NUMERICAL COMPUTATION OF THE FLOW AROUND TWO SQUARE CYLINDERS ARRANGED SIDE-BY-SIDE

The numerical method is used to calculate the flow around two square cylinders arranged side-by-side and the mean and fluctuating aerodynamic forces, and Strouhal numbers and power spectrum of lift force and drag force are obtained. An improved MAC method proposed by Chen Suqin et al.,which uses three order upwind scheme to discretize the convection term and uses multigrid method to solve the Poisson equation for pressure is applied to simulate the flow around two square cylinders arranged side-by-side. Results show that the interference characteristic of two square cylinders arranged side-by-side is completely different with the different spacing ratio. When the spacing ratio is smaller than a certain critical value, the gap flow between two cylinders is biased to one side in a stable or unstable manner.

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.

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.

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.

Numerical Simulation on Flow Past Two Side-by-Side Inclined Circular Cylinders at Low Reynolds Number

A series of three-dimensional numerical simulations is carried out to investigate the effect of inclined angle on flow behavior behind two side-by-side inclined cylinders at low Reynolds number Re=100 and small spacing ratio T/D=1.5 (T is the center-to-center distance between two side-by-side cylinders, D is the diameter of cylinder). The instantaneous and time-averaged flow fields, force coefficients and Strouhal numbers are analyzed. Special attention is focused on the axial flow characteristics with variation of the inclined angle. The results show that the inclined angle has a significant effect on the gap flow behaviors behind two inclined cylinders. The vortex shedding behind two cylinders is suppressed with the increase of the inclined angle as well as the flip-flop gap flow. Moreover, the mean drag coefficient, root-mean-square lift coefficient and Strouhal numbers decrease monotonously with the increase of the inclined angle, which follows the independent principle at small inclined angles.

Response of Two Unequal-Diameter Flexible Cylinders in A Side-by-Side Arrangement:Characteristics of FIV

Till now,little information is available on the flow-induced vibration(FIV)of multiple flexible cylinders with unequal diameters.Some FIV characteristics of unequal-diameter cylinders can be predicted based on the knowledge of equal-diameter cylinders,while there are still other features remaining unrevealed.In this paper,the FIV characteristics of two flexible cylinders with unequal diameters arranged side-by-side are experimentally investigated.The diameter ratio of the small cylinder(Small Cyl.)to the large cylinder(Large Cyl.)is nearly 0.5.The aspect ratios and mass ratios of the two flexible cylinders are 350/181 and 1.90/1.47,respectively.The centre-tocentre spacing ratio in the cross-flow(CF)direction is kept constant as 6.0 and the two cylinders can oscillate freely in both the CF and in-line(IL)directions.The towing velocity varies from 0.05 m/s to 1.00 m/s.The dominant modes and frequencies,CF and IL displacement amplitudes and response trajectories are discussed.Compared with the case of two identical cylinders in our previous study,the FIV responses demonstrate some similarities and differences.The similarities are as follows.Both cylinders exhibit multi-mode vibration features and they interact with each other.Meanwhile,the IL FIV shows a more complex behaviour than that in the CF direction.The difference is that as the diameter of one cylinder is increased,the effect on the smaller cylinder becomes more significant.For Large Cyl.,the FIV response is similar to its isolated counterpart,which indicates that Small Cyl.has a negligible effect on the FIV of the larger one.Whereas Large Cyl.perplexes the FIV of Small Cyl.during the vibration process.The spacing would change when both cylinders are oscillating.Proximity interference between the two cylinders and wake shielding effect of the Large Cyl.may occur.The dominant frequencies of Small Cyl.are reduced and the wake-induced flutter of Small Cyl.is observed from the response trajectories at different measuring points.

Application of Helical Strakes for Suppressing the Flow-Induced Vibration of Two Side-by-Side Long Flexible Cylinders

Helical strakes have been widely applied for suppressing the vibration of flexible cylinders undergoing vortexshedding in offshore engineering.However,most research works have concerned on the application of helical strakes for the isolated flexible cylinder subjected to vortex-induced vibration(VIV).The effectiveness of helical strakes attached to side-by-side flexible cylinders in vibration reduction is still unclear.In this paper,the response characteristics of two side-by-side flexible cylinders with and without helical strakes were experimentally investigated in a towing tank.The configuration of the helical strakes used in the experiment had a pitch of 17.5D and a height of 0.25D(where D is the cylinder diameter),which is usually considered the most effective for VIV suppression of isolated marine risers and tendons.The center-to-center distance of the two cylinders was 3.0D.The uniform flow with a velocity ranging from 0.05 m/s to 1.0 m/s was generated by towing the cylinder models along the tank.Experimental results,including the displacement amplitude,the dominant frequency,the dominant mode,and the mean drag force coefficient,were summarized and discussed.For the case where only one cylinder in the two-cylinder system had helical strakes,the experimental results indicated that helical strakes can remarkably reduce the flow-induced vibration(FIV)of the staked cylinder.For the case of two straked cylinders in a side-by-side arrangement,it was found that the performance of helical strakes in suppressing the FIV is as good as that for the isolated cylinder.

