Fluid–Solid Interaction in Particle-Laden Flows

Using a laser-Doppler split-phase measuring technique, the rates of fluctuation in horizontal and vertical directions of pipe flow containing solid particles were observed. Employing these observations the effect of particles on flow turbulence was analyzed and a formula for determining the initial condition of particles restraining the flow turbulence in the mainstream region was developed. The mechanisms affecting the energy loss of flow were then analyzed.     

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.     

Turbulence Characteristics in Flows Subjected to Boundary Injection and Suction

The influence of seepage (lateral flow) on the turbulence characteristics in free-surface flows over an immobile rough boundary is investigated. Steady flows having zero-pressure gradient over an immobile rough boundary created by uniform gravels of 4.1 mm in size were simulated experimentally with injection (upward seepage) and suction (downward seepage) applied through the boundary. A Vectrino (acoustic Doppler velocimeter) was used to measure the instantaneous velocities, which are analyzed to explore second- and third-order correlations, turbulent kinetic energy, turbulent energy budget, and conditional Reynolds shear stresses. It is observed that the second-order correlations decrease in presence of injection and increase in suction. The turbulent diffusivity and mixing length increase in presence of injection and decrease in suction. The third-order correlations suggest that the ejections are prevalent over the entire flow depth. The near-boundary flow is significantly influenced by the existence of upward seepage, which is manifested by a reduction in streamwise flux and the vertical advection of streamwise Reynolds normal stress. In addition, the upward flux and the streamwise advection of vertical Reynolds normal stress are also affected. The streamwise flux of turbulent kinetic is found to migrate upstream, while the vertical flux of turbulent kinetic energy is transported upward. The fluxes increase in presence of injection and decrease in suction. Energy budget evidences a lag between the turbulent dissipation and production and an opposing trend in the turbulent and pressure energy diffusions. A quadrant analysis for the conditional Reynolds shear stresses reveals that the ejection and sweep events are the primary contributions toward the total Reynolds shear stress production, with ejections dominating over the entire flow depth. The effect of seepage is shown to affect the magnitude of such events. However, in case of sweeps, this phenomenon is the opposite. The mean-time of occurrence of ejections and that of sweeps in suction are more persistent than those in no-seepage and injection.     

Analysis of Velocity Lag in Sediment-Laden Open Channel Flows

Laboratory experiments have recently confirmed that the streamwise particle velocity is largely less than that of the fluid in sediment-laden flows. This velocity lag is investigated analytically in the present study based on the drag force exerting on a particle in the presence of other neighbors. The normalized drag force or the hindrance coefficient is found generally dependent on the particle concentration, particle Reynolds number, and specific gravity. The velocity lag is then derived by relating the hindrance coefficient to the shear stress distribution for uniform sediment-laden open channel flows. The analysis shows that the profile of the velocity lag, when normalized by the shear velocity, is associated with the shear Reynolds number, dimensionless particle diameter, and specific gravity. For the dilute condition, the velocity lag distribution varies only with the shear Reynolds number, and the lag can be ignored if the shear Reynolds number is less than unity. The theoretical predictions are comparable to limited experimental results.     

Analysis of Suspended Sediment Transport in Open-Channel Flows: Kinetic-Model-Based Simulation

This paper presents a comprehensive analysis of suspended sediment transport in open channels under various flow conditions through a kinetic-model-based simulation. The kinetic model, accounting for both sediment-turbulence and sediment-sediment interactions, successfully represents experimentally observed diffusion and transport characteristics of suspended sediments with different densities and sizes. Without tuning any model coefficients, the nonmonotonic concentration distribution and the noticeable lag velocity with a negative value close to the wall are reasonably reproduced. Examination of flow conditions typical of suspension dominated rivers shows that the conventional method may overestimate or underestimate unit suspended-sediment discharge, depending on the Rouse number, sediment size, as well as shear velocity. The error may be less than 20% for dp<0.5?mm and might exceed 60% for dp>1.0?mm under typical flow conditions where shear velocity ranges from 1.0?to?12.5?cm/s and flow depth ranges from 1.0?to?5.0?m.     

