use force balance approaches to determine incipient motion conditions.     

Experimental Study of Fine Sand Particle Settling in Turbulent Open Channel Flows over Rough Porous Beds

Results are presented from laboratory studies investigating the behavior of fine sand particles within turbulent open channel flow conditions flowing over rough, porous beds. A particle tracking technique was employed to record and analyze sand particle motion within the flow, while mean and fluctuating flow velocities were measured by an acoustic Doppler velocimeter probe. Measured particle settling rates show a strong influence from flow turbulence, being generally enhanced in the near-bed and intermediate flow regions and retarded in the outer flow region, compared to their fall velocity in still water conditions. Experiments also reveal the relative degree of settling enhancement to increase with decreasing particle size. Correlation between particle and small-scale fluid motions is demonstrated through a quadrant analysis technique, with higher-order events for the two phases found to be dominated by ejections and sweeps associated with the bursting process. Particle interactions with large-scale turbulent flow structures, revealed through flow visualization with a moving frame of reference, are found to result in particle accumulation in peripheral trajectories on the downflow side of local eddy structures. Analytical and theoretical considerations suggest that both these turbulence scales provide preferential transportation mechanisms that will account for the enhanced sand particle settling rates observed.     

Near-Bed Turbulence Characteristics at the Entrainment Threshold of Sediment Beds

This experimental study is devoted to quantification of the near-bed turbulence characteristics at an entrainment threshold of noncohesive sediments. Near the bed, the departure in the distributions of the observed time-averaged streamwise velocity from the logarithmic law is more for immobile beds than for entrainment-threshold beds. In the Reynolds shear stress distributions, a damping that occurs near the bed for sediment entrainment is higher than that for immobile beds. Quadrant analysis reveals that in the near-bed flow zone, ejections and sweeps on immobile beds cancel each other, giving rise to the outward interactions, whereas sweeps are the dominant mechanism toward sediment entrainment. The bursting duration for entrainment-threshold beds is smaller than that for immobile beds. On the other hand, the bursting frequency for entrainment-threshold beds is larger than that for immobile beds. The third-order correlations indicate that during sediment entrainment, a streamwise acceleration associated with a downward flux and advection of streamwise Reynolds normal stress is prevalent. The streamwise and the downward vertical fluxes of turbulent kinetic energy (TKE) increase with sediment entrainment. The TKE budget proves that for sediment entrainment, the pressure energy diffusion changes drastically to a negative magnitude, indicating a gain in turbulence production.     

Bed-Load Effects on Hydrodynamics of Rough-Bed Open-Channel Flows

The extent to which turbulent structure is affected by bed-load transport is investigated experimentally using a nonporous fixed planar bed comprising mixed-sized granular sediment with a d50 of 1.95?mm. Three different sizes of sediment (d50 = 0.77, 1.99, and 3.96?mm) were fed into the flow at two different rates (0.003 and 0.006?kg/m/s), and subsequently transported as bed load. Particle image velocimetry (PIV) was used to determine the turbulence characteristics over the fixed bed during clear water and sediment feed cases. Mean longitudinal flow velocities at any given depth were lower than their clear water counterparts for all but one of the mobile sediment cases. The exception was with the transport of fine grains at the higher feed rate. In this case, longitudinal mean flow velocities increased compared to the clear water condition. The coarse grains tended to augment bed roughness, but fine grains saturated the troughs and interstices in the bed topography, effectively causing the influence of bed irregularities to be smoothed. The PIV technique permitted examination of both temporal and spatial fluctuations in flow variables: therefore many results are presented in terms of double-averaged quantities (in temporal and spatial domains). In particular, the form-induced stress, which arises from spatially averaging the Reynolds averaged Navier–Stokes equations and is analogous to the Reynolds turbulent stress, contributed between 15 and 35% of the total measured shear stress in the roughness layer. Flow around protrusive roughness elements produced a significant proportion of the turbulent kinetic energy shear production, suggesting that this process is highly intermittent near rough beds.     

