THREE-DIMENSIONAL SIMULATION OF MEANDERING RIVER BASED ON 3-D RNG κ-ε TURBULENCE MODEL

A 3-D numerical model for calculating flow in non-curvilinear coordinates was established in this article. The flow was simulated by solving the full Reynolds-averaged Navier-Stokes equations with the RNG κ-ε turbulence model. In the horizontal x-y-plane, a boundary-fitted curvilinear co-ordinate system was adopted, while in the vertical direction, a σ co-ordinate transformation was used to represent the free surface and bed topography. The water level was determined by solving the 2-D Poisson equation derived from 2-D depth averaged momentum equations. The finite-volume method was used to discretize the equations and the SIMPLEC algorithm was applied to acquire the coupling of velocity and pressure. This model was applied to simulate the meandering channels and natural rivers, and the water levels and the velocities for all sections were given. By contrasting and analyzing, the agreement with measurements is generally good. The feasibility studies of simulating flow of the natural fiver have been conducted to demonstrate its applicability to hydraulic engineering research.     

NUMERICAL SIMULATION OF 3-D TURBULENT FLOW IN THE MULTI-INTAKES SUMP OF THE PUMP STATION

In this article, a numerical model for three-dimensional turbulent flow in the sump of the pump station was presented. A reasonable boundary condition for the flow in the sump with several water intakes at different flow rates was proposed. The finite volume method was employed to solve the governing equations with the body fitted grid generated by the multi-block grid technique. By using the Fluent software, the fluid flow in a model sump of the pump station was calculated. Compared with the experimental result, the numerical result of the example is fairly good.     

Modeling of thermodynamics of ice and water in seasonal ice-covered reservoir

A width-averaged 2-D numerical model for simulating vertical distributions of flow and water temperature in reservoirs with an ice cover is developed. In this model, the 2-D flow and water temperature distributions are solved by the finite volume method with the k-? turbulent model. The heat conduction in the ice cover is modeled by the vertical heat transfer and the heat exchanges through the air-ice and ice-water interfaces. The model is applied to a 153 km long reservoir in Songhua River and the simulated results are in a good agreement with the field data of both the vertical water temperature and the ice thickness. The simulated results show that the ice cover thickness in the reservoir is not uniform, the maximum thickness appears in the middle reach, the outflow temperature has an obvious variation as compared with the natural temperature, and a buoyant flow occurs in the reservoir surface at the freeze-up and break-up periods. The model can effectively simulate the water temperature and the ice conditions of large reservoirs in cold regions.     

Two-dimensional shallow water equations with porosity and their numerical scheme on unstructured grids

In this study, porosity was introduced into two-dimensional shallow water equations to reflect the effects of obstructions, leading to the modification of the expressions for the flux and source terms. An extra porosity source term appears in the momentum equation. The numerical model of the shallow water equations with porosity is presented with the finite volume method on unstructured grids and the modified Roe-type approximate Riemann solver. The source terms of the bed slope and porosity are both decomposed in the characteristic direction so that the numerical scheme can exactly satisfy the conservative property. The present model was tested with a dam break with discontinuous porosity and a flash flood in the Toce River Valley. The results show that the model can simulate the influence of obstructions, and the numerical scheme can maintain the flux balance at the interface with high efficiency and resolution.     

THREE-DIMENSIONAL NUMERICAL MODEL FOR WINDING TIDAL RIVER WITH BRANCHES

Natural rivers are usually winding with branches and shoals,which are difficult to be simulated with rectangular grids. A 3-D current numerical model was established based on the orthogonal curvilinear coordinate system and vertical σ coordinate system. The equations were discretisized using a semi-implicit scheme. The “predictor” and “corrector” steps were applied for the horizontal momentum equations to meet the basic requirement that the depth-integrated currents obtained from the equations for 2-D and 3-D modes have identical values. And a modification of traditional method of dry/wet discriminance was proposed to determine accurately the boundary and ensure the continuity of variable boundary in the simulation. This model was verified with the data measured in a winding tidal river with branches in April,2004. The simulated data of water levels and velocities agree well with the measured ones,and the computed results reveal well the practical flow characteristics,including the vertical secondary flow in a winding reach.     

Assessment of water depth change patterns in 120° sharp bend using numerical model

In this study,FLUENT software was employed to simulate the flow pattern and water depth changes in a 120° sharp bend at four discharge rates.To verify the numerical model,a 90° sharp bend was first modeled with a three-dimensional numerical model,and the results were compared with available experimental results.Based on the numerical model validation,a 120° bend was simulated.The results show that the rate of increase of the water depth at the cross-section located 40 cm before the bend,compared with the cross-sections located 40 cm and 80 cm after the bend,decreases with the increase of the normal water depth in the 120° curved channel.Moreover,with increasing normal water depth,the dimensionless water depth change decreases at all cross-sections.At the interior cross-sections of the bend,the transverse water depth slope of the inner half-width is always greater than that of the outer half-width of the channel.Hence,the water depth slope is nonlinear at each crosssection in sharp bends.Two equations reflecting the relationships between the maximum and minimum dimensionless water depths and the normal water depth throughout the channel were obtained.     

