Numerical analysis of finite amplitude motion of waves and a moored floating body under severe storm conditions

The motion of a moored floating body under the action of wave forces, which is influenced by fluid forces, shape of the floating body and mooring forces, should be analysed as a complex coupled motion system. Especially under severe storm conditions or resonant motion of the floating body it is necessary to consider finite amplitude motions of the waves, the floating body and the mooring lines as well as non-linear interactions of these finite amplitude motions. The problem of a floating body has been studied on the basis of linear wave theory by many researchers. However, the finite amplitude motion under a correlated motion system has rarely been taken into account. This paper presents a numerical method for calculating the finite amplitude motion when a floating body is moored by non-linear mooring lines such as chains and cables under severe storm conditions.     

Fluid Flows Around Floating Bodies, I: The Hydrostatic Case

We consider the hydrostatic configuration of a body floating freely on a liquid. Under the influence of gravitational and capillary forces there exists an equilibrium solution with contact angle π/2. This solution is the minimizer of a variational problem with an obstacle condition; the corresponding free boundary consists of the curve where the capillary surface meets the floating body.     

反共振流体浮筏的隔振特性研究

基于反共振原理, 设计了一种新型的流体浮筏隔振器. 应用流体动量方程和结构振动理论推导了该隔振器的数学模型, 分析了其隔振特性, 得到了最优隔振频率和浮体浸入流体深度的关系式. 仿真结果表明, 当浮体浸入流体深度在有限的范围内变化时, 新型隔振器会在从低频到高频的宽带内发生反共振现象. 反共振条件下的力传递率可降至极低水平.流体浮筏隔振器具有很好的(尤其是低频)隔振效果.     

The Effect of the Walls of an Arbitrary Tank in the Problem of Separation–Free Impact on a Floating Body

An algorithm for constructing an asymptotic power series for large depths is proposed. It allows one to use the well–known solution of the problem of impact on a rigid body floating on the surface of a fluid half–space to obtain an approximate solution of the impact problem for the same body floating on the surface of a fluid in a bounded basin. The case where the domain occupied by the fluid has two perpendicular planes of symmetry is considered. Asymptotic expressions are given for the velocity potential on the wetted part of the body surface and for the added mass. Examples of solutions are considered.     

Interaction between elliptical and ellipsoidal inclusions under bending stress fields

Summary  This paper deals with interaction problems of elliptical and ellipsoidal inclusions under bending, using singular integral equations of the body force method. The problems are formulated as a system of singular integral equations with Cauchy-type or logarithmic-type singularities, where unknown functions are densities of body forces distributed in the x,y and r,θ,z directions in infinite bodies having the same elastic constants as those of the matrix and inclusions. In order to satisfy the boundary conditions along the elliptical and the ellipsoidal boundaries, the unknown functions are approximated by a linear combination of fundamental density functions and polynomials. The present method is found to yield the exact solutions for a single elliptical or spherical inclusion under a bending stress field. It yields rapidly converging numerical results for interface stresses in the interaction of inclusions. Received 9 September 1999; accepted for publication 15 January 2000     

Heat transfer and hydrodynamic studies on two- and three-phase fluidized beds of floating bubble breakers

Heat transfer characteristics in three-phase fluidized beds of floating bubble breakers have been studied in a 0.142 m I.D. x 2.0 m high Plexiglas column fitted with an axially mounted cylindrical heater.Effects of the liquid and gas velocities, the particle size, the volume ratio of floating bubble breaker to particles on phase holdup, the vertical bubble length, and the heat transfer coefficient have been determined.In the bubble-coalescing regime, the heat transfer coefficient in three-phase fluidized beds having the volume ratio V_f/V_s of 10–15% produced a maximum increase in heat transfer coefficient of about 20% in comparison to that in the bed without floating bubble breakers. Also, bubble length and gas-phase holdups exhibited their maximum and minimum values at a volume ratio of 10–15%. The heat transfer coefficient in three-phase fluidized beds of floating bubble breakers can be estimated from the surface renewal model with isotropic turbulence theory.Heat transfer coefficients expressed in terms of the Nusselt number have been correlated with the particle Reynolds number and the volume ratio of floating bubble breakers to particles.     

Variable spaced particle in mesh-free method to handle wave-floating body interactions

In this work, the motion of a two-dimensional rectangular freely floating body under waves is simulated using Improved Meshless Local Petrov-Galerkin method with Rankine Source function (IMLPG_R) with variable spacing resolutions. The IMLPG_R method is a particle method that solves Navier–Stokes equations using the fractional step method to capture the wave properties. However, many existing particle methods are computationally intensive to model the wave-floating body due to the requirement of fine particles, needing uniform distribution throughout the domain. To improve the computational efficiency and capture the body response properly, variable spaced particle distribution with fine resolution near the floating body and coarse resolution far from the body is implemented. Numerical schemes to handle variable resolutions are reported. An iterative scheme to handle the wave-floating body is implemented in the particle method. Two test cases, one with small wave and another with steep waves, are simulated for uniform particle distribution and the result shows good agreement with literature. Based on this, the performance of the variable spaced particle distribution is tested in coupling with floating body solver. The application of the method for wave impact load from the green water loading of the floating structure is also simulated.     

