Analytical Solution and Simplified Formula for Added Mass of Horizontal and Vertical Motions of Truncated Cylinders Under Earthquake Action

This paper investigates the hydrodynamic characteristics of floating truncated cylinders undergoing horizontal and vertical motions due to earthquake excitations in the finite water depth.The governing equation of the hydrodynamic pressure acting on the cylinder is derived based on the radiation theory with the inviscid and incompressible assumptions.The governing equation is solved by using the method of separating variables and analytical solutions are obtained by assigning reasonable boundary conditions.The analytical result is validated by a numerical model using the exact artificial boundary simulation of the infinite water.The main variation and distribution characteristics of the hydrodynamic pressure acting on the side and bottom of the cylinder are analyzed for different combinations of wide-height and immersion ratios.The added mass coefficient of the cylinder is calculated by integrating the hydrodynamic pressure and simplified formulas are proposed for engineering applications.The calculation results show that the simplified formulas are in good agreement with the analytical solutions.

Variation of Added Mass and Its Application to the Calculation of Amplitude Response for A Circular Cylinder

In the present study, analyzed are the variation of added mass for a circular cylinder in the lock-in （synchronization） range of vortex-induced vibration （VIV） and the relationship between added mass and natural frequency. A theoretical minimum value of the added mass coefficient for a circular cylinder at lock-in is given. Developed are semi-empirical formulas for the added mass of a circular cylinder at lock-in as a function of flow speed and mass ratio. A comparison between experiments and numerical simulations shows that the semi-empirical formulas describing the variation of the added mass for a cireular cylinder at lock-in are better than the ideal added mass. In addition, computation models such as the wake oscillator model using the present formulas can predict the amplitude response of a circular cylinder at lock-in more accurately than those using the ideal added mass.

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

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

NUMERICAL ANALYSIS OF FLUID FLOW AND ADDED MASS INDUCED BY VIBRATION OF STRUCTURE

The fluid flow induced by light-density, low-stiffness structures was treated as inviscid, incompressible irrotational and steady plane flow. On the basis of the dipole configuration method, a singularity distribution method of distributing sources/sinks and dipoles on interfaces of the structure and fluid was developed to solve the problem of fluid flow induced by the vibration of common structures, such as columns and columns with fins, deduce the expression of kinetic energy of the fluid flow, and obtain the added mass finally. The calculational instances with analytical solutions prove the reliability of this method.

Added Mass Effect and an Extended Unsteady Blade Element Model of Insect Hovering

During the insect flight, the force peak at the start of each stroke contributes a lot to the total aerodynamic force. Yet how this force is generated is still controversial. Two current explanations to this are wake capture and Added Mass Effect （AME） mechanisms. To study the AME, we present an extended unsteady blade element model which takes both the added mass of fluid and rotational effect of the wing into account. Simulation results show a high force peak at the start of each stroke and are quite similar to the measured forces on the physical wing model. We found that although the Added Mass Force （AMF） of the medium contributes a lot to this force peak, the wake capture effect further augments this force and may play a more important role in delayed mode. Furthermore, we also found that there might be an unknown mechanism which may augment the AME during acceleration period at the start of each stroke, and diminish the AME during deceleration at the end of each stroke.

Seismic and stress qualification of LMFR fuel rod and simple method for the determination of LBE added mass effect

In this study, two different designs of liquid metal fast reactor(LMFR) fuel rods wire-wrapped and nonwire-wrapped(bare) are compared with respect to different parameters as a means of considering the optimum fuel design. Nuclear seismic rules require that systems and components that are important for safety must be capable of bearing earthquake effects, and that their integrity and functionality should be guaranteed. Mode shapes, natural frequencies, stresses on cladding, and seismic aspects are considered for comparison using ANSYS. Modal analysis is compared in a vacuum and in lead–bismuth eutectic(LBE) using potential flow theory by considering the added mass effect. A simple and accurate approach is suggested for the determination of the LBE added mass effect and is verified by a manually calculated added mass, which further proved the usefulness of potential flow theory for the accurate estimation of the added mass effect. The verification of the hydrodynamic function(τ) over the entire frequency range further validated the finite element method(FEM) modal analysis results. Stresses obtained for fuel rods against different loading combinations revealed that they were within the allowable limits with maximum stress ratios of 0.25(bare) and 0.74(wire-wrapped). In order to verify the structural integrity of cladding tubes, stresses along the cladding length were determined during different transients and were also calculated manually for static pressure. The manual calculations could be roughly compared with the ANSYS results, and the two showed a close agreement. Contact analysis methodology was selected,and the most appropriate analysis options were suggested for establishing contact between the wire and cladding for the wire-wrapped design grid independence analysis,which proved the accuracy of the results, confirmed the selection of the appropriate procedure, and validated the use of the ANSYS mechanical APDL code for LMFR fuel rod analysis. The results provided detailed insight into the structural design of LMFR fuel rods by considering different structural configurations(i.e., bare and wire-wrapped) in the seismic loading;this not only provides a FEM procedure for LMFR fuel with complex configuration, but also guides the reference design of LMFR fuel rods.

