THE STUDY ON THREE-DIMENSIONAL MATHEMATICAL MODEL OF RIVER BED EROSION FOR WATER-SEDIMENT TWO-PHASE FLOW

Based on the tensor analysis of water-sediment two-phase how, the basic model equations for clear water flow and sediment-laden flow are deduced in the general curve coordinates for natural water variable-density turbulent how. Furthermore, corresponding boundary conditions are also presented in connection with the composition and movement of non-uniform bed material. The theoretical results are applied to the calculation of the float open caisson in the construction period and good results are obtained.

THREE-DIMENSIONAL MATHEMATICAL MODEL AND ITS APPLICATION IN THE NEIGHBORHOOD OF THE THREE GORGES RESERVOIR DAM IN THE YANGTZE RIVER

The calculation of flow and sediment transport is one of the most important tasks in river engineering. The task is particularly difficult because a number of complex physical phenomena should be accounted for more realistically in a model with a predictive power. Three-dimensional calculations of river flow and suspended sediment transport are performed in this paper with application in the Three Gorges Reservoir in the Yangtze River. A period of 76 years after the dam is built is simulated and the results are compared with laboratory measurements obtained by Tsinghua University whereby the model is verified and calibrated. Generally speaking, the calculated results agree well with the experiments, demonstrating that the present model can be used for flow and sediment transport prediction in rivers.

Three-dimensional tidal current numerical model of the Oujiang Estuary

The characteristics of three-dimensional （3-D） tidal current in the Oujiang Estuary are investigated according to in situ observations. The Oujiang Estuary has features of irregular coastline, complex topography, many islands, moveable boundary, and submerged dyke, therefore, σ 3-D numerical model oil an unstructured triangular grid has been degeloped. The σ coordinate transforination, the moveable boundary and submerged dyke treatment techniques were employed in the model so it is suitable for the tidal simulations in the Oujing Estuary with submerged dyke and moveable boundary problems. The model is evaluated with the in situ data, and the results show that the calculated water elevations at 19 stations and currents at 19 profiler stations are in good agreement with measured data both in magnitude and phase. This numerical model is applied to the 3-D tidal circulation simulations of experiments in stopping flow transport through the South Branch of the Oujiang Estuary, and the feasibility to cutoff the flow in the South Branch of the Oujiang Estuary is demonstrated by numerical simulation experiments. The developed numerical model simulated the 3-D tidal current circulations in complicated coastal and estuarine waters very well.

Three-Dimensional Water-Quality Simulation for River Based on VOF Method

In the present study, considering the transport and transformation processes of variables, a threedimensional water quality model for the river system was established, which coupled the volume of fluid(VOF) method with the k-ε turbulence mathematical model. Then, the water hydrodynamic characteristics and transport processes for BOD_5, NH_(3^-)N and TP were analyzed. The results showed that the water surface of convex bank was a little lower than that of concave bank due to the centrifugal force near the bend, and most concentrations were inferior to the type Ⅴ standard indexes of surface water environmental quality. The model validation indicated that the errors between the simulated and monitored values were comparatively small, satisfying the application demands and providing scientific basis and decision support for the restoration and protection of water quality.

岱山—洋山跨海通道水沙环境影响数值模拟研究

杭州湾是世界闻名的强潮河口,具有不规则的岸线边界、独特的地形地貌特征和复杂的水动力泥沙环境。岱山—洋山跨海通道位于杭州湾湾口水域,将岱山与洋山近35km连通,实现了上海—洋山—岱山—舟山—宁波跨海通道的全线贯通,其建设具有非常重要的意义。基于考虑波浪作用的潮流泥沙数值模型,讨论了岱山—洋山跨海通道几种工况对杭州湾大范围海域水沙环境的影响。研究结果表明:跨海通道实施后潮位变化在大桥轴线附近较为敏感,远离则基本没有影响,高低潮位变化幅度大多在2 cm以内。杭州湾涨落潮量减小小于0.6%。水流流态和水下地形仅在大桥附近水域存在明显变化。从对杭州湾水沙环境影响角度考虑,岱山—洋山跨海通道几种工况均可行,建议关注桥墩和人工岛附近的局部冲刷问题。

