A finite difference solution of the shear flow over a circular cylinder

The incompressible viscous shear flow past a circular cylinder is analyzed by solving two-dimensional Navier-Stokes equations and pressure Poisson equation using a finite difference method. The shear flow is calculated for Reynolds numbers from 80 to 1000, and shear parameters up to 0.25. The numerical results indicate that the vortex shedding persists at the shear parameters up to 0.25 for the present Reynolds number range. The Strouhal number and the drag coefficient decrease as the shear parameter increases. There is a transverse force acting from the high velocity side toward the low velocity side in the shear 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.     

近壁圆柱绕流水动力特性数值模拟与实验研究

通过数值模拟和物理模型实验,对距壁面一定高度的圆柱绕流水动力特性进行了研究。数值模拟采用有限体积法对标准k-ε模式方程进行离散,采用SIMPLE算法进行求解,模拟绕流流场。在物理模型实验中,将PVC圆管制作的实验模型安放在水槽内,在圆管的跨中沿表面周向均匀布置水下压力传感器,用于测量绕流圆柱体表面动水压力分布。通过改变Re数和间隙比来分析它们对近壁圆柱绕流水动力特性的影响。基于数值流动显示技术,给出了近壁绕流流场的尾流流态分析。通过数值结果与实验结果的对比,对近壁绕流圆柱体的升力系数及其表面动水压力分布进行了研究,对比结果显示了较好的一致性。     

Large-eddy simulation of the flow past a circular cylinder at sub- to super-critical Reynolds numbers

Large-eddy simulation of turbulent flow past a circular cylinder at sub- to super-critical Reynolds numbers is performed using a high-fidelity orthogonal curvilinear grid solver. Verification studies investigate the effects of grid resolution, aspect ratio and convection scheme. Monotonic convergence is achieved in grid convergence studies. Validation studies use all available experimental benchmark data. Although the grids are relatively large and fine enough for sufficiently resolved turbulence near the cylinder, the grid uncertainties are large indicating the need for even finer grids. Large aspect ratio is required for sub-critical Reynolds number cases, whereas small aspect ratio is sufficient for critical and super-critical Reynolds number cases. All the experimental trends were predicted with reasonable accuracy, in consideration the large facility bias, age of most of the data, and differences between experimental and computational setup in particular free stream turbulence and roughness. The largest errors were for under prediction of turbulence separation.     

Numerical simulation of solitary wave scattering by a circular cylinder array

The interaction of a solitary wave with an array of surface-piercing vertical circular cylinders is investigated numerically. The wave motion is modeled by a set of generalized Boussinesq equations. The governing equations are discretized using a finite element method. The numerical model is validated against the experimental data of solitary wave reflection from a vertical wall and solitary wave scattering by a vertical circular cylinder respectively. The predicted wave surface elevation and the wave forces on the cylinder agree well with the experimental data. The numerical model is then employed to study solitary wave scattering by arrays of two circular cylinders and four circular cylinders respectively. The effect of wave direction on the wave forces and the wave runup on the cylinders is quantified.     

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.     

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。     

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.     

Effect of turbulence modelling on the computation of the near-wake flow of a circular cylinder

An evaluation of four well-known Reynolds-Averaged Navier-Stokes (RANS)-based turbulence models was performed in comparison with the results of a dedicated experimental measurement on the near-wake of a circular cylinder in a large water (cavitation) tunnel using a state-of-the-art two-dimensional Digital Particle Image Velocimetry (DPIV) device.The turbulence models investigated were Spalart-Allmaras (S-A), Realizable k-ε (RKE), Wilcox k-ω (WKO) and Shear-Stress-Transport k-ω (SST), which were assessed based on their comparative performances in predicting some important flow field characteristics of the near-wake region of the experimental circular cylinder flow. Within the flow range investigated in this study, which implied a cylinder diameter-based Reynolds Number of 41,300, the qualitative and quantitative comparisons revealed that the application of the SST model to the wall-bounded unsteady flow - that experienced severe adverse pressure gradient, massive flow separation and vortex shedding - presents more successful predictions compared to other models investigated for such challenging flow conditions.     

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%.     

Interaction of uniform current with a circular cylinder submerged below an ice sheet

The problem of a uniform current passing through a circular cylinder submerged below an ice sheet is considered. The fluid flow is described by the linearized velocity potential theory, while the ice sheet is modelled through a thin elastic plate floating on the water surface. The Green function due to a source is first derived, which satisfies all the boundary conditions apart from that on the body surface. Through differentiating the Green function with respect to the source position, the multipoles are obtained. This allows the disturbed velocity potential to be constructed in the form of an infinite series with unknown coefficients which are obtained from the boundary condition. The result shows that there is a critical Froude number which depends on the physical properties of the ice sheet. Below this number there will be no flexural waves propagating to infinity and above this number there will be two waves, one on each side of the body. When the depth based Froude number is larger than 1, there will always be a wave at far upstream of the body. This is similar to those noticed in the related problem and is different from that in the free surface problem without ice sheet. Various results are provided, including the properties of the dispersion equation, resistance and lift, ice sheet deflection, and their physical features are discussed.     

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。     

亚临界区雷诺数下圆柱绕流场电磁力控制数值研究

在亚临界区雷诺数下,采用脱体涡模拟方法对弱电解质中电磁力作用下圆柱绕流场及其升阻力特性进行了数值模拟与分析。结果表明,电磁力可以提高圆柱体边界层内的流体动能,延缓圆柱体近壁面流动分离,减弱绕流场中流向和展向大尺度涡的强度,减小圆柱体阻力及其升力脉动幅值;当电磁力作用参数大于某个临界值后,流动分离角消失,在圆柱体尾部产生射流现象,电磁力产生净推力作用,出现负阻力现象,而且升力脉动幅值显著减小且接近于零。     

Steady streaming around a circular cylinder in an oscillatory flow

Steady streaming induced by an oscillatory flow around a circular cylinder is investigated using a numerical method. Two-dimensional Reynolds-averaged Navier-Stokes equations are solved using a finite element method with a k-ω turbulent model closure. The range of the Keulegan-Carpenter (KC) number investigated is between 2 and 40, which is substantially higher than those reported in literature related to steady streaming to date. A constant value of Stokes number (β) of 196 is chosen in this study. The steady streaming structures and velocity distribution are analysed in detail. It is found that the characteristics of steady streaming are strongly related to the vortex shedding flow regimes.     

Behavior of vortex-induced vibration of a circular cylinder near a deformable wall with two degrees of freedom in steady flow

The behavior of vortex-induced vibration of a two-degree-of-freedom cylinder near a deformable wall in steady flow is investigated experimentally.The typical phenomenon of the two-degree-of-freedom cylinder’s VIV is discussed.The influences of initial gap between the cylinder and the wall on the dynamic responses of the cylinder are analyzed.The comparison is made about dynamic responses of the cylinder with one and two degrees of freedom.Experimental results show that the vibration of the cylinder near a deformable wall with a small value of initial gap-to-diameter ratios can generally be divided into two phases.The initial gap-to-diameter ratios have a noticeable influence on the occurrence of transverse vibration.The transverse maximum amplitude of the cylinder with two degrees of freedom is larger than that of the cylinder with one degree of freedom under the condition with the same values of other parameters.However,the vibration frequency of the cylinder for the two degrees of freedom case is smaller than that for the one degree of freedom case at the same value of Vr number.