Interaction of free-surface waves with a floating dock

A new method to describe the interaction of waves with a rigid or flexible dock, with zero draft, is derived. By means of Green's theorem an integral equation along the platform for either the velocity potential or the deflection is obtained. In the two-dimensional case this equation is solved by means of a superposition of exponential functions. With a specific choice of the Green function the integration with respect to the space coordinate can be carried out analytically. The integration left is the integration in the k-plane that occurs in the chosen Green function. Subsequently the contour of this integral is modified in the complex plane. This results at first in a dispersion relation for the phase functions in the expansion. Then the set of algebraic equations for the amplitude coefficients follows from the same singularity analysis in the complex plane. These equations are very simple and easy to solve. In contrast to the classical approach of eigen-mode expansions, there is no need to split the problem in a symmetric and antisymmetric one. An other advantage is that the transmission and reflection coefficients are determined seperately by means of Green's theorem, applied at the free surface in the far field. The method is first explained for the semi-infinite rigid dock, followed by the rigid strip, the moving strip and the flexible moving platform. In the appendix it is explained how to derive a set of algebraic equations in the case when the incident wave is not perpendicular to the strip.     

On the use of boundary-integral equation methods for unsteady free-surface flows

The Mixed Eulerian-Lagrangian Methods (MEL) forfree-surface potential flows solved by boundary-integral equations (BIEs) is considered, and the diffusion and dispersion errors are studied in the discrete linearized problem. The diffusion error is the base for the stability analysis of the scheme; both the errors give indications on the accuracy of the numerical solution. The study is divided into two steps: comparison of the discrete dispersion relation with the analytical solution and coupling with different time-integration schemes. In particular, a stability analysis of the Runge-Kutta and Taylor-expansion schemes, previously not given in the literature, is addressed. It is shown that MEL methods based on first- and second-order explicit Runge-Kutta and Taylor-expansion schemes are unstable, regardless of the technique adopted to discretize the BIEs. Higher-order Runge-Kutta and Taylor-expansion schemes lead to conditionally stable methods. Known results for explicit, implicit and explicit-implicit Euler schemes are recovered by the present analysis. The theoretical predictions of the errors are confirmed for two different boundary-element techniques: a high-order panel method based on B-Splines to solve for the velocity potential and a spectrally-accurate method based on the Euler-McLaurin summation formula to solve directly for the velocity field.     

Generation of water waves and bores by impulsive bottom flux

The inviscid free-surface flow due to an impulsive bottom flux on constant depth is investigated analytically and numerically. The following classes of two-dimensional flow are considered: an upwelling flow which is uniform over a half-plane, a line source/sink, and a dipole aligned along the bottom. The bottom flux is turned on impulsively and may decay with time. The fully nonlinear problem is solved numerically. A small-time asymptotic expansion to third order is found for the nonlinear problem. An asymptotic large-time solution is found for the linearized problem. A steady source will generate a pair of symmetric bores, and their breaking is investigated. A steady sink generates a depression wave if it is weak, and dip instability if it is strong. Wave breaking will occur for intermediate sink strengths. A decaying source emits solitary waves.     

Free-surface wave interaction with a thick flexible dock or very large floating platform

In this paper the recently developed semi-analytic method to solve the free-surface wave interaction with a thin elastic plate is extended to the case of a plate of finite thickness. The method used is based on the reformulation of the differential–integral equation for this problem. The thickness of the plate is chosen such that the elastic behavior of the plate can be described by means of thin-plate theory, while the water pressure at the plate is applied at finite depth. The water depth is finite.     

Nonlinear capillary free-surface flows

Capillary free-surface flows are considered. The fluid is taken to be inviscid and incompressible and the flow to be irrotational. Particular attention is devoted to two-dimensional flows for which the free surfaces intersect rigid walls. These include cavitating flows and local flows at the front of a small object (probe or insect) moving at the surface of a fluid. A general study of the effect of surface tension on the possible singularities which can occur at the separation points is presented. The results confirm and generalise previous findings on the subject.     