Three-dimensional flow field mathematical model inside the pilot stage of the deflector jet servo valve

A new flow field mathematical model is proposed to describe accurately the flow field structure and calculate the static characteristics of the pilot stage in a deflector jet servo valve(DJSV). The flow field is divided into five regions, a 3D turbulent jet is adopted to describe the free jet region, and a velocity distribution expression of the jet is proposed. The jet entrainment model is put forward in the pressure recovery region to describe the coupling relationship between the pressure in the receiving chamber and the jet flow. The static characteristics, including pressure-flow characteristics, pressure characteristics,and flow characteristics of the pilot stage are obtained. The flow field structure and the static characteristics are verified by finite element analysis(FEA) and experiment, respectively, and the mathematical model results are in good agreement with the experimental and simulation results.

Effect of Development of Caofeidian Harbor Area in Bohai Bay on Hydrodynamic Sediment Environment

Based on the characteristics of waves, tidal currents, sediment and seabed evolution in the Caofeidian sea area in the Bohai Bay, a 2D sediment mathematical model of waves and tidal currents is employed to study the development schemes of the harbor. Verification of spring and neap tidal currents and sediment in the winter and summer of 2006 shows that the calculated values of tidal stages as well as flow velocities, flow directions and sediment concentration of 15 synchronous vertical lines are in good agreement with the measured data. Also, deposition and erosion of the sea area in front of Caofeidian ore terminal induced by suspended load under tidal currents and waves are verified; it shows that the calculated values of depth of deposition and erosion as well as their distribution are close to the measured data. Furthermore, effects of reclamation scheme of island in front of the land behind Caofeidian harbor on the hydrodynamic environment are studied, including changes of flow velocities in the deep channels at the south side of Caofeidian foreland and Laolonggou and in various harbor basins, as well as changes of deposition and erosion of seabed induced by the project.

Two-dimensional coupled mathematical modeling of fluvial processes with intense sediment transport and rapid bed evolution

Alluvial rivers may experience intense sediment transport and rapid bed evolution under a high flow regime,for which traditional decoupled mathematical river mod-els based on simplified conservation equations are not applicable. A two-dimen-sional coupled mathematical model is presented,which is generally applicable to the fluvial processes with either intense or weak sediment transport. The governing equations of the model comprise the complete shallow water hydrodynamic equa-tions closed with Manning roughness for boundary resistance and empirical rela-tionships for sediment exchange with the erodible bed. The second-order Total-Variation-Diminishing version of the Weighted-Average-Flux method,along with the HLLC approximate Riemann Solver,is adapted to solve the governing equations,which can properly resolve shock waves and contact discontinuities. The model is applied to the pilot study of the flooding due to a sudden outburst of a real glacial-lake.

A MATHEMATICAL MODEL FOR UNSTEADY SEDIMENT TRANSPORT IN NINGXIA REACH OF THE YELLOW RIVER

A one-dimensional mathematical model for unsteady sediment transport in the Ningxia reach of the Yellow River was developed. In the model, the formulas for the sediment carrying capacity and the manning roughness coefficient, which reflect the features of the Yellow River, were adopted. A coefficient of sediment distribution was defined to represent the ratio of the bottom to the average concentration under the equilibrium conditions, which is not constant and is evaluated by using an empirical expression obtained by integrating the sediment concentration along water depth. The concentration distributions and the mean diameter distributions of suspended sediment in the transversal direction were also estimated in this model. A four-point (Preismann type) finite difference scheme and TDMA were employed in the numerical simulation. The amount of sediment deposition during the period of 1993～1999 in the Ningxia reach of the Yellow River from Xiaheyan to Shizuishan with a length of 197.43km were numerically simulated with the model. The computed results, such as the amount of sediment deposition and water stage agree well with the field data. Finally the validated model was used to predict the riverbed deformation during the period of 1999～2019 in the Ningxia reach of the Yellow River.

