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LES two-phase modelling of suspended sediment transport using a two-way coupled Euler–Lagrange approach
Abstract
Sediment plume development was modelled using an Euler-Lagrangian two-way coupled large eddy simulation. Momentum exchange was calculated based on interaction forces in the Maxey-Riley equation. Validation showed good agreement with experimental data from literature. For analysis of interaction between sediment and fluid 6,859 particles were released into turbulent fluid flow. In order to ensure independence of the results from arbitrary turbulent velocity fluctuations in the initial fluid velocity field, 41 simulations of the test case starting from different initial flow fields were analysed. Results of these simulations are normally distributed. Mean values indicate three phases of the development of the sediment plume: (i) acceleration phase, (ii) transport phase and (iii) deposition phase. Significant slow down of fluid flow and particle sorting turned out to be relevant processes in the initial development of the sediment plume which are not accounted for in one-way coupled models.
... Over the past decade, extensive research has been conducted on sediment transport patterns and various numerical models have been utilized. They can be divided mainly into three categories, namely Euler-Euler model [7][8][9][10][11][12], Euler-Lagrange model [13][14][15][16] and Lagrange-Lagrange model [17][18][19][20][21][22]. The Euler-Euler model treats sediment phase as a continuum and sediment transport is modeled using an advection-diffusion equation. ...
... The motion equation for a spherical particle within an unsteady and non-uniform fluid field is expressed as [24]: d d = + + + + (15) where , , , , are body force, drag force, fluid acceleration due to local pressure gradient, added mass force, Basset history force, respectively. ...
Sediment-laden flow is a common phenomenon in nature and the deposition of sediments can make a great difference in landscape formation or marine systems. The complexity of this issue can be further increased with temporal variations in the free surface elevation. This paper aims to present a two-phase flow model that effectively integrates the non-hydrostatic free surface model with the Lagrangian point-particle model. The free surface elevation is conceptualized as a height function and is tracked using a Lagrangian-Eulerian method. This new model is validated by five test cases, showing a good agreement with analytical or experimental results. This demonstrates the model's proficiency in handling sediment-laden flow under various free surface flow conditions, particularly with surface waves. Consequently, the proposed model holds promise for investigating sediment-laden flow issues in coastal regions.
... However, although it is important, this aspect has not garnered widespread attention. For particle plumes, Wildt et al. 50 employed an Euler-Lagrangian two-way coupled LES to simulate sediment plume development. Liu et al. 51 coupled VOF and DPM models to simulate the three-dimensional diffusion of the plume. ...
The particle plume, a ubiquitous particle–fluid coupled phenomenon in tailing discharge from deep-sea mining, undergoes suspension and diffusion over distances transportation. Our study is motivated by predicting plume dispersion patterns driven by different initial momentums, relying on understanding complex fluid–particle interaction mechanics. To consider irregular particle shapes and discrete effects, a discrete element method and large-eddy simulation coupled model is established in our in-house solver to simulate particle plumes and investigate flow characteristics from a Lagrangian perspective. The influence of the initial incident velocity W0 on particle flow regimes, movement patterns, velocity, concentration, Reynold shear stress, fluid–particle interactions, and energy budget is explored. The results show that a counter-rotating vortex pair forms in the initial stage, with ambient fluid entrainment inducing coherent vortex splitting into numerous vortex filaments, causing significant radial diffusion. Plume transportation begins with rapid settling, followed by a decrease to a roughly constant level. Increasing W0 enhances the particle velocity, allowing plumes to advance faster. This results in particle diffusion rate and concentration dilution rate increasing with decreasing W0. Away from the nozzle centerline, negative axial velocity magnitudes increase as W0 decreases, prompting particle radial diffusion. Additionally, for cases with low W0, significant particle concentration in regions far from the nozzle dampens pulsatile velocity, resulting in decreased Reynolds stress with decreasing W0. Notably, despite the complexity of particle–fluid interactions in plumes, the conversion of initial gravitational potential energy into particle and fluid kinetic energy is limited across all W0.
... Sedimentladen flow fundamentally belongs to two-phase flow, and the main challenge in model development is to handle the phase interface and its associated discontinuities. 34,35 Treating the solid phase as a dispersed medium 8,32,36 can provide precise descriptions but requires substantial computational resources. Conversely, treating the solid phase as a continuous medium 37,38 does not require tracking the movement of individual particles, offering high computational efficiency and producing satisfactory results in sediment-laden turbulence. ...
We propose a model that integrates a drift flux model with a vegetation source term and the
shear stress transport with improved delayed detached eddy simulation turbulence model to simulate sediment-laden vegetated flows. The numerical model was validated using experimental data from Lu [“Experimental study on suspended sediment distribution in flow with rigid vegetation,” Ph.D. thesis (Hohai University, Nanjing, Jiangsu, China, 2008)] and Wang and Qian [“Velocity profiles of sediment-laden flow,” Int. J. Sediment Res. 7, 27–58 (1992)]. We analyzed the vertical profile characteristics and spatial distribution features of sediment-laden vegetated flows at different vegetation densities. A detailed analysis was conducted on the correlations between variables that could affect the suspended sediment distribution, including vorticity, vertical velocity, Reynolds stress, and turbulent kinetic energy (TKE) fields. It was found that the vorticity field is primarily correlated with the suspended sediment concentration (SSC) field at the vegetation canopy, while the vertical velocity field above the canopy has a positive correlation with the SSC field. Both the Reynolds stress and TKE fields above the canopy exhibit positive correlations with the sediment concentration field. However, below the canopy, both fields show negative correlations with the sediment concentration. The TKE field is closely related to the suspended sediment distribution near the bottom, whereas the Reynolds stress field influences the suspended sediment distribution near the surface. The overall correlation between Reynolds stress and TKE with sediment concentration is negative, with their correlation significantly higher than that of vorticity and vertical velocity, indicating a closer connection with the movement of suspended sediments than the other variables.
... Für das numerische Experiment zum Schwebstofftransport wurden knapp 7000 Sedimentpartikel mit gleichförmig verteilten Korngrößen zwischen 0,07 und 0,71 mm und einer Dichte von 2650 kg/m 3 von oben am Beginn der Versuchsrinne zugegeben (Wildt et al. 2022 ...
Zusammenfassung
In dieser Arbeit werden zwei numerische Grundlagenuntersuchungen vorgestellt, die das Prozessverständnis von Schwebstoff- und Geschiebetransport erweitern. Die Modellierungen werden mittels der hochauflösenden Large-Eddy-Simulation durchgeführt. Im Fall des Schwebstofftransports werden die ersten Sekunden nach der Verklappung von Feinsediment simuliert und die Geschwindigkeiten der Partikel in der Schwebstoffwolke im Vergleich zur Fließgeschwindigkeit analysiert. Es zeigt sich, dass der Schwebstoff bereits nach wenigen Sekunden keine nennenswerten Geschwindigkeitsunterschiede zur Strömungsgeschwindigkeit in Hauptströmungsrichtung mehr aufweist und somit eine Modellierung mithilfe einer Advektions-Diffusions-Gleichung ab diesem Zeitpunkt zulässig ist. Hinsichtlich des Geschiebetransports werden die Einwirkungen von turbulenten kohärenten Strukturen auf die Geschiebekörner untersucht. Hierbei wird deutlich, dass insbesondere asymmetrische turbulente Strukturen in der Größe der Körner die Druckverteilung und das Verhältnis von Strömungswiderstands- zu Auftriebsbeiwerten so zu ändern vermögen, dass eine Bewegung des Geschiebes eintreten kann. Diese Erkenntnisse werden es zukünftig erlauben, Geschiebetransportmodelle mithilfe hydromechanischer Ansätze zu verbessern.
