Wave forces on a large, horizontal submerged cylinder

A numerical boundary integral equation method combined with a non-linear time stepping procedure is used for the calculation of wave forces on a large, submerged, horizontal circular cylinder. As the method is based on potential theory, all computations are performed in the inertia dominated domain, that is, for small Keulegan-Carpenter numbers. Computations are carried out for the Eulerian mean current under wave trough level equal to zero. When the cylinder is moved towards the sea bed the computations show that the inertia coefficients increase significantly, which is associated with a blockage effect. Furthermore, the effect of the wave steepness is reduced when the submergence of the cylinder is increased. In the vicinity of the free water surface the vertical inertia coefficient is highly dependent upon the wave steepness, which tends to reduce it, whereas the horizontal inertia coefficient is only slightly dependent on the wave steepness. Computations are also carried out for cylinder diameters comparable with the wave length. Finally, inertia coefficients computed by the present method are compared with some analytical results by Ogilvie [(1963), First and second order forces on a cylinder submerged under a free surface. J. Fluid Mech. 16, 451–472]. As long as the assumptions leading to Ogilvie's theory are fulfilled (cylinder radius small compared to the wave length), the results are quite similar.     

Lateral ice force acting on a vertical cylinder

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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。     

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.     

Wave-current forces on bipiles in parallel array

The inline and lift forces on bipiles in parallel array induced by both irregular waves and currents were investigated experimentally in this paper. The characteristics in both time and frequency domains of inline, lift and resultant forces as well were analyzed. The grouping effect coefficients of inline and resultant forces on two piles related to KC number and relative spacing parameters are given. A comparison of the magnitude and direction of resultant forces on two piles in parallel array with the corresponding values for single cylinder is also made.     

Second-order wave loading on a horizontal rectangular cylinder of substantial draught

Approximate first- and second-order analytical solutions of wave diffraction of a semi-submerged horizontal cylinder of rectangular cross-section are presented. The solutions are based on the assumption that the pressure in the fluid domain underneath the cylinder is linearly dependent on the horizontal space coordinate. Basically, this approach is valid when the clearance between the bottom of the cylinder and the sea bottom is small in comparison with the wave length and is recommended for a cylinder of substantial draught where due to the small clearance other methods are difficult to apply. Boundary conditions are satisfied by a choice of a proper form of the potential functions and by making use of the properties of matching conditions. Theoretical results reveal that the magnitude of the vertical second-order time-dependent loads could be significant and even exceed the corresponding first-order quantities. This phenomenon, which occurs even at moderate steepnesses, as well as the assumption of a linear pressure distribution, are confirmed by experiments performed in a wave tank.     

Added mass and damping of horizontal circular cylinder sections

This note brings together and extends previously known results for the added masses and dampings of surface-piercing or completely submerged horizontal circular cylinders. For vertical (heave) motions, but not horizontal (sway) motions, a striking qualitative change occurs in these hydrodynamic coefficients when the cylinder breaks the surface. This is simply explained in terms of low-frequency asymptotics and the equivalent wavemaker method.     

Wave forces acting on a submerged horizontal circular cylinder in oblique waves and on a vertical cylinder in deep waves

This paper presents a method of estimating wave forces acting on a submerged horizontal circular cylinder fixed in oblique waves.The experiments show that drag and inertia coefficients in beam sea are available for calculating the wave forces in oblique waves.Wave forces exerted on a vertical circular cylinder in deep waves are also investigated.The experimental results show that wave forces acting on the vertical cylinder coincide approximately with hydrodynamic forces acting on a submerged circular cylinder in an oscillating fluid.     

Steady drift force on vertical cylinder - viscous vs. potential

The contribution of the steady drift force on a floating structure may arise from waves, wind and current. The component of the wave drift force may be due to the second-order diffraction theory or potential effect and may be due to the velocity squared force or viscous effect. The presence of current in waves increases the effect of the viscous force. The expressions for these terms for a vertical cylinder are derived and their relative importance is investigated. Plots are presented showing the regions where the viscous or potential drift force predominates. Experiments were conducted with both small and large diameter cylinders. The mean drift forces obtained in these tests are compared with the theory.     

