Numerical analysis of added mass and damping of floating production, storage and offloading system

An integral equation approach is utilized to investigate the added mass and damping of floating production,storage and offloading system(FPSO system).Finite water depth Green function and higher-order boundary element method are used to solve integral equation.Numerical results about added mass and damping are presented for odd and even mode motions of FPSO.The results show robust convergence in high frequency range and can be used in wave load analysis for FPSO designing and operation.     

Suspensions in turbulent liquid pipe flow: Kinetic modelling and added mass effects

We develop a Eulerian model for a particle suspension in fully developed turbulent liquid in a horizontal pipe. Virtual mass effects and hydrodynamic interactions are accounted for by an extension of the kinetic theory of Reeks and Swailes.     

Experimental study on the added mass and damping of a disk submerged in a partially fluid-filled tank with small radial confinement

The dynamic response of submerged and confined disk-like structures is of interest in engineering applications, such as in hydraulic turbine runners. This response is difficult to be estimated with accuracy due to the strong influence of the boundary conditions. Small radial gaps as well as short axial distances to rigid surfaces greatly modify the dynamic response because of the added mass and damping effects.In this paper, the influence of the axial nearby rigid distance on the dynamic response of a submerged disk is evaluated when the radial gap is very small. Moreover, the effects of the fluid depth and fluid viscosity on the natural frequencies and damping ratio of the submerged disk are studied. The study has been performed experimentally and numerically using structural–acoustic simulations.For the experimental investigation a test rig has been developed. It consists of a disk attached to a shaft and confined with a small radial gap inside a cylindrical container full of water. The disk can be moved up and down along the shaft to vary the axial distance to the nearby rigid surface. Piezoelectric patches are used to excite the disk and the response is measured with submersible accelerometers. Several excitation patterns can be used due to the disposition of these piezoelectric patches. For each configuration tested, the dynamic response of the structure is studied analyzing the natural frequencies and damping ratio of the disk attached to the shaft. The numerical results have been compared with the experimental results.     

SPH for 3D floating bodies using variable mass particle distribution

A floating body with substantial heave motion is a challenging fluid–structure interaction problem for numerical simulation. In this paper we develop SPH in three dimensions to include variable particle mass distribution using an arbitrary Lagrange–Eulerian formulation with an embedded Riemann solver. A wedge or cone in initially still water is forced to move with a displacement equal to the surface elevation of a focused wave group. A two‐dimensional wedge case is used to evaluate two forms of repulsive‐force boundary condition on the body; the force depending on the normal distance from the object surface produced closer agreement with the experiment. For a three‐dimensional heaving cone the comparison between SPH and experiment shows excellent agreement for the force and free surface for motion with low peak spectral frequencies while for a higher peak frequency the agreement is reasonable in terms of phase and magnitude, but a small discrepancy appears at the troughs in the motion. Capturing the entire three‐dimensional flow field using an initially uniform particle distribution with sufficiently fine resolution requires an extremely large number of particles and consequently large computing resource. To mitigate this issue, we employ a variable mass distribution with fine resolution around the body. Using a refined mass distribution in a preselected area avoids the need for a dynamic particle refinement scheme and leads to a computational speedup of more than 600% or much improved results for a given number of particles. SPH with variable mass distribution is then applied to a single heaving‐float wave energy converter, the ‘Manchester Bobber’, in extreme waves and compared with experiments in a wave tank. The SPH simulations are presented for two cases: a single degree‐of‐freedom system with motion restricted to the vertical direction and with general motion allowing six degrees‐of‐freedom. The motion predicted for the float with general motion is in much closer agreement with experimental data than the vertically constrained system. Using variable particle mass distribution is shown to produce close agreement with a computation time 20% of that required with a uniformly fine resolution. Copyright © 2012 John Wiley & Sons, Ltd.     

