Validation and application of nonlinear hydrodynamics from CFD in an engineering model of a semi-submersible floating wind turbine

Nonlinear hydrodynamics play a significant role in accurate prediction of the dynamic responses of floating wind turbines (FWTs), especially near the resonance frequencies. This study investigates the use of computational fluid dynamics (CFD) simulations to improve an engineering model (based on potential flow theory with Morison-type drag) by modifying the second-order difference-frequency quadratic transfer functions (QTFs) and frequency-dependent added mass and damping for a semi-submersible FWT. The results from the original and modified engineering models are compared to experimental data from decay tests and irregular wave tests. In general, the CFD results based on forced oscillation tests suggest increasing the frequency-depending added mass and damping at low frequencies compared to first order potential flow theory. The modified engineering model predicts natural periods close to the experimental results in decay tests (within 5%), and the underprediction of the damping is reduced compared to the original engineering model. The motions, mooring line tensions and tower-base loads in the low-frequency response to an irregular wave are underestimated using the original engineering model. The additional linear damping increases this underestimation, while the modified QTFs based on CFD simulations of a fixed floater in bichromatic waves result in larger difference-frequency wave loads. The combined modifications give improved agreement with experimental data in terms of damage equivalent loads for the mooring lines and tower base.     

Second-order wave run-up on a vertical cylinder adjacent to a plane wall based on the application of quadratic transfer function in bi-directional waves

A numerical model was developed in this study to simulate the wave diffraction caused by an arbitrarily shaped structure in the presence of bi-directional incident waves based on a higher-order boundary element method (HOBEM). Based on the developed model, the wave elevation quadratic transfer function (QTF) in bi-directional waves, which is defined as the second-order wave elevation caused by two incident waves of unit amplitude from two directions, can be determined. The developed model was subsequently used to investigate the wave interaction with a cylinder situated near a vertical wall. The image principle was applied to transform the original problem into an equivalent one of wave diffraction caused by two symmetrical cylinders in open seas exposed to bi-directional incident waves. The second-order wave run-up on the cylinder can then be determined using the wave elevation QTF obtained from an analysis of the equivalent problem. A detailed numerical analysis was then conducted. Numerical results revealed that the presence of the vertical wall can apparently disturb the wave diffraction process from the cylinder, and lead to significantly amplified second-order wave elevation within the region between the wall and cylinder. In addition, the respective contribution from the first- and second-order components to the overall wave elevation around the cylinder was discussed.     

粘性对方尾船波浪力的影响分析

航行船舶绕射问题的准确求解是预报船舶波浪中运动的基础.文章分别采用基于三维移动脉动源的边界元法和基于RANS方程的CFD方法求解了规则波中航行的方尾船模型的波浪力,并通过与试验结果比较验证了方法的可靠性.CFD计算时通过从波浪力中分离出粘性力,研究了粘性对方尾船波浪力的影响.结果表明,基于RANS方程的波浪力计算结果与试验结果和势流理论结果吻合良好,在长波中与试验值更接近.粘性对船模斜浪航行时的横摇力矩有较大影响.     

Wave analysis of porous geometry with linear resistance law

The wave diffraction-radiation problem of a porous geometry of arbitrary shape located in the free surface of a fluid is formulated by a set of integral equations, assuming a linear resistance law at the geometry. The linear forces, the energy relation and the mean horizontal drift force are evaluated for non-porous and porous geometries. A geometry of large porosity has an almost vanishing added mass. The exciting forces are a factor of 5–20 smaller compared to a solid geometry. In the long wave regime, the porous geometry significantly enhances both the damping and the mean drift force, where the latter grows linearly with the wavenumber. The calculated mean drift force on a porous hemisphere and a vertical truncated cylinder, relevant to the construction of fish cages, is compared to available published results.     

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.     

