UNSTEADY WAVES DUE TO AN IMPULSIVE OSEENLET BENEATH THE CAPILLARY SURFACE OF A VISCOUS FLUID

The two-dimensional free-surface waves due to a point force steadily moving beneath the capillary surface of an incompressible viscous fluid of infinite depth were analytically investigated. The unsteady Oseen equations were taken as the governing equations for the viscous flows. The kinematic and dynamic conditions including the combined effects of surface tension and viscosity were linearized for small-amplitude waves on the free-surface. The point force is modeled as an impulsive Oseenlet. The complex dispersion relation for the capillary-gravity waves shows that the wave patterns are characterized by the Weber number and the Reynolds number. The asymptotic expansions for the wave profiles were explicitly derived by means of Lighthill’s theorem for the Fourier transform of a function with a finite number of singularities. Furthermore, it is found that the unsteady wave system consists of four families, that is, the steady-state gravity wave, the steady-state capillary wave, the transient gravity wave, and the transient capillary wave. The effect of viscosity on the capillary-gravity was analytically expressed.     

UNSTEADY INTERFACIAL WAVES DUE TO SINGULARITIES IN TWO SEMI-INFINITE INVISCID FLUIDS

1.INTRODUCTION ThelinearCauchy Poissonproblems,which areconcernedwiththegenerationandpropagation offree surfacewavesduetoaninitialelevationor apointpressureactingonthefreesurfaceofanin compressibleinviscidfluid,havebeeninvestigated bymanyresearchersinviewofitstheoreticalinterestandpracticalimportance[15].Thetransient developmentoftwo dimensionalgravitywavesdue toanoscillatingsurfacepressurewasconsideredby Miles[6]whoproposedawell posedinitialvalue problemtocorrectStoker'sformulation[2].A…     

Large eddy simulation of free-surface flows

This paper introduces and discusses numerical methods for free-surface flow simulations and applies a large eddy simulation(LES) based free-surface-resolved CFD method to a couple of flows of hydraulic engineering interest. The advantages, disadvantages and limitations of the various methods are discussed. The review prioritises interface capturing methods over interface tracking methods, as these have shown themselves to be more generally applicable to viscous flows of practical engineering interest, particularly when complex and rapidly changing surface topologies are encountered. Then, a LES solver that employs the level set method to capture free-surface deformation in 3-D flows is presented, as are results from two example calculations that concern complex low submergence turbulent flows over idealised roughness elements and bluff bodies. The results show that the method is capable of predicting very complex flows that are characterised by strong interactions between the bulk flow and the free-surface, and permits the identification of turbulent events and structures that would be very difficult to measure experimentally.     

FREE-SURFACE WAVES AND FAR WAKES GENERATED BY A FLOATING BODY IN A VISCOUS FLUID

1 .　INTRODUCTIONThewavemotionduetoamovingdisturbancehasbeenoflong standinginterest .Butthecorre spondingwakestructuredidnotreceivemuchat tentionuntilthesyntheticapertureradarcollectedanumberofimagesofV likewakepatternsgener atedbyships (Milgram 1988;Brownetal.1989) .Thewakestructuresarethoughttobeclassifiedin tothreecategories :theKelvinwavewakes ,thetrubulentwakesandtheinternalwavewakes(Griffin 1988;Lydenetal.1988;GuandPhillips1994 ) .TheKelvinwakesarethefar fieldwavepatternsgenerate…     

SURFACE AND INTERFACIAL GRAVITY WAVES INDUCED BY AN IMPULSIVE DISTURBANCE IN A TWO-LAYER INVISCID FLUID

The transient gravity waves due to an impulsive source in a two-layer fluid system are investigated analytically.The fluid is assumed to be inviscid and incompressible.The density of each of the two layers is constant.Five different boundary conditions are considered.The depth of each of the two layers is infinite or finite.The upper fluid of finite depth is covered by a rigid lid or a free surface.Based on the assumption of small-amplitude waves,a linear system is established.The integral solutions for the free-surface and interfacial waves are obtained by means of the Fourier-Laplace transform.The corresponding asymptotic representations are derived for large time with a fixed distance-to-time ratio by the Stokes and Scorer methods of stationary phase.The analytical solutions show that there are two different modes,namely the free-surface and interfacial wave modes.The wave profiles observed depend on the relation between the distance-to-time ratio and the maximal group velocities and on the limiting values of the second derivatives of the frequencies as well.     

Ship bow waves

The bow wave generated by a ship hull that advances at constant speed in calm water is considered. The bow wave only depends on the shape of the ship bow (not on the hull geometry aft of the bow wave). This basic property makes it possible to determine the bow waves generated by a canonical family of ship bows defined in terms of relatively few parameters. Fast ships with fine bows generate overturning bow waves that consist of detached thin sheets of water, which are mostly steady until they hit the main free surface and undergo turbulent breaking up and diffusion. However, slow ships with blunt bows create highly unsteady and turbulent breaking bow waves. These two alternative flow regimes are due to a nonlinear constraint related to the Bernoulli relation at the free surface. Recent results about the overturning and breaking bow wave regimes, and the boundary that divides these two basic flow regimes, are reviewed. Questions and conjectures about the energy of breaking ship bow waves, and free-surface effects on flow circulation, are also noted.     