... The deposition rates of circular particles and angular particles are also different (Arora et al. 2022). Moreover, studies emphasized the effects of particle diffusion concentration (Wildt et al. 2022) and pipe wall roughness (Alihosseini and Thamsen 2019) on particle deposition. Establishing mathematical or physical models to quantify the particle deposition process is a common research method. ...
Deposition particles can lead to blockage, odor, and corrosion of pipes, and the deposition process of suspended particles is particularly complicated. In order to quantify the deposition process of suspended particles and mastered the critical conditions for the deposition in storm drainage, the process was simulated experimentally, and the deposition states of suspended particles under the different roughness of pipe wall, particle size, and density were analyzed. Two mathematical models of deposition critical velocity and easy deposition velocity were established. Results showed that with the increase of particle size and density, the gravity of particles increased and deposition was more likely to occur. In the rough pipeline, the kinetic energy consumption of water flow increased, the ability to carry particles was weakened, and the deposition rate would increase accordingly. The higher the flow velocity, the lower the deposition rate. The deposition states of particles in the pipeline could be divided into three types according to the deposition rates: “no deposition,” “minor deposition,” and “bulk deposition.” Verification showed that the difference rates between the calculated values and measured values of the deposition critical velocity ranged from − 3.23 to 2.86%, and the difference rates of the easy deposition velocity were − 4.14–4.72%, showing good consistency.
The article highlights the role of numerical modelling in research of the CD-Laboratory “Sediment research and -management”. Numerical models and their application are presented to investigate sediment transport, morphodynamics, and the ecological functions of water bodies. The application of modelling tools in basic research enables the deciphering of the mechanisms of the incipient motion of sediment grains and the transport of suspended particles with the flow. Applied research shows that both groynes and gravel islands have significant impacts on the hydrodynamics and morphodynamics of waterbodies. Groynes contribute to achieving morphological equilibrium and bed stabilization, while gravel islands offer multifunctional benefits, including improving habitat availability and regulating low water levels. The results also emphasize the importance of choosing appropriate model scales to minimize scale effects and increase the accuracy of the models. The insights gained contribute to a broader knowledge base of ecological hydraulic engineering measures in rivers and reservoirs and can be considered in future planning.
The Turbidity current (TC), a ubiquitous fluid-particle coupled phenomenon in the natural environment and engineering, can transport over long distances on an inclined terrain due to the suspension mechanism. A large-eddy simulation and discrete element method coupled model is employed to simulate the particle-laden gravity currents over the inclined slope in order to investigate the auto-suspension mechanism from a Lagrangian perspective. The particle Reynolds number in our TC simulation is and the slope angle is . The influences of initial particle concentration and terrain slope on the particle flow regimes, particle movement patterns, fluid-particle interactions, energy budget and auto-suspension index are explored. The results indicate that the auto-suspension particles predominantly appear near the current head and their number increases and then decreases during the current evolution, which is positively correlated with the coherent structures around the head. When the turbidity current propagates downstream, the average particle Reynolds number of the auto-suspension particles remains basically unchanged, and is higher than that of other transported particles. The average particle Reynolds number of the transported particles exhibits a negative correlation with the Reynolds number of the current. Furthermore, the increase in particle concentration will enhance the particle velocity, which allows the turbidity current to advance faster and improves the perpendicular support, thereby increasing the turbidity current auto-suspension capacity. Increasing slope angle will result in a slightly larger front velocity, while the effect of that on the total force is insignificant.
The turbidity current (TC), a ubiquitous fluid–particle coupled phenomenon in the natural environment and engineering, can transport over long distances on an inclined terrain due to the suspension mechanism. A large-eddy simulation and discrete element method coupled model is employed to simulate the particle-laden gravity currents over the inclined slope in order to investigate the auto-suspension mechanism from a Lagrangian perspective. The particle Reynolds number in our TC simulation is and the slope angle is . The influences of initial particle concentration and terrain slope on the particle flow regimes, particle movement patterns, fluid–particle interactions, energy budget and auto-suspension index are explored. The results indicate that the auto-suspension particles predominantly appear near the current head and their number increases and then decreases during the current evolution, which is positively correlated with the coherent structures around the head. When the turbidity current propagates downstream, the average particle Reynolds number of the auto-suspension particles remains basically unchanged, and is higher than that of other transported particles. The average particle Reynolds number of the transported particles exhibits a negative correlation with the Reynolds number of the current. Furthermore, the increase in particle concentration will enhance the particle velocity, which allows the turbidity current to advance faster and improves the perpendicular support, thereby increasing the turbidity current auto-suspension capacity. Increasing slope angle will result in a slightly larger front velocity, while the effect of that on the total force is insignificant.
A systematic variation of the exposure level of a spherical particle in an array of multiple spheres in a high Reynolds number turbulent open-channel flow regime was investigated while using the Large Eddy Simulation method. Our numerical study analysed hydrodynamic conditions of a sediment particle based on three different channel configurations, from full exposure to zero exposure level. Premultiplied spectrum analysis revealed that the effect of very-large-scale motion of coherent structures on the lift force on a fully exposed particle resulted in a bi modal distribution with a weak low wave number and a local maximum of a high wave number. Lower exposure levels were found to exhibit a uni-modal distribution.
The Maxey–Riley equation has been extensively used by the fluid dynamics community to study the dynamics of small inertial particles in fluid flow. However, most often, the Basset history force in this equation is neglected. Analytical solutions have almost never been attempted because of the difficulty in handling an integro-differential equation of this type. Including the Basset force in numerical solutions of particulate flows involves storage requirements which rapidly increase in time. Thus the significance of the Basset history force in the dynamics has not been understood. In this paper, we show that the Maxey–Riley equation in its entirety can be exactly mapped as a forced, time-dependent Robin boundary condition of the one-dimensional diffusion equation, and solved using the unified transform method. We obtain the exact solution for a general homogeneous time-dependent flow field, and apply it to a range of physically relevant situations. In a particle coming to a halt in a quiescent environment, the Basset history force speeds up the decay as a stretched exponential at short time while slowing it down to a power-law relaxation, , at long time. A particle settling under gravity is shown to relax even more slowly to its terminal velocity ( ), whereas this relaxation would be expected to take place exponentially fast if the history term were to be neglected. An important mechanism for the growth of raindrops is by the gravitational settling of larger drops through an environment of smaller droplets, and repeatedly colliding and coalescing with them. Using our solution we estimate that the rate of growth rate of a raindrop can be grossly overestimated when history effects are not accounted for. We solve exactly for particle motion in a plane Couette flow and show that the location (and final velocity) to which a particle relaxes is different from that due to Stokes drag alone. For a general flow, our approach makes possible a numerical scheme for arbitrary but smooth flows without increasing memory demands and with spectral accuracy. We use our numerical scheme to solve an example spatially varying flow of inertial particles in the vicinity of a point vortex. We show that the critical radius for caustics formation shrinks slightly due to history effects. Our scheme opens up a method for future studies to include the Basset history term in their calculations to spectral accuracy, without astronomical storage costs. Moreover, our results indicate that the Basset history can affect dynamics significantly.
