A Review on Vibration Control of Multiple Cylinders Subjected to FlowInduced Vibrations

The fatigue damage caused by flow-induced vibration(FIV)is one of the major concerns for multiple cylindrical structures in many engineering applications.The FIV suppression is of great importance for the security of many cylindrical structures.Many active and passive control methods have been employed for the vibration suppression of an isolated cylinder undergoing vortex-induced vibrations(VIV).The FIV suppression methods are mainly extended to the multiple cylinders from the vibration control of the isolated cylinder.Due to the mutual interference between the multiple cylinders,the FIV mechanism is more complex than the VIV mechanism,which makes a great challenge for the FIV suppression.Some efforts have been devoted to vibration suppression of multiple cylinder systems undergoing FIV over the past two decades.The control methods,such as helical strakes,splitter plates,control rods and flexible sheets,are not always effective,depending on many influence factors,such as the spacing ratio,the arrangement geometrical shape,the flow velocity and the parameters of the vibration control devices.The FIV response,hydrodynamic features and wake patterns of the multiple cylinders equipped with vibration control devices are reviewed and summarized.The FIV suppression efficiency of the vibration control methods are analyzed and compared considering different influence factors.Further research on the FIV suppression of multiple cylinders is suggested to provide insight for the development of FIV control methods and promote engineering applications of FIV control methods.

Study on scour around vertical large-size cylinder base due to combined action of wave and current

Based on the mechanism of local scour around vertical large-sized cylinder due to combined action of wave and current,the sour morphology,scour process and the maximum scour depth around the cylinders are studied experimentally.The influence of various ocean environmental parameters on local scour around the cylinder is considered in physical model test.The experimental results indicate that the principal effect factors on the scour in fine-sand seabed are wave height,wavelength,current velocity,ratio of diameter to wavelength and ratio of depth to wavelength when the ratio of cylinder diameter to wavelength is from 0.2 to 0.8.In this paper,dimensional analysis theory is utilized to establish a theoretical equation for forecasting maximum scour depth around large-sized round cylinder base due to the combined action of wave and current.The results computed with the theoretical equation are compared with the experimental results,and found to be in good consistency.The results in this studies can be used to estimate the maximum sour depth around analogous structures.

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.

A thermal stress loading technique for large-sized hot dry rock mechanical tests

Testing of large-sized specimens is becoming increasingly important in deep underground rock mechanics and engineering.In traditional mechanical loading,stresses on large-sized specimens are achieved by large host frames and hydraulic pumps,which could lead to great investment.Low-cost testing machines clearly always have great appeal.In this study,a new approach is proposed using thermal expansion stress to load rock specimens,which may be particularly suitable for tests of deep hot dry rock with high temperatures.This is a different technical route from traditional mechanical loading through hydraulic pressure.For the rock mechanics test system of hot dry rock that already has an investment in heating systems,this technology may reduce the cost of the loading subsystem by fully utilizing the temperature changes.This paper presents the basic principle and a typical design of this technical solution.Preliminary feasibility analysis is then conducted based on numerical simulations.Although some technical details still need to be resolved,the feasibility of this loading approach has been preliminarily confirmed.

Calculating the Wave Force on Partially Immersed Large-Scale Horizontal Cylinders

Large-scale interceptors constitute the main structure of offshore self-driven floating marine litter collection devices,and the structural stability of such interceptors under the action of waves directly influences the overall safety of the device.When the ratio of the diameter of a horizontal cylinder in such interceptors to the incident wavelength is larger than 0.25,the wave force can be calculated by using the diffraction theory,by considering the problem as that of the interaction between the waves and a partially immersed large-scale horizontal cylinder.In this study,an analytical approach to calculate the wave force on a partially immersed large-scale horizontal cylinder was formulated by using the stepwise approximation method.Physical model tests were conducted to investigate the effects of different factors(wave height,period,and immersion depth)on the wave force on a large-scale horizontal cylinder under conditions involving short-period waves.The results show that both horizontal and vertical wave forces on the cylinder increase as the wave height(immersion depth)increases in most cases.The vertical wave force decreases with the decrease of the period.For the horizontal wave force,it increases with the decrease of the period when the wavelength is larger than the diameter of the cylinder and decreases with the decrease of the period when the wavelength is smaller than the diameter of the cylinder.