Surface and interfacial gravity waves due to a disturbance steadily moving in a two-layer inviscid fluid

The generation and interaction of surface and interfacial gravity waves due to an submerged source moving in a two-layer fluid are investigated analytically for two-dimensional cases. The fluid is assumed to be inviscid and incompressible. The density of each of the two layers is constant. Two different boundary conditions are considered for the upper surface. The upper fluid of finite depth is bounded above by a rigid lid or a free surface. Based on the assumption of small-amplitude waves, a linear system is established. The integral solutions for the free-surface and interfacial elevations are obtained by means of the Fourier transform. Then the corresponding asymptotic representations are derived for far-field waves by the residue theorem. The critical Froude numbers for the existence of far-field waves are derived for the two-layer system bounded above by a rigid lid or a free surface. The effect of different upper boundary conditions on the wave generation are discussed.

     

用密度函数法对自由表面进行数值模拟

本文从二维非定常N-S方程出发，提出了一种处理自由表面问题的数值方法。引入密度函数法(density-function method)追踪自由表面，在密度函数的传输方程中采用TVD格式达到了二阶精度。对均匀来流中的非定常不可压方柱绕流进行了数值模拟。数值结果成功地捕捉了自由表面波动以及漩涡的生成、分离的时间发展历程。同时验证了本方法的有效性。     

波流联合作用下的物体上的波浪绕射力

本文研究了在波流联合作用下的任意三维物体的波浪绕射问题,建立了求解物体上的波浪绕射力的时域解理论模型。本文证明了对于任意三维物体,如果在自由面条件简化时,假设定常兴波势为有限量阶,则在波浪绕射力公式中,不存在含有绕射势的水线积分项。从数学上证明了水线积分项反映了自由面条件中定常兴波势和不定常势之间的耦合效应。在此基础上,本文提出了在波流联合作用情况下,作用在物体上的绕射力与辅助辐射势之间的关系式,从而不须求解绕射势便可得到绕射力。     

Numerical simulation of submarine landslide tsunamis using particle based methods

This paper presents the simulation of tsunamis due to rigid and deformable landslides with consideration of submerged conditions by using particle methods. The smoothed particle hydrodynamics(SPH), as a particle based method, is for solving problems of fast moving boundaries in the field of continuum mechanics. Other particle based methods, like the discrete element method(DEM), are suitable for modeling the displacement and the collision related to the rigid landslides. In the present work, we use the SPH and the DEM to simulate tsunamis generated by rigid and deformable landslides with consideration of submerged conditions. The viscous free-surface flows are solved by a weakly compressible SPH and the displacement and the rotation of the rigid body slides are calculated using a multi-sphere DEM allowing for modeling solids of arbitrarily complex shapes. The fluid-solid interactions are simulated by coupling the SPH and the DEM. A rheology model combining the Papanastasiou and the Herschel-Bulkley models is applied to represent the viscoplastic behavior of the non-Newtonian flow in the submarine deformable landslide cases. Submarine landslide tsunamis due to rigid and deformable landslides are both simulated as typical landslide cases in this investigation. Our simulated results and the previous experimental results in the literatures are in good agreement, which shows that the proposed particle based methods are capable of modeling the submarine landslide tsunamis.     

Shedding frequency of sheet cavitation around axisymmetric body at small angles of attack

Cavity shedding of cavitating flows around an axisymmetric body belongs to the unsteady cavitating flows in the condition of steady incoming current.The periodic characteristics of unsteady cavitating flows around an axisymmetric body at small angles of attack are investigated experimentally and numerically.The evolution and shedding process of the three-dimensional sheet cavitation are computed numerically by the Reynolds averaged Navier-Stokes equations and the RNG k-?model.The modification approach for eddy viscosity coefficient in the transition area of the two-phase flow is adopted to reproduce the shedding process of cavitating flows.The computed frequency of the cavity shedding coincides with the experimental data for the cases of unsteady cavitating flows around axisymmetric bodies with four headforms.Given the cavitation number,the shedding process of the cavitating flow depends heavily on the headform of the axisymmetric body.If the angle of attack of the axisymmetric body is greater than a critical value,the violent shedding of the sheet cavitation seems to be depressed.     

NUMERICAL SIMULATIONS OF CAVITATING FLOWS

BRIEFINTRODUCTIONOFTHEPAPER :　Thisthesismainlyresearchesonthehydrodynamiccharacteristicsandmechanismfor 3Dcavitatingflowsaroundaxisymmetricbodies ,aswellasthe2Dcavitatingflowsaroundhydrofoils .Anewcavi tatingflowmodel,whichinvolvesviscousandmul ti phaseeffects,isestablishedintwo phaseflowcategory .Accordingtothelocalizedvariationofdensitywithinpredominantlyincompressiblewatermediumandthecharacteristicsofsoundspeedinwater vapormixture ,arelationbetweendensityandpressureisassumed ,in…     

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.     

