流向Morison 型波浪力的高阶矩分析

通过理论研究定量地说明流向Morison波浪力,即拖曳力和惯性力的高阶统计矩随采样次数增加的规律.主要应用二阶Stokes波理论,推导了流向Morison波浪力的前四阶累积量.计算了作用于实际海底管线上的流向Morison波浪力的偏斜度和峰度.结果表明,随着采样次数的增加,拖曳力和惯性力的偏斜度和峰度驱于收敛.文中给出的方法为后续理论工作奠定了基础.     

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.     

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.     

Probability distribution of random wave forces in weakly nonlinear random waves

Based on the second-order random wave theory, the joint statistical distribution of the horizontal velocity and acceleration is derived using the characteristic function expansion method. From the joint distribution and the Morison equation, the theoretical distributions of drag forces, inertia forces and total random wave forces are determined. The distribution of inertia forces is Gaussian as that derived using the linear wave model, whereas the distributions of drag forces and total random forces deviate slightly from those derived utilizing the linear wave model. It is found that the distribution of wave forces depends solely on the frequency spectrum of sea waves associated with the first order approximation and the second order wave–wave interaction.     

半潜式平台内孤立波载荷计算方法及其试验验证

针对半潜式平台的立柱群和沉箱群,设计了两套独立的载荷测量系统,利用大型重力式密度分层水槽,在不同来波方向下对孤立波中半潜式平台载荷进行了系列模型试验。研究表明,对平台立柱部分,其内孤立波载荷可以用Morison公式进行计算,基于试验结果建立了Morison公式中其拖曳力系数以及惯性力系数的经验公式;对于半潜式平台的沉箱部分,当来波方向与其中纵剖面不平行时,其水平内孤立波载荷同样可以使用Morison公式进行计算,并建立了Morison公式中其拖曳力系数以及惯性力系数的经验公式;当来波方向与半潜式平台中纵剖面平行时,沉箱群的水平内孤立波载荷可以采用Froude-Krylov公式进行计算;同时,在不同来波方向下沉箱群的垂向载荷同样可以采用Froude-Krylov公式进行计算。     

Viscous drift forces in regular and irregular waves

A method to compute wave- and current-induced viscous drift forces and moments on floating platforms in regular and random waves is presented. The relative velocity drag term of Morison's equation is used in conjunction with frequency domain first-order motion transfer functions to compute the drift forces and moments. Mean viscous drift forces and moments in regular waves in all six degrees-of-freedom of a tension leg platform are computed. The relative importance of the free-surface force integration, steady current, wave-current interaction and platform motions on the computed drift forces and moments are discussed. The results from this method, in the frequency domain, are used to compute the drift forces and responses in irregular waves using existing methods developed for potential drift computations. Comparisons with results from time-domain computations are also presented and good agreement between the frequency-domain and time-domain results is found. Some comparisons with experimental data are also made. The frequency-domain method is found to be an efficient and useful tool for the analysis of semi-submersible and tension leg platforms during the preliminary design stage in which extensive parametric studies need to be undertaken.     

Numerical simulation of a partially buried pipeline in a permeable seabed subject to combined oscillatory flow and steady current

Hydrodynamic forces exerting on a pipeline partially buried in a permeable seabed subjected to combined oscillatory flow and steady current are investigated numerically. Two-dimensional Reynolds-Averaged Navier-Stokes equations with a k−ω turbulent model closure are solved to simulate the flow around the pipeline. The Laplace equation is solved to calculate the pore pressure below the seabed with the simulated seabed hydrodynamic pressure as boundary conditions. The numerical model is validated against the experimental data of a fully exposed pipeline resting on a plane boundary under various flow conditions. Then the flow with different embedment depths, steady current ratios and KC numbers is simulated. The amplitude of seepage velocity is much smaller than the amplitude of free stream velocity as expected. The normalized Morison inertia, drag and lift coefficients based on the corresponding force coefficients of a fully exposed pipeline are investigated. The normalized Morison force coefficients reduce almost linearly with the increase of embedment depth and that the KC only has minor effect on the normalized Morison coefficients. It is also found that the permeable seabed condition causes a slight increase on the inline force and has a little effect on the lift force, compared with corresponding conditions in an impermeable bed.     

Probability models for offshore structural response due to Morison wave loading: Part II: Inertia-only and total responses

Offshore structures are exposed to random wave loading in the ocean environment and hence the probability distribution of their response to wave loading is a minimum requirement for efficient probabilistic analysis of these structures. Due to nonlinearity of Morison wave loading and also due to intermittency of wave loading on members in the splash zone, the response is often non-Gaussian. Part I of this paper was devoted to the development and validation of a new probability model for drag-only responses (i.e. responses due to the drag component of Morison wave loading). This part is devoted to the development and validation of new probability models for both inertia-only and total responses.     