Modeling and Simulation of the Characteristics of Pneumatic Cushion Cylinders

The analysis of the characteristics of the cushion process of the pneumatic cushion cylinder is presented, and the nonlinear model of pneumatic cushion cylinders is built in the form of nonlinear differential equations. Besides, through the simulation of the pressure in the cushion chamber, the characteristics of the pneumatic cushion cylinder are obtained, which helps to understand the performance of the pneumatic cushion cylinder and improve or design the better cushion structure.

Associated rules between microstructure characterization parameters and contact characteristic parameters of two cylinders

The contact strength calculation of two curved rough surfaces is a forefront issue of Hertz contact theory and method. Associated rules between rough surface characterization parameters(correlation length, and root mean square deviation) and contact characteristic parameters(contact area, maximum contact pressure, contact number, and contact width) of two rough cylinders are mainly studied. The contact model of rough cylinders is deduced based on GW model. As there is no analytical solution for the pressure distribution equation, an approximate iterative solution method for the pressure distribution is adopted. Furthermore, the quantitative relationships among the correlation length, the root mean square deviation, the asperity radius of curvature and the asperity density are also obtained based on a numerical simulation method. The maximum contact pressure and the contact number decrease with the increase of correlation length, while the contact width and the contact area are on the contrary. The contact width increases with the increase of root mean square deviation while the maximum contact pressure, the contact area and the contact number decrease.

Scale-adaptive simulation of flow past wavy cylinders at a subcritical Reynolds number

The Xu ＆ Yan scale-adaptive simulation （XYSAS） model is employed to simulate the flows past wavy cylinders at Reynolds number 8 × 10 3.This approach yields results in good agreement with experimental measurements.The mean flow field and near wake vortex structure are replicated and compared with that of a corresponding circular cylinder.The effects of wavelength ratios λ/D m from 3 to 7,together with the amplitude ratios a /D m of 0.091 and 0.25,are fully investigated.Owing to the wavy configuration,a maximum reduction of Strouhal number and root-meansquare （r.m.s） fluctuating lift coefficients are up to 50% and 92%,respectively,which means the vortex induced vibration （VIV） could be effectively alleviated at certain larger values of λ/D m and a /D m.Also,the drag coefficients can be reduced by 30%.It is found that the flow field presents contrary patterns with the increase of λ/D m.The free shear layer becomes much more stable and rolls up into mature vortex only further downstream when λ/D m falls in the range of 5-7.The amplitude ratio a /D m greatly changes the separation line,and subsequently influences the wake structures.

Experimental Study on Ocean Internal Wave Force on Vertical Cylinders in Different Depths

A series of experimental studies about the force of internal solitary wave and internal periodic wave on vertical cylinders have been carried out in a two-dimensional layered internal wave flume. The internal solitary waves are produced by means of gravitational collapse at the layer thickness ratio of 0.2, and the internal periodic waves are produced with rocker-flap wave maker at the layer thickness ratio of 0.93. The wave parameters are obtained through dyeing photography. The vertical cylinders of the same size are arranged in different depths. The horizontal force on each cylinder is measured and the vertical distribution rules are researched. The internal wave heights are changed to study the impact of wave heights on the force. The results show that the horizontal force of concave type internal solitary wave on vertical cylinder in the upper-layer fluid has the same direction as the wave propagating, while it has an opposite direction in the lower-layer. The horizontal force is not evenly distributed in the lower fluid. And the force at different depths increases along with wave height. Internal solitary wave can produce an impact load on the entire pile. The horizontal force of internal periodic waves on the vertical cylinders is periodically changed at the frequency of waves. The direction of the force is opposite in the upper and lower layers, and the value is close. In the upper layer except the depth close to the interface, the force is evenly distributed; but it tends to decrease with the deeper depth in the lower layer. A periodic shear load can be produced on the entire pile by internal periodic waves, and it may cause fatigue damage to structures.