Numerical Analysis of Adaptation-to-capacity Length for Fluvial Sediment Transport

Over the last several decades,various sediment transport capacity formulations have been used by geomorphologists and engineers to calculate fluvial morphological changes.However,it remains poorly understood if the adaptation to capacity could be fulfilled instantly in response to differing inflow discharges and sediment supplies,and thus if the calculation of morphological changes in rivers based on the assumed capacity status is fully justified.Here we present a numerical investigation on this issue.The distance required for sediment transport to adapt to capacity(i.e.,adaptation-to-capacity length) of both bed load and suspended sediment transport is computationally studied using a coupled shallow water hydrodynamic model,in line with varied inlet sediment concentrations.It is found that the adaptation-to-capacity length generally decreases as the Rouse number increases,irrespective of whether the inlet sediment concentration increases or reduces.For cases with vanishing inlet sediment concentration a unified relationship is found between the adaptation-to-capacity length and the Rouse number.Quantitatively,the adaptation-to-capacity length of bed load sediment is limited to tens of times of the flow depth,whilst that of suspended sediment increases substantially with decreasing Rouse number and can be up to hundreds of times of the flow depth.The present finding concurs that bed load sediment transport can adapt to capacity much more rapidly than suspended sediment transport,and it facilitates a quantitative criterion on which the applicability of bed load or suspended sediment transport capacity for natural rivers can be readily assessed.

Coupling mechanism of mathematical models for sediment transport based on characteristic theory

This paper aims to explore the coupling mechanism between flow movement, sediment transport and riverbed evolution in currently widely used mathematical models for sediment transport. Based on characteristic theory, analytic forms of eigenvalues,eigenvectors and characteristic relationships of total-sediment transport model, bed-load transport model and suspenedload transport model were derived, respectively. The singular perturbation technology was implemented to obtain the asymptotic solutions to different families of eigenvalues. The results indicate that, interactions between motion variables were explicitly coupled in the characteristics of total-sediment transport model and bed-load transport model. Further qualitative and quantitative analysis demonstrates that high sediment transport intensity and significant riverbed change will inevitably affect the property of flow movement. In the process of deposition, sediment-laden flow will move faster when sediment transport intensity becomes stronger. In contrast, the wave of flow will propagate at slower speed as erosion intensity becomes stronger.For most existing suspended-load transport models, however, the characteristics are decoupled as the interactions between motion variables cannot be integrally illustrated in eigenvalues, eigenvectors and characteristic relationship.

Mathematical modeling of sediment transport jn estuaries and coastal regions

Based on the suspended sediment transport equation and transport capacity formula under the action of tidal currents and wind waves, a horizontal 2-D mathematical model of suspended sediment transport for estuaries and coastal regions is established. The verification of calculations shows that the sediment concentration distribution and sea bed deformation in the estuaries and coastal regions can be successfully simulated. Therefore, a new method for studying and solving the sediment problems in the estuarine and coastal engineering is presented.

Discussion at Maximum Sediment Discharge Theory

It is observed the gravel river sediment discharge with existing empirical regime relationships.The aim of the research is to give a mathematical model about the stable cross-section geometry and to determine a model for the stable slope of an alluvial channel which is in nature seldom stable.In an alluvial channel to reach an equilibrium condition,it changes its plane geometry until to have a stable condition in plane configuration.There are three different parameters in plan configuration about river behavior:width,depth and slope.

唐山丰南涧河口取水工程取水前池泥沙淤积数模研究

取水前池泥沙淤积和取水口含沙量是近海钢厂、电厂取排水工程重点关注的问题。以唐山丰南涧河口取水工程为例,建立了工程海域的三维潮流泥沙数学模型,在模型验证的基础上研究了工程区附近潮流、泥沙运动及取水前池泥沙淤积情况。研究结果表明,取水前池淤积与取水工程海域潮流运动、波浪、河道上游径流量等有密切关系。研究成果可为该取水工程设计提供参考。

