Vertical Distribution Of Sediment Concentration Research Articles

Application of Hausdorff fractal derivative to the determination of the vertical sediment concentration distribution

The Rouse formula and its variants have been widely used to calculate the steady-state vertical concentration distribution for suspended sediment in steady sediment-laden flows, where the diffusive flux is assumed to be Fickian. Turbulent flow, however, exhibits fractal properties, leading to non-Fickian diffusive flux for sediment particles. To characterize non-Fickian dynamics of suspended sediment, the current study proposes a Hausdorff fractal derivative based advection-dispersion equation (HADE) model, where the Fickian diffusive flux in the Rouse model is replaced by a fractal derivative re-scaled using a constant diffusivity. The order of the Hausdorff fractal derivative is designed to characterize the influence of the multi-fractal turbulence structure on sediment diffusion. Applications show that the HADE model, with the analytical solution expressed using a stretched exponential function, can accurately describe the observed vertical concentration profiles for suspended sediment with different sizes. This improvement well captures the non-exponential decay of the vertical sediment concentration in turbulent flow. Further analyses of measured sediment concentration profiles reveal that the Hausdorff fractal order decreases with the Rouse parameter, which describes the stronger impact of turbulent flow and a more uniform sediment concentration profile for smaller particles. Model comparisons also show that the HADE model provides better performance in describing the sediment concentration profiles than the improved Rouse formula and the standard fractional derivative advection-dispersion equation (FADE), which either under- or over-estimates vertical displacement of sediment particles, likely due to coherent turbulent structures.

Application of homotopy analysis method to the determination of vertical sediment concentration distribution with shear-induced diffusivity

Application of homotopy analysis method to the determination of vertical sediment concentration distribution with shear-induced diffusivity

Laboratory measurements of the fall velocity of fine sediment in an estuarine environment

The study of the fall velocity variation of fine sediment in estuarine areas plays an important role in determining how various factors affect the flocculation process. Previous experimental studies have focused solely on the relation between the median fall velocity and influencing factors, while in the current study, the variation of the fall velocity in quiescent water also was examined. The experimental results showed that the vertical distribution of sediment concentration was more uneven, and larger variations occurred earlier during the settling process under higher salinity and/or sediment concentration conditions. The fall velocity initially increased then decreased over time, peaking at ∼20 min after settling began, and stabilizing at a value similar to that in freshwater, regardless of the initial sediment concentration and salinity combinations. Along the water depth, the fall velocity increased monotonically with a gradually decreasing gradient. The median fall velocity increased then decreased with increased salinity. The salinity at which the peak fall velocity occurred depended on the initial sediment concentration. The relation between the median fall velocity and initial sediment concentration displayed an obvious two-stage pattern (i.e., accelerated flocculation and decelerated, hindered settling) at higher salinities; whereas the maximum median fall velocity was observed at two consecutive sediment concentration values under lower salinity conditions. Finally, an empirical equation estimating the median fall velocity of cohesive fine sediment was formulated, incorporating the effects of both salinity and sediment concentration.

Vertical Distribution of Sediment Concentration in Offshore Waters

Li, C.; Fu, X.; Xiao, Q.; Pan, X., and Cao, H., 2018. Vertical distribution of sediment concentration in offshore waters. In: Liu, Z.L. and Mi, C. (eds.), Advances in Sustainable Port and Ocean Engineering. Journal of Coastal Research, Special Issue No. 83, pp. 167–171. Coconut Creek (Florida), ISSN 0749-0208.The existing formulae of vertical distribution of sand concentration are difficult to integrate. Based on the formula of vertical distribution of the flow velocity obtained in the previous study and the suspended sediment diffusion equation in equilibrium, a formula of the distribution of suspended sediment is deduced. It can effectively avoid the phenomena that the Rouse formula equals zero at the water surface. The field measurement data of Jiangsu Sea is used to verify and analyze the deuced formula. And results show that it has a high accuracy and it solve the difficulties caused by lack of data in engineering, such as only the sediment concentration on the surface is given.

