Direct numerical simulation of flow over a slotted cylinder at low Reynolds number

Direct numerical simulation was conducted to investigate the flow past a slotted cylinder at low Reynolds number (Re) of 100. The slotting of cylinder affects the boundary layer separation, vortex formation position, recirculation region length and wake width, which are determined by the type of slit. The streamwise slit (SS1), T-shaped slit (SS3) and Y-shaped slit (SS4) act as passive jets, while the transverse slit (SS2) achieves an alternate self-organized boundary layer suction and blowing. The flow rate in slits fluctuates over time due to the alternate vortex shedding and fluctuating pressure distribution around the cylinder surface. One fluctuation cycle of flow rate is caused by a pair of vortices shedding for SS2, SS3 and SS4, while it is created by each vortex shedding for SS1. The wall shear stress and flow impact on the slit wall partly contribute to the hydrodynamic forces acting on the slotted cylinder. Taking into account the internal wall of slit, the transverse slit plays the best role in suppressing the fluid forces with drag reduction of 1.7% and lift reduction of 17%.     

动波浪壁圆柱绕流三维数值模拟

利用计算流体力学软件Fluent开展了三维动波浪壁圆柱绕流的数值模拟,建立了三维运动波浪壁圆柱模型,通过C语言自编程序实现波浪壁面的运动控制,并保证壁面变形时网格的高质量。在来流速度u=0.125 m/s、雷诺数Re=12 500的情况下,开展了动波浪壁波动速度w=0、0.062 5、0.125、0.187 5 m/s四个工况的计算分析,并比较了不同波动速度对流场结构、升力、阻力特性的影响。结果表明:动波浪壁圆柱能有效抑制流动的分离,消除交替脱落的尾涡,从而消除周期振荡的升力;在消除卡门涡街的同时,圆柱后驻点处的涡量值随波动速度增加而增加,其原因在于波形移动加大了壁面流体的速度,从而减小了圆柱前后的压力差,减小了阻力;随着波动速度的增大,平均阻力系数呈明显下降趋势,当波动速度为来流速度的1.5倍时,平均阻力系数相对于光滑圆柱下降了53.76%。     

Numerical Simulation of the Vortex-Induced Vibration of A Curved Flexible Riser in Shear Flow

A series of fully three-dimensional(3 D) numerical simulations of flow past a free-to-oscillate curved flexible riser in shear flow were conducted at Reynolds number of 185–1015. The numerical results obtained by the two-way fluid–structure interaction(FSI) simulations are in good agreement with the experimental results reported in the earlier study. It is further found that the frequency transition is out of phase not only in the inline(IL) and crossflow(CF) directions but also along the span direction. The mode competition leads to the non-zero nodes of the rootmean-square(RMS) amplitude and the relatively chaotic trajectories. The fluid–structure interaction is to some extent reflected by the transverse velocity of the ambient fluid, which reaches the maximum value when the riser reaches the equilibrium position. Moreover, the local maximum transverse velocities occur at the peak CF amplitudes, and the values are relatively large when the vibration is in the resonance regions. The 3 D vortex columns are shed nearly parallel to the axis of the curved flexible riser. As the local Reynolds number increases from 0 at the bottom of the riser to the maximum value at the top, the wake undergoes a transition from a two-dimensional structure to a 3 D one. More irregular small-scale vortices appeared at the wake region of the riser, undergoing large amplitude responses.     

不同雷诺数下倾斜圆柱绕流三维数值模拟研究

基于计算流体力学(CFD)开源代码OpenFOAM开展了不同雷诺数(Re=100、1500和3900)和倾斜角度(-60°≤α≤60°)工况下倾斜圆柱绕流流场的三维数值模拟,研究倾斜圆柱绕流的三维瞬时及时均尾流流场、流线拓扑、升阻力系数与旋涡脱落频率随雷诺数及倾斜角度变化的规律,探讨在顺流向及逆流向情况下独立性原则对倾斜圆柱绕流的适用性。研究结果表明:随着圆柱倾角的增大,倾斜圆柱尾流产生较为明显的轴向流,尾流旋涡脱落受到明显抑制,细碎旋涡逐渐消失,尾流宽度随之减小;随着雷诺数的增大,圆柱尾流涡管发生明显的变形,展向掺混使得大量细碎旋涡产生,呈现出明显的三维特性。在不同雷诺数下,阻力系数均值、升力系数均方根及无量纲涡脱频率在一定倾角范围内符合独立性原则。     