关于浮体的平衡与稳定性

本文讨论了浮体的平衡与稳定问题, 介绍了定倾中心的定义, 并结合一个具体的例子, 给出了浮体稳定性3种不同的判别方法, 最后, 根据能量方法说明了用定倾高度判定浮体稳定性的理论依据.     

Homogenization of scalar wave equations with hysteresis

The paper deals with a scalar wave equation of the form where is a Prandtl–Ishlinskii operator and are given functions. This equation describes longitudinal vibrations of an elastoplastic rod. The mass density and the Prandtl–Ishlinskii distribution function are allowed to depend on the space variable x. We prove existence, uniqueness and regularity of solution to a corresponding initial-boundary value problem. The system is then homogenized by considering a sequence of equations of the above type with spatially periodic data and , where the spatial period tends to 0. We identify the homogenized limits and and prove the convergence of solutions to the solution of the homogenized equation. Received June 17, 1999     

Parallel finite element simulation of mooring forces on floating objects

The coupling between the equations governing the free‐surface flows, the six degrees of freedom non‐linear rigid body dynamics, the linear elasticity equations for mesh‐moving and the cables has resulted in a fluid‐structure interaction technology capable of simulating mooring forces on floating objects. The finite element solution strategy is based on a combination approach derived from fixed‐mesh and moving‐mesh techniques. Here, the free‐surface flow simulations are based on the Navier–Stokes equations written for two incompressible fluids where the impact of one fluid on the other one is extremely small. An interface function with two distinct values is used to locate the position of the free‐surface. The stabilized finite element formulations are written and integrated in an arbitrary Lagrangian–Eulerian domain. This allows us to handle the motion of the time dependent geometries. Forces and momentums exerted on the floating object by both water and hawsers are calculated and used to update the position of the floating object in time. In the mesh moving scheme, we assume that the computational domain is made of elastic materials. The linear elasticity equations are solved to obtain the displacements for each computational node. The non‐linear rigid body dynamics equations are coupled with the governing equations of fluid flow and are solved simultaneously to update the position of the floating object. The numerical examples includes a 3D simulation of water waves impacting on a moored floating box and a model boat and simulation of floating object under water constrained with a cable. Copyright © 2003 John Wiley & Sons, Ltd.     

Variational principles in elasticity with nonlinear stress-strain relation

Since 1979, a series of papers have been published concerning the variational principles and generalized variational principles in elasticity such as [1] (1979), [6] (1980), [2,3] (1983) and [4,5] (1984). All these papers deal with the elastic body with linear stress-strain relations. In 1985, a book was published on generalized variational principles dealing with some nonlinear elastic body, but never going into detailed discussion. This paper discusses particularly variational principles and generalized variational principles for elastic body with nonlinear stress-strain relations. In these discussions, we find many interesting problems worth while to pay some attention. At the same time, these discussions are also instructive for linear elastic problems. When the strain is small, the high order terms may be neglected, the results of this paper may be simplified to the well-known principles in ordinary elasticity problems.     

Influence of unsteady wake on a turbulent separation bubble

 An experimental study was made of turbulent separated and reattaching flow over a blunt body, where unsteady wake was generated by a spoked-wheel type of wake generator with cylindrical rods. The influence of unsteady wake was scrutinized by altering the rotation direction (clockwise and counter-clockwise) and the normalized passing frequency (0 ≤ St _H  ≤ 0.20). The Reynolds number based on the cylindrical rod was Re _d =375. A phase-averaging technique was employed to characterize the unsteady wake. The effect of different rotation directions, which gave a significant reduction of x _R , was examined in detail. The wall pressure fluctuations on the blunt body were analyzed in terms of the spectrum and the coherence. Received: 15 January 2001 / Accepted: 17 July 2001     

Motion of a slender body in a fluid under a floating plate

This paper studies the three-dimensional unsteady problem of the hydroelastic behavior of a floating infinite plate under the impact of waves generated by horizontal rectilinear motion of a slender solid in a fluid of infinite depth. An analytic solution of the problem is found based on the known solutions for the unsteady motion of a point source of mass in a fluid of infinite depth under a floating plate. Asymptotic formulas are obtained which model the motion of a solid slender body in a fluid by replacing the body with a source-sink system. These formulas are used to numerically analyze the effect of plate thickness, depth of the body, its dimensions and the velocity of rectilinear motion on the amplitude of deflection of the floating plate. The motion of a submarine under a nonbreakable plate was modeled experimentally. Theoretical and experimental data are in good agreement.     

