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.     

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.     

NUMERICAL MODELLING OF FREE-SURFACE FLOWS WITH BOTTOM AND SURFACE-LAYER PRESSURE TREATMENT

A new non-hydrostatic numerical model with the three-dimensional Navier-Stokes equations on structured grids was constructed and discussed. The algorithm is based upon a staggered finite difference Crank-Nicholson scheme on a Cartesian grid. The eddy viscosity coefficient was calculated by the efficient k-ε turbulence model. A new surface-layer non-hydrostatic treatment and a local cell bottom treatment were introduced so that the three-dimensional model is fully non-hydrostatic and is free of any hydrostat...     

Application of CLEAR-VOF method to wave and flow simulations

A two-dimensional numerical model based on the Navier-Stokes equations and computational Lagrangian-Eulerian advection remap-volume of fluid (CLEAR-VOF) method was developed to simulate wave and flow problems. The Navier-Stokes equations were discretized with a three-step finite element method that has a third-order accuracy. In the CLEAR-VOF method, the VOF function F was calculated in the Lagrangian manner and allowed the complicated free surface to be accurately captured. The propagation of regular waves and solitary waves over a flat bottom, and shoaling and breaking of solitary waves on two different slopes were simulated with this model, and the numerical results agreed with experimental data and theoretical solutions. A benchmark test of dam-collapse flow was also simulated with an unstructured mesh, and the capability of the present model for wave and flow simulations with unstructured meshes, was verified. The results show that the model is effective for numerical simulation of wave and flow problems with both structured and unstructured meshes.     

EXPERIMENTS OF SEA ICE SIMULATION

As a substitute for the original displaced pole grids, a simple rotated spherical coordinate system was intro duced into the Community Sea Ice Model version 4（CSIM4）, which is a component of the Community Climate System Model（CCSM） of the American National Center of Atmospheric Researeh（NCAR）, to deal with the ＂pole problems＂. In the new coordinates, both the geographical North Pole and South Pole lie in the model equator and grid sizes near the polar region are more uniform. With reanalysis dataset of American National Centers for Environment Prediction （NCEP） and Levitus dataset without considering sub-mixed layer heat flux, the model was integrated for 100 years with thermodynamics proce.ss involved only in the former 49 years and both dynamic and thermodynamic processes involved in the left time. Inner consistency of model results was checked with no contradiction found. The results of last 10 years＇ model output were analyzed and it is shown that the simulated sea ice seasonal variation is rational whereas sea ice extent in the Barcnts Sea in winter is larger than that of observation, Numerical experiment on influence of sub-mixed layer heat flux was also carried out and it is shown that the sub-mixed layer heat flux can modulate seasonal variation of sea ice greatly. As a model component, the sea ice model with rotated spherical coordinates was coupled with other models （the oceanic general cir culation model is the LASG/IAP Climate System Ocean Model （LICOM） with reduced grid, other models are components of NCAR CCSM2） forming a climate system model and its preliminary results were also given briefly.     

Numerical Investigation of Performance of an Axial-Flow Pump With Inducer

The interaction of flow through the inducer and impeller of an axial-flow pump equipped with an inducer has significant effect on its performance. This article presents a recent numerical investigation on this topic. The studied pump has an inducer with 3 blades mounted on a conical hub and a 6-blade impeller. The blade angle of the impeller is adjustable to generate different relative circumferential angles between the inducer blade trailing edge and the impeller blade leading edge. A computational fluid dynamics code was used to investigate the flow characteristics and performance of the axial-flow pump. For turbulence closure, the RNG k-ε model was applied with an unstructured grid system. The rotor-stator interaction was treated with a Multiple Reference Frame (MRF) strategy. Computations were performed in different cases: 7 different relative circumferential angles ( Δθ ) between the inducer blade trailing edge and the impeller blade leading edge, and 3 different axial gaps (G) between the inducer and the impeller. The variation of the hydraulic loss in the rotator was obtained by changing Δθ . The numerical results show that the pressure generated is minimum in the case of ( G = 3%D), which indicates that the interference between inducer and impeller is strong if the axial gap is small. The pump performances were predicted and compared to the experimental measurements. Recommendations for future modifications and improvements to the pump design were also given.     

