Experimental study of forces on a cylinder in oscillatory flow with a cross current

Forces on a circular cylinder have been measured with nominally two-dimensional current and oscillatory flow at right angles. Previous results for purely oscillatory flow defined by a Keulegan-Carpenter number, Kc, have been extended for reduced velocities, Vr, in the range 3–10. For Kc<7 modification of the Karman street by oscillation is complex and locking-on has a dominant influence. For Kc > 7 simply adding forces due to the current and oscillation as though in isolation generally gives conservative results. The ‘current’ drag shows considerable variation and can even be negative. The Morison fit to the in-line force is generally less satisfactory when there is a current and can be wholly inadequate.     

In-line response of a cylinder in oscillatory flow

The most widely used mathematical model to represent flow-induced in-line forces on structures is based on the Morison¹ equation. The present paper investigates the validity of using an extension of Morison's equation for non-stationary structures, by comparing predictions with results from a simple laboratory experiment. An elastically-mounted circular cylinder is placed in the sinusoidal flow of a U-tube, and responds in-line with the flow. Cylinder forces and responses are recorded over a range of Keulegan Carpenter numbers up to 35. An equation of motion is solved simply by using relative coordinates and by employing equivalent linearisation. The linear results are compared over a wide variation of parameters with solutions using the full nonlinear equation. Thereafter experimental results are compared with linear predictions.     

In-line force on a cylinder translating in oscillatory flow

Experiments were conducted with smooth and sand-roughened cylinders moving with constant velocity in a sinusoidally oscillating flow to determine the drag and inertia coefficients and to examine the effect of wake biasing on the modified Morison equation. The various flow parameters such as the relative cylinder velocity. Reynolds number, and the Keulegan-Carpenter number were varied systematically and the in-line force measured simultaneously. The principal results, equally valid for both smooth and rough cylinders, are as follows: the drag coefficient decreases with increasing relative current for a given Reynolds number and Keulegan-Carpenter number; the effect of wake biasing on the drag and inertia coefficients is most pronounced in the drag-inertia dominated regime; and the two-term Morison equation with force coefficients obtained under no-current conditions is not applicable to the prediction of wave and current induced loads on circular cylinders.     

Drag force on a circular cylinder in unseparated laminar high Reynolds number nonlinear random oscillatory flow

The stochastic properties of the drag force maxima on a circular cylinder subjected to nonlinear random waves are investigated. Unseparated laminar high Reynolds number flow is considered. A simplified approach based on second order Stokes waves is presented, including the sum-frequency effect only. It is demonstrated how a drag force formula valid for regular linear waves can be used to find the cumulative distribution function of individual drag force maxima for nonlinear irregular waves. Here the [Wang, 1968] drag force coefficient is used.     

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.     

Measurements of higher harmonic wave forces on a vertical truncated circular cylinder

Wave forces on a vertical truncated circular cylinder in Stokes waves with the wave slopes ranging from 0.06 to 0.24, are measured in a wave tank. The higher harmonic wave forces are compared with the available values from theories of the FNV (Faltisen–Newman–Vinje) model and Varyani solution. The first harmonic horizontal forces measured are much larger than the theoretical values from the FNV model, while the first harmonic vertical forces are well predicted by the Varyani theory. It was also found that the FNV model significantly overpredicts the second harmonic horizontal forces in high frequency waves, but under predicts the third harmonic forces. The differences between the actual measurement and the theory, in the second and third harmonic horizontal forces, become smaller at low wave frequencies as the wave slope increases. In addition, the transverse instabilities in the incoming waves with high wave slope were observed, which is due to the nonlinear modulation. Measurements were, thus, carried out before the instability occurred.     

Hydrodynamic forces on a partially submerged cylinder at high Reynolds number in a steady flow

The hydrodynamic forces on the stationary partially submerged cylinder are investigated through towing test with Reynolds number ranging from 5 × 10⁴ to 9 × 10⁵. Three test groups of partially submerged cylinders with submerged depths of 0.25 D, 0.50 D, and 0.75 D and one validation group of fully submerged cylinders are conducted. During the experiments, the hydrodynamic forces on the cylinders are measured using force sensors. The test results show a considerable difference in the hydrodynamic coefficients for the partially submerged cylinders versus the fully submerged cylinders. A significant mean downward lift force is first observed for the partially submerged cylinders in a steady flow. The maximum of the mean lift coefficients can reach 1.5. Two distinct features are observed due to the effects of overtopping: random distributions in the mean drag coefficients and a clear quadratic relationship between the mean lift coefficients and the Froude number appear in the non-overtopping region. However, the novel phenomenon of a good linear relationship with the Froude number for the mean hydrodynamic coefficients is clearly shown in the overtopping region. In addition, fluctuating hydrodynamic coefficients are further proposed and investigated. These results are helpful to have a better understanding of the problem and to improve related structural designs.     

