Normalization of Hydrodynamic Coefficients in Morison Equation

The hydrodynamic coefficients C-d and C-m are not only dependent on the size of slender cylinder, its location in water, KC number and Re number, but also vary with environmental conditions, i.e., in regular waves or in irregular waves, in pure waves or in wave-current coexisting field. In this paper, the normalization of hydrodynamic coefficients for various environmental conditions is discussed. When a proper definition of KC number and proper characteristic values of irregular waves are used, a unified relationship between C-d, C-m and KC number for regular waves, irregular waves, pure waves and wave-current coexisting field can be obtained.

Comparison of Potential Theory and Morison Equation for Deformable Horizontal Cylinders

This study investigates the hydro-elastic behaviors of fully submerged horizontal cylinders in different regular waves.Two methods were proposed and compared in this study.The first method was based on potential theory in frequency domain and the discrete-module-beam(DMB)method,which discretizes a floating elastic structure into a sufficient number of rigid bodies while simultaneously representing the elastic behavior from beam elements with Euler-Bernoulli beam and Saint-Venant torsion.Moreover,the Morison method in time domain was employed;this method estimates wave forces from the semi-empirical Morison equation,and the elastic behavior is embodied by massless axial,bending,and torsional springs.Various parametric studies on cylinder diameter,submergence depth,and wave direction were conducted.Wave forces,dry/wet mode shapes/natural frequencies,and dynamic motions are presented and analyzed.

Comparisons of Wave Force Model Effects on the Structural Responses and Fatigue Loads of a Semi-Submersible Floating Wind Turbine

The selection of wave force models will significantly impact the structural responses of floating wind turbines.In this study,comparisons of wave force model effects on the structural responses and fatigue loads of a semi-submersible floating wind turbine(SFWT)were conducted.Simulations were performed by employing the Morison equation(ME)with linear or second-order wave kinematics and potential flow theory(PFT)with first-or second-order wave forces.A comparison of regular waves,irregular waves,and coupled wind/waves analyses with the experimental data showed that many of the simulation results and experimental data are relatively consistent.However,notable discrepancies are found in the response amplitude operators for platform heave,tower base bending moment,and tension in mooring lines.PFT models give more satisfactory results of heave but more significant discrepan-cies in tower base bending moment than the ME models.In irregular wave analyses,low-frequency resonances were captured by PFT models with second-order difference-frequency terms,and high-frequency resonances were captured by the ME models or PFT models with second-order sum-frequency terms.These force models capture the response frequencies but do not reasonably predict the response amplitudes.The coupled wind/waves analyses showed more satisfactory results than the wave-only analyses.However,an important detail to note is that this satisfactory result is based on the overprediction of wind-induced responses.

The Optimal Design of TMD for Offshore Structures

This paper presents the optimal design procedure of Tuned Mass Damper (TMD) for reducing vibration of an actual steel jacket offshore platform excited by random wave loading. In this study, a frequency domain is taken. The force on the structure is determined by use of the linearized Morison equation for an input Power Spectral Density (PSD) of wave elevation. The sensitivity of optimum values of TMD to characteristic parameters of random wave spectrum is analyzed. An optimized TMD design for the modeled platform is given based on design conditions and the findings of the study.

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

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

-Based on the extended Morison Equation and model tests, the in-line forces on small square cylinders caused by waves (regular and irregular) and currents are analyzed in detail in this paper. The hydrodynamic coefficient CD and Cu related to KC number and the effect of direction of wave incidence are also given, which can be used in engineering practice.

Investigation on the Dynamic Responses of a Truss Spar Platform for Different Mooring Line Groups

The dynamic responses of any floating platform arc dependent on the mass, stiffness and damping characteristics of the body as well as mooring system. Therefore, it is very essential to study the effect of individual contributions to the system that can finally help to economise their cost. This paper focuses on the effect of mooring stiffness on the responses of a truss spar platform, obtained by different grouping of lines. The study is part of our present researches on mooring systems which include the effect of line pretension, diameter and azimuth angles. The platform is modelled as a rigid body with three degrees-of-freedom and its motions are analyzed in time-domain using the implicit Newmark Beta technique. The mooring lines restoring force-excursion relationship is evaluated using a quasi-static approach. It is observed that the mooring system with lines arranged in less number of groups exhibits better performance in terms of the restoring forces as well as mean position of platform. However, the dynamic motions of platform remain unaffected for different line groups.

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,how-ever,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.

Experimental Study and System Identification of Hydrodynamic Force Acting on Heave Damping Plate

Although Morison equation is often applied for simulating hydrodynamic force of marine structure, it may give poor results when non-linear behavior is severe or random wave is encountered. This leads to some modifications of Morison equation or other methods for predicting hydrodynamic force. One of them is the system identification technique. In this paper, NARMAX model theory is firstly used to identify the hydrodynamic system of heave damping plates, which are commonly installed on spar platform. Both linear and non-linear models are obtained. The comparisons between the predieted results and measured data indicate that NARMAX model can predict hydrodynamic force of a heave damping plate very well. The measured data for identification originate from forced oscillation tests, which are random records with given spectrum. The forced oscillation forms in experiment also contain simple harmonic, multi-frequency ones.

Offshore Structural Control Considering Fluid Structure Interaction

Tuned Mass Damper （TMD） was applied to an offshore structure to control ocean wave-induced vibration, In the analysis of the dynamic response of the offshore structure, fluid-structure interaction is considered and the errors, which occur in the linearization of the interaction, are investigated. For the investigation of the performance of TMD in controlling the vibration, both regular waves with different periods and irregular waves with different significant wave heights are used. Based on the numerical analysis it is concluded that the fluid-structure interaction should be considered in the evaluation of the capability of TMD in vibration control of offshore structures.