Sediment saltation in a rough-wall turbulent boundary layer was simulated with a coupled model with large eddy simulation and a discrete element model. The aim is to quantify the saltation process using eddy-resolving fluid simulations and Lagrangian particle tracking. The four-way coupling approach in this work considered the fluid–particle, particle–particle, and particle–wall interactions. Five simulations were performed. For comparison, one simulation with the flow field replaced by a simple log-law profile was also performed. The simulated saltation trajectory, velocity, and collision angles were analysed and we found: (1) Turbulent fluctuation and random collision with the bed are two controlling factors for particle trajectory. Without turbulent fluctuation, the loss of saltation information is severer in the streamwise direction than in other directions. In the spanwise direction, bed collision plays a comparable role to turbulent fluctuation. (2) Particle velocities in the streamwise and vertical directions follow skew-normal distributions. (3) Turbulent fluctuations make the incidence angle wider and slightly enhance the correlation between the incidence and reflection angles.
Multiphase flows are relevant in several industrial processes mainly because they are present in the production of a large diversity of products. Hence, the availability of accurate numerical modeling tools, able to cope with this type of flows, is of major significance to provide detailed information about the system characteristics, in order to guide the design activity. This study presents a detailed assessment of a multiphase flow solver able to couple Eulerian and Lagrangian phases, the last modeled through the discrete particle method. The numerical code is already implemented in the open source computational fluid dynamics software package . The solver (DPMFoam) is firstly used to simulate the collision between two particles, for which a good correlation was obtained with the theoretical impulse force value. Subsequently, the solver is employed in the simulation of a pseudo 2D gas-solid flow in a fluidized bed. In this case study, the results obtained for the bubble patterns, time-average flow patterns, bed expansion dynamics and particle phase energy analysis are in agreement with the experimental and numerical results available in the literature. In addition, the numerical pressure drop for the fluidized bed is computed and compared with the analytical Ergun’s pressure drop equation. The accuracy of the numerical results was found to be sensitive to the solid fraction estimation.
A Reynolds-averaged Euler-Lagrange sediment transport model (CFDEM-EIM) was developed for steady sheet flow, where the inter-granular interactions were resolved and the flow turbulence was modeled with a low Reynolds number corrected k-ω turbulence closure modified for two-phase flows. To model the effect of turbulence on the sediment suspension, the interaction between the turbulent eddies and particles was simulated with an eddy interaction model (EIM). The EIM was first calibrated with measurements from dilute suspension experiments. We demonstrated that the eddy-interaction model was able to reproduce the well-known Rouse profile for suspended sediment concentration. The model results were found to be sensitive to the choice of the coefficient, C 0, associated with the turbulence-sediment interaction time. A value C0=3 was suggested to match the measured concentration in the dilute suspension. The calibrated CFDEM-EIM was used to model a steady sheet flow experiment of lightweight coarse particles and yielded reasonable agreements with measured velocity, concentration and turbulence kinetic energy profiles. Further numerical experiments for sheet flow suggested that when C 0 was decreased to C 0 < 3, the simulation under-predicted the amount of suspended sediment in the dilute region and the Schmidt number is over-predicted (Sc > 1.0). Additional simulations for a range of Shields parameters between 0.3 and 1.2 confirmed that CFDEM-EIM was capable of predicting sediment transport rates similar to empirical formulations. Based on the analysis of sediment transport rate and transport layer thickness, the EIM and the resulting suspended load were shown to be important when the fall parameter is less than 1.25.
A three-dimensional Eulerian two-phase flow model for sediment transport in sheet flow conditions is presented. To resolve turbulence and turbulence-sediment interactions, the large-eddy simulation approach is adopted. Specifically, a dynamic Smagorinsky closure is used for the subgrid fluid and sediment stresses, while the subgrid contribution to the drag force is included using a drift velocity model with a similar dynamic procedure. The contribution of sediment stresses due to intergranular interactions is modeled by the kinetic theory of granular flow at low to intermediate sediment concentration, while at high sediment concentration of enduring contact, a phenomenological closure for particle pressure and frictional viscosity is used. The model is validated with a comprehensive high-resolution dataset of unidirectional steady sheet flow (Revil-Baudard et al., 2015, Journal of Fluid Mechanics, 767, 1–30). At a particle Stokes number of about 10, simulation results indicate a reduced von Kármán coefficient of κ ≈ 0.215 obtained from the fluid velocity profile. A fluid turbulence kinetic energy budget analysis further indicates that the drag-induced turbulence dissipation rate is significant in the sheet flow layer, while in the dilute transport layer, the pressure work plays a similar role as the buoyancy dissipation, which is typically used in the single-phase stratified flow formulation. The present model also reproduces the sheet layer thickness and mobile bed roughness similar to measured data. However, the resulting mobile bed roughness is more than two times larger than that predicted by the empirical formulae. Further analysis suggests that through intermittent turbulent motions near the bed, the resolved sediment Reynolds stress plays a major role in the enhancement of mobile bed roughness. Our analysis on near-bed intermittency also suggests that the turbulent ejection motions are highly correlated with the upward sediment suspension flux, while the turbulent sweep events are mostly associated with the downward sediment deposition flux.
Debris flows represent some of the most relevant phenomena in geomorphological events. Because of the potential destructiveness of such flows, they are the subject of a vast amount of research. This paper addresses the need for a numerical model applicable to granularfluid mixtures featuring high spatial and temporal resolution, and thus capable of resolving the motion of individual particles, including all interparticle contacts. The DualSPHysics meshless numerical implementation based on smoothed particle hydrodynamics (SPH) is expanded with a distributed-contact discrete-element method (DCDEM) in order to explicitly solve the fluid and solid phases. The specific objective is to test the SPH-DCDEM approach by comparing its results with experimental data. An experimental setup for stony debris flows in a slit check dam is reproduced numerically, where solid material is introduced through a hopper, assuring a constant solid discharge for the considered time interval.With each sediment particle possibly undergoing several simultaneous contacts, thousands of time-evolving interactions are efficiently treated because of the model's algorithmic structure and the HPC implementation of DualSPHysics. The results, composed of mainly retention curves, are in good agreement with the measurements, correctly reproducing the changes in efficiency with slit spacing and density.
The settling of cohesive sediment is ubiquitous in aquatic environments. In the settling process, the silt particles show behaviors that are different from non-cohesive particles due to the influence of inter-particle cohesive force. While it is a consensus that cohesive behaviors depend on the characteristics of sediment particles (e.g., Bond number, particle size distribution), little is known about the exact influence of these characteristics on the cohesive behaviors. In the present work, three-dimensional settling process is investigated numerically by using CFD--DEM (Computational Fluid Dynamics--Discrete Element Method). The inter-particle collision force, the van der Waals force, and the fluid--particle interaction forces are considered. The numerical model is used to simulate the hindered settling process of silt based on the experimental setup in the literature. The results obtained in the simulations, including the structural densities of the beds, the characteristic lines, and the particle terminal velocity, are in good agreement with the experimental observations in the literature. To the authors' knowledge, this is the first time that the influences of non-dimensional Bond number and particle polydispersity on the structural densities of silt beds have been investigated separately. The results demonstrate that the cohesive behavior of silt in the settling process is attributed to both the cohesion among silt particles themselves and the particle polydispersity. To guide to the macro-scale modeling of cohesive silt sedimentation, the collision frequency functions obtained in the numerical simulations are also presented based on the micromechanics of particles. The results obtained by using CFD--DEM indicate that the binary collision theory over-estimated the particle collision frequency in the flocculation process at high solid volume fraction.