Validation of a Three-Dimensional Numerical Code in the Simulation of Pseudo-Natural Meandering Flows

Validation of a three-dimensional finite volume code solving the Navier–Stokes equations with the standard k-ε turbulence model is conducted using a high quality and high spatial resolution data set. The data set was collected from a large-scale meandering channel with a self-formed fixed bed, and comprises detailed bed profiling and laser Doppler anemometer velocity measurements. Comparisons of the computed primary and secondary velocities are made with those observed and it is found that the lateral momentum transfer is generally under predicted. At the apices this results in the predicted position of the primary velocity maximum having a bias towards the channel center, compared to the position where it has been measured. Using a simplified two zone roughness distribution whereby a separate roughness height was prescribed for the channel center and channel sides relative to a single distributed roughness height, generally led to a slightly improved longitudinal velocity distribution; the higher velocities were located nearer to the outside of the bend. Improving both the free surface calculation and scheme for discretization of the convection terms led to no appreciable difference in the computed velocity distributions. A more detailed study involving turbulence measurements and bed form height distribution should discriminate whether using distributed roughness height is a precursor to using an anisotropic turbulence representation for the accurate prediction of three-dimensional river flows.     

Flow Details near River Groynes: Experimental Investigation

Experiments have been carried out in a fixed-bed flume for a schematized straight river reach with groynes on one side to study the dynamics of the flow near groynes. The flume had a geometrical scale of 1∶40, based on typical dimensions of the Dutch River Waal. Both emergent and submerged groynes were studied. The measurements demonstrate the differences in the nature of the turbulence between submerged and emerged groynes stages; and provide insight into the flow pattern in the vicinity of groynes, the shape and the extent of the mixing layer at different flow stages, and the dynamic behavior of the velocity along the mixing layer between the main channel and the groyne fields. A parameterization of the turbulence characteristics of the flow near groynes is presented. Large-scale velocity fluctuations are found in all test cases, with timescales that vary with the flow stage. The large-scale u and v velocity fluctuations are in phase in the center of the mixing layer and out of phase for the points on the boundaries of the mixing layer.     

Eddy Taxonomy Methodology around a Submerged Barb Obstacle within a Fixed Rough Bed

Past research in environmental hydraulics has established the consideration that small- and large-scale turbulent eddy structures correspond to fast and slow fluctuations within a velocity time series measured at a fixed location. This work embraces this concept and develops an eddy taxonomy methodology to classify the prominent small- and large-scale eddies in the vicinity of an obstacle within a fixed rough bed. The previously documented visual interpretation technique is used in conjunction with a novel technique, which utilizes the statistical skew parameter, to quantify the moving-average time step at which large-scale eddies may be isolated from small-scale eddies. Thereafter, triple decomposition theory is employed and prominent spatial and temporal scales (i.e., integral length scales and periodicity) of small- and large-scale eddies are calculated. The eddy taxonomy methodology is implemented using acoustic Doppler velocimeter time-series measurements captured in the vicinity of an experimental model of a submerged barb obstacle—a hydraulic structure used for bank protection and increasing aquatic diversity. Implementation of the eddy taxonomy methodology using the streamwise velocity (u) time series and streamwise-vertical Reynolds stress (uw) time series provide similar results for the time step necessary to decompose large- from small-scale eddies. Eddy taxonomy results indicate the presence of large-scale, macroturbulent eddies throughout the barb test section with periodicity and length scales that agree with literature reported values. Additionally, small-scale bed derived eddies are most pronounced in the deflected flow regions where the barb obstacle has less influence upon the flow, while multiple small-scale eddies, including ejection, wake, and Kelvin–Helmotz associated eddies, persist in the downstream overtopping and wake regions of the barb obstacle.     

Flow Measurement Using Flying ADV Probes

An innovative measurement system of “flying” acoustic Doppler velocimeters was designed in order to allow rapid velocity measurement over a large flow field. Such measurements are necessary, for example, when measuring over a temporally varying and locally nonuniform rough bed. The measurement technique was verified by comparison with measurements taken in the same flows using a traditional stationary probe technique. Comparison showed that the flying-probe approach performs similarly to stationary measurements in capturing the mean flow field and turbulent fluctuations. The data obtained from flying probe experiments can be used to describe the flow in terms of double-averaged hydrodynamic variables, obtained by averaging in time and spatial domains within a thin slab parallel to the mean bed. Examples are presented of flow measurements over a fixed flat bed, a fixed dune bed, and over mobile developing bed forms. It is shown that near-bed measurements suffer from boundary reflection interference, though affected data can be filtered out based on the ADV-measured correlation coefficient. Measurement below roughness tops is possible, with in-bed records being detectable by spikes in measured signal-to-noise-ratio and by comparison with measured bed topography.     