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。     

振荡流作用下圆柱体结构的水动力特性研究

圆柱绕流作为流体力学领域中的经典问题,近年来得到了广泛的关注和研究。开展振荡流下二维圆柱的水动力特性和漩涡发放形态研究将为认识和理解圆柱绕流特性提供重要参考。基于RANS方程,采用k-ωSST湍流模型,首先通过对比雷诺数10 000时均匀流下的受迫振动试验数据,验证了研究方法的可行性,进而开展了振荡流下圆柱绕流的数值模拟,对比讨论了5种KC数下流体力系数变化情况及漩涡脱落模式,并开展了升力系数时历分析。结果表明:在低振幅、低频率下,小KC数时激励力系数变化较大,大KC数时流态趋向于均匀流,激励力系数变化较小。在大KC数时可以观察到较为明显的2S脱落模式,升力系数在每一周期内出现两次振幅调制现象,小KC数时流体变化较快,规律性相对较弱。     

Statistics of wave forces on large horizontal cylinders

To the first order in a Stokes expansion, the pressure force exerted by a sea state on a large horizontal cylinder represents a stationary random Gaussian process. A relationship is obtained between the spectrum of this process and the wave spectrum. As a consequence, the basic statistical properties of the height and period of the individual waves of the force-process are also obtained. It is proven that these statistical properties agree very well with the data from a small scale field experiment.     

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。     

The influence of corner radius on the forces experienced by cylindrical bluff bodies in oscillatory flow

Measurements are presented of the effects of corner radius on the hydrodynamic forces experienced by cylindrical bluff bodies in oscillatory flow over the Keulegan Carpenter number range from 1 to 100. The range of Reynolds number covered is from 200 to 2 × 10⁴ and two basic cross-sectional shapes, namely a square and a diamond, were used in the investigation. Drag coefficients in oscillatory flow are found to be more sensitive to corner radius than in steady flow. At a fixed Keulegan Carpenter number the drag coefficient of a diamond section decreases with increasing corner radius and the reduction is more marked at low Keulegan Carpenter numbers. The drag of a square section does not follow a consistent trend with corner radius and for high Keulegan Carpenter numbers the rounded square with a corner radius of 0.265D (where D is the width of the model normal to the flow) can have a drag coefficient equal to half the value for a circular cylinder.     

Application of the state space model to the system of wave energy conversion Analytical method for wave forces on single oscillating rectangular buoy

A new analytical method is proposed to analyze the force acting on a rectangular oscillating buoy due to linear waves. In the method a new analytical expression for the diffraction velocity potential is obtained first by use of the eigenfunction expansion method and then the wave excitation force is calculated by use of the known incident wave potential and the diffraction potential. Compared with the classical analytical method, it can be seen that the present method is simpler for a two-dimensional problem due to the comparable effort needed for the computation of diffraction potential and for that of radiated potential. To verify the correctness of the method, a classical example in the reference is recomputed and the obtained results are in good accordance with those by use of other methods, which shows that the present method is correct.     

近距离靠泊条件下钻井支持平台与生产平台相对运动研究

为了探究钻井支持平台及生产平台组成的复杂多浮体耦合系统在近距离靠泊状态下的相对运动情况,基于多浮体三维势流理论及时域耦合分析方法,计算了半潜式钻井支持平台和张力腿(TLP)生产平台耦合系统在三种不同环境方向,即迎浪、斜浪、横浪下两平台的相对运动和平台间连接栈桥的运动响应,为平台运动分析和栈桥设计提供指导。并将计算结果与水池模型试验结果进行对比,验证了数值方法的可靠性。为进一步了解多浮体间耦合水动力的影响,计算了该近距离靠泊系统在不考虑浮体间水动力相互干扰下的运动响应。研究表明除在横浪作用外,其他环境条件下的多浮体水动力干扰作用明显,对浮体运动响应的影响不可忽略,且有效波高在小范围内变化时,平台间的相对运动幅值基本与其呈线性关系。     

Experimetal Investigation of lift Forces on Horizontal Cylinder near Bottom in Oscillating Flow

The lift forces on horizontal cylinder near bottom is experimentally investigatde at Reynolds(Re)in the range lf 2500~10000and Keulegan~CARPENTER NUMBERS(kc) inthe intervalof5~20,and gap ratio (e/D) is from (a0)are analyzde by using the Fourier analyses method.It is found that found that both Cl& a0 are the functions lf the Kc number.     

Nonlinear effect on inertia component of wave forces on a cylinder

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Numerical prediction of hydrodynamic forces on a ship passing through a lock

While passing through a lock, a ship usually undergoes a steady forward motion at low speed. Owing to the size restriction of lock chamber, the shallow water and bank effects on the hydrodynamic forces acting on the ship may be remarkable, which may have an adverse effect on navigation safety. However, the complicated hydrodynamics is not yet fully understood. This paper focuses on the hydrodynamic forces acting on a ship passing through a lock. The unsteady viscous flow and hydrodynamic forces are calculated by applying an unsteady RANS code with a RNG k-ε turbulence model. User-defined function(UDF) is compiled to define the ship motion. Meanwhile, the grid regeneration is dealt with by using the dynamic mesh method and sliding interface technique. Numerical study is carried out for a bulk carrier ship passing through the Pierre Vandamme Lock in Zeebrugge at the model scale. The proposed method is validated by comparing the numerical results with the data of captive model tests. By analyzing the numerical results obtained at different speeds, water depths and eccentricities, the influences of speed, water depth and eccentricity on the hydrodynamic forces are illustrated. The numerical method proposed in this paper can qualitatively predict the ship-lock hydrodynamic interaction. It can provide certain guidance on the manoeuvring and control of ships passing through a lock.     

Effect of a base structure on the wave forces and pressures on a vertical cylinder

The influence of a square base placed at the bottom of a vertical cylinder on the wave induced forces and pressures on the cylinder is reported in this paper. In order to carry out this study, initially, the two dynamic variables on the cylinder in the absence of the base was studied so as to make sure the quality of measurements is satisfactory. The experimental results are compared with MacCamy and Fuchs' theory and the agreement found good.