Experimental investigation of TARMAX model for modeling of hydrodynamic forces on cylinder-like structures

A new approach that models lift and drag hydrodynamic force signals operating over cylindrical structures was developed and validated. This approach is based on stochastic auto regressive moving average with exogenous (ARMAX) input and its time-varying form, TARMAX. Model structure selection and parameter estimation were discussed while considering the validation stage. In this paper, the cylindrical structure was considered as a dynamic system with an incoming water wave and resulting forces as the input and outputs, respectively. The experimental data, used in this study, were collected from a full-scale rough vertical cylinder at the Delft Hydraulics Laboratory. The practicality of the proposed method and also its efficiency in structural modeling were demonstrated through applying two hydrodynamic force components. For this purpose, an ARMAX model is first used to capture the dynamics of the process, relating in-line forces provided by water waves;secondly, the TARMAX model was applied to modeling and analysis of the lift forces on the cylinder. The evaluation of the lift force by the TARMAX model shows the model is successful in modeling the force from the surface elevation.     

Assessment of uncertainty in the CFD simulation of the wave-induced loads on a vertical cylinder

The paper addresses different uncertainty analysis methods commonly used for uncertainty quantification in Computational Fluid Dynamics (CFD) studies and compares a constant Courant–Friedrichs–Lewy (CFL) number based approach for uncertainty estimation to the ITTC recommended grid and time-independent procedures. Four different uncertainty estimation procedures are presented and discussed. To compare their performance and better understand CFD related uncertainty quantification in wave load simulations on offshore structures, the methods are applied to a case study of the wave loads on a fixed vertical cylinder. The numerical or CFD wave tank is generated using the open-source CFD toolkit OpenFOAM. Uncertainty is assessed for the case study using four different uncertainty estimation procedures for verification and later, validation is attempted by comparing the CFD results with experiments. The study concludes that a constant CFL number based uncertainty study provides more stable results and is better suited for uncertainty estimation in CFD than the ITTC recommended individual grid and time step uncertainty study.     

直立圆柱体内孤立波载荷特性数值模拟

以三类内孤立波理论(KdV、eKdV和MCC)的适用性条件为依据,将内孤立波诱导上下层深度平均水平速度作为入口条件,采用Navier-Stokes方程为流场控制方程,建立了两层流体中内孤立波对直立圆柱体强非线性作用的数值模拟方法.结果表明,数值模拟所得内孤立波波形及其振幅与相应理论和实验结果一致,并且直立圆柱体内孤立波水平力、垂向力及其力矩数值模拟结果与实验结果吻合.直立圆柱体内孤立波载荷由波浪压差力、粘性压差力和摩擦力构成,其中摩擦力很小,可以忽略;对于水平力,其波浪压差力与粘性压差力量级相当,流体粘性的影响显著;对于垂向力,粘性压差力很小,流体粘性影响可以忽略.此外,直立圆柱体对内孤立波的波形及其诱导流场的影响很小,因此采用Morison公式和傅汝德—克雷洛夫力分别计算其内孤立波水平力和垂向力是可行的.     

数值波浪序列中的高频成分

可靠的波浪模拟方法对于海洋结构物水动力性能的评估而言至关重要。文章基于软件FLUENT,分别采用四种不同的网格模型,实现了对于规则波的模拟。文中采用VOF方法对自由液面进行捕捉,并采用动网格方法模拟摇板的运动从而实现造波。考虑到数值耗散及截断误差对数值模拟结果的影响,针对沿水池方向的波浪衰减情况进行了相关研究。为了避免造波板的初始运动所引起的波面扰动,引入了一种“缓入”方法使造波板缓慢地达到最大幅值的运动,有效地避免了初始扰动所带来的影响。数值模拟的结果分别与一阶和二阶理论解进行了对比。结果表明,该数值波浪模型能够给出可靠的预测,为下一步模拟强非线性波浪（如畸形波）奠定了基础。     

考虑高阶拖曳力的导管架平台极端载荷响应谱方法（英文）

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.     

基于CFD的规则波顺浪数值水池模拟

基于CFD（ Computational Fluid Dynamics）和粘性数值波浪水池技术,对顺浪航态的规则波波浪环境进行数值模拟,采用边界造波法进行波浪生成,VOF（Volume of Fluid）法模拟自由面。本文改进了传统的基于规则波的顶浪数值模拟方法,在特定波浪、不同航速条件下进行了顺浪航态的数值水池模拟。根据模拟呈现的动态效果,以及与Matlab仿真结果的对比,对试验的准确性进行验证。     