Mass Transport in Shallow Turbulent Wake Flow by Planar Concentration Analysis Technique

A planar concentration analysis (PCA) system is used for observing the transport and mixing of a tracer mass in a shallow turbulent free-surface wake flow of a large cylindrical obstacle. The nonintrusive, fieldwise PCA measuring technique is applied to evaluate depth-averaged mass concentrations by making use of light attenuation due to absorption and scattering processes related to a dissolved tracer mass. The scalar fields are decomposed into a low-frequency quasiperiodic part, the coherent flow, and a randomly fluctuating part. From accompanying near-surface velocity measurements, large-scale coherent structures are identified and related to the coherent mass fields. This allows one to assess the role of the large-scale vortices for advection and diffusion in shallow wake flows. The time–mean wake flow displays a self-similar spanwise distribution both for mass and velocity. The longitudinal development of shallow wakes initially shows the growth of unbounded wakes; in the wake far field an attenuated behavior applies.     

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.     

Surface Roughness Effects in Near-Bed Turbulence: Implications to Sediment Entrainment

In this study, the characteristics of near-bed turbulence were experimentally investigated for three distinct roughness regimes, namely (1) isolated; (2) wake interference; and (3) skimming. Spherical particles of the same size and density were placed upon a rough sediment bed to simulate the three regimes. Experimental runs for the aforementioned regimes were performed in a tilting water-recirculating flume. Flow measurements atop the spherical particles were performed by means of a 3D laser Doppler velocimeter. The aim of the tests was to provide further evidence that the structure of turbulence is affected throughout the boundary layer by the presence of roughness geometry. The measurements reported here include velocity profiles of the mean streamwise and vertical velocity components and of the Reynolds shear stress distribution. To further quantify the differences in turbulent structure under various surface roughnesses, a quadrant analysis was performed.     

New Solution of Classical Hydraulic Jump

This technical note, applying dimensional analysis and incomplete self-similarity, proposes a new functional relationship for the sequent depth ratio for hydraulic jumps over both smooth and rough horizontal beds. For the smooth bed condition, experimental measurements in the literature were used to calibrate the new relationship. For the rough bed condition the data of a previous investigation were used with new measurements carried out in a rectangular horizontal flume having a gravel bed. Finally, a generalized solution of the sequent depth ratio is proposed.     

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.     

LDV measurements and computation of a turbulent circular jet placed non-concentrically in a confining pipe

Quantitative and nonintrusive fluid velocity and turbulence measurements obtained using laser Doppler velocimetry (LDV) in a circular jet that is positioned nonconcentrically in a confining pipe are presented. The experimental findings are compared with the results obtained by the finite-element computational simulation of the flow. The measured and predicted contours of the time-averaged axial velocity reveal the presence of a three-dimensional (3-D) asymmetric reverse-flow region, with its radial and circumferential extent depending on the axial position and the eccentricity ratio. Due to the weakened radial mixing and spreading of the jet for the higher eccentricities, the transition to the fully developed state is delayed for the high eccentricity cases. Measured and predicted contours of the axial turbulence fluctuations exhibit the ringlike distribution, although it is observed in an offset position for a given eccentricity ratio. At the downstream stations, the ringlike distribution tends to become more symmetric. The basic phenomena of flow reversal, preferential mixing, and shear layer growth are recovered by the computational predictions based on the high-Reynolds-number turbulence model. The time-averaged velocity measurements compare well with the predictions, whereas only qualitative comparison can be observed between the measured and predicted turbulence fluctuations.     

Hydrodynamic Forces Generated on a Spherical Sediment Particle during Entrainment

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

Computational modelling of water flow inside laboratory Knelson concentrator bowl

Enhanced gravity concentrators such as Knelson concentrator (KC) are extensively used in the mineral processing industry. The complexities of KC bowl geometry and variation of feed characteristics have forced process engineers to design empirically new units using laboratory and pilot-scale Knelson concentrators. However, numerical modelling methods such as computational fluid dynamics (CFD) and discrete element method (DEM) provide a better insight of flow behaviour of fluid and particulate solid phases inside these processing units. This article reports findings of CFD simulations for single-phase water flow inside the laboratory KC. An available standard 7.5-cm laboratory KC bowl was numerically simulated using realisable k-ε turbulence model to resolve the turbulence dispersion of existing transitional flow regime. The effects of relative centrifugal force (RCF) intensity and bed fluidisation water flow rate on the water velocity and pressure distributions were studied. Simulations confirmed the swirling flow pattern governing inside the bowl. The results revealed that the impact of RCF intensity on the water field values is greater than that of bed fluidisation water flow rate. Both velocity and pressure variations inside the bowl rings followed a linear trend.