A multi-dimensional Eulerian two-phase model for sediment transport, called SedFoam, is presented. The model was developed under the open-source framework via the CFD toolbox OpenFOAM. With closures of particle stresses and fluid-particle interactions, the model is able to resolve processes in the concentrated region of sediment transport and hence does not require conventional bedload/suspended load assumptions. A modified k − ϵ closure was adopted for the carrier flow turbulence. The model was validated for Reynolds-averaged steady and oscillatory sheet flows and verified with empirical formulae for scour downstream of an apron. The model was used to study momentary bed failure (or plug flow) under sheet flow conditions. Model results revealed the existence of instabilities of the near-bed transport layer when momentary bed failure criteria was exceeded. These instabilities evolved into 5–10 cm billows and were responsible for the large transport rate. The instabilities were associated with a large erosion depth, which was triggered by the combination of large bed shear stresses and large horizontal pressure gradients. Further numerical experiments confirmed the conjecture by previous studies that a criterion for onset of momentary bed failure in oscillatory sheet flow was a function of both the Shields parameter and Sleath parameter.
In this paper, a monitoring and modelling concept for ecological optimized harbour dredging and fine sediment disposal in large rivers is presented. According to the concept, first a preliminary assessment should be performed previous to the dredging and dumping procedure to derive knowledge about the current status in hydrodynamics, morphology and instream habitat quality. During the performance of the maintenance work, a high-resolution monitoring program has to be organized to measure flow velocities, the suspended sediment concentrations and the extent of the occurring plume. These data can then be compared with natural suspended sediment conditions and serve as input data for numerical sediment transport modelling. Furthermore, bathymetric surveys and biotic sampling enable the detection of possible effects of dredging and disposal in the post-dumping stage. Based on sediment transport modelling approaches, short- to mid-term developments of the sediment plume can be predicted with an additional and final habitat evaluation at the end of the project. This concept was applied and optimized during the maintenance work at the case study winter harbour Linz at the Danube River. The findings of the presented study highlight the necessity of integrated monitoring and modelling approaches for harbour dredging especially in large river systems.
Development of algorithms and growth of computational resources in the past decades have enabled simulations of sediment transport processes with unprecedented fidelities. The Computational Fluid Dynamics--Discrete Element Method (CFD--DEM) is one of the high-fidelity approaches, where the motions of and collisions among the sediment grains as well as their interactions with surrounding fluids are resolved. In most DEM solvers the particles are modeled as soft spheres due to computational efficiency and implementation complexity considerations, although natural sediments are usually mixture of non-spherical particles. Previous attempts to extend sphere-based DEM to treat irregular particles neglected fluid-induced torques on particles, and the method lacked flexibility to handle sediments with an arbitrary mixture of particle shapes. In this contribution we proposed a simple, efficient approach to represent common sediment grain shapes with bonded spheres, where the fluid forces are computed and applied on each sphere. The proposed approach overcomes the aforementioned limitations of existing methods and has improved efficiency and flexibility over existing approaches. We use numerical simulations to demonstrate the merits and capability of the proposed method in predicting the falling characteristics, terminal velocity, threshold of incipient motion, and transport rate of natural sediments. The simulations show that the proposed method is a promising approach for faithful representation of natural sediment, which leads to accurate simulations of their transport dynamics. The proposed method also opens the possibility for first-principle-based simulations of the flocculation and sedimentation dynamics of cohesive sediments. Elucidation of these physical mechanisms can provide much needed improvement on the prediction capability and physical understanding of muddy coast dynamics.
The simulation of sediment transport by three-dimensional modelling is linked with the question how accurate such models are. The current paper provides a test where detailed field measurements of velocities and bed elevation changes over a three-month period from a prototype reservoir are compared with simulation results. The SSIIM software was used to compute water flow and sediment transport in the Iffezheim reservoir. The numerical model solved the Navier-Stokes equations on a 3D unstructured grid with dominantly hexahedral cells. The k-epsilon turbulence model was used, together with the SIMPLE method to find the pressure. The 3D convection-diffusion equation for suspended sediments was solved for nine sediment fractions.
The computed velocity pattern showed good correspondence with the measurements. Grid sensitivity tests showed that the main flow features were computed in different grid sizes, but more accurately so with the finest grid. The sediment deposits were reasonably well computed in location and magnitude. A sensitivity test revealed that the computed bed elevation changes were most sensitive to the fall velocities of the finest cohesive sediment particles and sediment cohesion. The sediment deposition computations were also to some degree sensitive to the sediment discharge formula, bed roughness, discretization scheme and the grid resolution.
A unified discretisation of rigid solids and fluids is introduced, allowing for resolved simulations of fluid-solid phases within a meshless framework. The numerical solution, attained by Smoothed Particle Hydrodynamics (SPH) and a variation of Discrete Element Method (DEM), the Distributed Contact Discrete Element Method (DCDEM) discretisation, is achieved by directly considering solid-solid and solid-fluid interactions. The novelty of the work is centred on the generalization of the coupling of the DEM and SPH methodologies for resolved simulations, allowing for state-of-the-art contact mechanics theories to be used in arbitrary geometries, while fluid to solid and vice versa momentum transfers are accurately described. The methods are introduced, analysed and discussed. Initial validations on the DCDEM and the fluid coupling are presented, drawing from test cases in the literature. An experimental campaign serves as a validation point for complex, large scale solid-fluid flows, where a set of blocks in several configurations is subjected to a dam-break wave. Blocks are tracked and positions are then compared between experimental data and the numerical solutions. A Particle Image Velocimetry (PIV) technique allows for the quantification of the flow field and direct comparison with numerical data. The results show that the model is accurate and is capable of treating highly complex interactions, such as transport of debris or hydrodynamic actions on structures, if relevant scales are reproduced.
Most theoretical and numerical studies employ diffusion theory to investigate suspended sediment distributions in fluvial rivers, yet diffusion-theory-based descriptions are strictly valid only in the limit of small particle inertia and low concentrations. This paper presents a transport equation for sediment in suspension based on a two-fluid model of solid/liquid two-phase flows. The transport equation is derived from the consideration of mass conservation for solid particles. The velocity of the solid phase is obtained from an asymptotic solution of the momentum conservation equation for solid phase. Moreover, this transport equation is a typical convection-diffusion equation that includes the conventional diffusion equation as a special case when particle inertia is small and concentrations are low. Retaining the essential features of two-fluid models, the transport equation is applicable to sediment-laden flows with a wide range of particle inertia and sediment concentrations. Comparisons of the results with available experimental observations are presented, and fairly good agreement is obtained.
The drift velocity, at which sediment disperses relative to the motion of water-sediment mixtures, is a key variable in two-phase mixture equations. A constitutive relation for the drift velocity, expressed as a power series in the particle bulk Stokes number, was obtained by solving the momentum equation for sediment with the perturbation approach. It shows that gravity and turbulent diffusion are the primary dispersion effects on sediment, whereas flow inertia, particle-particle interactions, and other forces such as lift are the first-order particle inertial corrections that also play significant roles in sediment suspension. Analysis proves that studies based on turbulent diffusion theory are the zeroth-order approximations to the present formulation with respect to the particle inertia effect. The vertical concentration and velocity distributions of sediment in simple flows were investigated with the two-phase mixture equations closed by the drift velocity acquired in the research reported in this paper. The calculated concentration profiles agree well with measurements when the first-order particle inertial effect is considered. The calculated velocity of sediment coincides with available experiments that sediment lags behind water in open-channel flows as a result of turbulence-induced drag.
A number of turbulence closure schemes can be employed to numerically investigate near-bed wave boundary layer and sediment transport problems. We present an extension of the widely used k-ωk-ω turbulence model to two-phase sediment transport modelling. In this model, a transport equation is solved for the turbulence specific dissipation rate ωω. For two-phase models, this equation is similar to the one for clear fluids with an additional term due to inter-phase interaction terms, which we will discuss. The new k-ωk-ω model is then applied to wave and current sheet flows. We compare the numerical results from the k-ωk-ω model and from an existing k-εk-ε model against sheet flow experimental data collected in oscillatory water tunnels. Both models provide broadly similar numerical results. Nevertheless, the k-ωk-ω and k-εk-ε models display different behaviour around flow reversal, and neither is able to fully reproduce observed suspension peak at flow reversal.
