NUMERICAL SIMULATION OF MOVING SCOUR BOUNDARY AND TURBULENCE FLOW AROUND SUBMARINE PIPELINES

A two dimensional vertical mathematical model is proposed in this paper for simulating the equilibrium profile of local scour around submarine pipelines. The current model is composed of a new k-ε turbulence model, fitting moving boundary with pre-meshed grid lines and incipient criterion of shear stress for sediments. Employing the proposed model, an instance is carried out numerically and compared with experiments. The calculation results agree well with the experiments. It shows that the improved two equation turbulence model, adopted in this paper is appropriate to simulating the turbulent flow ficld around submarine pipelines, fitting moving boundary with pre-mcshed grid lines method is efficient for moving boundary problems in a multiply connected domain and the stability evaluation method for seabed with critical shear stress based on log-wall law is a reliable choice.     

TIME DOMAIN SOLUTION OF UNSTEADY FLOW AROUND A SHIP

The unsteady flow around a ship advancing at constant speed is studied in time domain using a higher-order boundary element method. The Rankine source is employed and the ship hull and free surface are discretized into 8-node isoparametric elements. A modified Green formula is used to overcome the numerical difficulty arising from the singular or quasi-singular integrals in the integral equation. In the case of τ> 0. 25, a rigid wall condition is applied to the upstream and a numerical beach is applied downstream to absorb the outgoing waves. The numerical results are satisfactory, compared with the experimental results.     

A FINITE ELEMENT AND BOUNDARY ELEMENT METHOD OF NUMERICAL SIMULATION OF TWO DIMENSIONAL AND TWO PHASE FLOW

ＡＦＩＮＩＴＥＥＬＥＭＥＮＴＡＮＤＢＯＵＮＤＡＲＹＥＬＥＭＥＮＴＭＥＴＨＯＤＯＦＮＵＭＥＲＩＣＡＬＳＩＭＵＬＡＴＩＯＮＯＦＴＷＯＤＩＭＥＮＳＩＯＮＡＬＡＮＤＴＷＯＰＨＡＳＥＦＬＯＷＦａｎＪｉａｎｇ；ＱｕＤｅ－ｂｉｎ；ＺｈａｎｇＺｉ－ｘｉａｎｇ（Ｑｉｎ...     

NUMERICAL MODELING OF UNSTEADY SEPARATING FLOW AND ITS EXPERIMENT VERIFICATION

A simulation of unsteady separating flow in an expanding flume is presented inthis paper.The numerical modeling is based on a general horizontal 2-D mathematical model ofunsteady flow.It is verified that the flow pattern,whirlpool length and maximum reversalvelocity reasonably agree with the data from flume tests and this result could be an additionalproof for the validity of the earlier developed mathematical model.     

NUMERICAL SIMULATION OF TRANSIENT FLOW AROUND A SHIP IN UNSTEADY BERTHING MOTION

Ship berthing is a specific maneuver operation. The flow around a berthing ship and the forces acting on the hull are quite different from those for a ship in normal navigation. By solving the unsteady Reynolds-Averaged Navier-Stokes (RANS) equations, the transient flow field around a ship undergoing unsteady lateral motion is simulated and the varying lateral hydrodynamic force acting on the hull is evaluated in this article. The numerical results obtained with different turbulence models are analyzed and compared with experimental results and other numerical results published in literature, and a turbulence model more suitable for simulation of the viscous flow around a ship undergoing unsteady berthing is determined.     

NUMERICAL SOLUTION OF INCOMPRESSIBLE VISCOUS FLOW OVER AEROFOIL WITH H-TYPE GRID

The numerical solution of incompressible viscous flow over an aerofoil is obtainedby H-type grids and a special difference scheme. The method of mass flux corection is introducedwith success in order to accelerate convergence in iteration of velocity and pressure calculation.     

NUMERICAL SIMULATION OF NONLINEAR WAVE FLOW AROUND COCHLEA CHANNELED STERN SHIPS

A nonlinear method based on Gadd's model [1] [2] is developed to simulate the wave flow around cochlea-channeled stern ships. The subsurface division method is capable of dividing the complicated hull into panels and defining the computer simulated 3-D graphs. Good results are obtained and depicted by computer graphs.     