ANALYSIS OF WATER QUALITY IN SHALLOW LAKES WITH A TWO-DIMENSIONAL FLOW-SEDIMENT MODEL

The governing equation for sediment pollutions was derived based on the turbulent diffusion of pollutants in shallow lakes. Coupled with shallow water equations, a depth-averaged 2-D flow and water quality model was developed. By means of the conservation law, a proposed differential equation for the change of sediment pollutants was linked to the 2-D equations. Under the framework of the finite volume method, the Osher approximate Riemann solver was employed to solve the equations. An analytical resolution was used to examine the model capabilities. Simulated results matched the exact solutions especially well. As an example, the simulation of CODMn in the Wuli Lake, a part of the Taihu lake, was conducted, which led to reasonable results. This study provides a new approach and a practical tool for the simulation of flow and water quality in shallow lakes.     

Factors influencing thermal structure in a tributary bay of Three Gorges Reservoir

To better understand the factors influencing the thermal structure of tributaries in the Three Gorges Reservoir(TGR),a well validated three-dimensional hydrodynamic and water temperature model was proposed to simulate the water temperature distribution in the Xiangxi Bay, a representative tributary of TGR.The numerical results show that water temperature stratification seasonally occurred in the Xiangxi Bay, with stable vertical temperature profiles.It is found from the numerical experiments that three key factors are responsible for the formation of water temperature structure:(1) very often,the locations of thermocline are mainly determined by wind speeds, and the higher the wind speed is, the deeper the thermocline is located beneath the water surface,which could be expressed by a fitted exponential function,(2) the thermal structure is affected by static stability of water column, and the thermocline becomes closer to the water surface and its thickness increases with the increase of temperature, (3) due to the effect of the thermal density inflow, the water temperature of the hypolimnion tends to be uniform, however, even under the condition of larger inflow discharge,the influence of the inflow on the epilimnion and the thermocline is not significant.     

NUMERICAL SIMULATION OF TWO-DIMENSIONAL DAM-BREAK FLOWS IN CURVED CHANNELS

Two-dimensional transient dam-break flows in a river with bends were theoretically studied. The river was modeled as a curved channel with a constant width and a flat bottom. The water was assumed to be an incompressible and homogeneous fluid. A channel-fitted orthogonal curvilinear coordinate system was established and the corresponding two-dimensional shallow-water equations were derived for this system. The governing equations with well-posed initial and boundary conditions were numerically solved in a rectangular domain by use of the Godunov-type finite-difference scheme, which can capture the hydraulic jump of dam-break flows. The comparison between the obtained numerical results and the experimental data of Miller and Chaudry in a semicircle channel shows the validity of the present numerical scheme. The mathematical model and the numerical method were applied to the dam-break flows in channels with various curvatures. Based on the numerical results, the influence of river curvatures on the dam-break flows was analyzed in details.     

Numerical study of the flow in the Yellow River with non-monotonous banks

A 2-D depth averaged RNG k- ε model is developed to simulate the flow in a typical reach of the Upper Yellow River with non-monotonic banks. In order to take account of the effect of the secondary flow in a bend, the momentum equations are modified by adding an additional source term. A comparison between the numerical simulation and the field measurements indicates that the improved 2-D depth averaged RNG k- ε model can improve the accuracy of the numerical simulation. An arc spline interpolation method is developed to interpolate the non-monotonic river banks. The method can also be reasonably applied for the 2-D interpolation of the river bed level. Through a comparison of the water surface gradients simulated in the seven bends of the studied reach, some analytical formulae are improved to reasonably calculate the longitudinal and transverse gradients in meandering river reaches. Furthermore, the positions of the maximum water depth and the maximum velocity in a typical bend are discussed.     

THREE-DIMENSIONAL SIMULATION OF MEANDERING RIVER BASED ON 3-D RNG k-ε TURBULENCE MODEL

A 3-D numerical model for calculating flow in non-curvilinear coordinates was established in this article. The flow was simulated by solving the full Reynolds-averaged Navier-Stokes equations with the RNG k-ε turbulence model. In the horizontal x-y-plane, a boundary-fitted curvilinear co-ordinate system was adopted, while in the vertical direction, a co-ordinate transformation was used to represent the free surface and bed topography. The water level was determined by solving the 2-D Poisson equation derived from 2-D depth averaged momentum equations. The finite-volume method was used to discretize the equations and the SIMPLEC algorithm was applied to acquire the coupling of velocity and pressure. This model was applied to simulate the meandering channels and natural rivers, and the water levels and the velocities for all sections were given. By contrasting and analyzing, the agreement with measurements is generally good. The feasibility studies of simulating flow of the natural river have been conducted to demonstrate its applicability to hydraulic engineering research.     