CALCULATION OF ADDED MASS OF A VEHICLE RUNNING WITH CAVITY

A numerical method is developed to obtain the added mass coefficients of a vehicle running with cavity in numerical simulation for the multiphase flow of the vehicle which is imposed an added vibration and analyzing its hydrodynamic loads. The method is verified through the cases of non-cavitating sphere and ellipsoid. The changing rule of the added mass of a sphere during water exit is gained. Then the influence of cavitation on the added mass of a cylinder is studied. The results show that λ 11, λ22, λ26, λ66 all decrease as the cavitation number reduces and the length of the attached cavity increases. There is almost a linear relationship between the cavity length and λ22 .The base cavity has great influence on λ11 its contribution decreases more than 60%, when the cavitation number changes from 0.6 to 0.2.

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

Computational fuid 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,

Numerical analysis of added mass and damping of elastic hydrofoils

A numerical model is proposed for analyzing the effects of added mass and damping on the dynamic behaviors of hydrofoils.Strongly coupled fluid-structure interactions(FSIs)of hydrofoils are analyzed by using the 3-D panel method for the fluid and the finite element method for the hydrofoils.The added mass and damping matrices due to the external fluid of the hydrofoil are asymmetric and computational inefficient.The computational inefficiencies associated with these asymmetric matrices are overcome by using a modal reduction technique,in which the first several wet mode vectors of the hydrofoil are employed in the analysis of the FSI problem.The discretized system of equations of motion for the hydrofoil are solved using the Wilson-6 method.The present methods are validated by comparing the computed results with those obtained from the finite element analysis.It is found that the stationary flow is sufficient for determining the wet modes of the hydrofoil under the condition of single-phase potential flow and without phase change.In the case of relatively large inflow velocity,the added damping of the fluid can significantly affect the structural responses of the hydrofoil.

Hybrid algorithm for modeling of fluid-structure interaction in incompressible, viscous flows

The objective of this paper is to present and to validate a new hybrid coupling （HC） algorithm for modeling of fluid-structure interaction （FSI） in incompressible, viscous flows. The HC algorithm is able to avoid numerical instability issues associated with artificial added mass effects, which are often encountered by standard loosely coupled （LC） and tightly coupled （TC） algorithms, when modeling the FSI response of flexible structures in incompressible flow. The artificial added mass effect is caused by the lag in exchange of interfacial displacements and forces between the fluid and solid solvers in partitioned algorithms. The artificial added mass effect is much more prominent for light/flexible struc- tures moving in water, because the fluid forces are in the same order of magnitude as the solid forces, and because the speed at which numerical errors propagate in an incom- pressible fluid. The new HC algorithm avoids numerical instability issues associated with artificial added mass effects by embedding Theodorsen＇s analytical approximation of the hydroelastic forces in the solution process to obtain better initial estimates of the displacements. Details of the new HC algorithm are presented. Numerical validation studies are shown for the forced pitching response of a steel and a plastic hydrofoil. The results show that the HC algorithm is able to converge faster, and is able to avoid numerical insta- bility issues, compared to standard LC and TC algorithms, when modeling the transient FSI response of a plastic hydrofoil. Although the HC algorithm is only demonstrated for a NACA0009 hydrofoil subject to pure pitching motion, the method can be easily extended to model general 3-D FSI response and stability of complex, flexible structures in turbulent, incompressible, multiphase flows.

