Wind and wave induced behaviour of offshore guyed tower platforms

Offshore guyed tower platforms belong to the group of compliant offshore platforms which are most suited for deep water exploration. The basic feature of compliant offshore platforms is that they are designed to move with the waves, in at least some degrees-of-freedom. As far as excitation of wave frequencies is concerned, the system opposes wave forces by inertial effects. The offshore guyed tower derives its stability against lateral movement from its mooring system.In this study, the response of offshore guyed towers to random forces generated by wind and wave is investigated. The exposed portion of the tower is subjected to the action of turbulent wind, while the submerged portion is acted upon by random wave forces. The analysis includes the nonlinearities due to the Morison equation of drag force, the variable submergence effect due to waves, the instantaneous position of the tower and force excursion relation of the mooring lines. A parametric study is conducted to investigate the behaviour of the tower under waves, and the combined effect of wind and wave forces.     

Non-linear analysis of a dynamically positioned platform in stochastic seaway

Safety is the topmost priority considered by the designers of floating systems or any other structural systems. Reliability, economy and environmental pollutions and the liability of the structure in the case of accidents are also considered by the designers. The paper concentrates on the non-linear behavior of a moored floating platform in stochastic seaway generated using the Pierson–Moskowitz spectrum. Second-order wave forces (slow drift force) acting on the structure is considered as they contribute to a major percentage of the excursion of a large platform. Wave drift damping and skin friction damping have also been considered.It has been shown that the principal frequency of the second-order motion of the platform due to drift forces closely matches the natural frequency of the system in surge motion. This has been subsequently used in tuning a PID (proportionate integral and differential)-based control system for the surge mode, where reduction in the order of 90% has been observed.     

Nonlinear Dynamic Analysis of Deepwater Drilling Risers Subjected to Random Loads

Excited by ocean currents, random wave and vessel motion, deepwater drilling risers exhibit significant dynamic response. In time domain, a method is proposed to calculate the nonlinear dynamic response of deepwater drilling risers subjected to random wave and dynamic large displacement vessel motion boundary condition. Structural and functional loads, external and internal pressure, free surface effect of irregular wave, hydrodynamic forces induced by current and wave, as well as wave and low frequency (drift) motion of the drilling vessel are all accounted for. An example is presented which illustrates the application of the proposed method. The study shows that long term drift motion of the vessel has profound effect on the envelopes of bending stress and lateral displacement, as well as the range of lower flex joint angle of the deepwater riser. It can also be concluded that vessel motion is the principal dynamic loading of nonlinear dynamic response for the deepwater risers rather than wave force.     

Triangular Configuration Tension Leg Platform behaviour under random sea wave loads

This study investigates the dynamic response of a Triangular Configuration Tension Leg Platform (TLP) under random sea wave loads. The random wave has been generated synthetically using the Monte-Carlo simulation with the Peirson–Moskowitz (P–M) spectrum. Diffraction effects and second-order wave forces have not been considered. The evaluation of hydrodynamic forces is carried out using the modified Morison equation with water particle kinematics evaluated using Airy's linear wave theory. Wave forces are taken to be acting in the surge degree-of-freedom. The effect of coupling of various structural degrees-of-freedom (surge, sway, heave, roll, pitch and yaw) on the dynamic response of the TLP under random wave loads is studied. Parametric studies for random waves with different H_s and T_z under the presence of current have also been carried out. For the orientation of the TLP, surge, heave and pitch degrees-of-freedom responses are influenced significantly. The surge power spectral density function (PSDF) indicates that the mean square response is affected by the amplification at the natural frequency of the surge degree-of-freedom and also at the peak frequency of the wave loading. The PSDF of the heave response shows higher peak values near the surge frequency and near the peak frequency of the wave loading. Surge response, therefore, influences heave response to the maximum. Variable submergence seems to be a major source of nonlinearity and significantly enhances the responses in surge, heave and pitch degrees-of-freedom. In the presence of current, the response behaviour of the TLP is altered significantly introducing a non-zero mean response in all degrees-of-freedom.     

Minimization of drift force on a floating cylinder by optimizing the flexural rigidity of a concentric annular plate

The deployment of suitable configurations of mutually interacting floating bodies for efficiently controlling their hydrodynamic interactions towards the reduction of the wave drift forces and, thus, of the mooring lines’ loads, has, nowadays, gained a great scientific interest. In this paper, the hydrodynamic behaviour of a floating cylinder and a concentric annular flexible plate is analysed in the frequency domain aiming at the minimization of the drift forces acting on the cylinder by optimizing the flexural rigidity of the plate. The diffraction/radiation problem is solved using a higher-order boundary element method. The analysis is implemented assuming that both floating bodies oscillate freely in heave, while for the plate, flexible modes are, additionally, considered for describing its structural deformations. The required modes shapes are determined in vacuum (“dry” mode superposition approach) through analytical expressions. The flexural rigidity of the plate, D, is optimized at a specific wave number using a real-coded genetic algorithm. Initially, results are compared with numerical results of other investigators for the case of two rigid concentric floating cylinders. Next, extended results are presented, focusing on the effect of D, including its optimum value, on various physical quantities describing the behaviour of both the cylinder and the plate. Contrary to the isolated cylinder, the presence of the plate introduces sharp peaks in the variation pattern of the drift force of the cylinder, bounded at specific wave numbers, where resonance of the seiche mode of water motion in the annular cavity or of specific flexible modes of the plate occurs. However, by reducing D to its optimum value, the cylinder’s drift force obtains practically zero values at the target wave number, due to an efficient improvement of the wave field in the annular cavity around the cylinder. Moreover, a great reduction of the drift force compared to the isolated cylinder is achieved in the subsequent high frequency range.     

