A TURBULENCE MODEL FOR VARYING DENSITY FLOW IN GENERAL CURVILINEAR COORDINATES

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A NUMERICAL MODEL FOR 3-D FLOW IN OPEN CHANNELS

A 3-D model based on the Reynolds equations with closed k-ε turbulence model ispresented in this paper,which can be used to predict surface water flow in open channels.In-stead of the“rigid lid”approximation,the solution of the free surface equation is implemented inthe velocity-pressure iterative procedure on the basis of the conventional SIMPLE method.Thismodel was used to compute the flow in rectangular channels with trenches dredged across the bot-tom.The velocity,eddy viscosity coefficient,turbulent shear stress,turbulent kinetic energyand elevation of the free surface over the trenches dredged in the main channel,can be obtained.The computed results are in good agreement with existing experimentaing data.     

2-D CHARACTERISTICS-LIKE MODEL AND OPEN BOUNDARY CONDITION FOR UNSTEADY OPEN CHANNEL FLOW MODELING

1.　ＩＮＴＲＯＤＵＣＴＩＯＮＵｎｓｔｅａｄｙｏｐｅｎｃｈａｎｎｅｌｆｌｏｗｓｗｉｔｈｒａｐｉｄｃｈａｎｇｅｏｆｗａｔｅｒｌｅｖｅｌｏｆｔｅｎｏｃｃｕｒｓｉｎｔｈｅｍａｎｍａｄｅｃｈａｎｎｅｌｓａｎｄｎａｔｕｒａｌｒｉｖｅｒｓ.Ｔｈｅｄａｍｂｒｅａｋｆ?..     

A MODIFIED SIMPLE ALGORITHM FOR 2-D FLOW IN OPEN CHANNEL

1.　INTRODUCTIONSince the SIMPLE[1 ] algorithm was set up,it has been used to numerically simulateincompressible flow successfully.And later on,the improved algorithms such as SIMPLERalgorithm[2 ] and SIMPLEC algorithm[3] have been presented in succession.For all thealgorithms stated above,only when velocity field varies linearly with water pressure(i.e.,pressure flow) ,owing to the coefficients of the velocity correction formulae beingindependent of pressure,do the velocity corre…     

A VARIATIONAL MODEL FOR 2-D MICROPOLAR BLOOD FLOW

1 .　INTRODUCTIONMicropolarfluids[1] arefluidswithmicro structure.Theybelongtoaclassoffluidswithnonsysmmetricstresstensorthatwasfirstintro ducedbyEringen[2 ] in 1964,andiscalledpolarflu ids.The polarfluids ,whenthecouplingstressisnottakenintoaccount ,reducetothewell knownNavier Stokesmodelofclassicalfluids .Physically ,micropolarfluidsrepresentsuchfluidsconsistingofrigid ,randomlyoriented (orspherical) particlessuspendedinaviscousmedium ,wherethedeformationoffluidparticlesisignored .Itha…     

FINITE VOLUME METHOD FOR SIMULATION OF VISCOELASTIC FLOW THROUGH A EXPANSION CHANNEL

A finite volume method for the numerical solution of viscoelastic flows is given. The flow of a differential Upper-Convected Maxwell (UCM) fluid through an abrupt expansion has been chosen as a prototype example. The conservation and constitutive equations are solved using the Finite Volume Method (FVM) in a staggered grid with an upwind scheme for the viscoelastic stresses and a hybrid scheme for the velocities. An enhanced-in-speed pressure-correction algorithm is used and a method for handling the source term in the momentum equations is employed. Improved accuracy is achieved by a special discretization of the boundary conditions. Stable solutions are obtained for higher Weissenberg number (We), further extending the range of simulations with the FVM. Numerical results show the viscoelasticity of polymer solutions is the main factor influencing the sweep efficiency.     

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.     

3-D SHALLOW WATER FLOW COMPUTATION BY A SEMIIMPLICIT FINITE ELEMENT METHOD

A simi-implicit finite element method is developed for three-dimensional shallow water flow. By using water depth to scale the vertical coordinate, the governing equation is transformed into fixed computational domain. An efficient generalized conjugate gradient scheme is adopted for the solution of finite element analogy.     