CFD modeling of liquid–solid fluidization: Effect of drag correlation and added mass force

Computational fluid dynamics (CFD) has been widely used to study the hydrodynamics of gas–solid fluidization; however, its applications in liquid–solid fluidization are relatively rare. In this study, CFD simulations of a liquid–solid fluidized bed are carried out, focusing on the effect of drag correlation and added mass force on the hydrodynamics of liquid–solid fluidization. It is shown that drag correlation has a significant effect on the simulation results and the correlation proposed by Beetstra et al. (2007) gives the best agreement with experimental data. We further show that the added mass force does play an important role in CFD simulation of liquid–solid fluidization, and therefore should not be ignored in CFD simulations.     

New estimations of the added mass and damping of two cylinders vibrating in a viscous fluid,from theoretical and numerical approaches

This paper deals with the small oscillations of two circular cylinders immersed in a viscous stagnant fluid. A new theoretical approach based on an Helmholtz expansion and a bipolar coordinate system is presented to estimate the fluid forces acting on the two bodies. We show that these forces are linear combinations of the cylinder accelerations and velocities, through viscous fluid added coefficients. To assess the validity of this theory, we consider the case of two equal size cylinders, one of them being stationary while the other one is forced sinusoidally. The self-added mass and damping coefficients are shown to decrease with both the Stokes number and the separation distance. The cross-added mass and damping coefficients tend to increase with the Stokes number and the separation distance. Compared to the inviscid results, the effect of viscosity is to add a correction term which scales as $S{k}^{-1∕2}$. When the separation distance is sufficiently large, the two cylinders behave as if they were independent and the Stokes predictions for an isolated cylinder are recovered. Compared to previous works, the present theory offers a simple and flexible alternative for an easy determination of the fluid forces and related added coefficients. To our knowledge, this is also the first time that a numerical approach based on a penalization method is presented in the context of fluid–structure interactions for relatively small Stokes numbers, and successfully compared to theoretical predictions.     

The rule of affine similitude for the force coefficients of a body oscillating in a uniformly stratified fluid

 This paper presents a study on affine similitude for the force coefficients of an arbitrary body oscillating in a uniformly stratified fluid. A simple formula is derived that gives a relation between the force coefficients for a body oscillating in homogeneous and uniformly stratified ideal fluids. In particular, it implies the existence of a universal nondimensional similitude criterion for a family of affinely similar bodies, namely, the bodies that can be transformed into each other by vertical dilation of the initial coordinate system. Theoretical results are verified by experiments with a set of spheroids having different length-to-diameter ratios. The experimental technique for evaluation of the frequency-dependent force coefficients is based on Fourier analysis of the time-history of damped oscillation tests. Received: 25 September 2000 / Accepted: 6 July 2001 Published online: 29 November 2001     

The added mass coefficient of a dispersion of spherical gas bubbles in liquid

Models published in the two-phase flow literature for the added mass coefficient of a dilute bubbly dispersion are discussed and compared. It is shown that the differences between the models are mainly due to the different ways in which the added mass is defined. Also, approximate expressions for the added mass coefficient of non-dilute bubbly dispersions are given. Finally, the use of the models in an equation for the average motion of the bubbles is briefly discussed.     

The two-dimensional transmission and reflection of a solitary wave

In the present paper, limited to the discussion of weak non-linear shallow water waves, the transmission and reflection of a planar soliton on a two-dimensional structure are considered. The whole flow field is divided mainly into two subfields. One is in the vicinity of the structure, called the inner field; the other is far from the structure, called the outer field. In the outer field, according to its definition, the influence of the structure on the flow is negligible; to the order O(α, β) the governing equation for the flow is replaced by the Boussinesq equation. In the inner field the effect of the structure on the flow is significant, so the full Laplace equation is adopted as the governing equation for the flow field. Then the matched asymptotic expansion method is employed to connect smoothly the inner and outer solutions. Owing to the irregularity of the bottom of the structure, the boundary element method is incorporated. As an example, the case in which the incoming wave is a solitary wave is calculated and the time histories of transmitted and reflected waves are plotted.     