Wave uplift force on horizontal panels: a laboratory study

Accurate estimation of wave uplift force is essential to the designs of reliable coastal and marine structures.We presents a series of laboratory work here on the impact of regular waves on horizontal panels,from which an empirical formula to estimate accurately the wave uplift force on panels is established.The laboratory measurements show that the wave uplift force depends mainly on the incident wave height,the wave period,the wave length,the panel width,and the clearance between the subsurface of the panel and the still water level.Among these factors,the impact of the panel width on uplift forces is relatively complicated.Result shows that the relative panel width(i.e.,the ratio of panel width to wave length)plays a more important role in estimating the wave uplift force.Based on our comprehensive laboratory measurements,we further developed an empirical formula to compute wave uplift force on horizontal panels through dimensionless analysis.Compared with other empirical formulas,this formula uses dimensionless variables of clear physical meanings,thus can describe the interaction between waves and the panels in a better way.In addition,the efficiency of the formula to estimate wave uplift force on horizontal panels is verified against existing works.Therefore,the findings in this study shall be useful for understanding the mechanism of wave uplift force on horizontal panels and numerical model validation.     

The effect of horizontal Coriolis force on internal wave-mean flow interaction

-In this paper, an improvement and revision of the theory of Miiller (1974, 1976), has been made under two conditions: (1) the horizontal component of the Coriolis force has been taken into account in the equations of motion for the internal wave field; and (2) the role of internal waves with frequencies close to the inertial frequency has been considered. The values of the viscosity coefficients and the diffusivity coefficients obtained in this paper are: Theappearance of the cross-diffusion (vc) of momentum is a natural result from the effect of the horizontal Coriolis force. Therefore the role of the horizontal shear of the mean flow cannot be absolutely separated from that of the vertical shear. So far in testing Muller's theory, the approximation of effective wave stress obtained by Ruddick and Joyce (1979) was extensively used, but it has to be revised under the conditions of this paper. The revised approximation shows that the internal waves with low frequencies close to the inertial frequency pl     

Study on scattering wave force of horizontal and vertical plate type breakwaters

The interaction between wave and horizontal and vertical plates is investigated by the boundary element method,and the relations of wave exciting force with plate thickness,submergence and length are obtained.It is found that:1) The efficient wave exciting force exists while plate submergence is less than 0.5 m,and the plate is very thin with order O(0.005 m).2) The maximum heave wave exciting force exists,and it is the main factor for surface and submerged horizontal plate while the roll force can be ignored.3) The maximum sway wave exciting force exists,it is the main factor for surface or submerged vertical plate,and the roll force is about 20 times of horizontal plate.     

黏土中隔舱吸力式钢圆筒安装及水平受荷试验研究

近年来大直径钢圆筒结构在离岸人工岛工程中得到应用,如港珠澳大桥人工岛即采用振动下沉的方式安装钢圆筒,该方法对施工条件、装备以及施工控制技术要求较高。提出一种新型隔舱吸力式钢圆筒结构,在钢圆筒内部设置隔舱板,将结构分为上下两个隔舱,通过对下舱抽气实现隔舱吸力式钢圆筒在负压作用下的下沉安装。设计了隔舱吸力式钢圆筒安装及水平承载力模型试验,对比了负压贯入的隔舱吸力式钢圆筒和压力贯入的传统钢圆筒结构的贯入阻力及承载特性,分析了改变隔舱吸力式钢圆筒上下舱高度比L₁/L₂对其沉贯过程及承载特性的影响。结果表明,采用负压吸力沉贯的隔舱吸力式钢圆筒相比于采用压力贯入的传统钢圆筒结构的贯入阻力减小,水平极限承载力提高。在极限水平荷载作用下,随着隔舱吸力式钢圆筒的L₁/L₂从2.28减小到1.00、0.56,转动中心位置上移,水平极限承载力及弯矩承载力得到显著提高。     

Volterra series-based system analysis of random wave interaction with a horizontal cylinder