The effect of shroud on vortex shedding mechanism of cylinder

In the present study, flow characteristics were investigated experimentally using particle image velocimetry technique (PIV) in a gap between a solid cylinder and a shroud to reveal the effect of shroud diameter (D_s) and porosity (β) on the vortex shedding mechanism of the cylinder. Porosity (varied from β = 0.3 to 0.7) and diameter ratio (D/D_s = 0.4, 0.5 and 0.6) were main parameters examined at a Reynolds number of Re = 5000. For the porosity values of β ≤ 0.5, it is observed that vortex formation of the cylinder occurs only in the gap and shroud produces its own wake flow patterns. Penetrating flow through the shroud extends the shear layers on the both sides of the shroud through the downstream direction and prevents the interaction of shear layers in the near wake region. The diameter ratio and the porosity are impactful on the wake flow patterns in outer region of the shroud since they are determinant of the penetrating flow rate. Force measurements were also performed in the air tunnel in order to reveal the effect of shroud on the drag coefficient of cylinder. It is found that the drag coefficient of the cylinders are reduced significantly by shrouds when compared with that obtained from the bare cylinder case. However, the drag coefficient of the cylinder together with the shroud is higher than the bare cylinder for all cases since the shrouds enlarge the area exposed to the flow.     

Comparison of flow patterns in the near wake of a circular cylinder and a square cylinder placed near a plane wall

The flow patterns in the near wake of a cylinder (either circular or square in shape, D=25 mm) placed in the proximity of a fully developed turbulent boundary layer (thickness δ=0.4D) are investigated experimentally using particle image velocimetry (PIV). The effects of changing the gap height (S) between the cylinder bottom and the wall surface, over the gap ratio range S/D=0.1–1.0, have been investigated. The results show that both the ensemble-averaged and instantaneous flow fields are strongly dependent on S/D. The flow patterns for the two types of cylinders share many similarities with respect to the change in S/D, such as the reduced recirculation length and increased velocity fluctuation in the near wake with increasing S/D, as well as the trend of suppression of vortex shedding at small S/D and onset of vortex shedding at large S/D. However, developments of the shear layers, in terms of wake width, flow curvature, etc., are considerably different for these two types of cylinders. In general, the wake development and momentum exchange for the square cylinder are slower those for the circular cylinder at the same gap ratio. Correspondingly, it is shown that the periodic vortex shedding is delayed and weakened in the case of square cylinder, as compared to that of the circular cylinder at the same S/D.     

Flow induced vibrations of a sharp edge square cylinder in the wake of a circular cylinder

The response of an oscillating circular cylinder at the wake of an upstream fixed circular cylinder was classified by different researchers as galloping, wake induced galloping or wake induced vibration. Furthermore it is already known that a sharp edge square cylinder would undergo galloping if it is subjected to uniform flow. In this study the influence of the wake of a fixed circular cylinder on the response of a downstream square cylinder at different spacing ratios (S/D = 4, 8, 11) is experimentally investigated. The subject appears not to have received previous attention. The lateral displacements, lift forces and the pressure data from gauges mounted in the wake of the oscillating cylinder are recorded and analyzed. The single degree of freedom vibrating system has a low mass-damping parameter and the Reynolds number ranges from 7.7 × 10² to 3.7 × 10⁴.In contrast to that for two circular cylinders in tandem arrangement, the freely mounted downstream square cylinder displays a VIV type of response at all spacing ratios tested. There is no sign of galloping or wake induced galloping with the square cylinder. With increase at the spacing ratio the cross-flow oscillations decrease. It is shown that the vortices arriving from the upstream fixed circular cylinder play a major role on the shedding mechanism behind the downstream square cylinder and cause the square cylinder to shed vortices with frequencies above Strouhal frequency of the fixed square cylinder (St = 0.13). The VIV type of oscillations in the downstream square cylinder is most probably caused by the vortices newly generated behind the square cylinder.     