The flow over a circular cylinder at Reynolds number 3900 and Mach number 0.2 was predicted numerically using the technique of large-eddy simulation. The computations were carried out with an O-type curvilinear grid of size of 300 × 300 × 64. The numerical simulations were performed using a second-order finite-volume method with central-difference schemes for the approximation of convective terms. A conventional Smagorinsky and a dynamic k-equation eddy viscosity sub-grid scale models were applied. The integration time interval for data sampling was extended up to 150 vortex shedding periods for the purpose of obtaining a fully converged mean flow field. The present numerical results were found to be in good agreement with existing experimental data and previously obtained large-eddy simulation results. This gives an indication on the adequacy and accuracy of the selected large-eddy simulation technique implemented in the OpenFOAM toolbox.
Explicit equations are developed for the drag coefficient and for the terminal velocity of falling spherical and nonspherical particles. The goodness of fit of these equations to the reported experimental data is evaluated and is compared with that of other recently proposed equations.Accurate design charts for CD and ut are prepared and displayed for all particle sphericities.
The dynamics of a three-dimensional gravity current is investigated by both laboratory experiments and numerical simulations. The experiments take place in a rectangular tank, which is divided into two square reservoirs with a wall containing a sliding gate of width b. The two reservoirs are filled to the same height H, one with salt water and the other with fresh water. The gravity current starts its evolution as soon as the sliding gate is manually opened. Experiments are conducted with either smooth or rough surface on the bottom of the tank. The bottom roughness is created by gluing sediment material of different diameters to the surface. Five diameter values for the surface roughness and two salinity conditions for the fluid are investigated. The mathematical model is based on shallow-water theory together with the single-layer approximation, so that the model is strictly hyperbolic and can be put into conservative form. Consequently, a finite-volume-based numerical algorithm can be applied. The Godunov formulation is used together with Roe's approximate Riemann solver. Comparisons between the numerical and experimental results show satisfactory agreement. The behavior of the gravity current is quite unusual and cannot be interpreted using the usual model framework adopted for two-dimensional and axisymmetric gravity currents. Two main phases are apparent in the gravity current evolution; during the first phase the front velocity increases, and during the second phase the front velocity decreases and the dimensionless results, relative to the different densities, collapse onto the same curve. A systematic discrepancy is seen between the numerical and experimental results, mainly during the first phase of the gravity current evolution. This discrepancy is attributed to the limits of the mathematical formulation, in particular, the neglect of entrainment in the mathematical model. An interesting result arises from the influence of the bottom surface roughness; it both reduces the front velocity during the second phase of motion and attenuates the differences between the experimental and numerical front velocities during the first phase of motion.
The flow of an idealized granular material consisting of uniform smooth, but nelastic, spherical particles is studied using statistical methods analogous to those used in the kinetic theory of gases. Two theories are developed: one for the Couette flow of particles having arbitrary coefficients of restitution (inelastic particles) and a second for the general flow of particles with coefficients of restitution near 1 (slightly inelastic particles). The study of inelastic particles in Couette flow follows the method of Savage & Jeffrey (1981) and uses an ad
hoc distribution function to describe the collisions between particles. The results of this first analysis are compared with other theories of granular flow, with the Chapman-Enskog dense-gas theory, and with experiments. The theory agrees moderately well with experimental data and it is found that the asymptotic analysis of Jenkins & Savage (1983), which was developed for slightly inelastic particles, surprisingly gives results similar to the first theory even for highly inelastic particles. Therefore the ‘nearly elastic’ approximation is pursued as a second theory using an approach that is closer to the established methods of Chapman-Enskog gas theory. The new approach which determines the collisional distribution functions by a rational approximation scheme, is applicable to general flowfields, not just simple shear. It incorporates kinetic as well as collisional contributions to the constitutive equations for stress and energy flux and is thus appropriate for dilute as well as dense concentrations of solids. When the collisional contributions are dominant, it predicts stresses similar to the first analysis for the simple shear case.
Lagrangian-type numerical simulation was carried out on plug flow of cohesionless, spherical particles conveyed in a horizontal pipe. The motion of individual particles contacting each other was calculated using the equations of motion and a modified Cundall model. Forces between particles were expressed by using the Hertzian contact theory. The Ergun Equation was applied to give the fluid force acting on particles in a moving or stationary bed.The flow patterns obtained in the present work appear to be realistic. The wave-like motion of the flow boundary reported previously by several other researchers was observed clearly in the simulation. Also, good agreement was obtained for the relation between the height of the stationary deposited layer and the plug flow velocity. Due to the limitations of computation time, only the case of large particles (ie. d > 10 mm) could be considered here.
It is predicted that 60% of all new energy investments over the next 20 years will be in renewables. The estimation for new hydropower production is 25% of all new renewables primarily due to potential in China, Africa, Latin America and SouthEast Asia. Also in Europe a growth of hydropower production is aimed to achieve emission targets within the European Union by 2050. However, one of the main economic, technical and ecological challenges in future are the deposition, the treatment, and the disturbed dynamics of sediments in river catchments, which reduce the future market potential of hydropower substantially. Due to a lack in awareness of those sedimentological challenges (e.g. lack of process understanding), various huge economical, technical and ecological problems emerge with an increasing relevance for hydropower industry, water management authorities and the society in future. Based on a substantial literature review, (i) legal frameworks and (ii) reservoir management techniques including (iii) process understanding and numerical modelling are addressed in this article. Moreover, the relevant cost-effective aspects of abrasion are worked out for (iv) turbine runners and (v) sediment bypass systems as well as the (vi) the ecological relevance of sediments and possible disturbances are described in this manuscript to open a future discussion on technical opportunities. It was concluded, that all these issues should be addressed within the framework of the overall aim to minimize the costs under consideration of ecological requirements and standards by an improved sediment management in terms of hydro-power use. Moreover, it was stated that trans-and interdisciplinary research is required, to achieve those aims in future.
The state-of-the-art in fluvial hydrodynamics can be examined only through a careful exploration of the theoretical development and applied engineering technology. The book will be primarily focused, since most up-to-date research findings in the field will be presented, on the research aspects that involves a comprehensive knowledge of sediment dynamics in turbulent flows. It begins with the fundamentals of hydrodynamics and particle motion followed by turbulence characteristics related to sediment motion. Then, the sediment dynamics will be described from a classical perspective by applying the mean bed shear approach and additionally incorporating a statistical description for the role of turbulence. The book will finally describe the local scour problems at hydraulic structures and scale models. It is intended to design as a course textbook in graduate / research level and a guide for the field engineers as well, keeping up with modern technological developments. Therefore, as a simple prerequisite, the background of the readers should have a basic knowledge in hydraulics in undergraduate level and an understanding of fundamentals of calculus.