COMPRESSIBILITY BOUNDARY LAYER THEORY AND ITS SIGNIFICANCE IN COMPUTATIONAL HYDRODYNAMICS

ＣＯＭＰＲＥＳＳＩＢＩＬＩＴＹＢＯＵＮＤＡＲＹＬＡＹＥＲＴＨＥＯＲＹＡＮＤＩＴＳＳＩＧＮＩＦＩＣＡＮＣＥＩＮＣＯＭＰＵＴＡＴＩＯＮＡＬＨＹＤＲＯＤＹＮＡＭＩＣＳ￥ＣｈａｒｌｅｓＣ．Ｓ．Ｓｏｎｇ（ＵｎｉｖｅｒｓｉｔｙｏｆＭｉｎｎｅｓｏｔａ，Ｍｉｎｎｅａ...     

计及自由面兴波和螺旋桨非定常旋转效应的集装箱船舶绕流场计算研究

该文以商用软件FLUENT为平台,以KCS算例为对象,进行了计及自由面和螺旋桨非定常旋转效应的计算。考察了时间步长、自由面是否固化、湍流模式和网格数量、计算策略对计算结果的影响,确定了工程适用的计算方法,并应用于9000TEU集装箱船舶,与试验结果比较,吻合良好。     

Iterative Rankine HOBEM analysis of hull-form effects in forward-speed diffraction problem

A time-domain numerical algorithm based on the higher-order boundary element method and the iterative time-marching scheme is proposed for seakeeping analysis. The ship waves generated by a hull advancing at a constant forward speed in incident waves and the resultant diffraction forces acting on the hull are computed to investigate the hull-form effects on the hydrodynamic forces. A rectangular computational domain travelling at ship's speed is considered. An artificial damping beach for satisfying the radiation condition is installed at the outer portion of the free surface except the downstream side. An iterative time-marching scheme is employed for updating both kinematic and dynamic free-surface boundary conditions for numerical accuracy and stability. The boundary integral equation is solved by distributing higher-order boundary elements over the wetted body surface and the free surface. The hull-form effects on the naval hydrodynamics are investigated by comparing three different Wigley models. Finally, the corresponding unsteady wave patterns and the wave profiles around the hulls are illustrated and discussed.     

An iterative Rankine BEM for wave-making analysis of submerged and surface- piercing bodies in finite water depth

A 3-D iterative Rankine Boundary Element Method （BEM） for seakeeping problem in time domain is developed in the framework of linear potential theory. Waves generated by both submerged and surface-piercing bodies moving at a constant forward speed in otherwise calm water, and the resultant steady wave pattern, wave profile and resistance are computed to validate this newly-developed code. A rectangular computational domain moving with the same forward speed as the body is introduced, in which an artificial damping beach is installed at an outer portion of the free surface except the downstream side for satisfying the radiation condition. The velocity potential on the ship hull and the normal velocity on the free surface are obtained directly by solving the boundary integral equation, with the Rankine source used as the kernel function. An iterative time-marching scheme is employed for updating both kinematic and dynamic free surface boundary conditions to stabilize the calculation. Extensive results including the wave patterns, wave profiles and wave resistances for a submerged spheroid and a Wigley hull with forward speed are presented to validate the efficiency of the proposed 3-D time-domain higher-order approach. Finally, the sensitivity of ship-generated waves to the water depth is investigated. Computed results show satisfactory agreement with the corresponding experimental data and other numerical solutions.     

应用时域格林函数方法模拟有限水深中波浪对结构物的作用

该文采用时域内满足自由水面条件的格林函数方法对无限和有限水深中波浪与任意形状三维物体相互作用所产生的绕射和辐射问题进行了理论研究和数值计算。建立了不包含自由水面积分的积分方程,消除了自由项系数。文中计算了各种形状三维物体在无限水深和有限水深情况下所受到的绕射和辐射波浪力,并与解析解以及频域理论进行了对比,结果符合良好,验证了本文所提理论的正确性。     

A 3-D numerical study of solitary wave interaction with vertical cylinders using a parallelised particle-in-cell solver

This paper aims to provide a better understanding of the interaction between solitary waves and vertical circular cylinders. This is achieved via process based numerical modelling using the parallel particle-in-cell based incompressible flow solver PICIN. The numerical model solves the Navier-Stokes equations for free-surface flows and incorporates a Cartesian cut cell method for fluid-structure interaction. Solitary waves are generated using a piston-type wave paddle. The PICIN model is first validated using a test case that involves solitary wave scattering by a single vertical cylinder. Comparisons between the present results and experimental data show good agreement for the free surface elevations around the cylinder and the horizontal wave force on the cylinder. The model is then employed to investigate solitary wave interaction with a group of eleven vertical cylinders. The wave run-up and wave forces on the cylinders are discussed.     

AN APPROACH IN MODELING TWO-DIMENSIONAL PARTIALLY CAVITATING FLOW

1. INTRODUCTIONCavitation is a phenomenon that widely occurs in liquids. When the flow leads to the local pressure below the saturation vapor pressure of water (the fluid medium, in our research), usually incipient cavitation firstly occurs on the solid b…