长周期波大输沙量条件下海港平面布置方案

随着“一带一路”的建设,西非、地中海以及印度洋沿岸等海域由于其特定的自然条件导致具有明显的长周期波浪成分,且已对港口工程建设产生了严重影响。结合非洲某港口工程实例,其具有波浪周期长以及沿岸输沙量大两大特点;长周期波及大输沙量易引起港内泊稳条件差、泥沙淤积重,外海船舶施工风险大等问题,经对其平面布置方案研究后,决定采用挖入式港池布置方案,并通过波浪泥沙数学模型及物理模型试验等研究方法进行验证。结果表明,该挖入式港池方案能较好地解决以上问题。

A three-dimensional modeling of the morphological change in the Liaodong Bay

The morphology in the Liaodong Bay has undergone a marked change over the past decades due to the cutoff of nearby rivers. The fine sediment of the bay consists of both non-cohesive and cohesive fractions with relatively small particles over the seabed. Thus, a three- dimensional morphodynamic model accounting for non- cohesive and cohesive fractions is established to investi- gate the morphological change without sediment input from nearby rivers. A representative wave is chosen to compute the wave distribution in the Liaodong Bay and depth-dependent wave radiation stresses are employed by the hydrodynamic model. The advection-diffusion equa- tion is used to simulate the fine sediment transport under the representative wave and tidal currents. The erosion flux of non-cohesive and cohesive sediment is taken into account. The simulated results of tidal level, velocities, directions, and sediment concentrations are in agreement with the measured data. The results demonstrate that the present model, which takes the erosion flux of both non- cohesive and cohesive fractions into account, gives more reasonable values than when accounting for cohesive sediment alone. When the three-dimensional morphody- namic model is applied to predict morphological change over the course of a year, the deposition is shown to be relatively small and the range of the erosion is increased compared to previous results of sediment input from the river. It can be concluded that the erosion in the Liaodong Bay is increasing due to the cutoff of the river, and that morphological evolution must be taken into account if any type of coastal construction plans are to be carried out over the seabed.

不同特征水位对水电站库尾淤积分布模拟研究

以澜沧江流域某电站为例,针对初步拟定的不同正常蓄水位和汛期运行控制水位,采用数学模型和物理模型相互印证相互结合的方法,计算分析建库后不同特征水位对库尾淤积分布的影响。研究发现,库区淤积量随汛期控制水位和正常蓄水位的升高而增加,且汛期控制水位的影响程度相对较大;库尾淤积分布较天然情况表现为滩面淤积略有增加。研究成果可为水库特征水位选择兼顾生态保护提供依据。

汛期调度运行方式对径流式水电站防沙排沙条件的影响——以桐子林水电站为例

坝前防沙条件、排沙效率是影响径流式水电站使用寿命及厂房发电安全的重要因素。为研究径流式水电站在汛期采取不同调度运行方式对电站汛期排沙、防沙效果的影响,通过非工程措施改善坝前排沙、防沙条件,采用FLOW-3D数值模拟软件建立三维水沙数值模型,模拟了桐子林水电站在不同坝前来流情况下,采取不同的调度运行方案时,电站取水前池的流速、流态和泥沙输移情况。结果表明:不同的调度方案可改变坝前水动力轴线、推移质输移带走向,因此在满足电站安全运行的前提下,采取合理的调度运行方式可使电站防沙效果取得最佳;汛期电站排沙以集中开启泄洪闸排沙为宜;坝前来流较大时电站需开启冲沙底孔,关闭发电机组以保证生产安全。

ANALYSIS SOLUTION OF ONE-DIMENSIONAL MATHEMATICAL MODEL ABOUT HEAVY METAL TRANSPORT FOR RIVER WATER

Water quality model about heavy metal under general initial and boundary conditions was studied. The model includes adsorption of suspended sediment, adsorption of bed load, advective diffusion of flow water, which affect the concentration of heavy metal in river water. Laplace transforms method was adopted, its integral equation of the concentration of diluting heavy metal and solid heavy metal was given. The characteristic of the model under constant solution was discussed. Using this model the prediction of mercury (Hg) ions concentration distribution along a section of Yellow River in Lanzhou, China was performed. The computational value is approximately equal to the measured value.