Large eddy simulations of a circular cylinder at Reynolds numbers surrounding the drag crisis

Large eddy simulations of the flow around a circular cylinder at high Reynolds numbers are reported. Five Reynolds numbers were chosen, such that the drag crisis was captured. A total of 18 cases were computed to investigate the effect of gridding strategy, turbulence modelling, numerical schemes and domain width on the results. It was found that unstructured grids provide better resolution of key flow features, when a ‘reasonable’ grid size is to be maintained.When using coarse grids for large eddy simulation, the effect of turbulence models and numerical schemes becomes more pronounced. The dynamic mixed Smagorinsky model was found to be superior to the Smagorinsky model, since the model coefficient is allowed to dynamically adjust based on the local flow and grid size. A blended upwind-central convection scheme was also found to provide the best accuracy, since a fully central scheme exhibits artificial wiggles, due to dispersion errors, which pollute the solution.Mean drag, fluctuating lift Strouhal number and base pressure are compared to experiments and empirical estimates for Reynolds numbers ranging from 6.31 × 10⁴ to 5.06 × 10⁵. In terms of the drag coefficient, the drag crisis is well captured by the present simulations, although the other integral quantities (rms lift and Strouhal number) show larger discrepancies. For the lowest Reynolds number, the drag is seen to be more sensitive to the domain width than the spanwise grid spacing, while at the higher Reynolds numbers the grid resolution plays a more important role, due to the larger extent of the turbulent boundary layer.     

Large Eddy Simulation on Interaction Between in-Line and Cross-Flow Oscillation of A Circular Cylinder

This paper discusses numerical results from three-dimensional large eddy simulations of an oscillating cylinder under prescribed movements in uniform flow. Six cases,namely pure in-line,pure cross-flow and two groups of 'Figure of Eight' oscillation patterns are under investigation at Reynolds number Re=24000. The 'Figure of Eight' pattern in each group is with identical shape but opposite orbital directions. The numerical results on hydrodynamic forces,higher order force components,and vortex shedding mode...     

基于MPS方法模拟低雷诺数方柱绕流问题

柱体绕流问题是流体力学领域一个非常经典的问题。当流体流经柱体时,由于黏性的存在,会发生许多复杂的流动现象,如流动分离、涡旋周期性生成与脱落等,经常被作为标准验证算例。同时,柱体绕流广泛存在于实际工程中,并在一定工况下可能对工程产生巨大危害,因此对柱体绕流进行深入研究具有重要意义。研究中,拟将一种无网格类方法——半隐式移动粒子方法(moving particle semi-implicit method,简称MPS)引入到柱体绕流问题的数值研究中,并对不同雷诺数下二维方柱绕流问题进行数值模拟。首先,使用基于MPS方法自主开发的MLParticle-SJTU求解器,结合入口边界条件和出口边界条件,模拟了雷诺数Re分别为40、200和1 000时均匀来流条件下的方柱绕流。随后,将模拟的绕流结果与文献中试验和数值计算结果进行了对比,结果吻合较好,并且在雷诺数为200和1 000时,可以清晰地捕捉到方柱尾流中的卡门涡街现象,验证了MPS方法在柱体绕流问题模拟上的有效性和适用性。     

五圆柱体结构群绕流特性及互扰效应研究

基于Fluent流体计算平台,运用大涡模拟方法对亚临界雷诺数Re=3900下“X”形排列五圆柱体结构群三维绕流特性进行研究,主要分析来流攻角α与间距比L/D两个关键参数对五圆柱体结构群的尾流区三维涡结构演化与流体力系数的影响,并揭示其内在流动互扰机理。研究表明:来流攻角和间距比的变化对五圆柱体结构群流动控制及互扰效应的影响显著。在小间距比工况下,观察到柱体群间隙区域内流体高速流动的现象,导致五圆柱体之间的互扰作用十分强烈。间隙流对中间圆柱体和下游圆柱体有较强的冲击作用,对其表面的流体力分布特性有显著的影响。另外,大间距比工况下,当α=0°与L/D≥5.0工况时,柱体群尾流效应强于其间隙流效应。当α=22.5°与L/D=7.0时,位于下游与中间处的圆柱体流体绕流特性存在较大差异。而当α=45°与L/D≥6.0时,位于上游与中间处的圆柱体尾流区均会产生正负交替的漩涡结构。     

Large-eddy simulation of the turbulent near wake behind a circular cylinder: Reynolds number effect