Breaking and merging of liquid sheets and filaments

The surface of a sheet of liquid which contracts due to surface tension, breaks, and then pulls apart into two pieces, is calculated. Before breaking, the flow is the self-similar one found by Keller, Milewski and Vanden-Broeck. After breaking, it is the self-similar flow found by Keller and Miksis. A general numerical scheme, which includes the previous ones, is presented and new numerical results are discussed. There is an analogous flow of an axially symmetric liquid filament, but it is not calculated.     

Hydroelastic behaviour of compound floating plate in waves

The paper deals with the plane problem of the hydroelastic behaviour of floating plates under the influence of periodic surface water waves. Analysis of this problem is based on hydroelasticity, in which the coupled hydrodynamics and structural dynamics problems are solved simultaneously. The plate is modeled by an Euler beam. The method of numerical solution of the floating-beam problem is based on expansions of the hydrodynamic pressure and the beam deflection with respect to different basic functions. This makes it possible to simplify the treatment of the hydrodynamic part of the problem and at the same time to satisfy accurately the beam boundary conditions. Two approaches aimed to reduce the beam vibrations are described. In the first approach, an auxiliary floating plate is added to the main structure. The size of the auxiliary plate and its elastic characteristics can be chosen in such a way that deflections of the main structure for a given frequency of incident wave are reduced. Within the second approach the floating beam is connected to the sea bottom with a spring, the rigidity of which can be selected in such a way that deflections in the main part of the floating beam are very small. The effect of the vibration reduction is quite pronounced and can be utilized at the design stage.     

Starting flow generated by the impulsive start of a floating wedge

The initial stage of the plane unsteady flow caused by the impulsive vertical motion of a wedge initially floating on an otherwise flat free surface is investigated with the help of a combination of numerical and asymptotic methods. The liquid is assumed ideal and incompressible and its flow potential. Compressible effects give a negligible contribution to the flow close to the entering body at the stage considered in the present paper. The vertical velocity of the body is constant after the impulsive start. The flow domain is divided into an outer region, where the first-order solution is given by the pressure-impulse theory, and inner regions close to the intersection points between the free surface and the moving body. The relative displacement of the body plays the role of a small parameter. The inner solution is matched with the outer one. The outer solution is given in quadratures but the inner solution, which is shown to be nonlinear and self-similar, can be found only numerically. With the aim of deriving the inner solution, the inner region is divided into three parts. In the far-field zone the solution is given in terms of its asymptotic behavior while, in the jet region, attached to the wedge, the flow is described by a second-order shallow-water approximation. In the intermediate region a boundary-element method is used, which is suitably coupled with the solutions in both the jet and the far-field regions through an iterative pseudo-time stepping procedure. The procedure is dependent on the deadrise angle of the wedge. If the angle is equal or smaller than π/4, eigensolutions appear in the far-field asymptotics and their amplitudes are recovered together with the solution. The approach is applied to different values of the wedge deadrise angle. The obtained results can be used to improve the prediction of the hydrodynamic loads acting on floating bodies, the velocity of which changes rapidly.     

A high-order harmonic polynomial method for solving the Laplace equation with complex boundaries and its application to free-surface flows. Part I: Two-dimensional cases

A high-order harmonic polynomial method (HPM) is developed for solving the Laplace equation with complex boundaries. The “irregular cell” is proposed for the accurate discretization of the Laplace equation, where it is difficult to construct a high-quality stencil. An advanced discretization scheme is also developed for the accurate evaluation of the normal derivative of potential functions on complex boundaries. Thanks to the irregular cell and the discretization scheme for the normal derivative of the potential functions, the present method can avoid the drawback of distorted stencils, that is, the possible numerical inaccuracy/instability. Furthermore, it can involve stationary or moving bodies on the Cartesian grid in an accurate and simple way. With the proper free-surface tracking methods, the HPM has been successfully applied to the accurate and stable modeling of highly nonlinear free-surface potential flows with and without moving bodies, that is, sloshing, water entry, and plunging breaker.     

