Numerical prediction of turbidity currents on unsteady sediment-supply

A three-dimensional(3D) numerical model of unstable turbidity currents is developed based on the mechanism of sediment transport and turbulence theory.In this model,numerical simulation of turbidity currents without subsequent supply of muddy water was conducted using the same parameters as were used in the flume experiments.The evolution process of turbidity currents of completely losing supplies observed in the experiment was simulated by the model;validation of the numerical model and the algorithm was conducted.If momentarily interrupted process is regarded as a special case of the gradually interrupted,based on the preceding numerical simulation validity,it is feasible to simulate the motion law of turbidity currents under losing gradually supplies.By this method in this article,the characteristic of sediment-laden flow of losing gradually supplies was obtained,as well as its relationship between front velocity and sediment concentration.     

One-dimensional morphodynamic model for retrogressive erosion based on a sediment entrainment theory at high flow velocity

Retrogressive erosion is a high-speed erosion process that usually occurs during the rapid release of stored water in reservoirs built on sandy rivers.Retrogressive erosion has been utilized in the practice of reservoir sedimentation control,but accurate prediction of the bed deformation process by numerical models has rarely been reported.The current study presents a one-dimensional morphodynamic model for simulating the evolution process of retrogressive erosion induced by high-velocity flows on steep slopes.The governing equations apply a Cartesian coordinate system with a vertically oriented z axis.The bed surface gradient and friction terms in the flow equations include correction factors to take account of the effects of high slope on flow movement.The net vertical sediment flux term in the sediment transport and bed deformation equations is calculated using an equation of erosion velocity.Particularly,this equation is based on an empirical relation between the sediment entrainment rate and the Shields parameter in contrast to the traditional sediment transport capacity,and the critical Shields parameter is modified by taking into account the permeability of the sediment layer and the stability of particles on a slope.The feedback of scoured sediment on the flow movement is considered by additional terms in the governing equations.Flume experiments of retrogressive erosion in literature were simulated to validate the model.The temporal variations of the longitudinal profiles of the free surface and channel bed and the sediment transport rate were well predicted.The algorithm calculating sediment entrainment in the proposed model also was validated for an experiment measuring entrainment rate from the literature.More importantly,it was found that the morphodynamic model using the sediment transport capacity equation predicts the trend of cumulative erosion contrary to the measurements,while results of the proposed model can follow a similar trend with the observed data in the retrogressive erosion process.     

An analytical study on turbulence with mixed-flow model and two-phase model

Suspended sediment is carried by turbulent water flows in rivers.Traditional sediment-laden flow analysis treats the suspension as a mixed liquid,and recent two-phase flow model enables separate velocity measurement of the two coupling phases.A simplified theoretical analysis was presented to discuss the differences between the two models in reporting turbulence intensity in experimental research.The turbulence intensity of the mixture is lower than the weighted average of those of the two phases in mixed-flow experiments.The mixture’s turbulence intensity becomes higher than the average of the two phases in two-phase experiments due to the presence of velocity lag.The same set of data may lead to either an underestimation or an overestimation of actual turbulence levels when different models are used.     

NUMERICAL STUDY ON THE MIXING OF UNSORTED SEDIMENT PARTICLES DISCHARGED INTO A CROSS-FLOW BY MULTIPHASE PARTICLE-IN-CELL （MP-PIC） METHOD

The mixing characteristics of dredged sediments of variable size discharged into cross-flow are studied by an Eulerian-Lagrangian method. A three-dimensional (3D) numerical model has been developed by using the modified k-ε parameterization for the turbulence in fluid phase/water and a Lagrangian method for the solid phase/sediments. In the model the wake turbulence induced by sediments has been included as additional source and sink terms in the k-ε model; and the trajectories of the sediments are tracked by the Lagrangian method in which the sediment drift velocities in cross-flow are computed by a multiphase particle-in-cell (MP-PIC) method and the diffusion process is approximated by a random walk model. The hydrodynamic behavior of dumped sediment cloud is governed by the total buoyancy on the cloud, the drag force on each particle and velocity of cross-flow. The cross-flow destroys more or less the double vortices occurred in stagnant ambience and dominates the longitudinal movement of sediment cloud. The computed results suggest satisfactory agreement by comparison with the experimental results of laboratory.     