The spatial lag effect on sediment transport around a hydraulic structure is quantified through numerical simulation using a Eulerian-Lagrangian model. The Eulerian-Lagrangian model uses a deterministic approach of bed load motion and stochastic approach of Einstein's concept, which allows for a reasonable quantification of both non-equilibrium and equilibrium bed load transport rates. Numerical simulations are conducted for local scour around a spur dyke and a weir-type structure. As pointed out in previous experimental studies on the one-dimensional problem, Eulerian-Lagrangian simulation reveals an unsaturated bed load in a scour hole around a hydraulic structure. Furthermore, an oversaturated bed load is also found in the deposition region, particularly behind the structure. The validity of the linear adaptation equation is discussed using numerical results, revealing the possibility that the linear adaptation equation does not appropriately represent the existence of the strong spatial lag effect. The present study finds there are two modes in the response of the adaptation length to the unsaturated bed load, which depend on the clear-water scour condition or the live-bed scour condition. Findings of this study will contribute to multi-dimensional sediment transport simulations that consider the spatial lag effect.
In this work, a fully-coupled Computational Fluid Dynamics (CFD) model and Discrete Element Method (DEM) are used to simulate a unidirectional turbulent open-channel flow over the full range of sediment transport regimes. The fluid and particles are computed on separate grids using a dual-grid formulation to maintain consistency and avoid instability issues. The results of coupling the dispersed phase to a multiphase flow solver that uses volume-averaged Navier-Stokes equations are compared to those obtained from coupling through drag to a single flow solver. The current work also examines the applicability and limitations of lumping particles as a representative particle to reduce the cost of simulations. Insight to the impact of different turbulent events to the entrainment of particles is also given. The simulation results of sediment transport from both coupling techniques show good agreement with empirical formulas in the bedload regime, but under-predict sediment transport in the suspended load regime. In the suspended load regime, using partial coupling, the rate of sediment transport was found to be under-predicted as compared to full-coupling. The deviation in results in the suspended load regime was found to increase with increases in the applied shear stress. Both coupling methods revealed the same effect on the friction factor where friction increases in the bedload regime and decreases in the suspended load regime reaching a maximum at the transition between regimes. This result is contrary to past studies which have shown a discrete jump in the friction factor at the transition. Lumping particles as representative particles is shown to reduce the simulation cost by more than a factor of 5 when using a scaling factor of 2. By doing a quadrant analysis on information obtained from particle and flow field results, it was found that most of the particles are entrained by more frequent sweep events.
A coupled solenoidal Incompressible Smoothed Particle Hydrodynamics (ISPH) model is presented for simulation of sediment displacement in erodible bed. The coupled framework consists of two separate modules: (a) granular module, (b) fluid module. The granular module considers a friction based rheology model to calculate deviatoric stress components from pressure. The module is validated for Bagnold flow profile and two standardized test cases of sediment avalanching. The fluid module resolves fluid flow inside and outside porous domain. An interaction force pair containing fluid pressure, viscous term and drag force acts as a bridge between two different flow modules. The coupled model is validated against three dambreak flow cases with different initial conditions of movable bed. The simulated results are in good agreement with experimental data. A demonstrative scenario considering effect of granular column failure under full/partial submergence highlights the capability of the coupled model for application in generalized scenario.
Turbulent pipe flow velocity distribution at high Reynolds numbers is described by Coles' log-wake law for which the wake component is purely empirical. This research innovates Coles' wake law with another log-function, and thus combines the log- and the wake-laws into a single (complete) log-law, for which the von Kármán constant (0.39) is the only fit parameter. Specifically, the symmetrical velocity distribution about the centreline requires a symmetrical eddy viscosity model which is approximated by a quartic polynomial, leading to a complete log-law including the effects of the bottom and top walls as well as their interactions. The complete log-law is confirmed with data from both smooth and rough pipes; it also results in an accurate and explicit friction law for smooth pipe flow. Furthermore, the complete log-law is preliminarily tested with data from channels and boundary layers; the quartic eddy viscosity may be extended for ice-covered river flow in future studies.
This paper presents the results of a large-eddy simulation (LES) of turbulent flow over a channel bed artificially roughened by hemispheres. The Reynolds number of the flow based on the channel depth is 13,680 at a relatively low submergence of 3.42. First- and second-order statistics are compared with corresponding laboratory experiments to validate the LES. The effect of roughness heterogeneity on higher-order statistics is quantified and discussed. The contribution of the dominating turbulent events (i.e., sweeps, ejections) to the Reynolds stress and the anisotropy of turbulence are quantified. Visualizations of the complex three-dimensional turbulence structures reveal the occurrence of a number of different vortex types in the flow. The contribution of turbulence structures to the turbulent kinetic energy and their scaling is assessed through proper orthogonal decomposition. DOI: 10.1061/(ASCE)HY.1943-7900.0000454. (C) 2011 American Society of Civil Engineers.
In the present paper numerical simulations are used to investigate suspended sediment transport and its effect on the dynamics of the turbulent boundary layer. We use an Euler-Euler methodology based on single-phase approach. Large eddy simulation is employed to resolve the large scales of motion, whereas the contribution of the small scales is parametrized by the use of a dynamic Smagorinsky model. In order to account for sediment-induced buoyancy on momentum, a buoyancy term is considered in the three-dimensional Navier-Stokes equations through the use of the Boussinesq approximation. We consider four sediment sizes and the simulations are performed for both one-way and two-way coupling approaches to gain a better description of sediment-turbulence interaction. The level of stratification for each particle size is qualified by the bulk Richardson number which increases by decreasing the grain size. The analysis reveals that the reduction of sediment size produces a larger suspension and sediment concentration in the flow field, due to the concurrence of increased available concentration at the wall and reduced deposition velocity. Comparison of concentration profiles between one-way and two-way coupling clearly shows the remarkable effect of stratification on the velocity and concentration mean profiles. This is particularly true for small sediments which are more likely suspended in the fluid column. In agreement with experimental literature results, our study shows that suspended sediment concentration reduces the von Kàrmàn constant of the velocity profile. The analysis of second order statistics and energy power spectra show turbulent suppression due to stratification effects, in agreement with previous studies. The gradient Richardson number distribution along the channel height demonstrates the increased level of stratification along the fluid column by decreasing the grain size. Momentum and concentration diffusivity are also discussed. The non-dimensional concentration diffusivity compares very well with the Coleman’s experimental data in the range of parameters shared by the two studies. Overall, the results of our study confirm that a single-phase mathematical model is a good candidate to simulate suspended sediment transport. Our study also shows that differences between one-way and two-way coupling approaches are negligible for relatively large sediments, that, on the other hand, are more likely transported according to the bed-load mode. For smaller particles, transported according to the suspension-load mode, the two-way coupling approach reproduces the reduction of turbulence activity already observed in physical experiments.
DualSPHysics is a hardware accelerated Smoothed Particle Hydrodynamics code developed to solve free-surface flow problems. DualSPHysics is an open-source code developed and released under the terms of GNU General Public License (GPLv3). Along with the source code, a complete documentation that makes easy the compilation and execution of the source files is also distributed. The code has been shown to be efficient and reliable. The parallel power computing of Graphics Computing Units (GPUs) is used to accelerate DualSPHysics by up to two orders of magnitude compared to the performance of the serial version.
We study erosion depth and sediment fluxes for wave-induced sheet-flow, and their dependency on grain size and streaming. Hereto, we adopt a continuous two-phase model, applied before to simulate sheet-flow of medium and coarse sized sand. To make the model applicable to a wider range of sizes including fine sand, it appears necessary to adapt the turbulence closure of the model. With an adapted formulation for grain – carrier flow turbulence interaction, good reproductions of measured erosion depth of fine, medium and coarse sized sand beds are obtained. Also concentration and velocity profiles at various phases of the wave are reproduced well by the model. Comparison of sediment flux profiles from simulations for horizontally uniform oscillatory flow as in flow tunnels and for horizontally non-uniform flow as under free surface waves, shows that especially for fine sand onshore fluxes inside the sheet-flow layer increase under influence of progressive wave effects. This includes both the current-related and the wave-related contribution to the period-averaged sheet-flow sediment flux. The simulation results are consistent with trends for fine and medium sized sediment flux profiles observed from tunnel and flume experiments. This study shows that the present two-phase model is a valuable instrument for further study and parameterization of sheet-flow layer processes.
