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.     

THEORETICAL AND EXPERIMENTAL STUDY ON THE CONICAL SWIRLING WATER JET FLOW

This paper is concerned with theoretical and experimental study on theconical swirling water jet flow.Based upon the theoretical analysis,the experiment on thestructural characteristics of swirling water jet flow including the velocity and pressure dis-tribution laws,on which the parameters of the jet,nozzle and directional blades havemore or less influence,was carried out in CSSRC by using a 3-D LDV in order to optimizea new high-efficiency jet instead of swirling drilling bit for rock-breaking and continuouslydrilling,and to meet the demand of radial horizontal drilling technology.Meanwhile basedon the experimental results,the numerical simulation was conducted for the conicalswirling water jet in the immersed well-bottom flow by solving the RANS equations in the3-D body-fitted coordinate system with the k-ε turbulence model.The numerical resultsare consistent with the experimental data,and lead to some conclusions which are impor-tant for applying the conical swirling water jet to the petroleum drill     

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.     

THE WALL EFFECT ON VENTILATED CAVITATING FLOWS IN CLOSED CAVITATION TUNNELS

For ventilated cavitating flows in a closed water tunnel, the wall effect may exert an important influence on cavity shape and hydrodynamics, An isotropic mixture multiphase model was established to study the wall effect based on the RANS equations, coupled with a natural cavitation model and the RNG k-ε turbulent model. The governing equations were discretized using the finite volume method and solved by the Gauss-Seidel linear equation solver on the basis of a segregation algorithm. The algebraic multigrid approach was carried through to accelerate the convergence of solution. The steady ventilated cavitating flows in water tunnels of different diameter were simulated for a conceptual underwater vehicle model which had a disk cavitator. It is found that the choked cavitation number derived is close to the approximate solution of natural cavitating flow for a 3-D disk. The critical ventilation rate falls with decreasing diameter of the water tunnel. However, the cavity size and drag coeflicient are rising with the decrease in tunnel diameter for the same ventilation rate, and the cavity size will be much different in water tunnels of different diameter even for the same ventilated cavitation number.     

SIMULATION OF SEDIMENT-LADEN FLOW BY DEPTH-AVERAGED MODEL BASED ON UNSTRUCTURED COLLOCATED GRID

The 2-D depth-averaged mathematical model for sediment-laden flows has been widely used in river control and other related engineering problems, and now it is usually solved on structured grids. Since the natural river is usually very complicated in plane boundary, and unstructured grids are more attractive in solving the problems with complicated domains, the following questions about solving 2-D depth-averaged model were discussed in this article: (1) a modified Bowyer algorithm was suggested to generate unstructured grids for natural rivers, (2) the Finite Volume Method (FVM) is employed to discretize the governing equations of the 2-D depth-averaged model and an implicit scheme was suggested with unstructured collocated grids, (3) the observed hydrological data of the Chenglingji Reach in the Yangtze River are used for verification of the presented method. It seems that the suggested numerical scheme works very well, and the simulation results of both hydraulic characteristics and river bed deformation are in good agreement with the observed ones.     

A SPLIT-CHARACTERISTIC FINITE ELEMENT MODEL FOR 1-D UNSTEADY FLOWS

An efficient and accurate solution algorithm was proposed for 1-D unsteady flow problems widely existing in hydraulic engineering. Based on the split-characteristic finite element method, the numerical model with the Saint-Venant equations of 1-D unsteady flows was established. The assembled finite element equations were solved with the tri-diagonal matrix algorithm. In the semi-implicit and explicit scheme, the critical time step of the method was dependent on the space step and flow velocity, not on the wave celerity. The method was used to eliminate the restriction due to the wave celerity for the computational analysis of unsteady open-channel flows. The model was verified by the experimental data and theoretical solution and also applied to the simulation of the flow in practical river networks. It shows that the numerical method has high efficiency and accuracy and can be used to simulate 1-D steady flows, and unsteady flows with shock waves or flood waves. Compared with other numerical methods, the algorithm of this method is simpler with higher accuracy, less dissipation, higher computation efficiency and less computer storage.     

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.     

BASIC THEORY AND MATHEMATICAL MODELING OF URBAN RAINSTORM WATER LOGGING

In this paper, a mathematical model for the urban rainstorm water logging was established on the basis of one- and two-dimensional unsteady flow theory and the technique of non-structural irregular grid division. The continuity equation was discretized with the finite volume method. And the momentum equations were differently simplified and dis-cretized for different cases. A method of “special passage” was proposed to deal with small-scale rivers and open channels. The urban drainage system was simplified and simulated in the model. The method of “open slot” was applied to coordinate the alternate calculation of open channel flow and pressure flow in drainage pipes. The model has been applied in Tianjin City and the verification is quile satisfactory.     