THREE DIMENSIONAL NUMERICAL MODELLING OF FLOW AND SEDIMENT TRANSPORT IN RIVERS

The 3D numerical model, ECOMSED (open source code), was used to simulate flow and sediment transport in rivers. The model has a long history of successful applications to oceanic, coastal and estuarine waters. Improvements in the advection scheme, treatment of river roughness parameterization and shear stress partitioning were necessary to reproduce realistic and comparable results in a river application. To account for the dynamics of the mobile bed boundary, a model for the bed load transport was included in the code. The model reproduced observed secondary currents, bed shear stress distribution and erosion-deposition patterns on a curved channel. The model also successfully predicted the general flow patterns and sediment transport characteristics of a 1-km long reach of the River Klar?lven, located in the north of the county of V?rmland, Sweden.     

Numerical analysis of synthetic granulate deposition in a physical model study

The current study focuses on the application of a three-dimensional numerical model for the prediction of morphological bed changes. The sediment deposition in a reservoir during a 10-year-flood was investigated and the results of the simulation were validated with data derived from a physical model study. Because of the small grain sizes in the prototype, synthetic granulate was used in the physical model. The numerical computation domain was a reproduction of the physical model, including the grain sizes and the density of the particles, in order to ensure comparability. The CFD code SSIIM, which solves the RANS-equations in three-dimensions, was used for the simulations. The sediment transport in SSIIM is divided into suspended sediment transport, computed by solving the convection-diffusion equation, and bed-load transport, calculated by an empirical formula. The results of the numerical simulation correspond well to the results of the physical model study. The simulated location and the pattern of the sediment deposition in the reservoir are an accurate representation of the observed distribution in the physical model.     

One-dimensional numerical simulation of non-uniform sediment transport under unsteady flows

One-dimensional numerical models are popularly used in sediment transport research because they can be easily programmed and cost less time compared with two- and three-dimensional numerical models. In particular, they possess greater capacity to be applied in large river basins with many tributaries. This paper presents a one-dimensional numerical model capable of calculating total-load sediment transport. The cross-section-averaged sediment transport capacity and recovery coefficient are addressed in the suspended load model. This one-dimensional model, therefore, can be applied to fine suspended loads and to hyperconcentrated flows in the Yellow River. Moreover, a new discretization scheme for the equation of unsteady non-uniform suspended sediment transport is proposed. The model is calibrated using data measured from the Yantan Reservoir on the Hongshui River and the Sanmenxia Reservoir on the Yellow River. A comparison of the calculated water level and river bed deformation with field measurements Shows that the improved numerical model is capable of predicting flow, sediment transport, bed changes, and bed-material sorting in various situations, with reasonable accuracy and reliability.     

A two-phase model for fast geomorphic shallow flows

The paper introduces a 2D shallow water model based on a two-phase formulation for the analysis of fast geomorphic transients occurring in the context of river morphodynamics.Mass and momentum conservation principles are separately imposed for both phases.The model naturally accounts for non-equilibrium solid transport,since neither instantaneous adaptation hypothesis nor any lag equation is employed to represent sediment dynamics.The hyperbolic character of the proposed model is shown to be preserved independently on the flow conditions.Results from numerical simulations of both 1D and 2D test-cases are compared with literature experimental data and with available numerical solutions.     