An analytical approach for the calculation of random wave forces on submerged tunnels

This paper deals with the random forces produced by high ocean waves on submerged horizontal circular cylinders. Arena [Arena F, Interaction between long-crested random waves and a submerged horizontal cylinder. Phys Fluids 2006;18(7):1–9 (paper 076602)] obtained the analytical solution of the random wave field for two dimensional waves by extending the classical Ogilvie solution [Ogilvie TF, First- and second-order forces on a cylinder submerged under a free surface. J Fluid Mech 1963;16:451–472; Arena F, Note on a paper by Ogilvie: The interaction between waves and a submerged horizontal cylinder. J Fluid Mech 1999;394:355–356] to the case of random waves. In this paper, the wave force acting on the cylinder is investigated and the Froude Krylov force [Sarpkaya T, Isaacson M, Mechanics of wave forces on offshore structures, Van Nostrand Reinhold Co.; 1981], on the ideal water cylinder, is calculated from the random incident wave field. Both forces represent a Gaussian random process of time. The diffraction coefficient of the wave force is obtained as quotient between the standard deviations of the force on the solid cylinder and of the Froude Krylov force. It is found that the diffraction coefficient of the horizontal force C_do is equal to the C_dv of the vertical force. Finally, it is shown that, since a very large wave force occurs on the cylinder, it may be calculated, in time domain, starting from the Froude Krylov force. It is then shown that this result is due to the fact that the frequency spectrum of the force acting on the cylinder is nearly identical to that of the Froude–Krylov force.     

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.     

Second-order oscillatory forces on a body in waves

When a small amplitude, water-wave train is incident upon a fixed body, a second-order analysis predicts that the body experiences a steady force and a force at twice the frequency of the incident wave. The double-frequency force is comprised of integrals of products of linear quantities over the surface of the body and the mean waterline and a term due to the second-order potential. An application of Green's theorem to the first-order potential and its horizontal derivative shows that the integral of the first order terms over the body is related in a simple way to the waterline integral and the far-field representation of the linear, diffraction potential. A minor modification of the analysis yields the farfield formulae for the drift force.     

Wave forces on a single and on a group of cylinders in response to two wave spectra of same significant wave height

Spectral analysis is used to determine the wave force characteristics on structures exposed to random waves. Considerable work has been carried out to determine the magnitude of random wave forces acting on a single cylinder, but little information is available in the case of a group of cylinders in random waves. Such situations arise when structures comprise multiple tubular members which are in close proximity, and wave forces cannot be calculated precisely by analytical methods due to complicated flow conditions past the group. Experimental studies are also required for proper understanding and analysis. An experimental scheme was carried out to study the wave force characteristics on a single cylinder and on a group of cylinders in response to two different wave spectra with the same significant wave height, and the results are compared.     

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.     

Fatigue damage induced by nonGaussian bimodal wave loading in mooring lines

Catenary mooring lines are typically subjected to bimodal loads, comprising of a wave frequency (WF) component due to the first-order wave forces and a low frequency (LF) component induced by the second-order wave forces. For moored vessels, the LF forces due to current and wind also play a role. Only dynamic wave loads are considered herein, while current and wind loads are modeled as constant forces. Because of the nonlinearities of the mooring line characteristics, the dynamic line tension and the second-order responses, both the WF and LF line tensions are in principle nonGaussian. These facts make it difficult to estimate the combined fatigue damage of mooring lines in the frequency domain. A fatigue combination rule based on the Jiao and Moan’s theory has been extended to cover the nonGaussian case. The purpose of this paper is to improve and validate the frequency-domain method by time-domain analysis based on a simplified, but accurate mechanical model of the dynamic line tension. Improvements on the LF and combined fatigue damage estimation have been made by considering the nonsymmetrical property of the LF line tension distribution. Both the WF and LF mooring line tensions due to wave loading have been simulated in the time domain for different sea states and the combined fatigue damage has been estimated by using the rainflow cycle counting algorithm. The accuracy of the frequency-domain method for estimating the bimodal nonGaussian fatigue damage of mooring lines has been verified by the time-domain simulations and is considered to be acceptable.     

Second order frequency domain analysis of moored vessels

A frequency domain analysis method for the dynamic response of a vessel moored in a random sea is presented, in which second order wave forces are included. The non-linearities occurring in the equations of motion of the vessel are accounted for by using the equivalent linearisation technique, leading to an iterative solution scheme for the mean values and covariances of the response. Application of the method to a moored drill ship indicates that the required computer time is relatively low. The method is intended for use in the preliminary stages of design where a parametric study may be required and the costs of a time domain analysis are prohibitive.     