船舶在进出船厢运动中的附加质量的计算

采用三维有限元方法，计算船在进出船厢运动中的附加质量。文中对单圆柱体在无限域和半无限域中运动的附加质量及双圆柱体同心放置时内圆柱运动的附加质量分别进行了计算，计算值与理论值吻合很好；对船在进出船厢运动中的附加质量做了大量的计算，结果表明：随着船与船厢侧壁间距的减小，船的附加质量系数增大；随着船厢中水深的减小，船的附加质量系数增大，随着船离船厢封闭端的距离的减小，附加质量系数增大。     

Impact of mass lumping on gravity and Rossby waves in 2D finite‐element shallow‐water models

The goal of this study is to evaluate the effect of mass lumping on the dispersion properties of four finite‐element velocity/surface‐elevation pairs that are used to approximate the linear shallow‐water equations. For each pair, the dispersion relation, obtained using the mass lumping technique, is computed and analysed for both gravity and Rossby waves. The dispersion relations are compared with those obtained for the consistent schemes (without lumping) and the continuous case. The P₀?P₁, RT₀ and P?P₁ pairs are shown to preserve good dispersive properties when the mass matrix is lumped. Test problems to simulate fast gravity and slow Rossby waves are in good agreement with the analytical results. Copyright © 2008 John Wiley & Sons, Ltd.     

压电质量传感器检测灵敏度分析

压电质量传感器是一种利用压电谐振器对质量的敏感性,通过谐振器吸附待测物后频率的变化实现对被测物质进行检测的传感器。由于附着物质引起的质量变化很小,因此测试精度将强烈依赖于结构频率对质量变化的敏感程度,而敏感程度与传感器感知部分的几何尺寸密切相关。本文主要研究压电材料悬臂梁式质量传感器的检测敏感度分析问题,推导传感器自振频率变化对质量变化的灵敏度与传感器各部分结构几何尺寸设计参数依赖关系的计算格式,并讨论了结构尺寸、截面形状以及谐振模态对传感器检测灵敏度的影响。     

附加质量变化率在航行体出水过程中的影响研究

航行体出水运动过程中,附加质量逐渐减小,在一些研究其出水运动的模型中,只考虑了随状态变化的附加质量值,而没有充分考虑附加质量的变化过程。本文通过建立航行体出水运动物理模型和对航行体出水过程的受力分析,构建了出水过程的动力学方程。为了更加准确模拟航行体出水情况,在进行理想流体作用力求解时,引入附加质量变化率研究附加质量在出水过程中的变化以及对出水过程的影响。通过对数学模型的仿真分析表明,在计算模型中考虑附加质量变化率能显著提高模型的计算精度。     

An experimental and numerical study of heave added mass and damping of horizontally submerged and perforated rectangular plates

Forced harmonic heave motions of horizontally submerged and perforated rectangular plates are studied experimentally and numerically at both a deep and shallow submergence. The steady-state vertical forces are expressed in terms of added mass and damping coefficients. The numerical results are partly obtained by combining potential flow with linear free-surface conditions and a nonlinear viscous pressure loss condition at the mean oscillatory plate position. A domain decomposition technique is applied with a boundary element method in the inner domain and an analytical representation of the velocity potential in the outer domain. A drag term accounts for the vortex shedding at the outer plate edges. The numerically predicted Keulegan–Carpenter number dependent heave added mass and damping coefficients agree reasonably with experimental values, in particular for the deeper submergence.     