General velocity formula of boundary layer above mobile sediment bed induced by asymmetric waves

Sediment movement in the wave boundary layer above a mobile sediment bed is complex.A velocity formula for the boundary layer is proposed for sheet flow induced by asymmetric waves above a mobile sediment bed.The formula consists of a free stream velocity and a defect function which contains a phase-lead,boundary layer thickness and mobile sediment bed.Phase-lag of sediment movement is considered in the formula for the mobile sediment bed.The formula needs six dependent variables about asymmetric wave and sediment characteristics.Asymmetry effects on parameters(orbital amplitude,roughness height,bed shear stress,and boundary layer thickness)are properly considered such that the formula can yield velocity differences among onshore,offshore,acceleration,and deceleration stages.The formula estimates the net boundary layer velocity resulting from the mobile sediment bed and asymmetric boundary layer thickness.In addition,a non-constant phase-lead also contributes to the net boundary layer velocity in asymmetric oscillatory sheet flow.Results of the formula are as good as that of a two-phase numerical model.Sheet flow transport induced by asymmetric waves,and the offshore net sediment transport rate with a large phase-lag under velocity-skewed waves,can be adequately estimated by the formula with a power sediment concentration function.     

Numerical simulation of tidal current and erosion and sedimentation in the Yangshan deep-water harbor of Shanghai

Yangshan near-shore sea area is the multi-island and multi-channel area with strong flow velocity and high suspended sediment concentration. Based on the characteristics of tidal currents, waves, and sediment in the Yangshan area, a two-dimensional numerical model of tidal currents, sediment transport, and sea bed deformation is developed. In the model, the effects of tidal currents and wind waves on sediment transport are considered. According to characteristics of the study area, unstructured grids are applied to fit the boundaries of the near-shore sea area. The results show that the calculated values are in good agreement with the measured data. The field of tidal currents, suspended sediment concentrations, and the deformation of the seabed can be successfully simulated.     

2D NUMERICAL SIMULATION OF FLOOD AND FLUVIAL PROCESS IN THE MEANDERING AND ISLAND-BRAIDED MIDDLE YANGTZE RIVER

The characteristics of water flow and sediment transport in a typical meandering and island-braided reach of the middle Yangtze River is investigated using a two-dimensional （2D） mathematical model. The major problems studied in the paper include the carrying capacity for suspended load, the incipient velocity and transport formula of non-uniform sediment, the thickness of the mixed layer on the riverbed, and the partitioning of bed load and suspended load. The model parameters are calibrated using extensive field data. Water surface profiles, distribution of flow velocities, riverbed deformation are verified with site measurements. The model is applied to a meandering and island-braided section of the Wakouzi-Majiazui reach in the middle Yangtze River, which is about 200 km downstream from the Three Gorges Dam, to study the training scheme of the navigation channels. The model predicts the processes of sediment deposition and fiver bed erosion, changes of flow stage and navigation conditions for the first 20 years of impoundment of the Three Gorges Project.     

Simulation of dam-break waves on movable beds using a multi-stage centered scheme

This paper presents the application of the multi-stage first-order centered scheme GMUSTA to solve a two-phase flow model with four equations for simulating dam-break floods without and with sediment transport.Computation of generalized Riemann invariants can be particularly complex and costly in simulating dam-break floods with sediment transport.GMUSTA numerical scheme,which does not require complete knowledge of the eigenstructure of the hyperbolic mathematical model,offers a suitable and attractive option.The quality of the dam-break flood simulations with GMUSTA scheme is verified by comparing the results against laboratory tests and some experimental data available in the literature,on fixed and mobile bed conditions,with different bed materials and flush or stepped bottoms.The numerical results reproduce quite well the experimental evidence,proving that the model is capable of predicting the temporal evolution of the free-surface and the bed.The GMUSTA scheme,which is not only simple to implement but also both accurate and computationally efficient,is proposed as an appropriate tool for integrating non-equilibrium sediment-transport models.     