The Structure of A Turbulent Jet in A Crossflow-Effect of Jet-Crossflow Velocity

A comprehensive numerical study on the three-dimensional structure of a turbulent jet in crossflow is performed. The jet-to-crossflow velocity ratio (R) varies in the range of 2 - 16; both vertical jets and inclined jets without excess streamwise momentum are considered. The numerical results of the Standard two-equation k-ε model show that the turbulent structure can be broadly categorised according to the jet-to-crossflow velocity ratio. For strong to moderate jet discharges, i.e. R> 4, the jet is characterized by a longitudinal transition through a bent-over phase during which the jet becomes almost parallel with the main freestream, to a sectional vortex-pair flow with double concentration maxima; the computed flow details and scalar mixing characteristics can be described by self-similar relations beyond a dimensionless distance of around 20-60. The similarity coefficients are only weakly dependent on R. The cross-section scalar field is kidney-shaped and bifurcated, vvith distinct double concentration maxima; the aspect ratio is found to be around 1.2. A loss in vertical momentum is ob-served and the added mass coefficient of the jet motion is found to be approximately 1. On the other hand, for weak jets in strong crossflow, i. e. R ≥ 2, the lee of the jet is characterized by a negative pressure region. Although the double vortex flow can stili be noted, the scalar field becomes more symmetrical and no longer bifurcated. The similarity coeffcients are al-so noticeably different. The predicted jet flovv characteristics and mixing rates are well supported by experimental and field dala

Experimental study on interaction between membrane structures and wind environment

The interaction between membrane structures and their environment can be either static or dynamic. Static interaction refers to interaction with static air, while dynamic interaction refers to wind and its effects. They can be evaluated by two parameters, added mass and radiation/aerodynamic damping, which are experimentally investigated in this study. The study includes the effects of both the static and dynamic interaction on structural dynamic characteristics, and the relationship between the interaction parameters and the covered area of a membrane structure for the static interaction and the relationship between the interaction parameters and wind direction and speed for the dynamic interaction. Experimental data show that the dynamic interaction is strongly correlated with the structural modes, i.e., the interaction of the symmetric modes is much larger than the anti-synmletric modes; and the influence of the dynamic interaction is significant in wind-induced response analysis and cannot be ignored. In addition, it is concluded that the structural natural frequency is remarkably decreased by this interaction, and the frequency band is significantly broadened.

Seismic response analysis of arch dam-water-rock foundation systems

The effect of water compressibility on the seismic responses of arch dams is not well understood.In this paper,a numerical model is developed with rigorous representation of the dynamic interaction between arch dam-water- rock foundation.The model is applied to the seismic response analysis of an arch dam with a height of 292m designed to a seismic intensity of IX.It is shown that consideration of the water compressibility clearly decreases the stress responses at key positions of the dam,while the added mass model gives a conservative estimate.

Coupled vibrations and frequency shift of compound system consisting of quartz crystal resonator in thickness-shear motions and micro-beam array immersed in liquid

The dynamic characteristics of a quartz crystal resonator（QCR） in thicknessshear modes（TSM） with the upper surface covered by an array of micro-beams immersed in liquid are studied. The liquid is assumed to be inviscid and incompressible for simplicity. Dynamic equations of the coupled system are established. The added mass effect of liquid on micro-beams is discussed in detail. Characteristics of frequency shift are clarified for different liquid depths. Modal analysis shows that a drag effect of liquid has resulted in the change of phase of interaction（surface shear force）, thus changing the system resonant frequency. The obtained results are useful in resonator design and applications.

Study on Hydrodynamic Coefficients of Double Submerged Inclined Plates

Added mass and damping coefficients are very important in hydrodynamic analysis of naval structures. In this paper,a double submerged inclined plates with ‘/\’ configuration is firstly considered. By use of the boundary element method(BEM) based on Green function with the wave term, the radiation problem of this special type structure is investigated. The added mass and damping coefficients due to different plate lengths and inclined angles are obtained. The results show that: the added mass and damping coefficients for sway are the largest. Heave is the most sensitive mode to inclined angles. The wave frequencies of the maximal added mass and damping coefficients for sway and roll are the same.

固定海上平台遭受水下爆炸载荷的非线性动态响应

In this paper,the dynamic response of a fixed offshore platform subjected to the underwater explosion(UNDEX)and probable events following it have been investigated.The pressure load due to UNDEX in a specified depth has been applied with a model that considers the effect of blast bubble fluctuations into account.The effect of water on the natural frequency and Fluid-Structure interaction has been modeled as equivalent added mass formulation.The effect of explosion distance on platform response is studied.In this regard,three cases of near,medium,and far-distance explosions are considered.For a case study,a real fixed offshore jacket platform,installed in the Persian Gulf,has been examined.Only the UNDEX pressure load is considered and other dynamic loads such as surface water waves and winds have been neglected.Dead loads,live loads and hydrostatic pressure has been considered in the static case based on the design codes.The results indicated that in near-distance explosions,the UNDEX pressure load can locally damage parts of the platform that are located at the same level as that of explosive material and it can destabilize the platform.In the medium to far distance explosion,a very large base shear was applied to the platform because more elements were exposed to the UNDEX load compared to the near-distance explosion.Therefore,precautionary measures against UNDEX such as risk assessment according to design codes are necessary.As a result of this,member strengthening against explosion may be required.