LARGE EDDY SIMULATION AND SPECTRUM ANALYSIS OF FLOW AROUND TWO SQUARE CYLINDERS ARRANGED SIDE BY SIDE

Large eddy simulation cooperated with the second order full extension ETG(Euler-Taylor-Galerkin) finite element method was applied to simulate the flow around two square cylinders arranged side by side at a spacing ratio of (1.5.) The second order full extension ETG finite element method was developed by Wang and He. By means of Taylor expansion of terms containing time derivative, time derivative is replaced by space derivative. The function of it is equal to introducing an artificial viscosity term. The streamlines of the flow at different moments were obtained. The time history of drag coefficient, lift coefficient and the streamwise velocity on the symmetrical points were presented. Furthermore, the symmetrical problem of the frequency spectrum of flow around two square cylinders arranged side by side were studied by using the spectral analysis technology. The data obtained at the initial stage are excluded in order to avoid the influence of initial condition on the results. The power spectrums of drag coefficient, lift coefficient, the streamwise velocity on the symmetrical points were analyzed respectively. The results show that although the time domain process of dynamic parameters is non-symmetrical, the frequency domain process of them is symmetrical under the symmetrical boundary conditions.

Physical mechanism for origin of streamwise vortices in mode A of a square-section cylinder

In the present paper, physical mechanism responsible for origin of streamwise vortices in mode A appeared in the threedimensional (3-D) wake transition of a square-section cylinder is investigated. Direct numerical simulations at a Reynolds number of 180 firstly show that such streamwise vorticity is not originated from lateral surfaces. Then through the analysis of local flow field in the immediate neighborhood of rear surface, based on the theory of vortex-induced vortex, a new physical mechanism is identified. At first, the vertical vorticity on rear surface is generated by the intrinsic three-dimensional instability with the same instability wavelength of mode A. Then the streamwise vorticity at a specific sign is induced by such vertical vorticity, convected and concentrated in the shear layers. Finally, streamwise vortices are formed and shed with alternatively shedding spanwise vortices in the near wake. Moreover, the effect of induced spanwise vorticity on original two-dimensional (2-D) spanwise vorticity is also presented in detail.

Numerical simulation of flow around square cylinder using different low-Reynolds number turbulence models

ABE-KONDOH-NAGANO,ABID,YANG-SHIH and LAUNDER-SHARMA low-Reynolds number turbulence models were applied to simulating unsteady turbulence flow around a square cylinder in different phases flow field and time-averaged unsteady flow field.Meanwhile,drag and lift coefficients of the four different low-Reynolds number turbulence models were analyzed.The simulated results of YANG-SHIH model are close to the large eddy simulation results and experimental results,and they are significantly better than those of ABE-KONDOH-NAGANO,ABID and LAUNDER-SHARMR models.The modification of the generation of turbulence kinetic energy is the key factor to a successful simulation for YANG-SHIH model,while the correction of the turbulence near the wall has minor influence on the simulation results.For ABE-KONDOH-NAGANO,ABID and LAUNDER-SHARMA models satisfactory simulation results cannot be obtained due to lack of the modification of the generation of turbulence kinetic energy.With the joint force of wall function and the turbulence models with the adoption of corrected swirl stream,flow around a square cylinder can be fully simulated with less grids by the near-wall.

Two-Dimensional Simulation of the Navier-Stokes Equations for Laminar and Turbulent Flow around a Heated Square Cylinder with Forced Convection

Few studies jointly investigate thermal and turbulent effects. In general, these subjects are treated separately. The purpose of this paper is to use the Immersed Boundary Method (IBM) coupled with the Virtual Physical Model (VPM) to investigate incompressible two-dimensional Newtonian flow around a heated square cylinder at constant temperature on its surface with forced convection and turbulence. The VPM model dynamically evaluates the force that the fluid exerts on the immersed surface and the thermal exchange between both in the Reynolds numbers (Re) window 40 ≤ Re ≤ 5×103 . For simulations of turbulence the Smagorinsky and Spalart-Allmaras models are used. The first model uses the Large Eddy Simulation (LES) methodology and is based on the local equilibrium hypothesis for small scales associated with the Boussinesq hypothesis, such that the energy injected into the spectrum of the turbulence balances the energy dissipated by convective effects. The second model uses the concept Unsteady Reynolds Averaged Navier-Stokes Equations (URANS), with only one transport equation for turbulent viscosity, being calibrated in pressure gradient layers. The goal of this work is to analyse the combination of the heat-transfer phenomena with the turbulence for the thermo-fluid-structure interaction in a square cylinder. For this, it was developed a C/C++ code that requires low computational costs in regards to memory and computer facilities. It is observed that, with the increase of the Reynolds number, an increase of the drag coefficient occurs, as well as reinforces the influence of the pressure distribution downstream of the cylinder, which is strongly influenced by the formation and detachment of vortices on the upper and lower sides of the square cylinder.