A MODEL FOR PREDICTING PHASE INVERSION IN OIL-WATER TWO-PHASE PIPE FLOW

1. INTRODUCTION Flows consisting of mixtures of two immisciblefluids such as oil and water are encountered frequentlyin many areas of the process industry and in thepetrochemical industry. The phase inversion refers toa phenomenon where, with a small chan…     

NUMERICAL SOLUTION FOR TIDAL FLOW IN OPENING CHANNEL USING COMBINED MACCORMACK-FINITE ANALYSIS METHOD

A new numerical scheme for solving the tidal flow in an opening channel using the advective-diffusion shallow-water equations as the governing equations is proposed based on the combination of the MacCormack and the finite analysis methods. In the present scheme, the finite analysis method is used to discretize the momentum equation and the MacCormack technique is used to discretize the continuity equation in a single grid system. The matrix of the discretized momentum equation is characterized by predominantly main diagonal elements, which ensures favorable convergence and stability for the numerical simulation by the combined method. To verify the present method, hydraulics simulation is carried out for a section down mainstream of the Huangpu River. The computational results agree with the measured data. By use of orthogonal curvilinear coordinate system, the methods can be easily extended to the numerical simulation of the tidal flow in a tortuous channel.     

A NEW FINITE DIFFERENCE SCHEME FOR 2-D FLOWS AT LARGE Re

Based on the conventional ADI method and SOR method for solving the Navier-Stokes equations, averaging those linkage terms which also are the terms of vary-ing coefficients of the equations, a new finite difference scheme-Averaging Finite Diffe-rence (AFD) scheme for 2-D flows was proposed. A 2-D driven cavity flow was calculated numerically as an example with the presented scheme at Re= 100, 1000, 2000, 3200, 10000. The results were discussed and compared to those obtained with the conventional methods as well as experimental data. It showed that a slight change of the approximation pattern of the conventional scheme in the terms of varying-coefficients of the governing equations seems to have an obvious influence on the solutions at high Re which will be erro- neous if the conventional schemes was employed.     

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.     

SIMULATION OF LAGRANGIAN DISPERSION USING A LAGRANGIAN STOCHASTIC MODEL AND DNS IN A TURBULENT CHANNEL FLOW

The mean square displacements of fluid particles in a turbulent channel flow at Re_τ = 100 are investigated using a modified Langevin equation, and are compared with DNS results. Both the Lagrangian integral time scales directly obtained from DNS and the predicted values using an empirical relation between the Eulerian and the Lagrangian integral time scales are used in the modified Langevin equation to test the effects of integral time scales on the dispersion of particles. The results show that the slight variation of the Lagrangian integral time scale has little influence on the dispersion. The agreement between results of the model equation and those of DNS is satisfactory except the streamwise dispersion for intermediate times (20 <t^* < 300), where the results of the model equation are slightly overestimated compared to those of DNS. The cause of such discrepancy is discussed.     

A COUPLED THERMO-HYDRAULIC MODEL FOR STEAM FLOW IN PIPE NETWORKS

This article aims to establish a coupled thermo-hydraulic mathematical model for steam network by adopting a set of equations, i.e., the continuity equation, motion equation, energy equation, state equation and enthalpy equation and considering the interaction of hydraulic and thermal working conditions. The model is simplified according to steam flow features in pipe networks. The unsteady flow model is simplified to a steady one with considering engineering practice and the solution to the governing equations are obtained by using the standard fourth-order Runge-Kutta method. Many factors of steam flow are generally considered, such as condensability, change of state, friction and heat transfer in the model. It is concluded that coupled iteration can be employed in steam network thermo-hydraulic computation. The numerical results with the model are basically in accordance with practical operation data.     

3-D NUMERICAL SIMULATIONS OF FLOW LOSS IN HELICAL CHANNEL

The flow loss of a helical channel Magnetohydrodynamic(MHD) thruster without MHD effect was numerically studied with 3-D simulations,and a flow loss coefficient was defined to quantify the flow loss and its influencing factors were studied.The results show that decreases in a first-order exponential manner with the pitch of a helical wall and the Reynolds number,and it declines slowly when and,a flow guide makes the flow more smooth and uniform,especially in the flow guide and helical wall sub-regions and thus reduces the flow loss greatly,by about 30% with the averaged value of from 0.0385 to 0.027,a rectifier weakens the helical flow and strengthens the axial one in the rectifier and outlet sub-regions,thus reduces the rotational kinetic pressure with the averaged value of declining about 4% from 0.0385 to 0.037,and decreases with a rectifier’s axial length when.     