Preface; Nomenclature; Part I. Fundamentals: 1. Introduction; 2. The
equations of fluid motion; 3. Statistical description of turbulence; 4.
Mean flow equations; 5. Free shear flows; 6. The scales of turbulent
motion; 7. Wall flows; Part II. Modelling and Simulation: 8. Modelling
and simulation; 9. Direct numerical simulation; 10. Turbulent viscosity
models; 11. Reynolds-stress and related models; 12. PDF models; 13.
Large-eddy simulation; Part III. Appendices; Bibliography.
Particle-driven gravity currents frequently occur in nature, for instance as turbidity currents in reservoirs. They are produced by the buoyant forces between fluids of different density and can introduce sediments and pollutants into water bodies. In this study, the propagation dynamics of gravity currents is investigated using the FLOW-3D computational fluid dynamics code. The performance of the numerical model using two different turbulence closure schemes namely the renormalization group (RNG)
scheme in a Reynold-averaged Navier-Stokes framework (RANS) and the large-eddy simulation (LES) technique using the Smagorinsky scheme, were compared with laboratory experiments. The numerical simulations focus on two different types of density flows from laboratory experiments namely: Intrusive Gravity Currents (IGC) and Particle-Driven Gravity Currents (PDGC). The simulated evolution profiles and propagation speeds are compared with laboratory experiments and analytical solutions. The numerical model shows good quantitative agreement for predicting the temporal and spatial evolution of intrusive gravity currents. In particular, the simulated propagation speeds are in excellent agreement with experimental results. The simulation results do not show any considerable discrepancies between RNG
and LES closure schemes. The FLOW-3D model coupled with a particle dynamics algorithm successfully captured the decreasing propagation speeds of PDGC due to settling of sediment particles. The simulation results show that the ratio of transported to initial concentration C
o
/C
i
by the gravity current varies as a function of the particle diameter d
s
. We classify the transport pattern by PDGC into three regimes: (1) a suspended regime (d
s
is less than about 16 μm) where the effect of particle deposition rate on the propagation dynamics of gravity currents is negligible i.e. such flows behave like homogeneous fluids (IGC); (2) a mixed regime (16 μm < d
s
<40 μm) where deposition rates significantly change the flow dynamics; and (3) a deposition regime (d
s
> 40 μm) where the PDGC rapidly loses its forward momentum due to fast deposition. The present work highlights the potential of the RANS simulation technique using the RNG
turbulence closure scheme for field scale investigation of particle-driven gravity currents.
We document a new method for including collisional return-to-isotropy in particle velocity distributions calculated by the MP-PIC method for numerical simulation of particle/fluid flows. Mathematically, we include the new method by adding to the transport equation for the particle distribution function (PDF), a Bhatnager, Gross, and Krook (BGK) collision term that causes velocity distributions to relax to isotropic Gaussian distributions. The numerical implementation is by a splitting technique in which we randomly sample from velocity distributions obtained as solutions to the PDF transport equation with just the return-to-isotropy source. Thus, collisions cause numerical particles to scatter in MP-PIC calculations, just as physical particles do in particle/fluid flows. The method is implemented in the Barracuda© code, and two computational examples verify proper implementation of the method and show that more realistic results are obtained in calculations of impinging particle jets. In an appendix, we derive the particle continuum-flow (PCF) equations implied by the MP-PIC method in the collision dominated limit, and we obtain the collisional relaxation time for return-to-isotropy by matching the shear viscosity of the MP-PIC PCF equations, and the kinetic part of the shear viscosity used in PCF equations in the literature.
It is shown that a sphere moving through a very viscous liquid with velocity V relative to a uniform simple shear, the translation velocity being parallel to the streamlines and measured relative to the streamline through the centre, experiences a lift force 81·2 the magnitude of the velocity gradient, and μ and v the viscosity and kinematic viscosity, respectively. The relevance of the result to the observations by Segrée & Silberberg (1962) of small spheres in Poiseuille flow is discussed briefly. Comments are also made about the problem of a sphere in a parabolic velocity profile and the functional dependence of the lift upon the parameters is obtained.
Direct numerical simulations (DNS) of incompressible turbulent channel flows coupled with Lagrangian particle tracking are performed to study the characteristics of ejections that surround solid particles. The behavior of particles in dilute turbulent channel flows, without particle collisions and without feedback of particles on the carrier fluid, is studied using high Reynolds number DNS (Re=12,500). The results show that particles moving away from the wall are surrounded by ejections, confirming previous studies on this issue. A threshold value separating ejections with only upward moving particles is established. When normalized by the square root of the Stokes number and the square of the friction velocity, the threshold profiles follow the same qualitative trends, for all the parameters tested in this study, in the range of the experiments. When compared to suspension thresholds proposed by other studies in the Shields diagram, our simulations predict a much larger value because of the measure used to characterize the fluid and the criterion chosen to decide whether particles are influenced by the surrounding fluid. However, for intermediate particle Reynolds numbers, the threshold proposed here is in fair agreement with the theoretical criterion proposed by Bagnold (1966) [Bagnold, R., 1966. Geological Survey Professional Paper, vol. 422-1]. Nevertheless, further studies will be conducted to understand the normalization of the threshold.
The present paper reports results obtained with image velocimetry to provide new insights into the two-phase nature of sediment-laden flows. The resulting two-phase flow perspective is compared with the traditional mixed-flow (or combined phase) perspective that treats sediment-laden flows essentially as flow of a single fluid. The insights are from flume experiments entailing the use of fully suspended natural sand and neutrally buoyant particles conveyed in a turbulent open channel flow of water. They confirm that suspended particles (irrespective of particle density) may affect a turbulent flow throughout its depth. Suspended particles modify flow turbulence, the main effects quantified being decreases in the bulk water velocity and in the von Kárman constant, while the flow's friction velocity remains approximately constant. Comparison of the results obtained with the two particle densities reveals differences in particle influences on water flow. In the flows conveying sand the characteristics of water and particle movement are strongly coupled, yet distinct; that is, there is a lag in the mean velocity between local water and particle movement, and intensities of water turbulence differ from intensities of particle motion turbulence. These results confirm and extend prior two-phase flow perspectives on suspended-particle transport and indicate the inaccuracies in some assumptions associated with the mixed fluid formulation of suspended-particle transport.
Using a two-phase formulation, the vertical and horizontal momentum equations for sediment are used to obtain the concentration and velocity profiles of a dilute suspension of particles in a 2D uniform flow. Assuming the form of the vertical turbulent intensities and dilute concentrations of sediment, one can solve the equations analytically and compare them with experimental data. No empirical coefficients in the model are tuned to match individual experiments, for which the experimental data cover a large range of particle sizes and densities. The models are shown to accurately predict two experimentally observed but theoretically unexplained phenomena: the increased diffusive flux of large particles, and the measurable velocity lag of particles. The increased diffusion of large particles is shown to originate from the added diffusive nature of the sediment's Reynolds stresses. The horizontal velocity lag of particles is due to an induced velocity, termed the drift velocity, resulting from the correlation of particle concentration with areas of low horizontal velocity fluid.