FORECAST OF WATER TEMPERATURE IN RESERVOIR BASED ON ANALYTICAL SOLUTION

The water temperature in reservoirs is difficult to be predicted by numerical simulations. In this article, a statistical model of forecasting the water temperature was proposed. In this model, the 3-D thermal conduction-diffusion equations were converted into a system consisting of 2-D equations with the Fourier expansion and some hypotheses. Then the statistical model of forecasting the water temperature was developed based on the analytical solution to the 2-D thermal equations. The~ simplified statistical model can elucidate the main physical mechanism of the temperature variation much more clearly than the numerical simulation with the Navier-Stokes equations. Finally, with the presented statistical model, the distribution of water temperature in the Shangyoujiang reservoir was determined.     

A coupled 1-D and 2-D channel network mathematical model used for flow calculations in the middle reaches of the yangtze river

A coupled one-dimensional (1-D) and two-dimensional (2-D) channel network mathematical model is proposed for flow calculations at nodes in a channel network system in this article.For the 1-D model, the finite difference method is used to discretize the Saint-Venant equations in all channels of a looped network.The Alternating Direction Implicit (ADI) method is adopted for the 2-D model at the nodes.In the coupled model, the 1-D model provides a good approximation with small computational effort, while the 2-D model is applied for complex topography to achieve a high accuracy.An Artificial Neural Network (ANN) method is used for the data exchange and the connectivity between the 1-D and 2-D models.The coupled model is applied to the Jingjiang-Dongting Lake region, to simulate the tremendous looped channel network system, and the results are compared with field data.The good agreement shows that the coupled hydraulic model is more effective than the conventional 1-D model.     

SIMULATION OF LOW-CONCENTRATION SEDIMENT-LADEN FLOW BASED ON TWO-PHASE FLOW THEORY

Low concentration sediment-laden flow is usually involved in water conservancy, environmental protection, navigation and so on. In this article, a mathematical model for low-concentration sediment-laden flow was suggested based on the two-phase flow theory, and a solving scheme for the mathematical model in curvilinear grids was worked out. The observed data in the Zhang River in China was used for the verification of the model, and the calculated results of the water level, velocity and river bed deformation are in agreement with the observed ones.     

A COUPLED MODEL OF HYDRODYNAMICS AND WATER QUALITY FOR YUQIAO RESERVOIR IN HAIHE RIVER BASIN

In order to simulate the characteristics of hydrodynamic field and mass transport processes in the Yuqiao Reservoir （YQR）, a 2-D coupled model of hydrodynamics and water quality was developed, and the water-quality related state variables in this model included CODMn, TN and TP. The hydrodynamic model was driven by employing observed winds and daily measured flow data to simulate the seasonal water cycle of the reservoir. The simulation of the mass transport and transformation processes of CODMn, TN and TP was based on the unsteady diffusion equations, driven by observed meteorological forcing and external loadings, with the fluxes form the bottom of reservoir and the plant photosynthesis and respiration as internal sources and sinks. A finite volume method and Alternating Direction Implicit （ADI） scheme were used to solve these equations. The model was calibrated and verified by using the data observed from YQR in two different years. The results showed that in YQR, the wind-driven current was an important style of lake current, while the concentration of water quality item was decreasing from east to west because of the external pollutant loadings. There was a good agreement between the simulated and measured values, with the minimal calculation error percent of 0.1% and 2.6% and the mean error percent of 44.0% and 51.2% for TN and TP separately. The simulation also showed that, in YQR, the convection was the main process in estuaries of inflow river, and diffusion and biochemical processes dominate in center of reservoir. So it was necessary to build a pre-pond to reduce the external loadings into the reservoir.     

MODELING DAM-BREAK FLOOD OVER NATURAL RIVERS USING DISCONTINUOUS GALERKIN METHOD

A well-balanced numerical model is presented for two-dimensional, depth-averaged, shallow water flows based on the Discontinuous Galerkin (DG) method. The model is applied to simulate dam-break flood in natural rivers with wet/dry bed and complex topography. To eliminate numerical imbalance, the pressure force and bed slope terms are combined in the shallow water flow equations. For partially wet/dry elements, a treatment of the source term that preserves the well-balanced property is presented. A treatment for modeling flow over initially dry bed is presented. Numerical results show that the time step used is related to the dry bed criterion. The intercell numerical flux in the DG method is computed by the Harten-Lax-van Contact (HLLC) approximate Riemann solver. A two-dimensional slope limiting procedure is employed to prevent spurious oscillation. The robustness and accuracy of the model are demonstrated through several test cases, including dam-break flow in a channel with three bumps, laboratory dam-break tests over a triangular bump and an L-shape bend, dam-break flood in the Paute River, and the Malpasset dam-break case. Numerical results show that the model is robust and accurate to simulate dam-break flood over natural rivers with complex geometry and wet/dry beds.     