EXPERIMENTAL STUDIES AND NUMERICAL CALCULATION ON TURBULENT BOUNDARY LAYER OF WATER FLOW ALONG CURVED SURFACE

This paper will introduce experimental studies and numerical calculation onturbulent boundary layer of water flow along curved surface in our country in recent years.Onthe basis of the experimental studies,the effects of curvature and roughness on velocitydistribution and pressure distribution and the change of turbulent flow boundary layer onoverflow bucket concave surface is discussed.We proposed the empirical formula of velocity,pressure and the change of turbulent flow boundary layer on outlet bucket concave.According tothe momentum principle,we have deduced the momentum integral equation full water depthboundary layer and using the element as control unit inside the boundary layer on concavesurface of bucket.Combining with continuity equation,we have computed the boundary layerdevelopment on the bucket of a spillway.Compared with the field experimental data,thecalculation results are available.Under polar coordinates,a mathematical model for simulatingtime-averaged flow characteristics in concave surface of bucket is established.The turbulent flowfield on concave surface of bucket is calculated by SIMPLE method and this mathematicalmodel.The flow velocity field,pressure field,distribution of turbulent kinetic energy,distribution of turbulent energy dissipating rate and distribution of shear stress are available.Thecalculation value is consistent with measured test data.     

CALCULATION OF VISCOUS FLOW AROUND CIRCULAR CYLINDER WITH THREE-DIMENSIONAL NUMERICAL SIMULATION

1 .　ＩＮＴＲＯＤＵＣＴＩＯＮＴｈｅｆｌｏｗａｒｏｕｎｄａｃｉｒｃｕｌａｒｃｙｌｉｎｄｅｒｉｓｖａｌｕａｂｌｅｉｎｏｉｌｃｏｍｐａｎｉｅｓｏｒｏｆｆｓｈｏｒｅｉｎｄｕｓｔｒｙｔｈａｔｒｅｌｙｉｎｍｏｓｔｃａｓｅｓｏｎｓｕｂｓｅａｐｉｐｅｌｉｎｅｏｒｒｉｓｅｒｓｔｏｔｒａｎｓｐｏｒｔｇａｓａｎｄｏｉｌｆｒｏｍｏｃｅａｎｇｒｏｕｎｄｓｔｏｌａｎｄｏｒｓｕｒｆａｃｅｐｌａｔｆｏｒｍ .Ｗｅｓｈｏｕｌｄｅｎｓｕｒｅｔｈａｔｔｈｅｓｅｏｆｆｓｈｏｒｅｓｔｒｕｃｔｕｒｅｓａｒｅｒｅｓｉｓ ｔａｎｔａｎｄｓｔａｂ…     

NUMERICAL SIMULATION OF DISCONTINUOUS FLOW IN CIRCULAR CONDUITS

ＮＵＭＥＲＩＣＡＬ　ＳＩＭＵＬＡＴＩＯＮ　ＯＦ　ＤＩＳＣＯＮＴＩＮＵＯＵＳ　ＦＬＯＷ　ＩＮ　ＣＩＲＣＵＬＡＲ　ＣＯＮＤＵＩＴＳＮＵＭＥＲＩＣＡＬＳＩＭＵＬＡＴＩＯＮＯＦＤＩＳＣＯＮＴＩＮＵＯＵＳＦＬＯＷＩＮＣＩＲＣＵＬＡＲＣＯＮＤＵＩＴＳ￥ＭａｏＺｅ...     

INTEGRAL ANALYSIS ON INTERACTION OF DUAL-JET FLOW

This work reports the analysis of the flow characteristics of two plane,paralleljets that merge as they issue into stagnant surroundings.The predicted results based on a simpleintegral analysis of the flowfield are compared with the experimental data.It shows that thesimple analysis predicts the major variables of the dual-jet reasonably well and the spreadingparameter σ=15 for plane dual-jet.     

THEORETICAL ANALYSIS AND NUMERICAL SIMULATION OF TURBULENT FLOW AROUND SAND WAVES AND SAND BARS

Natural rivers usually possess sand waves and sand bars. In this article, the rapid distortion theory was used to study the turbulent flow over sand waves. The results show that the pre-existing shearing motion and upstream anisotropy of the turbulence flow would have significant effect on the turbulent structures, and hence the memory effect should be taken into consideration. Furthermore, the 2-D mathematical model was employed to simulate the unsteady flow around the Taiping Sand Bar in the lower reach of the Yangtze River and the time step effect on the unsteady flow simulation with the implicit scheme was discussed at the same time. The results show that the implicit scheme keeps effective until the time step reaches a certain number, and the calculated water levels and velocities are in agreement with the observed data.     

NUMERICAL STURDY OF GRAVITATIONAL GRANULAR FLOW

The mechanics of flowing granular materials such as coal,sand, metal ores etc. , has received considerable attention in the recent years as it has relevance to several important technological problems. The governing equations for the flow of granular materials, are derived using a model based on the kinetic theory approach [cf. Boyle and Mas-soudi (1990)]. For a fully developed flow of these meterials down an inclined plane, the equations reduce to a system of coupled non-linear ordinary differential equations. The resulting boundary value problem is solved numerically and a parametric study is carried out to delineate how the various non-dimensional parameters affect the structure of the solution.     