The pre-stack migration imaging technique for damages identification in concrete structures

Pre-stack migration imaging (PMI) method, which is used in geophysical exploration by the performance of single side detection and visually display, can be used to identify the location, orientation, and severity of damages in concrete structure. In particular, this letter focuses on the experimental study by using a finite number of sensors for further practical applications. A concrete structure with a surface-mounted linear PZT transducers array is illustrated. Three types of damages, horizontal, dipping and V-shaped crack damage, have been studied. A pre-stack reverse time migration technique is used to back-propagate the scattering waves and to image damages in concrete structure. The migration results from the scattering waves of an artificial damage are presented. It is shown that the existence of the damage in concrete structure is correctly revealed through migration process.     

质量对结构优化理性准则法计算结果的影响研究

在结构优化中,质量作为设计资源能改善结构性能,但质量会引起自重与惯性载荷等问题,因而质量还会导致结构性能劣化。虚功准则方程组忽略了载荷对设计变量的导数,不能考虑质量导致结构性能劣化的一面。对于航空航天器、高速运行的车辆、机械和高精度天线等以自重和惯性载荷为主的工程结构,这种忽略导致虚功法得到的解与最优解相差甚远。导重法是严密推导的理性准则法,克服了虚功法准则不准的缺陷,优化效果较虚功法大幅提高。但对于考虑自重载荷的三杆、五杆桁架等简单结构优化问题,虚功法也可以得到与导重法相同的最优解计算结果,从拉格朗日条件出发解释该问题,给出考虑载荷对设计变量的导数时虚功法也可求得最优解的条件,这对于结构理性准则法及其工程应用的深入研究均具有重要理论与实践意义。     

The MFS for the Cauchy problem in two-dimensional steady-state linear thermoelasticity

We study the reconstruction of the missing thermal and mechanical fields on an inaccessible part of the boundary for two-dimensional linear isotropic thermoelastic materials from over-prescribed noisy (Cauchy) data on the remaining accessible boundary. This problem is solved with the method of fundamental solutions (MFS) together with the method of particular solutions (MPS) via the MFS-based particular solution for two-dimensional problems in uncoupled thermoelasticity developed in Marin and Karageorghis, 2012a, Marin and Karageorghis, 2013. The stabilisation/regularization of this inverse problem is achieved by using the Tikhonov regularization method (Tikhonov and Arsenin, 1986), whilst the optimal value of the regularization parameter is selected by employing Hansen’s L-curve method (Hansen, 1998).     

结构主动开闭环多重调谐质量阻尼器（AMTMD）新控制策略

提出了一种新控制策略——主动开闭环多重调谐质量阻尼器(AMTMD)。AMTMD控制系统频率呈线性分布。AMTMD中的MTMD保持相同的刚度和阻尼系数但质量变化。基于TMD的工作原理定义了AMTMD的主动控制力构成即保持相同的位移和速度反馈增益系数但变化结构和地震加速度反馈增益系数。基于结构的广义振型模型，导出了设置AMTMD时结构的动力放大系数(DMF)，于是优化准则可定义为：Min．Min．Max．DMF．通过最优搜寻，研究了反映AMTMD有效性和鲁棒性的参数。这些参数包括：频率间隔、平均阻尼比、调谐频率比、总数、质量比和标准化加速度反馈增益系数。为了比较，多重调谐质量阻尼器(MTMD)和主动开闭环调谐质量阻尼器(ATMD)也被考虑。     

A second-order radiation boundary condition for the shallow water wave equations on two-dimensional unstructured finite element grids

A second-order radiation boundary condition (RBC) is derived for 2D shallow water problems posed in ‘wave equation’ form and is implemented within the Galerkin finite element framework. The RBC is derived by matching the dispersion relation for the interior wave equation with an approximate solution to the exterior problem for outgoing waves. The matching is correct to second order, accounting for curvature of the wave front and the geometry. Implementation is achieved by using the RBC as an evolution equation for the normal gradient on the boundary, coupled through the natural boundary integral of the Galerkin interior problem. The formulation is easily implemented on non-straight, unstructured meshes of simple elements. Test cases show fidelity to solutions obtained on extended meshes and improvement relative to simpler first-order RBCs.