Wave-Current Forces on Small Square Cylinders (Part II)

Based on model tests, the lift and resultant forces on small square cylinders caused by waves (regular and irregular) and currents are analyzed in this paper. The lift and resultant force coefficients CL and Cf related to KC number and the effect of direction of wave propagation are also given, which may be useful for practical engineering application.     

Wave-Current Forces on Vertical Cylinders in Side-by-Side Arrangement for Irregular Waves Combined With Opposing Current

- The wave-current forces on vertical piles in side-by-side arrangement induced by irregular waves with opposing current are investigated experimentally in this paper. The characteristics in both time and frequency domain of in-line, lift and resultant forces are analyzed. The grouping effect coefficients of inline, lift and resultant forces on piles related to KC number and relative spacing parameters are given. These results are compared with those in the case of irregular waves combined with following currents. It is found that the results in these two cases are quite different. The range of KC number tested is 10- 60, the range of Reynolds number is (0.55-3.43) ×104.     

Wave-Current Forces on Slender Circular Cylinders

- A series model tests of wave forces by both regular and irregular waves combined with currents on single piles and bipiles in tandem and parallel arrays have been carried out. Based on Morison Equation, linear wave theory and linear wave spectrum theory as well, the characteristics of inline, lift and resultant forces on cylinders have been analyzed respectively. The drag, inertia and lift coefficients CD, CM and CL f皉 single piles related to KC number and the grouping effect coefficients of inline, lift and resultant forces on bipiles in tandem and parallel arrays related to KC number are given in this paper.     

The Lift Forces Acting on a Submarine Composite Pipeline in a Wave-Current Coexisting Field

- A composite pipeline is defined as a main big pipe composed of one or several small pipes. The flow behaviour around a submarine composite pipeline is more complicated than that around a single submarine pipeline. A series model test of composite pipelines in a wave-current coexisting field was conducted by the authors. Both in-line and lift forces were measured, and the resultant forces were also analyzed. The results of lift forces and resultant forces are reported in this paper. It is found that the lift force coefficients for composite pipelines are well related to the KC number. The lift force coefficients for an irregular wave-current coexisting field are smaller than those for a regular wave-current coexisting field. The frequency of lift force is usually twice the wave frequency or higher. The authors test indicates that the resultant forces are about 10 to 20 percent larger than in-line forces (horizontal forces). The effect of water depth is analyzed. Finally, the relationship between lift f     

Hydrodynamic Forces on Smooth Inclined Cyh''''nders in Oscillatory Flow

-The hydrodynamic forces on a smooth inclined circular cylinder exposed to oscillating flow were experimentally investigated at Reynolds number (Re) in the range 40000-200000 and Keulegan-Capenter number (KC) in the interval from 5-40. In the test, Re number and KC number were varied systematically. The inertia force coefficient (Cu) and the drag force coefficient (CD) in Morison equation were determined from the measured loads and the water particle kinematics. In this analysis a modified form of Morison equation was used since it uses the normal velocity and acceleration. Thus, the applicability of the Cross Flow Principle was assumed. This principle, simply stated, is as follows: the force acting in the direction normal to the axis of a cylinder placed at some oblique angle with the direction of flow is expressed in terms of the normal component of flow only, and the axial component is disregarded. Both the total in-line force coefficient (CF) and transverse force (lift) coefficient (Cf) were analyzed     

Hydrodynamic Forces on Inclined Cylinder due to Waves with Crossing Current

Based on Morison's Equation and linear wave theory, hydrodynamic forces acting on inclined cylinders due to waves and crossing current at an angle of a, are analyzed. A method for calculating exciting forces is proposed. Experimental results show that the proposed method in this paper is feasible and can be used in engineering practice.     

A Finite Element Solution of Wave Forces on Submerged Horizontal Circular Cylinders

In this paper, a numerical model is established for estimating the wave forces on a submerged horizontal circular cylinder. For predicting the wave motion, a set of two-dimensional Navier-Stokes equations is solved numerically with a finite element method. In order to track the moving non-linear wave surface boundary, the Navier-Stokes equations are discretized in a moving mesh system. After each computational time step, the mesh is modified according to the changed wave surface boundary. In order to stabilize the numerical procedure, a three-step finite element method is applied in the time integration. The water sloshing in a tank and wave propagation over a submerged bar are simulated for the first time to validate the present model. The computational results agree well with the analytical solution and the experimental data.Finally, the model is applied to the simulation of interaction between waves and a submerged horizontal circular cylinder.The effects of the KC number and the cylinder depth on the wave forces are studied.     