Vertical Dispersion of Fine and Coarse Sediments in Turbulent Open-Channel Flows

Through using a kinetic model for particles in turbulent solid–liquid flows, underlying mechanisms of sediment vertical dispersion as well as sediment diffusion coefficient are investigated. Four hydrodynamic mechanisms, namely gravitational settling, turbulent diffusion, effect of lift force, and that of sediment stress gradient, coexist in two-dimensional (2D) uniform and steady open-channel flows. The sediment diffusion coefficient consists of two independent components: one accounts for the advective transport of sediment probability density distribution function due to sediment velocity fluctuations, and the other results from sediment–eddy interactions. Predictions of the kinetic model are in good agreement with experimental data of 2D open-channel flows. In such flows, it is shown that: (1) the parameter γ (i.e., the inverse of the turbulent Schmidt number) may be greater than unity and increases toward the bed, being close to unity for fine sediments and considerably large for coarse ones; (2) effects of lift force and sediment stress gradient become significant and need to be considered below the 0.1 flow depth; and (3) large errors may arise from the traditional advection–diffusion equation when it is applied to flows with coarse sediments and/or high concentrations.     

Numerical Calculation of Turbulence Structure in Depth-Varying Unsteady Open-Channel Flows

Unsteady depth-varying open-channel flows are really observed in flood rivers. Owing to highly accurate laser Doppler anemometers (LDA), some valuable experimental databases of depth-varying unsteady open-channel flows are now available. However, these LDA measurements are more difficult to conduct in open-channel flows at higher unsteadiness, in comparison with unsteady wall-bounded flows such as oscillatory boundary layers and duct flows. Therefore, in this study, a low-Reynolds-number k–ε model involved with a function of unsteadiness effect was developed and some numerical calculations were conducted using the volume of fluid method as a free-surface condition. The present calculated values were in good agreement with the existing LDA data in the whole flow depth from the wall to the time-dependent free surface. These values were also compared with those of unsteady wall-bounded flows. The present calculations were able to predict the distributions of turbulence generation and its dissipation, and consequently the unsteadiness effect on turbulence structure was discussed on the basis of the outer-variable unsteadiness parameter α, which is correlated with the inner-variable unsteadiness parameter ω+ in unsteady wall-bounded flows.     

Turbulence Measurements of Dye Concentration and Effects of Secondary Flow on Distribution in Open Channel Flows

This paper presents simultaneous turbulence measurements of velocity and tracer concentration using a combination of laser Doppler anemometer (LDA) and laser induced fluorescence (LIF) in rectangular and compound channels. Secondary flow, Reynolds stresses, Reynolds fluxes, and dye concentration distributions were measured near the water surface in both channels. An investigation of the effect of secondary flow on passive contaminant diffusion processes was carried out with relatively weak secondary flow in the rectangular channel and relatively strong secondary flow in the compound channel. The results show that the secondary flow clearly influences the spreading of the tracer concentration and the location of concentration peak, being different from the injection location. The transport rate of solute due to the secondary flow is not significant in the rectangular channel case but significant in the compound channel case. The transverse eddy viscosity is demonstrated to be equal to the transverse eddy diffusivity. The transverse eddy diffusivity near the water surface is larger than the vertical one. The Fickian law is valid in most regions investigated, but there are some regions where the Reynolds flux and concentration gradients are locally of the same sign due to the influence of secondary flow on the concentration distribution.     

Local Time Stepping for Modeling Open Channel Flows

This paper presents two time accurate local time stepping (LTS) algorithms developed within aeronautics and develops the techniques for application to the Saint-Venant equations of open channel flow. The LTS strategies are implemented within an explicit finite volume framework based on using the Roe Riemann solver together with an upwind treatment for the source terms. The benefits of using an LTS approach over more traditional global time stepping methods are illustrated through a series of test cases, and a comparison is made between the two LTS algorithms. The results demonstrate how local time stepping can reduce computer run times, increase the reliability of the error control, and also increase the accuracy of the solution in certain regions.     

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.     