关于小直径垂直桩柱结构的波浪力研究

本文归纳了应用Morison方程中涉及的研究成果。分别从阻力系数和惯性力系数。规则波与不规则波，二阶力和线性化，桩群受力等方面进行了论述。对目前该领域的研究给出了系统的介绍。     

A Prediction Method of Internal Solitary Wave Loads on the Semi- Submersible Platform

An investigation into the prediction method for internal solitary waves (ISWs) loads on the columns and caissons of the semi-submersible platform found on three kinds of internal solitary wave theories and the modified Morison Equation is described. The characteristics of loads exerted on the semi-submersible platform model caused by the ISWs have been observed experimentally, and the inertial and drag coefficients in Morison Equation are determined by analyzing the forces of experiments. From the results, it is of interest to find that Reynolds number, KC number and layer thickness ratio have a considerable influence on the coefficients. The direction of incoming waves, however, is almost devoid of effects on the coefficients. The drag coefficient of columns varies as an exponential function of Reynolds number, and inertia coefficient of columns is a power function related to KC number. Meanwhile, the drag coefficient of caissons is approximately constant in terms of regression analysis of experimental data. The results from different experimental conditions reveal that the inertia coefficient of caissons appears to be exponential correlated with upper layer depths.

     

Wave forces on submarine pipelines near a plane boundary

Forces induced by regular waves on submarine pipelines resting on as well as near a plane boundary and aligned parallel to wave fronts of the oncoming waves are investigated experimentally. The inline hydrodynamic coefficients of drag and inertia are evaluated through the use of Morison equation and the least squares method. The transverse force is analysed in terms of maximum transverse force and transverse root mean square (r.m.s.) coefficients. The resulting inline and transverse hydrodynamic coefficients are correlated with the period parameter or Keulegan-Carpenter number and relative clearance of the pipeline from the plane boundary. The effect of depth parameter on these coefficients and the correlation between maximum transverse force and transverse r.m.s. coefficients are also reported.     

Probability models for offshore structural response due to Morison wave loading Part I: Drag-only response

Offshore structures are exposed to random wave loading in the ocean environment and hence the probability distribution of their response to wave loading is a minimum requirement for efficient probabilistic analysis of these structures. Due to nonlinearity of Morison wave loading and also due to intermittency of wave loading on members in the splash zone, the response is often non-Gaussian. Analysis of simulated data has, however, shown that neither of the two probability models proposed in the literature can accurately predict the tails of the response distribution. New probability models are therefore required to overcome this deficiency. This paper is composed of two parts: Part I is devoted to the development and validation of a new probability model for drag-only responses (i.e. responses due to the drag component of Morison wave loading), while Part II is devoted to the development and validation of new probability models for both inertia-only and total responses.     

Probability distribution of random wave–current forces

Based on the second-order solutions obtained for the three-dimensional weakly nonlinear random waves propagating over a steady uniform current in finite water depth, the joint statistical distribution of the velocity and acceleration of the fluid particle in the current direction is derived using the characteristic function expansion method. From the joint distribution and the Morison equation, the theoretical distributions of drag forces, inertia forces and total random forces caused by waves propagating over a steady uniform current are determined. The distribution of inertia forces is Gaussian as that derived using the linear wave model, whereas the distributions of drag forces and total random forces deviate slightly from those derived utilizing the linear wave model. The distributions presented can be determined by the wave number spectrum of ocean waves, current speed and the second order wave–wave and wave–current interactions. As an illustrative example, for fully developed deep ocean waves, the parameters appeared in the distributions near still water level are calculated for various wind speeds and current speeds by using Donelan–Pierson–Banner spectrum and the effects of the current and the nonlinearity of ocean waves on the distribution are studied.     

Dynamic Response Analysis of Risers Subjected to Combined Wave and Current Loading

A dynamic response analysis in the frequency domain is presented for risers subjected to combined wave and current loading. Considering the effects of current, a modified wave spectrum is adopted to compute the linearized drag force. An additional drag force convolution term is added to the linearized drag force spectrum, therefore the error is reduced which arises from the truncation of higher order terms in the drag force auto-correlation function. An expression of linearized drag force spectrum is given taking the relative velocity into account. It is found that the additional term is a fold convolution integral. In this paper dynamic responses of risers are investigated, while the influence of floater motion on risers is considered. The results demonstrate that the accuracy of the present method reaches the degree required in time domain analysis.     