NUMERICAL SIMULATION OF FLOW FIELDS IN A NATURAL DRAFT WET-COOLING TOWER

The flow field in the hyperbolic natural draft wet-cooling tower, which has great effects on the economy and security of power plant, was studied through numerical simulation. The mathematical model was established and analyzed in order to optimize the cooling-tower and to evaluate its efficiency. Various working conditions were considered and compared with each other, such as the circulating water flux, air temperature and tower resistance. It is concluded that when the cooling-tower runs without wind, there is a vacuum region inside the tower and the pressure rises with the increase of the tower height. Meanwhile, the inner flow field is axisymmetrical. The air velocity achieves its climax at the axis. It is also found that the effect of circulating water temperature is equivalent to that of the water flux.     

STUDY AND APPLICATION OF STEADY FLOW AND UNSTEADY FLOW MATHEMATICAL MODEL FOR CHANNEL NETWORKS

Based on the Preissmann implicit scheme for the one-dimensional Saint-Venant equation, the mathematical model for one-dimensional river networks and canal networks was developed and the key issues on the model were expatiated particularly in this article. This model applies the method of three-steps solution for channel-junction-channel to simulate the river networks, and the Gauss elimination method was used to calculate the sparse matrix. This model was applied to simulate the tree-type irrigation canal networks, complex looped channel networks and the Lower Columbia Slough networks. The results of water level and discharge agree with the data from the Adlul and field data. The model is proved to be robust for simulating unsteady flows in river networks with various degrees of complex structure. The calculated results show that this model is useful for engineering applications in complicated river networks. Future research was recommended to focus on setting up ecological numerical model of water quality in river networks and canal networks.     

COMPUTATIONAL RESEARCH ON WAVE MAKING OF MOVING WIGLEY HULL IN TIME DOMAIN

Based on Green＇s theorem, a time domain numerical model was constructed to simulate wave making phenomenon caused by a moving ship. In this article, the Rankine sources and dipoles were placed on boundary surfaces （i.e., the ship surface and free surface）, and a time-stepping scheme was employed. Its unique characteristic is that steady state can be realized from initial value by employing the time-stepping scheme and unsteady free surface conditions. In time domain, if the results of unsteady flow problem tend to data stabilization after many time steps of computation, they could be regarded as the data of steady ones. This model could be employed to steady or unsteady problems. Theoretical reasoning and computational process of this method was described in detail The linear and nonlinear boundary conditions on body surface were studied, and the relative means to realize these boundary conditions in iterative computation were also discussed. Some proper parameters about the model of the Wigley hull were determined by many numerical tests, and their influences on wave making resistance and wave pattern were discussed. According to the comparison between numerical results and data available in relative references, the method used in this work is proven to be a reliable method in time domain. And the lattice reorganization in every time step computation is a feasible numerical approach.     

Unstructured finite volume method for water impact on a rigid body

A new method is presented for the water impact simulation, in which the air-water two phase flow is solved using the pressure-based computational fluid dynamics method. Theoretically, the air effects can be taken into account in the water structure interaction. The key point of this method is the air-water interface capture, which is treated as a physical discontinuity and can be captured by a well-designed high order scheme. According to a normalized variable diagram, a high order discrete scheme on unstructured grids is realised, so a numerical method for the free surface flow on a fixed grid can be established. This method is implemented using an in-house code, the General Transport Equation Analyzer, which is an unstructured grid finite volume solver. The method is verified with the wedge water and structure interaction problem.     

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.     