Distribution of sediment concentration in debris flow using Rényi entropy

Debris flow is a destructive natural phenomenon that normally occurs in mountainous regions or steeply sloping areas. Its destructive force is so high that whatever comes in its way is obliterated. It is therefore difficult to collect field observations of debris flow. This study developed a model of the vertical distribution of sediment concentration in debris flow by maximizing Rényi entropy. The model contains a parameter, called entropy parameter, which is a combination of Lagrange multipliers and has a physical justification. An expression for the equilibrium sediment concentration is also developed, and is found to be a function of the entropy parameter and an entropy index. The proposed model is validated with experimental data and is compared with other entropy-based models reported in the literature. It is observed that the prediction accuracy of the proposed models is superior to that of the other models. Errors, namely relative error and relative root-mean-squared error, are computed and are reported in the paper in support of the derived model.

Vertical Sediment Concentration Distribution in High-Concentrated Flows: An Analytical Solution Using Homotopy Analysis Method

Transport of suspended sediment in open channel flow has an enormous impact on real life situations, viz. control and management of reservoir sedimentation, geomorphic evolution such as dunes, rivers, and coastlines etc. Transport entails advection and diffusion. Turbulent diffusion is governed by the concept of Fick’s law, which is based on the molecular diffusion theory, and the equation that represents the distribution of sediment concentration is the advection-diffusion equation. The study uses the existing governing equation which considers different phases for solid and fluid, and then couples the two phases. To deal with high-concentrated flow, sediment and turbulent diffusion coefficients are taken to be different from each other. The effect of hindered settling on sediment particles is incorporated in the governing equation, which makes the equation highly non-linear. This study derives an explicit closed-form analytical solution to the generalized one-dimensional diffusion equation representing the vertical sediment concentration distribution with an arbitrary turbulent diffusion coefficient profile. The solution is obtained by Homotopy Analysis Method, which does not rely on the small parameters present in the equation. Finally, the solution is validated by comparing it with the implicit solution and the numerical solution. A relevant set of laboratory data is selected to check the applicability of the model, and a close agreement shows the potential of the model in the context of application to high-concentrated sediment-laden open channel flow.

Simplified Entropic Model for the Evaluation of Suspended Load Concentration

Suspended sediment concentration is a key aspect in the forecasting of river evolution dynamics, as well as in water quality assessment, evaluation of reservoir impacts, and management of water resources. The estimation of suspended load often relies on empirical models, of which efficiency is limited by their analytic structure or by the need for calibration parameters. The present work deals with a simplified fully-analytical formulation of the so-called entropic model in order to reproduce the vertical distribution of sediment concentration. The simplification consists in the leading order expansion of the generalized spatial coordinate of the entropic velocity profile that, strictly speaking, applies to the near-bed region, but that provides acceptable results also near the free surface. The proposed closed-form solution, which highlights the interplay among channel morphology, stream power, secondary flows, and suspended transport features, allows reducing the needed number of field measurements and, therefore, the time of field activities. Its accuracy and robustness were successfully tested based on the comparison with laboratory data reported in literature.

Hydrodynamic interaction in suspended sediment distribution of open channel turbulent flow

In the present study, a theoretical model is proposed to predict the vertical distribution of suspended sediment in open channel turbulent flow. We derive our mathematical model based on the six prominent hydrodynamic mechanisms, which are upward sediment flux due to the turbulent diffusion, downward gravitational settling of the sediment, hindered settling phenomenon, secondary current, fluid induced lift force on the suspended particles and the gradient of Reynolds normal stress of the suspended sediment. The importance of the hydrodynamics is described by the changes of suspended sediment concentration profile in terms of the particle-flow interaction caused by those mechanisms. We also address the significance of the co-existence of those mechanisms for estimating the suspended sediment concentration profile. The present model agrees satisfactorily with a wide spectrum of experimental data in available literature. Unlike the previous researchers, we select a broad range of previously published models of vertical sediment concentration distribution for comparison analysis, and the proposed model shows better prediction accuracy which is confirmed by error analysis.

Calculation Method about Vertical Distribution of Saturated Sediment Concentration Based on Exchange Equilibrium

Diffusion theory is the leading one which is used to study the vertical distribution of sediment concentration. And diffusion coefficient is a key parameter to determine the vertical distribution of suspended sediment. First of all, the calculation methods are introduced based on the momentum transfer theory and fluctuating velocity. According to the sediment equation of exchange equilibrium in vertical, the new expression is obtained for sediment diffusion coefficient and the vertical distribution of sediment concentration. By the flume experimental data and field data in natural river, the difference is analyzed among the different expressions.