Comparative Experimental and Numerical Study of Wave Loads on A Monopile Structure Using Different Turbulence Models

This study numerically and experimentally investigates the effects of wave loads on a monopile-type offshore wind turbine placed on a 1:25 slope at different water depths as well as the effect of choosing different turbulence models on the efficiency of the numerical model.The numerical model adopts a two-phase flow by solving Unsteady Reynolds-Averaged Navier−Stokes(URANS)equations using the Volume Of Fluid(VOF)method and three differentk-ωturbulence models.Typical environmental conditions from the East China Sea are studied.The wave run-up and the wave loads applied on the monopile are investigated and compared with relevant experimental data as well as with mathematical predictions based on relevant theories.The numerical model is well validated against the experimental data at model scale.The use of different turbulence models results in different predictions on the wave height but less differences on the wave period.The baseline k-ωturbulence model and Shear-Stress Transport(SST)k-ωturbulence model exhibit better performance on the prediction of hydrodynamic load,at a model-scale water depth of 0.42 m,while the laminar model provides better results for large water depths.The SST turbulence model performs better in predicting wave run-up for water depth 0.42 m,while the laminar model and standard k-ωmodel perform better at water depth 0.52 m and 0.62 m,respectively.

Response Spectrum Method for Extreme Wave Loading With Higher Order Components of Drag Force

Response spectra of fixed offshore structures impacted by extreme waves are investigated based on the higher order components of the nonlinear drag force. In this way, steel jacket platforms are simplified as a mass attached to a light cantilever cylinder and their corresponding deformation response spectra are estimated by utilizing a generalized single degree of freedom system. Based on the wave data recorded in the Persian Gulf region, extreme wave loading conditions corresponding to different return periods are exerted on the offshore structures. Accordingly, the effect of the higher order components of the drag force is considered and compared to the linearized state for different sea surface levels. When the fundamental period of the offshore structure is about one third of the main period of wave loading, the results indicate the linearized drag term is not capable of achieving a reliable deformation response spectrum.

Concept Design of a New Deep Draft Platform

The authors analyzed requirements for a new deepwater platform, from conceptual design to hydrodynamic analysis.The design incorporated Deep Draft Multi-Spar (DDMS) that allowed easy fabrication, reduced costs, and provided favorable motion performance.It also provided a dry tree system and other benefits.The conceptual design process included dimension estimation, general arrangements, weight estimation, weight distribution, stability analysis, etc.A high order boundary element method based on potential theory and the modified Morison equation was used to predict the hydrodynamic and viscous effects of this new concept platform.The response amplitude operators (RAOs) were acquired and compared with those of a typical Truss Spar.The response of the platform to the JONSWAP spectra of 3 different extreme ocean conditions was analyzed to evaluate the seakeeping ability of the new concept.The results revealed favorable motion performance due to all the degrees of freedom available.

THREE-DIMENSIONAL INSTABILITY OF AN OSCILLATING VISCOUS FLOW PAST A CIRCULAR CYLINDER

A systematically numerical study of the sinusoidally oscillating viscous flow around a circular cylinder was performed to investigate vortical instability by solving the three_dimensional incompressible Navier_Stokes equations. The transition from two_ to three_dimensional flow structures along the axial direction due to the vortical instability appears,and the three_dimensional structures lie alternatively on the two sides of the cylinder. Numerical study has been taken for the Keulegan_Carpenter(KC) numbers from 1 to 3.2 and frequency parameters from 100 to 600. The force behaviors are also studied by solving the Morison equation. Calculated results agree well with experimental data and theoretical prediction.

Shear Effects in Shakedown Analysis of Offshore Structures

In this paper, a formulation for shakedown analysis of elastic-plastic offshore structures under cyclic wave loading is presented. In this formulation, a fast numerical solution method is used, suitable for the Finite Element Method (FEM) analysis of large offshore structures on which shear effects in addition to bending and axial effects are taken into account. The Morison equation is adopted for converting the velocity and acceleration terms into resultant forces and it is extended to consider arbitrary orientations of the structural members. The theoretical methods of the shakedown analysis are discussed in detail and the formulation is applied to an offshore structure to verify the concept employed and its analytical capabilities.

Forces of fully nonlinear interfacial periodic waves on a cylindrical pile in a two-layer fluid with free-surface boundary conditions

In the frame of fully nonlinear potential flow theory,series solutions of interfacial periodic gravity waves in a two-layer fluid with free surface are obtained by the homotopy analysis method(HAM),and the related wave forces on a vertical cylinder are analyzed.The solution procedure of the HAM for the interfacial wave model with rigid upper surface is further developed to consider the free surface boundary.And forces of nonlinear interfacial periodic waves are estimated by both the classical and modified Mori-son equations.It is found that the estimated wave forces by the classical Morison equation are more conservative than those by the modified Morison’s formula,and the relative error between the total inertial forces calculated by these two kinds of Morison’s formulae remains over 25%for most cases unless the upper and lower layer depths are both large enough.It demonstrates that the convective acceleration neglected in the classical Morison equation is rather important for inertial force exerted by not only internal solitary waves but also interfacial periodic waves.All of these should further deepen our understanding of internal periodic wave forces on a vertical marine riser.