Omission of Critical Reynolds Number for Open Channel Flows in Many Textbooks

During the analysis of an open channel flow experiment, students were asked to determine whether the flow was laminar or turbulent. The array of answers highlighted the different information carried in fluid mechanics textbooks. It was noted that approximately 50% of the books did not mention the fact that the critical Reynolds number would be different in open channels as compared to circular pipes flowing full.     

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.     

Outer Scaling for Open Channel Flow over a Gravel Bed

Similarity analysis is performed for hydraulically rough open channel flow over a gravel bed to provide mixed outer scaling of the mean-velocity profile. The analysis is based on equilibrium turbulent boundary-layer theory derived using the asymptotic invariance principle. Outer scaling based on the similarity theory is validated with velocity measurements from the laboratory and field, having a Reynolds number range that includes 1×104, 1×105, and 1×106 and a Froude number range from 0.26 to 0.83. The results show that the free-stream velocity is an appropriate outer scale for gravel-bed river flows at moderate and bankfull stage. The results agree well with the velocity measurements and collapse laboratory and field data, which allow an important connection between open channel research in the laboratory and the applications for which the research is performed in the field. The results show that the R/aD84 roughness parameter is consistent with the mixed scale used in boundary-layer velocity scaling. This is in agreement with the consistent turbulent structure of the flow for both flat plate boundary-layer and open channel flow scenarios. While R/D84 has been used empirically with depth-averaged velocity and roughness laws for many years, this roughness parameter is shown in a theoretical context due to its influence on the turbulent structure of the flow. The results are applicable to modeling the velocity distribution under fundamental gravel-bed flow cases that span to the bankfull flow regime, which provides a contribution to stream engineering.     

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.     

Open Channel Flow Resistance

In 1965, Rouse critically reviewed hydraulic resistance in open channels on the basis of fluid mechanics. He pointed out the effects of cross-sectional shape, boundary nonuniformity, and flow unsteadiness, in addition to viscosity and wall roughness that are commonly considered. This paper extends that study by discussing the differences between momentum and energy resistances, between point, cross-sectional and reach resistance coefficients, as well as compound/composite channel resistance. Certain resistance phenomena can be explained with the inner and outer laws of boundary layer theory. The issue of linear-separation approach versus nonlinear approach to alluvial channel resistances also is discussed. This review indicates the need for extensive further research on the subject.     

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.     

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.     

Turbulence Modeling of Flows over Circular Spillways

To predict the characteristics of flows over circular spillways, a turbulence model based on the Reynolds stress model (RSM) is presented. Circular spillways are used to regulate water levels in reservoirs. The flow over the spillway is rapidly varied with highly curvilinear streamlines. The isotropic eddy-viscosity models such as k-ε models are based on the Boussinesq eddy viscosity approximation that assumes the components of the turbulence Reynolds stress tensor linearly vary with the mean rate of strain tensor. Hence, they cannot very precisely predict the characteristics of flows over the spillway. On the other hand, the non-isotropic turbulence models such as the turbulence Reynolds stress models (RSM) that calculate all the components of the Reynolds stress tensor can accurately predict the characteristics of these flows. The k-ε models and RSM were applied in the present study to obtain the flow parameters such as the pressure and velocity distributions as well as water surface profiles. The previously published experimental results were used to validate the simulation predictions. For flow over a circular spillway, RSM appears to properly validate the characteristics of the flow under various conditions in the field, without recourse to expensive experimental procedures.     

Numerical Simulation of Flows in Cut-Throat Flumes

A numerical simulation is presented to obtain the flow characteristics of cut-throat flumes in rectangular open channels. Cut-throat flumes with a horizontal floor are used as simple devices for flow measurement in open channels. Since the flow in the throat section is highly three dimensional and curvilinear, the three-dimensional turbulence Reynolds stress model was applied in the present study to obtain the flow parameters such as the water surface profiles, the pressure distributions, and the mean velocity distributions. The volume of fluid scheme was used to determine the shape of the free surface by computing the fraction of each near-interface cell of a fixed grid that is partially filled with water. The previously published experimental data as well as data based on a new test related to cut-throat flumes were used to validate the simulation results.