The purpose of the present work is <!–<query>The highlights are in an incorrect format. Hence they have been deleted. Please refer the online instructions: http://www.elsevier.com/highlights and provide 3-5 bullet points.</query>–>to study the effect of the Reynolds number on the near-wake structure and separating shear layers behind a circular cylinder. Three-dimensional unsteady large-eddy simulation is carried out and two different subgrid scale models are applied in order to evaluate the turbulent wake reasonably. The Reynolds number based on the free-stream velocity and the cylinder diameter is ranging from Re = 5500–41,300, corresponding to the full development of the shear-layer instability in the intermediate subcritical flow regime. For a complete validation of this numerical study, hydrodynamic bulk coefficients are computed and compared to experimental measurements and numerical studies in the literature. Special focus is made on the variations of both the large-scale near-wake structure and the small-scale shear-layer instability with increasing Reynolds numbers. The present numerical study clearly shows the broadband nature of the shear-layer instability as well as the dependence of the shear-layer frequency especially on the high Reynolds numbers.     

Heave motion suppression of a Spar with a heave plate

Vortex shedding flow of an oscillating vertical cylinder with a disk attached at its keel is considered. This configuration is of interest for the offshore oil and gas industry. A finite difference method is employed to solve the incompressible Navier–Stokes equations in the primitive-variables formulation. Test cases were used to guide selection of the size of flow domain, numerical parameters, and to verify that the resultant method was both convergent and accurate. Numerical simulations have shown that the geometry configurations of the cylinder and disk, such as aspect ratio of the disk t_d/D_d and diameter ratio, D_d/D_c have significant influence on the vortex shedding modes and associated hydrodynamic properties, e.g. hydrodynamic damping and added mass coefficients. These in turn affect the performance in heave motion control of the structures.     

Computational study on near wake interaction between undulation body and a D-section cylinder

We present a numerical study on the hydrodynamic performance of undulation NACA0012 foil in the near wake of D-section cylinder. Computations are conducted using unsteady incompressible Navier-Stokes equations with a moving adaptive mesh based on laminar flow. Investigations are focused on the effect of distance ratio between foil tip and centre of cylinder (L/D≤2.0) on the thrust/drag performance of foil and cylinder at various foil undulation frequency (St). We found that, foil thrust coefficient (C_t) increases considerably with the appearance of cylinder and an optimal distance exists at which C_t reaches maxima. The maximum increment is about eleven times that of its counterpart of single foil, which is obtained at St=0.23 and L/D=0.5. Our results for the cylinder drag coefficient (C_d) observed the existence of optimal parametric map, combined with various gap ratios and foil frequencies. With these parameters, insertion of an undulation foil can significantly lead to the drag reduction indicating that undulating foil could work efficiently as a passive vortex control device for cylinder drag reduction.     

Validation of a finite difference method for the simulation of vortex-induced vibrations on a circular cylinder

The Karman Vortex Street generated by a circular cylinder is investigated by the numerical solution of the compressible Navier–Stokes equations in the incompressible Mach number range (Mach<0.3) using the Beam and Warming implicit scheme. The agreement with the fully incompressible projection method (Chorin, 1968) is fairly good while convergence time is very much better. The investigation suggests that the compressible Navier–Stokes equations may be used as an efficient alternative to study incompressible flows as well. Mach numbers just below 0.3 are enough to simulate incompressible flow behavior and at the same time do not cause numerical ill-conditioning in the solution. In addition, some relevant features of the vortices generated and carried by the wake of the cylinder could be fairly well captured.     

Forces on a pitching plate: An experimental and numerical study

A flat plate in pitching motion is considered as a fundamental source of locomotion in the general context of marine propulsion. The experimental as well as numerical investigation is carried out at a relatively small Reynold number of 2000 based on the plate length c and the inflow velocity U_∞. The plate oscillates sinusoidally in pitch about its 1/3 − c axis and the peak to peak amplitude of motion is 20°. The reduced frequency of oscillation k = πfc/U_∞ is considered as a key parameter and it may vary between 1 and 5. The underlying fluid-structure problem is numerically solved using a compact finite-differences Navier–Stokes solution procedure and the numerical solution is compared with Particle Image Velocimetry (PIV) measurements of the flow field around the pitching foil experimental device mounted in a water-channel. A good agreement is found between the numerical and experimental results and the threshold oscillation frequency beyond which the wake exhibits a reverse von Kármán street pattern is determined. Above threshold, the mean velocity in the wake exhibits jet-like profiles with velocity excess, which is generally considered as the footprint of thrust production. The forces exerted on the plate are extracted from the numerical simulation results and it is shown, that reliable predictions for possible thrust production can be inferred from a conventional experimental control volume analysis, only when besides the wake's mean flow the contributions from the velocity fluctuation and the pressure term are taken into account.     