Forced convection heat transfer due to different inclination angles of splitter behind square cylinder

A numerical investigation is carried out to study the effect of splitter＇s inclination angle behind an inclined square cylinder on the forced convection heat transfer in a plan channel using the lattice Boltzmann method （LBM）. The simulations are conducted for the pertinent parameters in the following ranges： the Reynolds number Re=50-300, the gap ratio G/d = 2, and the splitter＇s inclination angle 8 = 0°-90°. The results show that with the increase in the angle of the splitter, the drag coefficient initially decreases and then increases. Moreover, the time-averaged Nusselt number at a certain angle increases noticeably.

Grid Convergence Property of Three-Dimensional Measurement-Integrated Simulation for Unsteady Flow behind a Square Cylinder with Karman Vortex Street

The purpose of this study was to clarify grid convergence property of three-dimensional measurement-integrated (3D-MI) simulation for a flow behind a square cylinder with Karman vortex street. Measurement-integrated (MI) simulation is a kind of the observer in the dynamical system theory by using CFD scheme as a mathematical model of the system. In a former study, two-dimensional MI (2D-MI) simulation with a coarse grid system showed a fairly good result in comparison with a 2D ordinary (2D-O) simulation, but the results were degraded with grid refinement. In this study, 3D-MI simulation and three-dimensional ordinary (3D-O) simulation were performed with three grid systems of different grid resolutions, and their grid convergence properties were compared. As a result, all 3D-MI simulations reproduced the vortex shedding frequency identical to that of the experiment, and the flow fields obtained were very close, within 5% difference between the results, while the results of the 3D-O simulations showed variation of the solution under convergence. It is shown that the grid convergence property of 3D-MI simulation is monotonic and better than that of 3D-O simulation, whereas those of 2D-O and 2D-MI simulations for streamwise velocity fluctuation are divergent. The solution of 3D-MI simulation with a relatively coarse grid system properly reproduces the basic three-dimensional structure of the wake flow as well as the drag and lift coefficients.

A New Method of Computing the Transient Response of a Dielectric Square Cylinder

The vulume intesral equation and Fourier transform are applied to solve thetransient response of a dielectric square cylinder. if the dielectric square cylinderis only two-dimensional inhoniogeneous and the source is three-dimensional,Fourier transformation is used to reduce the three-dimensional source into thesuperposition of two diniensional source.

Control of Vortex Shedding and Drag Reduction through Dual Splitter Plates Attached to a Square Cylinder

在这份报纸，我们在旋涡流的控制上做了数字研究并且由依附薄 splitter 盘子拖柱体的减小。有依附的 splitter 盘子的方形的剖面图的柱体的 wake 结构为雷纳兹数字的一个范围被分析，基于事件溪流和柱体的高度，在 laminar 范围。管理流动的海军司烧方程被控制体积方法在蹒跚的格子安排上解决。我们为连接压力的方程使用了半含蓄的方法(简单) 为计算的算法。我们的结果证明柱体在上游的一个 splitter 盘子的存在减少 drag，但是它在当板长度在 1.5 次以后是柱体的高度时，流频率的旋涡上有小影响。一个下游的 splitter 盘子的存在阻抑流频率的旋涡。进内部方面的液体的乘火车分开砍层被下游的 splitter 板妨碍。我们的结果建议由依附柱体在上游、下游的同轴的 splitter 盘子，流的旋涡能被压制，以及减小在拖被获得。我们做了参量的研究决定这些 splitter 盘子的最佳的长度以便完成低拖并且低旋涡流频率。

Features of Flow Past Square Cylinder with a Perforated Plate

A numerical investigation was performed on the reduction of the fluid forces acting on the square cylinder in the laminar flow regime with a perforated plate. The effects of geometric parameters such as the distance between the square cylinder and the perforated plate on the wake of the square cylinder were discussed. Furthermore, the flow characteristics such as the drag coefficient, lift coefficient, Strouhal number and flow pattern were obtained. It can be concluded that the drag force of the square cylinder reduces to some extent due to the addition of the perforated plate. The flow structure varies when the perforated plate is located behind the square cylinder. Moreover, the recirculation zone augments with the increase of L/D, and the vortex trace on the upper and lower surface of the square cylinder moves gradually backwards until a stable recirculation zone formed between the square cylinder and the perforated plate.