BOUSSINESQ MODELLING OF NEARSHORE WAVES UNDER BODY FITTED COORDINATE

A set of nonlinear Boussinesq equations with fully nonlinearity property is solved numerically in generalized coordinates,to develop a Boussinesq-type wave model in dealing with irregular computation boundaries in complex nearshore regions and to facilitate the grid refinements in simulations.The governing equations expressed in contravariant components of velocity vectors under curvilinear coordinates are derived and a high order finite difference scheme on a staggered grid is employed for the numerical implementation.The developed model is used to simulate nearshore wave propagations under curvilinear coordinates,the numerical results are compared against analytical or experimental data with a good agreement.     

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.     

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.     

NUMERICAL SIMULATION OF TURBULENT FREE SURFACE FLOW OVER OBSTRUCTION

A two-dimensional hybrid numerical model, FEM-LES-VOF, for free surface flows is proposed in this study, which is a combination of three-step Taylor-Galerkin finite element method, large eddy simulation with the Smagorinsky sub-grid model and Computational Lagrangian-Eulerian Advection Remap Volume of Fluid （CLEAR-VOF） method. The present FEM-LES-VOF model allows the fluid flows involving violent free surface and turbulence subject to complex boundary configuration to be simulated in a straightforward manner with unstructured grids in the context of finite element method. Numerical simulation of a benchmark problem of dam breaking is conducted to verify the present model. Comparisons with experimental data show that the proposed model works well and is capable of producing reliable predictions for free surface flows. Using the FEM-LES-VOF model, the free surface flow over a semi-circular obstruction is investigated. The simulation results are compared with available experimental and numerical results. Good performance of the FEM-LES-VOF model is demonstrated again. Moreover, the numerical studies show that the turbulence plays an important role in the evolution of free surface when the reflected wave propagates upstream during the fluid flow passing the submerged obstacle.     

SIMULATION OF STRONG TURBULENCE FLOW WITH FREE SURFACE INCLUDING THE EFFECTS OF STREAMLINE CURVATURE

This paper is concerned with a mathematical model for two-dimensional strong turbulence flow with free surface including the effects of streamline curvature in orthogonal curvilinear coordinate system, with which the characteristics of the turbulence flow field on the ogee spillway was numerical simulated. In the numerical simulation, the flow control equations in orthogonal curvilinear coordinate system were discretized by the finite volume method, the physical parameters（ P, U,V,K,ε,γt , etc. ） were arranged on a staggered grid, the discretized equations were solved with the SIMPLEC method, and the complex free surface was dealt with VOF method. The computed results show that the velocity fields, pressure field, shear stress distribution and kinetic energy of turbulent flow on the ogee spillway are in agreement with experimental data. This confirms that the model can be used for numerieal simulation of the turbulence flow on ogee spillway.     

Numerical method for multi-body fluid interaction based on Immersed Boundary Method

A Cartesian grid based on Immersed Boundary Method (IBM), proposed by the present authors, is extended to unstructured grids.The advantages of IBM and Body Fitted Grid (BFG) are taken to enhance the computation efficiency of the fluid structure interaction in a complex domain.There are many methods to generate the BFG, among which the unstructured grid method is the most popular.The concept of Volume Of Solid (VOS) is used to deal with the multi rigid body and fluid interaction.Each body surface is represen...     

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.     

MATHEMATICAL MODELS AND NUMERICAL SIMULATION FOR DENSE PARTICULATE FLOWS

Sedimentation of particles in inclined and vertical vessels is numerically simulated by the Eulerian two-fluid model. The numerical results show an interesting phenomenon with two circulation vortexes in a vertical vessel but one in the inclined vessel. Sensitivity tests indicate that the boundary layer effect is the key to induce this phenomenon. A numerical method based on 2D unstructured meshes is presented to solve the hard-sphere discrete particle model. Several applications show the numerical method has a good performance to simulate dense particulate flows in irregular domains without regard to element types of the mesh.