Experiment of Suspended Load with Hyperconcentration in Rectangle Open Channel

In view of the abnormal phenomenon that a flood peak increased in August 2004 and July 2005 along the lower Yellow River, the experiments of this abnormal phenomenon is studied. It is found that the flood increase was due to the decrease the channel roughness in the propagation of high concentrated flood carrying the extra fine sediment which was discharged from xiaolangdi reservoir. Experiments with hyper-concentration flowing over the rough beds prove that the resistance of the flow may be considerably reduced by suspended sediment. Especially in hyper-concentration, the phenomenon of drag-reducing is more obvious when the sediment contents exceed the flocculation sediment contents. It has the significant value for the flood control and flood prediction of hyper-concentration. It is found that the location of the maximum velocity appears below free surface by a series of experiments on velocity distribution and the distribution of sediment concentration in open channel flows. The classic log law and exponential law can not meet the command of experiment. Because the vertical distribution of sediment concentration is dependent on the velocity distribution, based on the diffusion theory, the deriving equation about the distribution of sediment concentration is got according the corrected the equation of velocity distribution. The results indicate that the deriving equation in this paper is well coincident with those observed data in open channel. The equation has important application value.

Fluvial hydraulics of hyperconcentrated floods in Chinese rivers

AbstractHyperconcentrated floods, with sediment concentrations higher than 200 kg/m3, occur frequently in the Yellow River and its tributaries on the Loess Plateau. This paper studies the fluvial hydraulics of hyperconcentrated floods by statistical analysis and comparison with low sediment concentration floods. The fluvial process induced by hyperconcentrated floods is extremely rapid. The river morphology may be altered more at a faster rate by one hyperconcentrated flood than by low sediment concentration floods over a decade. The vertical sediment concentration distribution in hyperconcentrated floods is homogeneous. The Darcy–Weisbach coefficient of hyperconcentrated floods varies with the Reynolds number in the same way as normal open channel flows but a representative viscosity $h\ +\ {{2R} \over {3U}}\tau _B$ is used to replace the viscosity, η. If the concentration is not extremely high and the Reynolds number is larger than 2000, the flow is turbulent and the Darcy–Weisbach coefficient for the hyperconcentrated floods is almost the same as low sediment concentration floods. Serious channel erosion, which is referred to as ‘ripping up the bottom’ in Chinese, occurs in narrow‐deep channels during hyperconcentrated floods. However, in wide‐shallow channels, hyperconcentrated floods may result in serious sedimentation. Moreover, a hyperconcentrated flood may cause the channel to become narrower and deeper, thus, reducing the flood stage by more than 1 m if the flood event lasts longer than one day. The fluvial process during hyperconcentrated floods also changes the propagation of flood waves. Successive waves may catch up with and overlap the first wave, thus, increasing the peak discharge of the flood wave during flood propagation along the river course. Copyright © 2009 John Wiley & Sons, Ltd.

Vertical distribution of sediment concentration

A simple formula is proposed to predict the vertical distribution of a suspended load concentration in a 2D steady turbulent flow. The proposed formula significantly improves the well-known Rouse formula where sediment concentration has an infinitely large value at the channel bottom and a zero value at the water surface. Based on this formula and the logarithmic velocity profile, a theoretical elementary function for the transport rate of a suspended load is developed. This equation improves the Einstein equation in which the unit-width suspended sediment discharge must be solved by numerical integration and a contradiction between the lower limit of the integral and that of velocity distribution exists.

Sediment-copper distributions in hyper-concentrated turbulent solid-liquid system

This study presents a special problem on vertical distribution for sediment and copper in hyper-concentrated turbulent solid-liquid system that is essentially different from the ordinary low-concentrated turbulent system. A resonance type turbulent simulation equipment is used for the experimental study in which a vertically uniform turbulent field of the mixture of loess and water is produced in a testing cylinder with a grille stirrer that moves up and down harmoniously with varying vibration frequencies. In order to compare the variations of the vertical profiles of sediment and copper in low- and hyper-concentrated solid-liquid system, different scenarios for input sediment content ranging from 5 to 800 kg/m 3 was considered in the experimental studies. It was found that solids copper content increases with input sediment content, S 0, and reaches its peak as S 0 goes to 10 kg/m 3 and then decreases rapidly with increasing input sediment content. Such a behavior is possibly resulted from the joint effect of the specific adsorption of copper on loess, precipitation of carbonate and hydroxide of copper due to high carbonate content in the loess and the so-called “particulate concentration effect” due to the present of the sediment variation in water. The vertical sediment concentration distribution resulted from the uniform turbulence is generally uniform, but slight non-uniformity does occur as sediment concentration exceeds certain value. However, the vertical concentration distributions of soluble copper seem not to be affected much by the variation of sediment concentrations.