Least Square Finite Element Method for Viscous Splitting of Unsteady Incompressible Navier–Stokes Equations

In order to solve unsteady incompressible Navier–Stokes(N–S) equations, a new stabilized finite element method,called the viscous-splitting least square FEM, is proposed. In the model, the N–S equations are split into diffusive and convective parts in each time step. The diffusive part is discretized by the backward difference method in time and discretized by the standard Galerkin method in space. The convective part is a first-order nonlinear equation.After the linearization of the nonlinear part by Newton’s method, the convective part is also discretized by the backward difference method in time and discretized by least square scheme in space. C0-type element can be used for interpolation of the velocity and pressure in the present model. Driven cavity flow and flow past a circular cylinder are conducted to validate the present model. Numerical results agree with previous numerical results, and the model has high accuracy and can be used to simulate problems with complex geometry.

并列切角方柱风致干扰效应的大涡模拟研究

针对并列切角高层建筑间的干扰影响问题,本文采用大涡模拟方法研究雷诺数22 000的均匀流场下并列切角(切角率10%)方柱的干扰效应。基于模型的网格收敛性分析及模型准确性验证,对比分析不同间距比下并列切角方柱的气动干扰效应和流场分布,并探寻风压干扰效应的影响规律和形成机理。结果表明:对于并列切角方柱,平均阻力系数主要呈放大效应,脉动升力系数主要呈减小效应。在并列切角方柱处于小间距(B/L=1.2)时,由于风与壁面的相互作用,产生风压力,风压力与方柱表面力叠加,对正压区域产生加强效果,表现为放大效应,对负压区域进行削弱,出现减小效应;当B/L=1.5时,结构干扰最剧烈,其中相邻立面后流场的切角处放大效明显,干扰因子最大值为2.58;当B/L≥4.0时,除相邻立面外的其他立面与切角干扰效应趋于消失;当B/L=8.0时,相邻立面仍然存在28%的放大效应。

融入几何先验的圆柱表面三维应变场双目视觉测量方法

针对现有基于双目视觉的圆柱表面三维应变场测量方法从位移场计算应变场效率低下的问题,将圆柱结构几何先验信息融入子域投影法理论,利用圆柱标准坐标变换替代大量冗余的局部切平面最小二乘拟合求解,提出了一种融合圆柱拟合和子域投影的表面三维应变场计算方法;然后采用数值模拟方式,在不同应变区域和位移场噪声条件下,将所提方法与一般曲面子域投影法进行对比分析;最后开展圆柱拉伸实验,分别从单点和全场两个角度将所提方法的应变计算结果与应变片测量结果进行了对比。研究结果表明:在保证计算精度和位移场噪声鲁棒性的同时,所提方法将计算效率提高了约20%,且与应变片实验测量结果吻合较好,验证了该方法能够实现圆柱结构表面三维应变场的高效测量,也为规则结构表面三维应变场的计算提供了新思路。

正方形布置四圆柱结构流致振动响应特性研究

通过风洞实验研究了正方形布置四圆柱的流致振动特性,实验雷诺数Re=3200~28900,圆柱间距比S/D=1.5~4.0(S为两圆柱圆心间距,D为圆柱直径),质量比m^(*)≈345.0.结果表明,当S/D≤2.0时,上游圆柱1和2呈现涡激振动和类弛振耦合响应,下游圆柱3和4呈现涡激共振和尾流弛振耦合响应;当S/D=2.5~3.0,上游圆柱1和2除了在约化速度超过一定值时存在弱振动外,基本接近单圆柱涡激振动响应,下游圆柱3和4表现为分离的涡激共振和尾流弛振响应;当S/D=4.0时,上游圆柱1和2振动响应几乎和单圆柱一样,而圆柱3和4仍呈现分离的涡激共振和尾流弛振响应.当圆柱呈现涡激振动(上游圆柱)或涡激共振(下游圆柱)时,涡脱频率f_(s)锁定于固有频率f_(n)的1倍谐频,而当圆柱呈现剧烈的类弛振响应(上游圆柱)或尾流弛振响应(下游圆柱)时,f_(s)则会出现明显的多倍谐频;圆柱模型振动频率f_(o)主频始终锁定于fn的1倍谐频.通过对比正方形四圆柱和双圆柱流致振动特性,发现双圆柱动力学响应规律在一定程度上仍适用于正方形布置四圆柱.