温排水对湖泊、水库富营养化影响的数值模拟

本文针对大型火、核电厂温排水对湖泊、水库富营养化影响预测的迫切需要，建立了一套以改型分步杂交法为计算手段，对二维守恒型浅水环流方程及能量方程求解，在正确模拟流场及温度场的基础之上，继续求解单步一级生态动力学模型，并用单因素分析法考虑水温对藻类生长过程影响的计算模式．并结合一大型火电厂的建设，对该模式进行了验证和实际工作应用．     

近岸海域电厂温排水数值模拟

 建立了守恒性好且能贴体模拟工程区域的二维水流-温水扩散数学模型,采用三角形网格划分计算区域,有限体积法求解水深积分方程。通过实测潮位潮流资料验证了模型的合理性,并在此基础上对近岸海域某电厂温排水的空间分布进行了预测计算,其结果为电厂设计和环境评价提供了依据。     

Effects of Selective Withdrawal on Hydrodynamics of a Stratified Reservoir

In water supply reservoirs, selective withdrawal is commonly implemented to control released water temperature for quality purposes. This study investigated the effects of selective withdrawal on hydrodynamics of a stratified reservoir through numerical modeling and analytical analysis. A 3-D hydrodynamic model was applied where observations of water temperature time series recorded every 30 min at the thermocline and measured temperature profiles along the water column were used to validate the numerical model. The effect of selective withdrawal from four outlets located along the water intake structure of Tahtali Reservoir in Turkey on water temperatures was investigated and the effects on thermal stratification structure were discussed. Withdrawal of the water at the bottom outlet was found to be the most effective choice encouraging the mixing of the water column and thus reducing anoxia. The results of this study can be used to guide the further investigations in stratified lakes for better management practices.     

A scheme for improving computational efficiency of quasi-two-dimensional model

The quasi-2D model, taking into account the axial velocity profile in the cross section and neglecting the convective term in the 2-D equation, can more accurately simulate the water hammer than the 1-D model using the cross-sectional mean velocity. However, as compared with the 1-D model, the quasi-2D model bears a higher computational burden. In order to improve the computational efficiency, the 1-D method is proposed to be used to solve directly the pressure head and the discharge in the quasi-2D model in this paper, based on the fact that the pressure head obtained as the solution of the two-dimensional characteristic equation is identical to that solved by the 1-D characteristic equations. The proposed scheme solves directly the 1-D characteristic equations for the pressure head and the discharge using the MOC and solves the 2-D characteristic equation for the axial velocities in order to calculate the wall shear stress. If the radial velocity is needed, it can be evaluated easily by an explicit equation derived from the explicit 2-D characteristic equation. In the numerical test, the accuracy and the efficiency of the proposed scheme are compared with two existing quasi-two-dimensional models using the MOC. It is shown that the proposed scheme has the same accuracy as the two quasi-2D models, but requires less computational time. Therefore, it is efficient to use the proposed scheme to simulate the 2-D water hammer flows.     

基于大气环流和海温场的降水组合预报模型

针对降水具有混沌性和随机性,准确进行长期降水预报难度高的问题,提出时变海温多极指数和因子预报意见指数,基于大气环流和海温场构建长期降水组合预报模型,以三峡水库流域为例进行了验证。结果表明:组合预报模型在三峡水库流域1961—2020年汛期的月降水预报中有较好的适用性,特别在6月和9月降水预报上表现优异;与多因子回归、随机森林数理统计模型和CFSv2、ECMWF system 4动力数值模型相比,该模型更为稳健、预报精度提高显著。     

A NON-UNIFORM SEDIMENT TRANSPORT MODEL WITH THE BOUNDARY-FITTING ORTHOGONAL COORDINATE SYSTEM

1. INTRODUCTIONSome problems have to be considered in the mathematical modeling for river engineering. The riverbed is always in the manner of deposition and erosion. The sediment transport is often in the state of non-equilibrium. General, the compositio…     

THE COMPARATIVE STUDY OF VENTILATED SUPER CAVITY SHAPE IN WATER TUNNEL AND INFINITE FLOW FIELD

In order to understand the difference of ventilated supercavity in water tunnel and infinite flow field, 3-D numerical simulations are carried out to obtain the ventilated supercavity in above mentioned conditions based on RANS equations, using the finite volume method and SST turbulence model in the framework of the two fluid multiphase flow model. The numerical method adopted in this article for the infinite flow field and water tunnel experiments is validated by comparing results with those of empirical formulas and experimental data. On this basis the difference between water tunnel experiments and infinite flow field is studied, including the influence of the route loss and the blocking effect in the water tunnel. Finally, some suggestions are made for water tunnel experiments.