Dynamic response of a tanker moored to an articulated loading platform

An analytical model was developed for the dynamic analysis of an articulated loading platform in an operation condition, while remaining in a head seas position. The environmental excitation considered, resulting from groups of regular waves, included first- and second-order force contributions. The nylon hawser connecting the tanker to the ALP was modeled as a nonlinear spring. The hydrodynamic load on the tower was evaluated using Morison's equation, which was modified to account for the relative motion of the tower and the fluid particles. The hydrodynamic load on the tanker was calculated using linear diffraction theory based on the 2-D Helmholtz equation. The “near field” approach of Pinkster was used to evaluate the drift force.     

冰区四季通用灯浮标的二阶波浪力计算

冰区四季通用灯浮标是一种为满足北方冬季冰冻港口一年四季的助航服务需求研制的新型灯浮标,二阶波浪力对其漂浮姿态和漂移运动有较大影响。文中研究了浮标受到的二阶波浪力的数值计算方法,计算了不同流速下罐形和锥形灯浮标的二阶波浪力。研究结果显示,罐形和锥形灯浮标受到的一阶波浪力相差不大,罐形的二阶波浪力明显小于锥形,具有一定的外形优势。     

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.     

Wave force prediction using an autoregressive model

An autoregressive wave force model is developed which is capable of accounting for localized flow history effects. It was developed in conjunction with the analysis of a series of experiments performed to study the wave-induced forces acting on a free-to-surge vertical cylinder in random waves. The wave force model incorporates a relative motion form of the Morison equation. The formulation presented in this study is quite general, but the filter coefficients in the model must be uniquely determined for each data set. The optimal length of the filter and its sensitivity are illustrated using data from small-scale wave tank tests. A high frequency wave force component observed in the experimental data is reproduced using this model. Lastly, the autoregressive wave force model is used to predict the response of a tension-leg platform to a wave train. A comparison of the results obtained both with and without the filter model are presented.     

海上风电单桩式支撑结构冰激振动及参数敏感性分析

针对渤海湾某风电场的海上固定式风机支撑结构,采用适用于大直径单桩结构的PSI曲线模拟桩土相互作用,并采用SACS软件建立支撑结构的动力分析模型。首先对支撑结构进行模态分析;其次考虑海冰结构的随机振动作用模式,根据适用于渤海湾的随机冰力谱构造随机冰载荷时程曲线,基于半耦合的时域方法,采用SACS软件对支撑结构进行冰激振动分析,输出塔筒顶部加速度、单桩基底剪力及倾覆力矩等响应参数的时程曲线和响应功率谱;最后针对冰厚、冰速和海冰强度等海冰参数对支撑结构的冰激振动进行敏感性分析。研究结果表明,在随机振动模式下,冰载荷及结构动力响应对冰厚和海冰强度较为敏感,在进行冰激振动分析时应合理确定冰厚和海冰强度等参数。     

Dynamic Analysis of a Turret-Moored Tanker

—In this paper,the second-order perturbation method in frequency domain is used to calculateRAO and spectra of motion and mooring line tension of a turret-moored tanker in ballast condition.Thecalculated results are compared with corresponding experiment results.In the experiment the wave head-ing is 180°,and the wave spectra is the P-M spectrum and white noise spectrum.In the theoretical calcu-lations,the damping coefficient of slow oscillation of the tanker is determined on the basis of the dampingobtained from a test of irregular waves where the mooring system is replaced by a nonlinear spring withnonlinear stiffness similar to that of the mooring system.From the comparison between theoretical calcula-tions and experimental results,it can be found that the theoretical results obtained by the second-orderperturbation method in frequency domain are in good agreement with the experimental results,indicatingthat the damping coefficient of slow oscillation of the tanker required in frequency domain calcu     

Nonlinear hydroelastic analysis of a moored floating body

By integration of the second-order fluid pressure over the instantaneous wetted surface, the generalized first- and second-order fluid forces used in nonlinear hydroelastic analysis are obtained. The expressions for coefficients of the generalized first- and second-order hydrodynamic forces in irregular waves are also given. The coefficients of the restoring forces of a mooring system acting on a flexible floating body are presented. The linear and nonlinear three-dimensional hydroelastic equations of motion of a moored floating body in frequency domain are established. These equations include the second-order forces, induced by the rigid body rotations of large amplitudes in high waves, the variation of the instantaneous wetted surface and the coupling of the first order wave potentials. The first-order and second-order principal coordinates of the hydrelastic vibration of a moored floating body are calculated. The frequency characteristics of the principal coordinates are discussed. The numerical results indicate that the rigid resonance and the coupling resonance of a moored floating body can occur in low frequency domain while the flexible resonance can occur in high frequency domain. The hydroelastic responses of a moored box-type barge are also given in this paper. The effects of the second-order forces on the modes are investigated in detail.