MATHEMATICAL MODEL FOR 2-D TIDAL FLOW AND WATER QUALITY WITH ORTHOGONAL CURVILINEAR COORDINATES

1 .　INTRODUCTIONThedischargeofpollutedwaterisbecominganincreasingthreattotheresourcesintidalareas.Thenumericalsimulatingthe 2 Dtidalflowandwaterqualityisthebasisofwaterresource plan ningandmanagement.Inrecentyears,althoughconsiderableattentionhasbeenfocusedonthisproblem ,thecomputationaldifficultiesinnaturaltidalriversremaintobeabigproblem ,suchasthecomplicatedboundaryconfigurations ,the greatdisparitybetweenlengthandwidth ,etc .Inthefollowing ,a 2 Dnumericalmodelbasedonthealternating…     

THE LINEAR HOMOGENEOUS FLOW MODEL FOR TWO-PHASE FLOW INSTABILITY IN BOILING CHANNELS

ＮＯＭＥＮＣＬＡＴＵＲＥＤ　ｉｎｎｅｒｄｉａｍｅｔｅｒ (ｍ)Ｑ　ｈｅａｔｆｌｕｘ (ｋｗ/ｍ2 )ｆ　ｆｒｉｃｔｉｏｎａｌｒｅｓｉｓｔａｎｃｅｃｏｅｆｆｉｃｉｅｎｔＴ　ｔｅｍｐｅｒａｔｕｒｅ (°Ｃ)Ｇ　ｍａｓｓｆｌｏｗｖｅｌｏｃｉｔｙ (ｋｇ/ｓ.ｍ2 )ｔ　ｔｉｍｅ (     

MEASUREMENT OF A WALL-BOUNDED TURBULENT MIXING LAYER FLOW

1.INTRODUCTION Wall boundedturbulentmixinglayerflowsare ofprimarysignificancetovariousindustrialand militaryapplications.Amongothers,thewall boundedturbulentmixinglayerflowoveranopen ingstep,e.g.,gaseductorconfiguration,received agreatdealofattention.Thesecondaryflowen trainedfromtheopeningbythecoherentstruc tures,whicharequasi deterministicallyembedded inthemixinglayer,ismixedwiththemainflow.Suchflowiscloselyrelatedtoplanemixinglayer flowandreattachingflow.However,fewstudies ofitsturbule…     

NUMERICAL FLOW VISUALIZATION OF A MIXING LAYER

The Kelvin-Helmhotz rollup of three-dimensional time-developing mixing layers is simulated numerically. Dye lines or fluid interfaces, often visualized in experiments, are presented by computing the passive scalar at high Peclet number. The scalar contours reveal the mushroom-shaped streaklines observed in many experiments [l]and uncover by far more exquisite structures beyond experimental observations. The hydric bubbles released at a constant time interval are also simulated numerically. To help understand the visualization results, we analyze the behavior of the coherent structures, such as the streamwise ribs and the spanwise rollers. A comparison between the vortical structure and the passive scalar contours indicates that the wrapping by the vortices largely dominates the evolution of the passive scalar.     

HYBRID FINITE ANALYTIC SOLUTION FOR THREE-DIMENSIONAL TIDAL FLOW WITH SIGMA COORDINATE SYSTEM

1.　INTRODUCTIONTounderstandthecirculationandpollutanttransportinestuarineandcoastalwaters,numericalmodelshavebeenextensivelydevelopedduringthelasttwodecades.Thetransportofsalinity,heat,sedimentandwaterqualityconstituentwasdescribedbyadvectionanddiffusioninnumericalsimulations.Toconsidertheverticalvariation,inmanythree-dimensionaltransportmodels(SwansonandSpaulding1985;BlumbergandMllor1987;andSheng1987)thewell-knownσ-transformation(Philips1957)wasemployedinthepresenceofirrgularbathymtr…