波浪与外壁透空双筒柱的相互作用

对于波浪与透空外壁同轴双筒柱的相互作用问题,利用速度势的特征函数展开式和透空壁内流体速度与两壁间压力差成正比的线性模型,建立了一个线性解析解。应用这一模型开展了数值实验,用以检验孔隙系数和透空部分大小以及内外柱径之比对双筒柱上波浪力和波面高度的影响。计算结果表明,外壁孔隙系数和透空部分大小对波面升高和波浪荷载有很大影响,通过调整各个系数,应用双筒透空柱可以减小周围的波面高度及其上的波浪荷载。     

Diffraction of elastic waves by four rigid strips embedded in an infinite orthotropic medium

In the present paper, the elastodynamic response of four coplanar rigid strips embedded in an infinite orthotropic medium due to elastic waves incident normally on the strips is analyzed. The resulting mixed boundary-value problem is solved by an integral-equation method. The normal stress and the vertical displacement are derived in closed analytic form. Numerical values of stress-intensity factors at the edges of the strips and vertical displacements at point in the plane of the strips for several orthotropic materials are calculated and plotted graphically to show the effect of material orthotropy.     

An algorithm for modelling the interaction of a flexible rod with a two‐dimensional high‐speed flow

We present an algorithm for modelling coupled dynamic interactions of a very thin flexible structure immersed in a high‐speed flow. The modelling approach is based on combining an Eulerian finite volume formulation for the fluid flow and a Lagrangian large‐deformation formulation for the dynamic response of the structure. The coupling between the fluid and the solid response is achieved via an approach based on extrapolation and velocity reconstruction inspired in the Ghost Fluid Method. The algorithm presented does not assume the existence of a region exterior to the fluid domain as it was previously proposed and, thus, enables the consideration of very thin open boundaries and structures where the flow may be relevant on both sides of the interface. We demonstrate the accuracy of the method and its ability to describe disparate flow conditions across a fixed thin rigid interface without pollution of the flow field across the solid interface by comparing with analytical solutions of compressible flows. We also demonstrate the versatility and robustness of the method in a complex fluid–structure interaction problem corresponding to the transient supersonic flow past a highly flexible structure. Copyright © 2005 John Wiley & Sons, Ltd.     

The effect of grease on the activated sludge process in wastewater treatment

Abstract

The purpose of this paper is to introduce the major potentials and perspectives of applications of finite element analysis in solving the problems of shallow water wave equations. One‐dimensional and two‐dimensional shallow water wave equations will both be incorporated into the modeling procedures. For one‐dimensional flows, the models will cover the typical single channels, confluence channels system, division channels system, and natural river systems. As far as two‐dimensional flows are concerned, the overland flows are investigated. The simulation results are compared with the data obtained by physical modeling and field observation and with the results of other existing literature. The models were found to be very feasible in modeling the complex flow fields of shallow water wave equation problems.     

漂浮式光伏发电装置在海浪影响下的光照性能研究

针对海洋漂浮式太阳能发电装置,为分析海浪运动对其光照性能的影响,对比陆地环境下相同面积光伏电池的光照性能,分析两者之间的差距.首先总结了倾斜表面太阳辐射能的计算方法,分析了在海洋环境下应用这一模型的差异性,再将海浪简化,分析浮体在海浪中的运动特性及角度摆动规律,同时运用AQWA仿真软件,对浮体运动进行仿真,以验证浮体摆动角度计算的准确性,最后将静态的太阳辐射能计算模型与动态的浮体角度摆动相结合,得出海浪影响下光伏电池表面所接收到的太阳辐射能.将其与相同条件下以最佳接收角度固定安装的光伏电池所接收的太阳辐射能相比较,得出在海浪影响下浮体及光伏电池所接收的辐射能能够达到陆地最佳接收情况下的87.5％.     