大幅船舶横摇运动非线性附加质量惯性矩和阻尼矩特性的非参数识别

This study aims to investigate the nonlinear added mass moment of inertia and damping moment characteristics of largeamplitude ship roll motion based on transient motion data through the nonparametric system identification method.An inverse problem was formulated to solve the first-kind Volterra-type integral equation using sets of motion signal data.However,this numerical approach leads to solution instability due to noisy data.Regularization is a technique that can overcome the lack of stability;hence,Landweber’s regularization method was employed in this study.The L-curve criterion was used to select regularization parameters(number of iterations)that correspond to the accuracy of the inverse solution.The solution of this method is a discrete moment,which is the summation of nonlinear restoring,nonlinear damping,and nonlinear mass moment of inertia.A zero-crossing detection technique is used in the nonparametric system identification method on a pair of measured data of the angular velocity and angular acceleration of a ship,and the detections are matched with the inverse solution at the same discrete times.The procedure was demonstrated through a numerical model of a full nonlinear free-roll motion system in still water to examine and prove its accuracy.Results show that the method effectively and efficiently identified the functional form of the nonlinear added moment of inertia and damping moment.

Evaluation of Hydrodynamic Coefficients of Ships Oscillating in A Numerical Wave Tank

A technique for the evaluation of the hydrodynamic coefficients of ships is outlined for ship oscillating in a numerical wave tank, which is established on Computational Fluid Dynamics （CFD） theories. The numerical simulation of ship sections and bodies forced oscillating in the tank are carried out. The added mass and damping coefficients are obtained by the decomposition of the computational results, which agree well with the corresponding ones of potential theories.

HYDRODYNAMIC INTERACTION BETWEEN TWO VERTICALCYLINDERS IN WATER WAVES

The hydrodynamic interaction between two vertical cylinders in water waves is investigated based on the linearized potential flow theory. One of the two cylinders is fixed at the bottom while the other is articulated at the bottom and oscillates with small amplitudes in the direction of the incident wave. Both the diffracted wave and the radiation wave are studied in the present paper. A simple analytical expression for the velocity potential on the surface of each cylinder is obtained by means of Graf's addition theorem. The wave-excited forces and moments on the cylinders, the added masses and the radiation damping coefficients of the oscillating cylinder are all expressed explicitly in series form. The coefficients of the series are determined by solving algebraic equations. Several numerical examples are given to illustrate the effects of various parameters, such as the separation distance, the relative size of the cylinders, and the incident angle, on the first-order and steady second-order forces, the added masses and radiation-damping coefficients as well as the response of the oscillating cylinder.

3D Effects on Vortex-Shedding Flow and Hydrodynamic Coefficients of A Vertically Oscillating Cylinder with A Bottom-Attached Disk

Vortex-shedding flow induced by the vertical oscillation of a cylinder with bottom-attached disks of different diameter ratio Dd/Dc and thickness ratio td/Dc is studied by a 3D （three-dimensional） numerical model developed in this paper, and compared with the results obtained through 2D （two-dimensional） numerical model. The high-order upwind scheme is applied to stabilize the computation, and convergence is accelerated by the multi-grid method. Qualitative and quantitative analyses of the differences between the 2D and 3D simulation results reveal the 3D effect on the flow field characteristics and hydrodynamic coefficients of the vertically oscillating cylinder with a bottom-attached disk. The 3D effect on the fluid field is mainly reflected in the significance of three vortex-shedding patterns： ωx has a greater effect on the flow fields around the sharp edges relative to the vortices generated in the 2D simulation. In the slice along the axial orientation, the vortex effect of ωy along the radial axis is smaller than that of ωx along the circumferential direction, indicating the radial effect on the velocity more pronounced than the circumferential effect around the sharp edges of the disk. The rotational interaction ωz of the fluid in the horizontal plane during the heave motion is insignificant. Based on the 2D and 3D simulation results, the turning points that separate the increasing regimes of the added mass coefficient and damping ratio are identified. The dependence of the turning point on the diameter ratio Dd/Dc and thickness ratio td/Dc are discussed in detail.