Three-dimensional saltating processes of multiple sediment particles

The purpose of this study was to investigate the interacting mechanism between the saltating particles near a channel bed. A three-dimensional real-time flow visualization technique was developed to measure the interparticle collision behaviors during the saltating process. Based on the experimental data, the distribution of the collision points was found to be symmetric. This confirms the assumption that the projections of the collision points onto the reasonable plane are uniformly distributed. A three-dimensional saltating model was also developed. This model produced satisfactory results. The model is able to simulate the continuous saltating trajectories of several particles. The simulated dimensionless saltating height, longitudinal and vertical saltation velocity components were found to increase as the dimensionless particle diameter and the dimensionless flow transport capacity parameter increase, while the simulated lateral saltation velocity component varies inversely with the dimensionless flow transport capacity parameter. A regression equation for the bed load transport rate was also obtained.     

Three-dimensional modeling of pollutants transportation in the flow field around a spur dyke

Pollutants are carried by sediment-laden flow dissolved in water or adsorbed on sediment particles. A transient three-dimensional model based on a compressible VOF(volume of fluid) method was developed to simulate the transport of dissolved and particulate pollutants.VOF is a numerical technique for acquiring and tracking the free surface of water flow.Local scouring,deposition and re-suspension were simulated and the processes of adsorption and desorption of pollutants on suspended sediment were analyzed.A series of experiments and numerical simulations were performed to study the transportation and dispersion of pollutants in the flow around a non-submerged spur dyke in a straight flume of rectangular shape.The simulation results agreed well with the experimental results.A certain volume of pollutants solution was released into the flow at upstream of the spur dyke.The concentration reduced with time.The concentration reduction was slower in the circumfluence zone than in the main flow.The ratio of adsorption to desorption coefficients was different for pollutants on suspended sediment with different diameter.The peak concentration of dissolved pollutants increased with the ratio of the adsorption to the desorption coefficients.The angle of the spur dyke affected the peak concentration around the dyke.The effect of the angle on dissolved pollutants decreased with the ratio of adsorption to desorption coefficients.The adsorption and desorption coefficients,as well as the saturated adsorption capacity had no effect on the concentration of particulate pollutants.     

Resonance vibration approach in soil densification: laboratory experiences and numerical simulation

This paper describes the improvement effect and mechanism of strengthening a liquefied sand foundation using the cross-vibration wing resonance method,through an indoor model test and numerical simulation.The results obtained from the model test showed that a vertical drainage tube was formed during vibration compaction,and finally a crater with a depth of 40 mm and a radius of 150 mm was formed with sloping sides.The sand layer obtained a good improvement effect after resonance vibration,especially in the middle-lower sand deposit.The variation in excess pore water pressure showed different behavior in three stages of the vibration process,and the value after treatment was less than before with a decrease of 18.81%.The vibration energy in the horizontal direction gradually decreased to zero,however the absorption of vibration energy of the soil presented obvious nonuniformity along the depth direction.The results of the numerical simulation were similar to the model test results,including the scope and variation of pore water pressure,and the ground settlement after treatment.     

Well-balanced numerical modelling of non-uniform sediment transport in alluvial rivers

The last two decades have witnessed the development and application of well-balanced numerical models for shallow flows in natural rivers.However,until now there have been no such models for flows with non-uniform sediment transport.This paper presents a 1D well-balanced model to simulate flows and non-capacity transport of non-uniform sediment in alluvial rivers.The active layer formulation is adopted to resolve the change of bed sediment composition.In the framework of the finite volume Slope Llmiter Centred(SLIC) scheme,a surface gradient method is incorporated to attain well-balanced solutions to the governing equations.The proposed model is tested against typical cases with irregular topography,including the refilling of dredged trenches,aggradation due to sediment overloading and flood flow due to landslide dam failure.The agreement between the computed results and measured data is encouraging.Compared to a non-well-balanced model,the well-balanced model features improved performance in reproducing stage,velocity and bed deformation.It should find general applications for non-uniform sediment transport modelling in alluvial rivers,especially in mountain areas where the bed topography is mostly irregular.     

