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 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.

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.

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.

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.

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.

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

In this paper we have made a numerical study on the control of vortex shedding and drag reduction of a cylinder by attaching thin splitter plates. The wake structure of the cylinder of square cross-section with attached splitter plates is analyzed for a range of Reynolds number, based on the incident stream and height of the cylinder, in the laminar range. The Navier-Stokes equations governing the flow are solved by the control volume method over a staggered grid arrangement. We have used the semi-implicit method for pressure-linked equation （SIMPLE） algorithm for computation. Our results show that the presence of a splitter plate upstream of the cylinder reduces the drag, but it has a small impact on the vortex shedding frequency when the plate length is beyond 1.5 time the height of the cylinder. The presence of a downstream splitter plate dampens the vortex shedding frequency. The entrainment of fluid into the inner side of the separated shear layers is obstructed by the downstream splitter plate. Our results suggest that by attaching in-line splitter plates both upstream and downstream of the cylinder, the vortex shedding can be suppressed, as well as a reduction in drag be obtained. We made a parametric study to determine the optimal length of these splitter plates so as to achieve low drag and low vortex shedding frequency.

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.

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.

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.

Numerical simulation of viscous flow past an oscillating square cylinder using a CIP-based model

The flow past an in-line forced oscillating square cylinder at Reynolds number of 200 is studied using an in-house code, named constrained interpolation profile method developed in Zhejiang University （CIP-ZJU）. The model is established in the Cartesian coordinate system using the CIP method to discretise the Navier-Stokes equations. The fluid-structure interaction is treated as a multiphase flow of the liquid and solid phases to be solved simultaneously. An immersed boundary method is used to deal with the boundary of the solid body. The CFD model is first applied to the computation of the flow past a fixed square cylinder for its validation. Computations are then performed for the flow past a square cylinder oscillating in the streamwise direction. Considerable attention is paid to the symmetric and anti-symmetric modes of the vortex shedding in the oscillating square cylinder wake. Various oscillation amplitudes and frequencies are simulated and their effects on the vortex shedding modes are analyzed via Lissajous patterns of the unsteady lift coefficient. The relationship among the lift coefficient, the drag coefficient and the lock-on range is also investigated quantitatively.

RANS and hybrid LES/RANS simulations of flow over a square cylinder

Unsteady RANS(URANS),hybrid LES/RANS and IDDES simulations were conducted to numerically investigate the velocity field around,and pressures distribution and forces over a square cylinder immersed in a uniform,steady oncoming flow with Reynolds number Re=21,400.The vortex shedding responses in terms of Strouhal number,the pressure distribution,the velocity profile and the velocity fluctuations obtained by numerical simulations are compared with experimental data.Compared with 2D URANS simulation,3D simulations using hybrid LES/RANS and IDDES models provide more accurate prediction on the responses in the wake,including mean streamwise velocity profile and rms velocity fluctuations.This also results in more accurate prediction of time-averaged surface pressure coefficient on the rear surface obtained by 3D hybrid LES/RANS and IDDES simulations than by URANS simulation.When a hybrid LES/RANS model or IDDES model is used,a more accurate prediction for either pressure coefficient or velocity profile(especially in the far wake region)is not guaranteed by increasing the mesh resolution along the spanwise direction of the square cylinder.

Numerical simulation of flow past a square cylinder with a circular bar upstream and a splitter plate downstream

A numerical investigation of flow past a square cylinder with a circular bar upstream and a splitter plate downstream is carried out in this paper by lattice Boltzmann method(LBM).The combination of the three obstacles and LBM is the main novelty of the present study.The flow patterns are analyzed by a uniform flow of Reynolds number 100 based on the side length of the square cylinder,D.Numerical simulations are performed in the range of 1≤Ds/D≤5,0≤G/D≤7 and 1≤L/D≤6,where Ds,G and L are the center-to center distance,surface-to-surface distance and the splitter plate length,respectively.Six flow patterns are observed in the present study.The maximum percentage reduction in mean drag coefficient is 68.76%at(ds,g,l)=(2.5,0,3)which is in pattern VI.The vortex shedding from the square cylinder and the circular bar can be completely suppressed in pattern VI.The small distance between the square cylinder and the splitter plate plays a more vital role in suppression of vortex shedding as compared with large distance and length.

融合LSC和REHSM的地壳形变分析模型

将块体运动偏离整体旋转和均匀应变的地壳形变看作信号,利用信号对块体内部偏离整体旋转与均匀应变的形变部分进行补偿,建立了融合最小二乘配置与整体旋转-均匀应变模型的地壳形变分析模型。对喜马拉雅-西藏块体的GPS速度场数据进行拟合分析结果表明,该方法有效地提高了拟合精度。

翼板角部处理方柱全风向角风致振动性能风洞试验研究

方形结构和构件在工程结构中应用广泛,其风致振动问题随着高度和跨度的增加而更加突出,角部处理是方形截面结构工程中常用的一种气动措施。为了研究翼板角部处理对方柱全风向角风致振动性能的影响,开展了标准方柱和翼板角部处理方柱的全风向角节段模型风洞试验,分析了标准方柱和带翼方柱全风向角涡激振动和驰振性能。结果表明:(1)翼板角部处理减小了方柱发生涡激振动的风向角范围,但是,最大涡激振动振幅和风速锁定区间明显大于标准方柱,翼板并未改善方柱的涡激振动性能,反而不利于方柱的涡激振动;(2)翼板角部处理没有提高方柱的驰振临界风速,但减小了发生驰振的风向角工况,整体而言,翼板角部处理并没有改善方柱的驰振性能;(3)在全风向角范围内,带翼方柱观测到涡激振动、驰振耦合状态振动和非耦合状态振动,表明风向角是改变柱体驰振类型的一个重要因素。

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.