波浪要素对水平圆柱杆件水动力系数影响研究

通过试验研究了波浪要素对水平固定圆柱杆件水动力系数的影响。试验利用垂直杠杆原理,提取了杆件在波浪下的水平受力历时曲线,基于改造的莫里森方程,计算了不同波浪要素下的水动力系数C_D和C_M取值。定义分析了新的波高参数KH,周期参数KT和雷诺数Re对水动力系数的影响。研究表明,整体拟合法与四点拟合法获得的水动力系数在数值上差异不大。KH、KT及Re均对水动力系数的取值有较显著影响:1)随着波高KH的增大,C_D、C_M整体呈幂指数衰减,且C_M的衰减更为迅速;2)随着波周期KT的增大,C_D、C_M整体亦呈衰减趋势;3)相同波高条件下,C_M随Re数增大而增大,而C_D值相对稳定。最后给出了波浪条件下水动力系数C_D和C_M的经验计算公式。     

Study on Current-Random Wave Forces Acting on a Framework

—The forces of random wave plus current acting on a simplified offshore platform(jacket)mod-el have been studied numerically and experimentally.The numerical results are in good agreement withexperiments.The mean force can be approximated as a function of equivalent velocity parameter and theroot-mean-square force as a function of equivalent significant wave height parameter.     

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.     

Wave Forces Acting on Vertical Walls

Regular and irregular wave forces acting on vertical walls are studied by a previously developed numerical model. The computed wave forces are compared with the available experimental data to verify the numerical model, and satisfactory agreements are obtained. The variation of wave forces with incident angles and the shape of simultaneous pressure distribution are investigated, and the comparisons between numerical results and Goda＇ s predictions are also carried out. It is concluded that the maximum wave forces acting on the unit length of vertical wall is often induced by the obliquely incident waves instead of normally incident waves, while Goda＇ s formula may be inapplicable for oblique wave incidence. The shape of simultaneous pressure distribution is not significantly influenced by incident angles, and it can be favorably predicted by Goda＇ s formula. When regular wave heights are taken as the same as irregular wave height H1%, the irregular wave forces Ph. 1% are slightly larger than regular wave forces in most cases.     

海洋结构物小尺度桩柱的水动力系数研究与进展

本文主要归纳了基于Morison方程求解小尺度桩柱的水动力系数方面的研究成果。分别从单桩柱和群桩两个方面对水动力系数的研究成果,包括纯波、波流混合、横向力、直立桩柱、倾斜桩柱、复杂结构桩柱、粗糙度等进行了阐述,给出了在波流条件下水动力系数的变化规律;归纳了当前水动力系数的求解方法;介绍了在水动力系数的物模实验、数值仿真以及实验数据处理方法上的研究进展,并提出了相关研究的建议。     

Nonlinear effect on inertia component of wave forces on a cylinder

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Experimental Study on Ocean Internal Wave Force on Vertical Cylinders in Different Depths

A series of experimental studies about the force of internal solitary wave and internal periodic wave on vertical cylinders have been carried out in a two-dimensional layered internal wave flume. The internal solitary waves are produced by means of gravitational collapse at the layer thickness ratio of 0.2, and the internal periodic waves are produced with rocker-flap wave maker at the layer thickness ratio of 0.93. The wave parameters are obtained through dyeing photography. The vertical cylinders of the same size are arranged in different depths. The horizontal force on each cylinder is measured and the vertical distribution rules are researched. The internal wave heights are changed to study the impact of wave heights on the force. The results show that the horizontal force of concave type internal solitary wave on vertical cylinder in the upper-layer fluid has the same direction as the wave propagating, while it has an opposite direction in the lower-layer. The horizontal force is not evenly distributed in the lower fluid. And the force at different depths increases along with wave height. Internal solitary wave can produce an impact load on the entire pile. The horizontal force of internal periodic waves on the vertical cylinders is periodically changed at the frequency of waves. The direction of the force is opposite in the upper and lower layers, and the value is close. In the upper layer except the depth close to the interface, the force is evenly distributed; but it tends to decrease with the deeper depth in the lower layer. A periodic shear load can be produced on the entire pile by internal periodic waves, and it may cause fatigue damage to structures.     