The response of a long flexible cylinder excited by random waves in a large model basin was investigated. The linear and non-linear physical mechanisms associated with the wave–cylinder interaction were analysed using system identification and modelling techniques. A third-order frequency domain Volterra model and its orthogonalized counterpart were used to analyse the relationships between wave elevations at various locations in the vicinity of the cylinder and cylinder acceleration data at various cylinder longitudinal locations. It was found that linear mechanisms dominate, particularly at the frequency band where the majority of the wave energy is located. At higher frequencies, the cubic component of the Volterra model is the main contributor to the total model coherence, i.e. the fraction of the measured output power that can be approximated by the model output, whereas the quadratic component's contribution to the total model coherence was in general quite small. This process of identification and quantification of the non-linear mechanisms of the unknown physical system can lead to the design of improved parametric models for the cylinder response, which should by design simulate non-linearities such as the ones identified by the Volterra model. The estimated linear and non-linear Volterra transfer functions were also used to predict the cylinder acceleration under excitation inputs not used in the estimation of the model transfer functions. The good match between predicted and measured output auto-power spectra suggests that the estimated transfer functions are indeed true models of the underlying physical mechanisms of the interaction. However, the latter can only be achieved if a minimum number of data segments, as determined by an error analysis involving modelling and prediction errors, is used in the estimation of the Volterra transfer functions.     

A numerical model for predicting the jump of lift force on an oscillating cylinder

The fluid force coefficients on a transversely oscillating cylinder are calculated by applying two-dimensional large eddy simulation method. Considering the “jump” phenomenon of the amplitude of lift coefficient is harmful to the security of the submarine slender structures, the characteristics of this “jump” are dissertated concretely. By comparing with experiment results, we establish a numerical model for predicting the jump of lift force on an oscillating cylinder, providing consultation for revising the hydrodynamic parameters and checking the fatigue life scale design of submarine slender cylindrical structures.     

Transient fluid motion due to the forced horizontal oscillations of a vertical cylinder

The problem of the forced horizontal oscillations of a vertical cylinder extending throughout the fluid depth is considered on the basis of the linearised theory of water waves. A new integral form is given for the frequency-domain solution and the procedure is then used to obtain an explicit time-domain solution.     

Simplified CFD modeling for bilge keel force and hull pressure distribution on a rotating cylinder

A horizontal, circular cylinder fitted with one bilge keel is forced to rotate harmonically around its axis. The bilge keel load and hull pressure distribution are investigated. A fully submerged condition (infinite fluid), and three partly-submerged conditions are considered. A two-dimensional numerical study is performed, and the results are validated against recently published experimental data by van’t Veer et al. [30]. In addition, comparisons for mass and drag coefficients are also made with experimental data for plate in infinite fluid (Keulegan and Carpenter [8]), and wall-mounted plate (Sarpkaya and O’Keefe [9]) in oscillatory flow.A Navier–Stokes solver based on the Finite Volume Method is adopted for solving laminar flow of incompressible water. The free-surface condition is linearized by neglecting the nonlinear free-surface terms and the influence of viscous stresses in the free surface zone, while the body-boundary condition is exact. This simplified modeling of the problem required the mesh to be fine only around the bilge keels, leading to a total number of cells around N ≃ 1 ×10⁴, which reduced computational cost significantly.The influence of draft and amplitude of oscillations on the bilge keel force and hull pressure distribution are considered. The bilge keel force is presented in terms of non-dimensional drag and mass coefficients including higher harmonic components. The numerical results are also compared with the industry standard empirical method for calculation of roll damping proposed by Ikeda et al. [4]. In general, a good agreement between the results of the present numerical method and the experimental data is obtained and the differences with those predicted by the empirical method are addressed.     

Artificial neural network ability in evaluation of random wave-induced inline force on a vertical cylinder

An approach based on artificial neural network (ANN) is used to develop predictive relations between hydrodynamic inline force on a vertical cylinder and some effective parameters. The data used to calibrate and validate the ANN models are obtained from an experiment. Multilayer feed-forward neural networks that are trained with the back-propagation algorithm are constructed by use of three design parameters (i.e. wave surface height, horizontal and vertical velocities) as network inputs and the ultimate inline force as the only output. A sensitivity analysis is conducted on the ANN models to investigate the generalization ability (robustness) of the developed models, and predictions from the ANN models are compared to those obtained from Morison equation which is usually used to determine inline force as a computational method. With the existing data, it is found that least square method (LSM) gives less error in determining drag and inertia coefficients of Morison equation. With regard to the predicted results agreeing with calculations achieved from Morison equation that used LSM method, neural network has high efficiency considering its convenience, simplicity and promptitude. The outcome of this study can contribute to reducing the errors in predicting hydrodynamic inline force by use of ANN and to improve the reliability of that in comparison with the more practical state of Morison equation. Therefore, this method can be applied to relevant engineering projects with satisfactory results.