带横隔板开孔沉箱所受波浪力的研究

研究了斜向波与无限多开孔沉箱的相互作用。依照结构物的几何形状,整个流域被分成无限多个子域,在每个子域内应用特征函数展开法求解速度势。对于沉箱内的波浪运动,引入相位差概念;同时,在构造反射波模型时,考虑了结构物的几何形状影响。进行了数值试验,分析了开孔沉箱水平波浪力及横隔板受力特点,详细讨论了波浪入射频率、入射角度、相对消浪室宽度及开孔影响系数对开孔沉箱波浪力的影响。     

规则波作用下近岸透空式结构物的波浪上托力研究

基于对透空码头结构物波浪上托力研究现状的分析,运用垂向二维CFD数值波浪水槽建立模拟规则波作用下水平板波浪上托力的数值模型.通过物理模型和数值模型所获波浪压力结果的对比分析,总结平板底部流场和测点压强的分布特点,探讨不同周期波浪的最大冲击压强随波浪相对超高变化的规律.试验结果表明,规则波作用下波浪上托力的数值模拟结果与...     

多孔介质中波浪传播的高阶Boussinesq方程*

准确模拟波浪在多孔介质中传播变形对于研究抛石防波堤等结构的消能作用是十分必要的。对Laplace方程、自由表面处的运动学方程和动力学方程以及海底运动学方程进行无因次化,且以自由表面处速度势为切点,进行幂级展开,最终给出4个不同的高阶Boussinesq水波方程。在常水深下对这些方程的一维问题进行了理论研究,并将无因次相速度和无因次虚波数与解析解结果进行对比,方程的相速度与解析解吻合程度较好,虚波数与解析解基本吻合,表明高阶Boussinesq方程可用于模拟波浪在多孔介质中的传播变形。     

Higher-order boundary element method for the interaction of a floating body with both waves and slow current

A hybrid boundary element method is suggested to solve the problem of the interaction of floating structures with both waves and slow current. A pulsating source and its mirror image referring to the sea bottom are adopted as the Green's function. The velocity potentials are expanded into an eigenfunction expansion in the outer region of the fluid domain while higher order elements are used to discretize the boundary surface surrounding the inner region. The method is validated by comparing calculated results for a circular cylinder with the semi-analytical solutions. The method is then applied to ellipsoids of various breadth and draft to investigate the influence of body shape on the wave drift damping.     

三维完全非线性波浪水槽的数值模拟

用有限元求解拉普拉斯方程,采用满足完全非线性自由表面条件的半拉格朗日法追踪流体自由表面,离散单元采用20节点的六面体二次等参数单元,建立了三维完全非线性数值波浪水槽.把数值计算结果与水面初始升高产生箱体内流体运动解析解和二阶斯托克波理论解进行了对比,结果表明该模型是稳定的、守恒的,能精确模拟非线性波浪的产生和传播,为今后研究非线性波浪对船舶等非规则物体的作用提供了参考.     

Stochastic modelling of quadratic wave components

This paper deals with stochastic wave models and their influence on wave load modelling of marine structures. The need for more refined theories is underlined for some applications and an entirely new quadratic model for the wave elevation is outlined. Finally, a number of physical phenomena relevant to waves are illustrated which are likely to be important for marine structures and could, in the near future, require ad hoc modelling.     

3D numerical modeling of wave forces on tandem fixed cylinders using the BEM

In this paper a 3D numerical model was developed to study the complicated interaction between waves and a set of tandem fixed cylinders.The fluid was considered to be inviscid and irrotational.Therefore,the Helmholtz equation was used as a governing equation.The boundary element method（BEM） was adopted to discretize the relevant equations.Open boundaries were used in far fields of the study domain.Linear waves were generated and propagated towards tandem fixed cylinders to estimate the forces applied on them.Special attention was paid to consideration of the effect on varying non-dimensional cylinder radius and distance between cylinders,ka and kd on forces and trapped modes.The middle cylinder wave forces and trapped modes in a set of nine tandem cylinders were validated utilizing analytical data.The comparisons confirm the accuracy of the model.The results of the inline wave force estimation on n tandem cylinders show that the critical cylinder in the row is the middle one for odd numbers of cylinders.Furthermore the results show that the critical trapped mode effect occurs for normalized cylinder radiuses close to 0.5 and 1.0.Finally the force estimation for n tandem cylinders confirms that force amplitude of the middle cylinder versus normalized separation distance fluctuates about that of a single cylinder.