Experimental Study on Diversion and Discharge of Suspended Load in a Headrace

We are proposing a new sediment removal system using existing headraces as a countermeasure against reservoir sedimentation. This is a method in which sediments which flowed into the headrace are removed and discharged from the large density sediment layer at the bottom of the pipe flow before they reach the turbine. In order to rationally design the bypass system, vertical sediment concentration distribution and diversion ratios of sediment at the diversion pipe have been studied experimentally. In this paper the formula of vertical sediment concentration distribution is expressed under the conditions in which the experiment was carried out and also it is shown that the shape of the diversion point we proposed efficiently separates sediment from turbid water.

現地遡上域の岸沖漂砂特性

Using a vertical array of four streamer-type traps, the on-offshore sand transport rates were measured in the swash zone on three beaches. At the same time, water velocity and water level were measured. The vertical distribution of sediment concentration was obtained from the measurements. Concentration of onshore sediment transport was uniform from bottom to the upper part. The corresponding distribution for the offshore transport rate indicated that the sand transport was concentrated in the bottom layer.

Drift Velocity Concept for Sediment-Laden Flows

The vertical distribution of suspended sediment concentration in open channel flows is usually described by the advection-diffusion equation. Hence, only the mechanisms of advection and diffusion affect the movement of sediment particles. However, recent publications show that the equation could not describe fully the sediment concentration distribution in open channels. A new model for particle migration in sediment-laden turbulent flow is presented. The model assumes there is an additional mechanism influencing the particle movement in sediment-laden flows. A new mechanism, which is called the drift, acts independently of advection and turbulent diffusion. Based on all three mechanisms, a new equation for the concentration distribution is derived. The equation describes the vertical distribution of sediment concentration more accurately than the advection-diffusion equation.

Transitional sediment concentration profiles

An important problem of the theory of nonequilibrium sediment transport is shown in Figure 1. It arises when a fully developed, steady, two-dimensional turbulent stream of clean water flowing over a rigid apron moves over a flat erodible bed and starts interacting with the cohesionless uniform sand of the bed. Beginning at the edge of the erodible bed, sediment particles commence diffusion into the bulk of the turbulent flow, making the concentration of the suspended solids increase in the downstream direction up to a distance where the vertical sediment concentration distribution becomes invariant.

Turbulent Structure of Open Channel Flows with Sudden Change in Bottom Roughness

Before and behind the bed protection works in natural rivers, the bed roughness abruptly changes from smooth to rough and rough to smooth. This paper deals with the water surface profile and turbulent structure of open channel flows with sudden change in bottom roughness experimentally and theoretically. Changes in vertical distribution of sediment concentration under the fully suspended condition are also discussed. The transition of flow depth was found to be mainly depend on the bed slope and classified into three types of flow patterns. In the downstream reach after roughness change, the velocity and turbulent Property distributions vary with development of the internal boundary layer, in w hich the transfer of turbulent energy by convection and vertical diffusion is dominant factor in the turbulent energy budget. The calculated results of the k-e and sediment transport models agree well with the experimental ones.

Sediment Suspension in Turbulent Pipe Flow

An analytical model of nonhomogenous low-concentration sediment suspension in turbulent flow of a liquid in a pipe is developed from the generalized, two-dimensional continuity-diffusion equation for suspended sediment. The equation is solved for the case in which the radial and azimuthal sediment fluxes are everywhere separately in balance, to yield a relation between the radial and azimuthal diffusion coefficients. The continuity equation is then solved for the case of homogeneous, isotropic diffusivity. The predicted exponential vertical distribution of sediment concentration was compared with results from five experiments in which concentration distributions were measured along seven radii. The experimental data were found to be in excellent conformity with the analytical results. The turbulent diffusion coefficient for sediment was found to be about 50% greater than that for momentum.