DEVELOPMENT AND APPLICATION OF A EUTROPHICATION WATER QUALITY MODEL FOR RIVER NETWORKS

The Preissmann implicit scheme was used to discretize the one-dimensional Saint-Venant equations, the river-junction-fiver method was applied to resolve the hydrodynamic and water quality model for river networks, and the key issues on the model were expatiated particularly in this article. This water quality module was designed to compute time dependent concentrations of a series of constituents, which are primarily governed by the processes of advection, dispersion and chemical reactions. Based on the theory of Water Quality Analysis Simulation Program （WASP） water quality model, emphasis was given to the simulation of the biogeochemical transformations that determine the fate of nutrients, in particular, the simulation of the aquatic cycles of nitrogen and phosphorus compounds. This model also includes procedures for the determination of growth and death of phytoplankton. This hydrodynamic and water quality model was applied to calculate two river networks. As illustrated by the numerical examples, the calculated water level and discharge agree with the measured data and the simulated trends and magnitudes of water quality constituents are generally in good agreement with field observations. It is concluded that the presented model is useful in the pollutant control and in the determination of pollutant-related problems for river networks.     

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.     

REAL-TIME FLOOD FORECASTING METHOD WITH 1-D UNSTEADY FLOW MODEL

A real-time forecasting method coupled with the 1-D unsteady flow model with the recursive least-square method was developed. The 1-D unsteady flow model was modified by using the time-variant parameter and revising it dynamically through introducing a variable weighted forgetting factor,such that the output of the model could be adjusted for the real time forecasting of floods. The application of the new real time forecasting model in the reach from Yichang to Luoshan of the Yangtze River was demonstrated. Computational result shows that the forecasting accuracy of the new model is much higher than that of the original 1-D unsteady flow model. The method developed is effective for flood forecasting,and can be used for practical operation in the flood forecasting.     

Flow and transport simulation of Madeira River using three depth-averaged two-equation turbulence closure models

This paper describes a numerical simulation in the Amazon water system, aiming to develop a quasi-three-dimensional numerical tool for refined modeling of turbulent flow and passive transport of mass in natural waters. Three depth-averaged two-equation turbulence closure models, , , and , were used to close the non-simplified quasi-three-dimensional hydrodynamic fundamental governing equations. The discretized equations were solved with the advanced multi-grid iterative method using non-orthogonal body-fitted coarse and fine grids with collocated variable arrangement. Except for steady flow computation, the processes of contaminant inpouring and plume development at the beginning of discharge, caused by a side-discharge of a tributary, have also been numerically investigated. The three depth-averaged two-equation closure models are all suitable for modeling strong mixing turbulence. The newly established turbulence models such as the model, with a higher order of magnitude of the turbulence parameter, provide a possibility for improving computational precision.     

A NEW NUMERICAL MODEL FOR THREE DIMENSIONAL SURFACE WATER FLOWS

A three dimensional numerical model based on the Reynolds equations is presented that can be used to predictthe surface water flow in open channels.The model uses a computational mesh that conforms to the free water sur-face and the bottom of the channel so that the accuracy of boundary condition application,code complexity,and e-conomy could be enhanced.The k-ε turbulence model is used to estimate the eddy viscosity coefficient.Instead ofusing the“rigid-lid”approximation a 2-D equation derived from integrating the continuity equation over the totaldepth is adopted to determine the elevation of the free water surface.A new algorithm is presented based on theconventional SIMPLE procedure.The block correction technique is employed to enhance rate of convergence.The model presented is applied to a bottom discharge into a rectangular straight channel for three dimensionalphenomena to obtain the free water surface configuration,velocities and pressure.The computed results are ingood agreement with the previous experimental values.     

NUMERICAL STUDY OF TURBULENT FLOW AROUND TWIN PLATE AT LARGE ATTACK ANGLE

The present work is mainly aimed to study the fluid dynamic force on twin plate in a turbulent flow by solving the governing equations numerically with the well known approach SIMPLE, in which the multiple time scale turbulent k-ε model has been employed to determine the eddy viscosity of turbulent flow field. The turbulence model is used with a restriction for the kinetic energy of smaller turbulent scale to achieve numerical stability. The lengths of recirculation zone for the turbulent flow around twin plate with the definite angle of attack AOA = 50° and constant flow blockage ratio 10% are in good agreement with experimental data, which indicates the wall functions used in the numerical investigation are acceptable as well. It is found that the drag force and distribution of wall pressure are intimately influenced by the arrangement of twin plate at constant flow blockage. The results of multiple time scale k-εmodel are compared with single time scale k-εmodel, indicating that the drag force of     

ONE-AND TWO-DIMENSIONAL COUPLED HYDRODYNAMICS MODEL FOR DAM BREAK FLOW

1-D and 2-D mathematical models for dam break flow were established and verified with the measured data in laboratory. The 1-D and 2-D models were then coupled, and used to simulate the dam break flow from the reservoir tail to the dam site, the propagation of dam break waves in the downstream channel, and the submergence of dam break flow in the downstream town with the hydrodynamics method. As a numerical example, the presented model was employed to simulate dam break flow of a hydropower station under construction. In simulation, different dam-break durations, upstream flows and water levels in front of dam were considered, and these influencing factors of dam break flow were analyzed, which could be referenced in planning and designing hydropower stations.