低雷诺数下圆柱强迫振动特性光滑粒子流体动力学模拟

基于光滑粒子流体动力学(SPH)方法,开发了能够准确描述水流作用下圆柱强迫振动特性的数学模型。通过引入适合于无网格粒子法的开边界算法,来模拟出入流边界条件,建立了具有造流功能的SPH数值水槽。圆柱及计算域的上下边界均采用修正的动力边界条件进行模拟。借助于粒子位移矫正和压力修正算法,避免了圆柱周围流体粒子压力大幅震荡以及结构下游区域出现空腔等非物理性现象。使用典型的圆柱绕流数据,验证了所建SPH模型的计算性能,研究了固定圆柱在低雷诺数情况下的尾涡脱落模式和升阻力变化规律。明确了低雷诺数下强迫振动圆柱在频率锁定以及非锁定区间内的升力变化规律,量化了升力与外界激励频率之间的关系。     

基于粘性流模型的筒型基础防波堤波浪力数值分析

筒型基础防波堤是一种新型港口海岸工程结构,其基础上部是由连续排列的圆筒构成的直立防浪墙.采用粘性流数值模型,研究连续圆筒防波堤上波浪力竖向分布、水平(沿圆筒环向)分布和波浪力合力特性,并对粘性流数值模型计算的平面直墙波浪力与海港水文规范方法计算结果;粘性流数值模型计算的连续圆筒墙面波浪力与平面直墙波浪力;无限长连续圆筒墙面波浪力与有限长连续圆筒墙面波浪力进行比较分析.针对所选工程算例,建议按<海港水文规范>中平面直墙波浪力计算方法确定连续圆筒防波堤上的波浪力时,波峰时考虑0.90左右的折减系数,波谷时考虑0.95左右的折减系数.     

PIV measurements of hull wake behind a container ship model with varying loading condition

Flow characteristics of the hull wake behind a container ship model were investigated under different loading conditions (design and ballast loadings) by employing the particle image velocimetry (PIV) technique. Measurements were made at four transverse locations and two longitudinal planes for three Reynolds numbers (Re) (=U₀Lpp/ν, where U₀ is the freestream velocity, Lpp is the length between two perpendiculars of the ship model and ν is the kinematic viscosity) of 5.08×10⁵, 7.60×10⁵, and 1.01×10⁶. It was observed that symmetric, large-scale, longitudinal counter-rotating vortices (with respect to centerline) of nearly the same strength were formed in the near wake. For the ballast-loading condition, the vortices appear at propeller plane below the propeller-boss. The vortex center exhibits a significant upward shift near the propeller-boss as the Reynolds number increase, and as the flow moves downstream. Under the design-loading condition, the vortices first appear at a further downstream location than that for the ballast-loading condition above the propeller-boss. This difference in the flow structure can significantly change the inflow conditions to the propeller blades, such as the streamwise mean velocity profiles and turbulence intensity distributions at the propeller plane. In particular, under the ballast-loading condition, asymmetric inflow may weaken the propulsion and cavitation performance of the marine propeller.     

Investigation of drag crisis phenomenon using CFD methods

When fluid flow passes a cylinder, the drag crisis phenomenon occurs between the sub-critical and the super-critical Reynolds numbers. The focus of the present studies was on the numerical prediction of the drag crisis based on CFD methods. In this work, block structured meshes with refined grids near the cylinder surface and in the downstream were employed. Both 2D and 3D simulations were performed using various turbulence models, including the SST k − ω model, the k − ϵ model, the SST with LCTM, the DES model, and the LES model. In the convergence studies, the effects of the grid size, the time step, the first grid size and the aspect ratio (for 3D simulations) on the solutions were examined. The errors due to spatial and time discretizations were quantified according to a V&V procedure. Validation studies were carried out for various Reynolds numbers between Re = 6.31 × 10⁴ and 7.57 × 10⁵. The averaged drag force, the RMS of lift force and the Strouhal number were compared with experimental data. The studies indicated that standard 2D and 3D RANS methods were inadequate to capture the drag crisis phenomenon. The LES method however has the potential to address the problem.