Wave Uplift Forces on the Bottom of a Circular Cylinder

The analysis of the data of model tests of two large deep wharves and monographic experimental studies show that two aspects are to be improved so as to predict the wave uplift forces on the bottom of a circular cylinder. The first aspect is the uplift pressure distribution on the bottom, and the second is the correct determination of the phase for maximum horizontal wave forces. The second problem has been solved. Synthesizing the results of theoretical analysis and experiments, we suggest a diagram for the determination of the phase when the maximum horizontal wave force appears. On the basis-ef the diagram the simultaneous wave uplift forces can be obtained for the structural stability analysis.     

Numerical Analysis of Wave Forces on Arbitrarily Shaped Multi-Pillars Over Varying Topography

The modified hybrid element method (MHEM) is utilized to predict and analyze wave forces on arbitrarily shaped multiple bodies. This method can be applied to waves of all water depths, i. e. shallow, intermediate, and deep waters, on slowly varying seabed. The MHEM employs the ICCG method to save CPU and storage, thus the computation of wave forces for large multi-body systems can be carried out on microcomputers. Numerical results of the present method are compared with experimental data and other solutions. It is shown that the MHEM provides more accurate solutions of the wave forces than other numerical methods do. Therefore, the methodology presented herein can be used in the design of coastal and ocean structures.     

浅浸没水平圆柱浮子波浪力计算研究

以海漂垃圾收集装置浮式围栏的圆柱浮子为研究对象,基于圆柱浮子的浅浸没特性,改进了Morison方程,并结合物理模型试验,对波浪与浅浸没水平圆柱浮子作用问题进行探讨。结果表明,改进的Morison方程可对水平圆柱浮子的波浪力做精确预测,并揭示了波幅、浸没深度以及周期对圆柱浮子波浪力的影响规律。对于浅浸没的圆柱浮子,所受水平波浪力随波高的增大而增大,随周期的增大而衰减到某一特定值。波浪力的正向大小分布要大于负向,而正负向大小的差异主要受浸没深度的影响。     

南海北部陆坡内孤立波对桩柱作用力的极值推算

内孤立波的发生常伴随着大振幅波动和突发性强流,对桩柱等海中结构物产生强烈破坏作用。基于KdV方程和Morison公式,在忽略高阶模态的情况下,探讨内孤立波对桩柱的单位作用力、总作用力、剪力和弯矩的极值问题,并利用2016-07南海北部陆坡的实测资料对理论结果进行检验。结果表明:1)在内孤立波最大振幅所在的垂向剖面上,上层与下层各存在一个单位作用力极值,且二者方向相反,上层总作用力强于下层,最大剪力和弯矩分别发生于水平流速的转向层和海底;2)各水层中,沿着内孤立波的传播方向,所有作用力的数值均随时间的推移先递增后递减,存在正向或负向的最大值;3)全水层总作用力极值发生在半周期,其值与波动振幅和水平波速有关,其他作用力极值发生于最大振幅时刻之前,作用力极值与振幅和非线性波速正相关,与水平特征宽度负相关;4)单位作用力极值的时间提前量与振幅和水平特征宽度强相关,与非线性波速弱相关。     

A Time-Domain Coupled Model for Nonlinear Wave Forces on A Fixed Box-Shaped Ship in A Harbor

A 2-D time-domain numerical coupled model is developed to obtain an efficient method for nonlinear wave forces on a fixed box-shaped ship in a harbor.The domain is divided into an inner domain and an outer domain.The inner domain is the area beneath the ship and the flow is described by the simplified Euler equations.The other area is the outer domain and the flow is defined by the higher-order Boussinesq equations in order to consider the nonlinearity of the wave motions.Along the interface boundaries between the inner domain and the outer domain,the volume flux is assumed to be continuous and the wave pressures are equal.Relevant physical experiment is conducted to validate the present model.It is shown that the numerical results agree with the experimental data.Compared with the coupled model with the flow in the inner domain governed by the Laplace equation,the present coupled model is more efficient and its solution procedure is more simple,which is particularly useful for the study on the effect of the nonlinear wave forces on a fixed box-shaped ship in a large harbor.