Mikusinski’s operators solution of three-order linear difference equation with variable coefficients

This paper proceeds the papers [3] [4], we make use of the idea of the variable number operators and some concepts and conclusions of the shifting operators series with variable coefficients in the operational field of Mikusinski, it is devoted to the solution of the general three-order linear difference equation with variable coefficients, and it is also devoted to the better solution formula for the some special three-order linear difference equations with variable coefficients: in addition, we try to provide the idea and method for realizing solution of the more than three-order linear difference equation with variable coefficients. Project Supported by the Science Foundation of Anhui Province     

Variation of the stress intensity factor along the front of a 3-D rectangular crack subjected to mixed-mode load

Summary  The singular integral equation method is applied to the calculation of the stress intensity factor at the front of a rectangular crack subjected to mixed-mode load. The stress field induced by a body force doublet is used as a fundamental solution. The problem is formulated as a system of integral equations with r ⁻³-singularities. In solving the integral equations, unknown functions of body-force densities are approximated by the product of polynomial and fundamental densities. The fundamental densities are chosen to express two-dimensional cracks in an infinite body for the limiting cases of the aspect ratio of the rectangle. The present method yields rapidly converging numerical results and satisfies boundary conditions all over the crack boundary. A smooth distribution of the stress intensity factor along the crack front is presented for various crack shapes and different Poisson's ratio. Received 5 March 2002; accepted for publication 2 July 2002     

Comparison of linear spring and nonlinear FEM methods in dynamic coupled analysis of floating structure and mooring system

This paper compares the dynamic coupled behavior of floating structure and mooring system in time domain using two numerical methods for the mooring lines such as the linear spring method and the nonlinear FEM (Finite Element Method). In the linear spring method, hydrodynamic coefficients and forces on the floating body are calculated using BEM (Boundary Element Method) and the time domain equation is derived using convolution. The coupled solution is obtained by simply adding the pre-determined spring constants of the mooring lines into the floating body equation. In FEM, the minimum energy principle is applied to formulate the nonlinear dynamic equation of the mooring system with a discrete numerical model. The ground contact model and Morison formula for drag forces are also included in the formulation. The coupled solution is obtained by iteratively solving the floating body equation and the FEM equation of the mooring system. Two example structures such as weathervane ship and semi-submersible structure are analyzed using linear spring and nonlinear FEM methods and the difference of those two methods are presented. By analyzing the cases with or without surge-pitch or sway-roll coupling stiffness of mooring lines in the linear spring method, the effect of coupling stiffness of the mooring system is also discussed.     

Variable Order and Distributed Order Fractional Operators

Many physical processes appear to exhibit fractional order behavior thatmay vary with time or space. The continuum of order in the fractionalcalculus allows the order of the fractional operator to be considered asa variable. This paper develops the concept of variable and distributedorder fractional operators. Definitions based on the Riemann–Liouvilledefinition are introduced and the behavior of the new operators isstudied. Several time domain definitions that assign different argumentsto the order q in the Riemann–Liouville definition are introduced. Foreach of these definitions various characteristics are determined. Theseinclude: time invariance of the operator, operator initialization,physical realization, linearity, operational transforms, and memorycharacteristics of the defining kernels.A measure (m ₂) for memory retentiveness of the order history isintroduced. A generalized linear argument for the order q allows theconcept of `tailored' variable order fractional operators whose m ₂ memory may be chosen for a particular application. Memory retentiveness (m ₂) andorder dynamic behavior are investigated and applications are shown.The concept of distributed order operators where the order of thetime based operator depends on an additional independent (spatial)variable is also forwarded. Several definitions and their Laplacetransforms are developed, analysis methods with these operators aredemonstrated, and examples shown. Finally operators of multivariable anddistributed order are defined and their various applications areoutlined.     

Analysis of free vibration of coupled Reissner's plate-liquid-spring system

Based on Reissner's plate theory, the dynamic behaviour of an offshore circular plate with moderate thickness floating on a liquid of finite constant depth and anchored by uniformly distributed springs to the sea bed is investigated. The frequency equation governing the motion of the coupled Reissner's plate-liquid-spring system is analytically obtained by means of the linear potential flow theory and the expansion theorem in modal analysis. Several numerical examples are presented to illustrate the variation in fundamental frequencies of Reissner's floating circular plates with free edge due to the stiffnesses of distributed springs and the depths of liquid.The author is grateful to Mr. W.M. Cheng for his help in completing the numerical calculations.     

A multiblock operator‐splitting algorithm for unsteady flows at all speeds in complex geometries

This paper describes a non‐iterative operator‐splitting algorithm for computing all‐speed flows in complex geometries. A pressure‐based algorithm is adopted as the base, in which pressure, instead of density, is a primary variable, thus allowing for a unified formulation for all Mach numbers. The focus is on adapting the method for (a) flows at all speeds, and (b) multiblock, non‐orthogonal, body‐fitted grids for very complex geometries. Key features of the formulation include special treatment of mass fluxes at control volume interfaces to avoid pressure–velocity decoupling for incompressible (low Mach number limit) flows and to provide robust pressure–velocity–density coupling for compressible (high‐speed) flows. The method is shown to be robust for all Mach number regimes for both steady and unsteady flows; it is found to be stable for CFL numbers of order ten, allowing large time steps to be taken for steady flows. Enhancements to the method which allow for stable solutions to be obtained on non‐orthogonal grids are also discussed. The method is found to be very reliable even in complex engineering applications such as unsteady rotor–stator interactions in turbulent, all‐speed turbomachinery flows. Copyright © 2004 John Wiley & Sons, Ltd.