Elastic and viscoelastic solutions to rotating functionally graded hollow and solid cylinders

Analytical solutions to rotating functionally graded hollow and solid long cylinders are developed. Young＇s modulus and material density of the cylinder are assumed to vary exponentially in the radial direction, and Poisson＇s ratio is assumed to be constant. A unified governing equation is derived from the equilibrium equations, compatibility equation, deformation theory of elasticity and the stress-strain relationship. The governing second-order differential equation is solved in terms of a hypergeometric function for the elastic deformation of rotating functionally graded cylinders. Dependence of stresses in the cylinder on the inhomogeneous parameters, geometry and boundary conditions is examined and discussed. The proposed solution is validated by comparing the results for rotating functionally graded hollow and solid cylinders with the results for rotating homogeneous isotropic cylinders. In addition, a viscoelastic solution to the rotating viscoelastic cylinder is presented, and dependence of stresses in hollow and solid cylinders on the time parameter is examined.

Wave-Current Forces on Small Square Cylinders (Part I)

-Based on the extended Morison Equation and model tests, the in-line forces on small square cylinders caused by waves (regular and irregular) and currents are analyzed in detail in this paper. The hydrodynamic coefficient CD and Cu related to KC number and the effect of direction of wave incidence are also given, which can be used in engineering practice.

Wave-Current Forces on Small Square Cylinders (Part II)

Based on model tests, the lift and resultant forces on small square cylinders caused by waves (regular and irregular) and currents are analyzed in this paper. The lift and resultant force coefficients CL and Cf related to KC number and the effect of direction of wave propagation are also given, which may be useful for practical engineering application.

Use of Helical Strakes for FIV Suppression of Two Inclined Flexible Cylinders in A Side-by-Side Arrangement

The experimental studies on flow-induced vibrations(FIV) reduction of two side-by-side flexible cylinders inclined at 45° by using the helical strakes were carried out in a towing tank. The main aim of the experiment is to check whether the helical strakes with a pitch of 17.5 D and a height of 0.25 D, which is considered as the most effective vibration suppression device for the isolated cylinder undergoing vortex-shedding, still perform very well to reduce FIV of two inclined flexible cylinders in a side-by-side arrangement. The vibration of two identical inclined cylinders with a mass ratio of 1.90 and an aspect ratio of 350 was tested in the experiment. The center-to-center distance between the two cylinders was 3.0 D. The uniform flow was simulated by towing the cylinder models along the tank.The towing velocity varied from 0.05 to 1.0 m/s with an interval of 0.05 m/s. The maximum Reynolds number can be up to 1.6×104. Three cases were experimentally studied in this paper, including two side-by-side inclined smooth cylinders, only one smooth cylinder fitted with helical strakes in the two side-by-side inclined cylinders system and both two cylinders attached with helical strakes. The variations of displacement amplitude, dominant frequency, FIV suppression efficiency and dominant mode for the two side-by-side inclined cylinders with reduced velocity were shown and discussed.

Shear flow induced vibrations of long slender cylinders with a wake oscillator model

A time domain model is presented to study the vibrations of long slender cylinders placed in shear flow. Long slender cylinders such as risers and tension legs are widely used in the field of ocean engineering. They are subjected to vortex-induced vibrations（VIV） when placed within a transverse incident flow. A three dimensional model coupled with wake oscillators is formulated to describe the response of the slender cylinder in cross-flow and in-line directions. The wake oscillators are distributed along the cylinder and the vortex-shedding frequency is derived from the local current velocity. A non-linear fiuid force model is accounted for the coupled effect between cross-flow and in-line vibrations. The comparisons with the published experimental data show that the dynamic features of VIV of long slender cylinder placed in shear flow can be obtained by the proposed model,such as the spanwise average displacement,vibration frequency,dominant mode and the combination of standing and traveling waves. The simulation in a uniform flow is also conducted and the result is compared with the case of nonuniform flow. It is concluded that the flow shear characteristic has significantly changed the cylinder vibration behavior.

Effect of Temperature and Ram Speed on Isothermal Extrusion for Large-size Tube with Piece-wing