Behavior of large post-liquefaction deformation in saturated Nanjing fine sand

Laboratory tests on the large post-liquefaction deformation of saturated Nanjing fine sand were performed by using a hollow cylinder apparatus. The stress-strain responses and the characteristics of excess pore water pressure after liquefaction were studied. It was found that the relationship between deviatoric stress and axial strain presented a sigmoid curve, and there was a good linearity relationship between normalized pore water pressure and deviatoric stress. On this basis, a constitutive model of stress-strain responses and a dissipation model of excess pore water pressure were established. It was found that the results predicted by the two models were in good agreement with the experimental data. The influence of relative densities and confi ning pressure on the characteristics of liquef ied soil were studied. The results showed the relative densities and initial effective confining pressure all had an important influence on the stress-strain responses of liquefi ed saturated Nanjing fine sand. However, the dissipation model of excess pore water pressure after liquefaction was only affected by the confining pressure.     

Physical and coupled fully three-dimensional numerical modeling of pressurized bottom outlet flushing processes in reservoirs

Sediment deposition in reservoirs is an important research topic in engineering practice. Reservoir sedimentation has the potential to affect ood levels, drainage for agricultural land, pump station and hydropower operation as well as navigation. This paper describes the development of a coupled fully three-dimensional (3D) numerical model for the prediction of the local sediment ushing scour upstream of the bottom outlet. The presented numerical model solves the Navier-Stokes equations in conjunction with the k- turbulence model which includes both sediment transport and hydrodynamic parameters. The proposed coupled fully 3D numerical model is used to simulate experimental tests based on non-cohesive sediment. The geometric features of the scour hole (temporal and spatial hole devel- opment) upstream of the bottom outlet were reasonably well predicted compared to the experimental data. Furthermore, the velocity eld upstream of the bottom outlet was in good agreement with mea- surements. The proposed numerical model for bottom outlet ushing was, therefore, validated because of its ability to accurately predict the scour hole development during the ushing process. The proposed numerical model can be considered reliable provided that the model is correctly calibrated and set up to re ect the conditions of a particular case study.     

Bedload resistance in supercritical flow

The movement of bedload in subcritical flow produces additional roughness as compared to flow in a rigid bed. The magnitude of this bed load roughness is proportional to the thickness of the sediment layer moving along the bed, the particle size and the sediment concentration. In a supercritical flow, however, further resistance is expected due to the momentum absorption by the high flow velocity. In this study the effect of sediment movement on the flow resistance in supercritical flow was experimentally investigated. The experiments included flows over smooth and rough beds carrying sediment of mean diameters D50=2.80, 5.42 and 7.06 mm in a rigid rectangular channel. The results show that the sediment transport may increase the friction factor by up to 90% and 60% in smooth and rough beds, respectively. Bedload extracts its momentum from the flow, which causes a reduction of near bed flow velocity and steeper velocity gradient near the bed resulting in an increase in shear velocity as well as in roughness height. The increase in friction factor is directly related to bedload concentration and particle size.     

DEPTH-AVERAGED 2-D CALCULATION OF TIDAL FLOW,SALINITY AND COHESIVE SEDIMENT TRANSPORT IN ESTUARIES

A depth-averaged 2-D numerical model for unsteady flow, salinity and cohesive sediment transport in estuaries is established using the finite volume method on the non-staggered, curvilinear grid. The convection terms are discretized by upwind schemes, the diffusion terms are by the central difference scheme, and the time derivative terms are by the three-time-level implicit scheme. The coupling of flow velocity and water level in the 2-D shallow water equations is achieved by the SIMPLEC algorithm with the Rhie and Chow‘s momentum interpolation method. The sediment model calculates the settling, deposition, erosion and transport of cohesive sediment, taking into account the influence of sediment size, sediment concentration, salinity and turbulence intensity on the flocculation of cohesive sediment. The flow model is first tested against the measurement data in the Tokyo Bay and San Francisco Bay, showing good agreements. And then, the entire model of flow, salinity and sediment transport is verified in the Gironde Estuary. The water elevation, flow velocity, salinity and sediment concentration are well predicted.