运动状态下柔性关节机器人关节面参数辨识研究

针对柔性关节机器人系统,提出了一种机构系统运动状态下关节面参数辨识的新方法。首先,将机器人柔性关节等效为弹性扭转轴,将应用于结构中的行波分析方法与机器人关节旋转变换矩阵相结合,建立机构系统的波导方程;其次,根据系统各结点力平衡与位移边界条件,建立运动状态下系统环境预测模型,并根据预测出的系统激励以及实验测得的关节扭转角等因素,建立系统振动方程;再次,利用最小二乘法对上述模型进行求解,推导出关节动态刚度和阻尼;最后,以两种不同的运动轨迹驱动3自由度机械臂,对其进行辨识实验研究。实验结果表明,该辨识方法是有效的,为后续系统的动态控制提供了重要参考。     

Scattering of inhomogeneous plane waves by a slit formed with impedance and perfectly electric conducting half planes

Scattering of an inhomogeneous plane wave with an arbitrary angle of incidence travelling through a slit made of perfectly electric conducting and impedance half planes is investigated. For the investigation of the scattering phenomena evaluation of the modified theory of physical optics integrals are evaluated asymptotically. An inhomogeneous plane wave is taken into consideration by assuming the incident angle of a homogeneous plane wave as a complex parameter. Uniform asymptotic results will be employed for the correct solution of an incoming inhomogeneous plane wave scattering problem. Asymptotic evaluation is carried out for the reflected and diffracted fields. Diffracted fields are uniformly expressed in terms of the Fresnel functions. To obtain correct plots of the diffracted fields, complex detour parameter decomposition method is applied. Obtained resultant fields are plotted numerically.     

Diffraction of short waves modelled using new mapped wave envelope finite and infinite elements

We consider a two‐dimensional wave diffraction problem from a closed body such that the complex progressive wave potential satisfies the Sommerfield condition and the Helmholtz equation. We are interested in the case where the wavelength is much smaller than any other length dimensions of the problem. We introduce new mapped wave envelope infinite elements to model the potential in the far field, and test them for some simple Dirichlet boundary condition problems. They are used in conjuction with wave envelope finite elements developed earlier [1] to model the potential in the near field. An iterative procedure is used in which an initial estimate of the phase is iteratively improved. The iteration scheme, by which the wave envelope and phase are recovered, is described in detail. Copyright © 1999 John Wiley & Sons, Ltd.     

柔性ITO衬底上铜酞菁薄膜有序生长的X射线衍射研究

采用石英晶体微天平实时监测薄膜生长速率,通过控制衬底温度与薄膜生长速率,在柔性ITO导电衬底上真空蒸发沉积了铜酞菁薄膜.X射线衍射分析表明,适当提高衬底温度与薄膜生长速率,可促进薄膜的有序生长.当衬底温度为90℃,生长速率为10nm/min时,薄膜的有序度最高,薄膜晶型呈(相和(200)晶面.     

Inverse-heat-conduction problems with boundary elements: analysis of a corner effect

A transient two-dimensional inverse-heat-conduction problem is investigated. It consists in the determination of both temperature and heat-flux density in the vicinity of an angle (≤ 180°) when some internal temperatures are known. Such a problem is solved by using a boundary-element approach with a time- and space-dependent fundamental solution. It uses a time-marching scheme that involves future time steps and a regularization procedure. An exhaustive study of sensitivity to the leading parameters of the problem is produced, and it is especially pointed out that the accuracy of the resolution is strongly affected as the corner angle decreases. In order to overcome this difficulty, a localized regularization procedure is suggested.     

轴向流作用下柔性简支梁静态与动态稳定性分析

对于一个轴向流作用下的柔性简支梁流固耦合模型,基于一定的假设,建立了系统的流固耦合非线性动力学方程,并运用参数无量纲化、假设模态、高阶模态截断等方法导出了有限自由度无量纲状态空间方程。根据静态分岔理论,对系统线性化扰动方程的Jacobi系数矩阵特征多项式进行了分析,理论上求得系统发生静态分岔时的临界流速。数值计算结果表明当流速大于临界流速时,系统发生静态失稳,在外界扰动作用下,梁随机地向上或向下弯曲。基于动态Hopf分岔理论与相关的实系数多项式特征根代数判据,证明了系统不会出现振颤失稳。