Comparisons of internal solitary wave and surface wave actions on marine structures and their responses

In this paper, a time-domain numerical model is established for computing the action of internal solitary wave on marine structures and structure motion responses. For a cylindrical structure, its side and bottom are discretized by pole and surface elements, respectively. The drag and inertial forces in the perpendicular direction of the structure are computed by the Morison equation from the pole elements, and the Froude–Krylov force in the axial direction of the structure due to internal wave motion is computed by integration of the dynamic pressure over the surface elements. The catenary theory is used to analyze the reaction force due to mooring lines, and the motion equation of the marine structure is solved by the fourth-order Runge–Kutta method in the time domain. The model is used to calculate the interaction of the internal solitary wave with a Spar platform with mooring system, and the surface wave action with the platform has also been computed by a frequency-domain boundary element method for comparison. Through the comparison based on a practical internal wave and surface wave states, it can be concluded that the internal wave force on the structure is only 9% of the one due to surface waves. However, the motion response due to the internal wave is much greater than the one due to the surface waves. It shows that the low-frequency effect of internal solitary waves is a great threat to the safety of marine structures.     

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.     

An experimental investigation of hydrodynamic coefficients for a vertical truncated rectangular cylinder due to regular and random waves

The research into hydrodynamic loading on ocean structures has concentrated mostly on circular cross-section members and relatively limited work has been carried out on wave loading on other cross-sections such as rectangular sections. These find applications in many offshore structures as columns and pontoons in semi-submersibles and tension-leg platforms. The present investigation demonstrates the behaviour of rectangular cylinders subject to wave loading and also supplies the hydrodynamic coefficients for the design of these sections.This paper presents the results of wave forces acting on a surface piercing truncated rectangular cylinder set vertically in a towing tank. The experiments are carried out in a water depth of 2.2 m with regular and random waves for low Keulegan–Carpenter number up to 6. The rectangular cylinder is of 2 m length, 0.2 m breadth and 0.4 m width with a submergence depth of 1.45 m from still water level. Based on Morison equation, the relationship between inertia and drag coefficients are evaluated and are presented as a function of KC number for various values of frequency parameter β, for two aspect ratios of cylinders, equals to 1/2 and 2/1. Drag and inertia coefficients obtained through regular wave tests are used for the random wave analysis to compute the in-line force spectrum.The results of the experiments show the drag and inertia coefficients are strongly affected by the variation in the aspect ratios of the cylinder. The drag coefficients decreases and inertia coefficients increases with increase in Keulegan–Carpenter number up to the range of KC number tested. The random wave results show a good correlation between measured and computed force spectrums. The transverse forces in both regular and random waves are found to be small compared to in-line forces.     

计算水位分布的标准差－偏度－峰度方法(BPF法)

海面水位各种高度的出现频率在海洋工程和航运中具有重要意义。为了得出其分布，最直接和可靠的方法当然是利用长期实测资料进行统计。但是在需要获得水位分布的地点往往没有足够长期的资料，这时就必须采用其他的方法来推算。 我国近海引起水位升降的主要因素是天文潮，故利用潮汐调和常数推算天文潮并考虑到到非天文因素的水位变化是一个比较可靠的办法。这个方法比较准确，但需要进行潮汐预报，计算量比较大。本文提出的方法所涉及的计算量很小，但仍能获得较好的效果。这个方法的基本出发点是：由于不同地点海面水位分布有一定的共性，水位分布和它的数字特征之间有密切的关系，而数字特征又决定于潮汐调和常数及非天文水位标准差，因而可利用潮汐调和常数及非天文水位标准差求得数字特征，然后进一步得出水位分布。这个方法所用到的数字特征为标准差、偏度和峰度，它们汉语拼音的第一个字母分别为B,P和F，故这个方法被称为BPF 法。 1977年我们提出 BPF 法时，主要应用于海图深度基准面，应用中的有关问题将另文讨论。     

聚焦波作用下平面网衣结构的水动力特性研究

由于沿海区域的限制以及愈加严重的环境污染,渔业养殖正从近海走向深远海。深远海海域的海况更加恶劣,给养殖装备的设计与性能评估带来新的挑战。为解决该问题,对极端波浪与养殖装备网衣结构的相互作用开展研究。基于waves2Foam建立数值波浪水池,极端波浪模拟采用基于NewWave理论的聚焦波模型,网衣结构模拟采用多孔介质模型,并通过与Morison模型计算的网衣受力等效分析,获得多孔介质模拟网衣结构阻力系数的直接估计方法。然后将多孔介质模型嵌入waves2Foam中,开展聚焦波与网衣结构相互作用的数值模拟,同时开展水槽试验,验证数值模拟的准确性。基于数值模拟结果,系统地分析了不同网衣密实度及不同波浪参数下网衣结构的升阻力特性以及网衣结构对波浪场的扰动规律。研究表明：聚焦波波峰幅值和网衣密实度对网衣结构的升阻力影响较大,且升力峰值出现在阻力为0的时刻;网衣结构对聚焦波的时空演化特性有影响,改变了聚焦波波形。     

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