Heat energy change during the extrusion of 7075 aluminium alloy large-size tube with piece-wing in a container was analyzed. Extrusion load vs ram displacement diagrams and exit temperature vs ram displacement diagrams at various speeds were obtained by 3D FEM simulation. Results show that the exit temperature becomes higher as the ram speed and displacement increase. For large-size tube with piece-wing, there is certainly a curve of ram speed decreasing with increasing ram displacement, which enables isothermal extrusion to be achieved. Therefore,an attempt was made to divide the working stroke into five different zones. Each of them has a preset speed that decreases from the ram displacement beginning to the ending. And then, new exit temperature vs ram displacement diagram was obtained by 3D FEM simulation for the five different speeds. It is shown that the variation of exit temperature is very small. Through the above research, a basic method for realizing isothermal extrusion of 7075 large-size tube with piece-wing was obtained, that is, the working stroke was divided into several different zones with a decreasing speed during extrusion, each zonest speed was real-time adjusted on the feedback signal of exit temperature by proportional hydraulic valve through closed-loop control. The engineering experiment verification was carried out on 100 MN aluminium extrusion press with oil-driven double action. The experimental results of the exit temperature agrees with the simulation ones. The achievements of this study may serve as a significant guide to the practice of the relevant processes, particularly for isothermal extrusion. The verified method has been used in the design and manufacture of 125 MN aluminium extrusion press with oil-driven double action.

Numerical simulation of low-Reynolds number flows past two tandem cylinders of different diameters

The flow past two tandem circular cylinders of different diameters was simulated using the finite volume method. The diameter of the downstream main cylinder （D） was kept constant, and the diameter of the upstream control cylinder （d） varied from 0.1D to D. The studied Reynolds numbers based on the diameter of the downstream main cylinder were 100 and 150. The gap between the control cylinder and the main cylinder （G） ranged from 0.1D to 4D. It is concluded that the gap-to-diameter ratio （G/D） and the diameter ratio between the two cylinders （d/D） have important effects on the drag and lift coefficients, pressure distributions around the cylinders, vortex shedding frequencies from the two cylinders, and flow characteristics.

In-line response of vertical cylinders in regular and random waves

The in-line response of a vertical flexibly mounted cylinder in regular and random waves is reported. Both theoretical analyses and experimental measurements have been performed. The theoretical predictions are based on the Morison equation which is solved by the incremental harmonic balance method. Experiments are then performed in a wave flume to determine the accuracy of the Morison equation in predicting the in-line response of the cylinder in regular and random waves. The interaction between waves and vibrating cylinders are investigated.

Analysis of Interaction of Plane Waves with Multiple Circular Cylinders

The interaction of water waves with multiple circular cylinders is analysed briefly in this paper. The formula obtained by Linton and Evans is improved to introduce a relation of phase between cylinders. The condition for the existence of the solution has been proved. The numerical results are compared with analytic solutions (Linton and Evans), numerical solutions and experimental data (Isaacson), and good agreement has been found.

A Finite Element Solution of Wave Forces on Submerged Horizontal Circular Cylinders

In this paper, a numerical model is established for estimating the wave forces on a submerged horizontal circular cylinder. For predicting the wave motion, a set of two dimensional Navier Stokes equations is solved numerically with a finite element method. In order to track the moving non linear wave surface boundary, the Navier Stokes equations are discretized in a moving mesh system. After each computational time step, the mesh is modified according to the changed wave surface boundary. In order to stabilize the numerical procedure, a three step finite element method is applied in the time integration. The water sloshing in a tank and wave propagation over a submerged bar are simulated for the first time to validate the present model. The computational results agree well with the analytical solution and the experimental data. Finally, the model is applied to the simulation of interaction between waves and a submerged horizontal circular cylinder. The effects of the KC number and the cylinder depth on the wave forces are studied.

Fully Nonlinear Simulations of Wave Resonance by An Array of Cylinders in Vertical Motions

The finite element method （FEM） is employed to analyze the resonant oscillations of the liquid confined within multiple or an array of floating bodies with fully nonlinear boundary conditions on the free surface and the body surface in two dimensions. The velocity potentials at each time step are obtained through the FEM with 8-node quadratic shape functions. The finite element linear system is solved by the conjugate gradient （CG） method with a symmetric successive overelaxlation （SSOR） preconditioner. The waves at the open boundary are absorbed by the combination of the damping zone method and the Sommerfeld-Orlanski equation. Numerical examples are given by an array of floating wedge- shaped cylinders and rectangular cylinders. Results are provided for heave motions including wave elevations, profiles and hydrodynamic forces. Comparisons are made in several cases with the results obtained from the second order solution in the time domain. It is found that the wave amplitude in the middle region of the array is larger than those in other places, and the hydrodynamic force on a cylinder increases with the cylinder closing to the middle of the array.