Fine sediment is carried in suspension by turbulent flow under steady conditions, provided that similar material is present on the bed. An equation is deduced for the variation with depth of the sediment concentration for two-dimensional flow. It is found necessary to take account of the volume occupied by the sediment, this being particularly important near the bed. The result agrees with recent observations by Vanoni (1946). A velocity distribution obtained by Karman, using a linear variation of shear with depth, is generalized by omitting the infinite velocity gradient condition at the bed and is found to be in good agreement with Vanoni's measurements. A slight difference is found between the mean sediment velocity in the direction of flow and that of the water.
A powerful two-color Laser Doppler Anemometer (LDA) system, with direct digital signal processing has been used to measure accurately the longitudinal and vertical velocity components in two-dimensional, fully-developed open-channel flow over smooth beds. The law of the wall and the velocity defect law were re-examined because the log-law has been often applied to open channels without detailed verification. It was found that the log-law can be applied strictly only to the near-wall region. In this region, the von K´rm´n constant &kgr; and the integral constant A are truly universal, having values of κ=0.412 and A=5.29 irrespective of the Reynolds and Froude number. As the Reynolds number becomes larger, the deviation from the log-law cannot be neglected in the outer region. This deviation can be expressed well by Coles’ wake function which involves a Reynolds-number dependent parameter Π. The distributions of eddy viscosity and mixing length were evaluated and found to depend on Π. All the data including the turbulence intensities will offer valuable information for the further understanding of open-channel flow and for the development and testing of calculation methods.
The effect of turbulence on particle concentration fields and the modification of turbulence by particles has been investigated using direct numerical simulations of isotropic turbulence. The particle motion was computed using Stokes’ law of resistance and it was also assumed the particle volume fraction was negligible. For simulations in which the particles do not modify the turbulence field it was found that light particles collect preferentially in regions of low vorticity and high strain rate. For increased mass loading the particle field attenuated an increasing fraction of the turbulence energy. Examination of the spatial energy spectra showed that the fraction of turbulence kinetic energy in the high wave numbers was increased relative to the energy in the low wave numbers for increasing values of the mass loading. It was also found that the turbulence field was modified differently by light particles than by heavy particles because of the preferential collection of the light particles in low‐vorticity, high‐strain‐rate regions. Correlation coefficients between the second invariant of the deformation tensor and pressure showed little sensitivity to increased loading while correlations between enstrophy and pressure were decreased more by the light particles than by the heavy particles for increased mass loading.
The forces on a small rigid sphere in a nonuniform flow are considered from first principles in order to resolve the errors in Tchen's equation and the subsequent modified versions that have since appeared. Forces from the undisturbed flow and the disturbance flow created by the presence of the sphere are treated separately. Proper account is taken of the effect of spatial variations of the undisturbed flow on both forces. In particular the appropriate Faxen correction for unsteady Stokes flow is derived and included as part of the consistent approximiation for the equation of motion.
The distinct element method is a numerical model capable of describing the mechanical behavior of assemblies of discs and spheres. The method is based on the use of an explicit numerical scheme in which the interaction of the particles monitored contact by contact and the motion of the particles modelled particle by particle. The main features of the distinct element method are described. The method is validated by comparing force vector plots obtained from the computer program BALL with the corresponding plots obtained from a photoelastic analysis.
The present paper gives an analysis of fully developed channel flow at Reynolds number of Re=uτδ/ν=4000 based on the friction velocity, uτ, and half the channel height, δ. Since the Reynolds number is high, the LES is coupled to a URANS model near the wall (hybrid LES–RANS) which acts as a wall model. It it found that the energy spectra is not a good measure of LES resolution; neither is the ratio of the resolved turbulent kinetic energy to the total one (i.e. resolved plus modelled turbulent kinetic energy). It is suggested that two-point correlations are the best measures for estimating LES resolution. It is commonly assumed that SGS dissipation takes place at high wavenumbers. Energy spectra of the fluctuating velocity gradients show that this is not true; the major part of the SGS dissipation takes place at low to midrange wavenumbers. Furthermore, the energy spectra of the fluctuating velocity gradients reveals that the accuracy of the predicted velocity gradients at the highest resolved wavenumbers is very poor.
Laboratory experiments show that the propagation and sedimentation patterns of particle-laden gravity currents are strongly influenced by the size of suspended particles. The main series of experiments consisted of fixed-volume releases of dilute mixtures containing two sizes of silicon carbide particles (25 μm and 69 μm mean diameter) within a 6-m flume. Polydisperse experiments involved mixtures of five different particle sizes and variation of the amounts of the finest and coarsest particles. All variables apart from the initial relative proportions of particles were identical in the experiments. The effects of mixing different proportions of fine and coarse particles is markedly non-linear. Adding small amounts of fine sediment to a coarse-grained gravity current has a much larger influence on flow velocity, run-out distance and sedimentation patterns than adding a small amount of coarse sediment to a fine-grained gravity current. The experiments show that adding small amounts of fine particles to a coarse-grained current results in enhanced flow velocities because the fine sediment remains suspended and maintains an excess current density for a much longer time. Thus, the distance to which coarse particles are transported increases substantially as the proportion of fines in the flow is increased. Our experiments suggest that sandy turbidity currents containing suspended fines will be much more extensive than turbidity currents composed of clean sand.
A multiphase particle-in-cell (MP-PIC) method has been developed. This numerical technique draws upon the best of Eulerian/Eulerian continuum models and Eulerian/Lagrangian discrete models. The MP-PIC method uses an accurate mapping from Lagrangian particles to and from a computational grid. While on the grid, continuum derivative terms that treat the particle phase as a fluid are readily evaluated and then mapped back to individual particles. The result of this procedure is a computational technique for multiphase flows that can handle particulate loading ranging from dense to dilute, a distribution of particle sizes and a range of particle materials. The dense particulate model represents separated flows of particles and includes drag exerted by a gas phase, inter-particle stresses, particle viscous stresses and gas pressure gradients. Six problems are presented to demonstrate the MP-PIC method. This MP-PIC method has important applications in fluidized beds (combustion, catalytic cracking), sedimentation, separation and many other granular flows.
We present results of a series of large-scale experiments to measure the coefficient of restitution for 1-m-diameter rocky bodies in impacts with collision speeds up to ∼1.5 m s−1. The experiments were conducted in an outdoor setting, with two 40-ton cranes used to suspend the ∼1300-kg granite spheres pendulum-style in mutual contact at the bottoms of their respective paths of motion. The spheres were displaced up to ∼1 m from their rest positions and allowed to impact each other in normal-incidence collisions at relative speeds up to ∼1.5 m s−1. Video data from 66 normal-incidence impacts suggest a value for the coefficient of restitution of 0.83 ± 0.06 for collisions between ∼1-m-scale spheres at speeds of order 1 m s−1. No clear trend of coefficient of restitution with impact speed is discernable in the data.
A three-dimensional, incompressible, multiphase particle-in-cell method is presented for dense particle flows. The numerical technique solves the governing equations of the fluid phase using a continuum model and those of the particle phase using a Lagrangian model. Difficulties associated with calculating interparticle interactions for dense particle flows with volume fractions above 5% have been eliminated by mapping particle properties to an Eulerian grid and then mapping back computed stress tensors to particle positions. A subgrid particle, normal stress model for discrete particles which is robust and eliminates the need for an implicit calculation of the particle normal stress on the grid is presented. Interpolation operators and their properties are defined which provide compact support, are conservative, and provide fast solution for a large particle population. The solution scheme allows for distributions of types, sizes, and density of particles, with no numerical diffusion from the Lagrangian particle calculations. Particles are implicitly coupled to the fluid phase, and the fluid momentum and pressure equations are implicitly solved, which gives a robust solution.