AN EXPERIMENTAL AND NUMERICAL INVESTIGATION OF THE STARTING FLOW OF A UNIFORMLY ACCELERATING CIRCULAR CYLIINDER

The starting flow around a uniformly accelerated circular cylinder is investigatedby flow visualization techncque and solving N-S equations numerically in detail.The results ofthe starting flow are similar with those of the impulsively started one.At lower Re_α,numbers the“phenomenon a”is revealed;the“phenomenon β”appears at higher Re_α numbers,but withonly one secondary vortex.At the early stage of the starting vortex formation,the flow islaminar;at the later stage,the flow transforms into turbulent flow.The velocity distribution inthe flow field is measured with the multiwires installment.The calculational results are comparedwith the results of experiment,and both are in agreement with each other.     

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.     

NUMERICAL SIMULATION OF FLOW FOLD OF A RIVER WITH COMPLICATED BOUNDARIES

ＮＵＭＥＲＩＣＡＬ　ＳＩＭＵＬＡＴＩＯＮ　ＯＦ　ＦＬＯＷ　ＦＩＥＬＤ　ＯＦ　Ａ　ＲＩＶＥＲ　ＷＩＴＨ　ＣＯＭＰＬＩＣＡＴＥＤ　ＢＯＵＮＤＡＲＹＳＮＵＭＥＲＩＣＡＬＳＩＭＵＬＡＴＩＯＮＯＦＦＬＯＷＦＯＬＤＯＦＡＲＩＶＥＲＷＩＴＨＣＯＭＰＬＩＣＡＴＥＤＢ...     

NUMERICAL SIMULATION OF ATOMIZATION RAINFALL AND THE GENERATED FLOW ON A SLOPE

This article studies the atomization rainfall and the generated flow on a slope by numerical simulations.The atomization rainfall is simulated by a unified model for splash droplets and a suspended mist,and the distribution of the diameter of splash rain drops is analyzed.The slope runoff generated by the atomization rainfall is simulated by a depth-averaged 2-D model,and the localization of the rainfall intensity in space is specially considered.The simulation results show that:(1) the median rain size of the atomization rainfall increases in the longitudinal direction at first,then monotonously decreases,and the maximum value is taken at the longitudinal position not in consistent with the position where the maximum rain intensity is taken.In the lateral direction the median rain size monotonously decreases,(2) since the atomization rainfall is distributed in a strongly localized area,it takes a longer time for its runoff yield to reach a steady state than that in the natural rainfall,the variation ranges of the water depth and the velocity in the longitudinal and lateral directions are larger than those in the natural rainfall.     

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.     

GRID GENERATION AND NUMERICAL SIMULATION OF 2-D RIVER FLOW

1 .　ＩＮＴＲＯＤＵＣＴＩＯＮＩｎｎａｔｕｒａｌｒｉｖｅｒ,ｔｈｅｓｈａｐｅｓｏｆｂｏｕｎｄａｒｉｅｓａｎｄｓｅｃ ｔｉｏｎｓａｒｅｏｆｔｅｎｉｒｒｅｇｕｌａｒ ,ｗｈｉｃｈｉｓａｄｉｆｆｉｃｕｌｔｐｒｏｂｌｅｍｆｏｒｎｕｍｅｒｉｃａｌｓｉｍｕｌａｔｉｏｎ .Ｔｏｓｏｌｖｅｔｈｉｓｐｒｏｂｌｅｍ ,ａｃｏｏｒｄｉ ｎａｔｅｔｒａｎｓｆｏｒｍａｔｉｏｎｍｅｔｈｏｄｉｓｏｆｔｅｎｕｓｅｄｔｏｔｒａｎｓｆｏｒｍｔｈｅｉｒｒｅｇｕｌａｒｒｅｇｉｏｎｉｎｔｈｅｐｈｙｓｉｃａｌｐｌａｎｅ(Ｘ ,Ｙ)ｔｏｔｈｅｒｅｇｕｌａ…     

NUMERICAL EXPERIMENTS ABOUT GROWTH OF THE ENERGY OF DISTURBANCE IN A BAROCLINIC FLOW

This article is concerned with the growth of energy of disturbances in a baroclinic flow within a finite time period. The implicit difference scheme was applied to the linearized vorticity equation, and the disturbance energy was computed for three kinds of vertical shears. It turns out that all the disturbance energy rapidly increases initially, and during the succeeding period there are several stages of growth and decay of energy of disturbances, and from a certain time on, all the disturbance energy begins to decrease.