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This study presents a comparative analysis of hydrodynamic forces on cylindrical offshore piles with both constant and linearly varying diameters utilizing computational fluid dynamics (CFD) simulations. The classical Morison equation is evaluated alongside an extended version to address limitations in predicting forces on geometrically complex structures. Mesh convergence studies are performed to select the optimum grid size for separate wave and current simulations. The focus is on test cases characterized by small Keulegan-Carpenter (KC) numbers and relatively high Reynolds (Re) numbers within both inertia-dominated and diffraction zones. Numerical simulation results are utilized to compare the force predictions of the classical Morison equation and the extended Morison equation. It is observed that the classical Morison equation performs adequately for constant diameter piles, but it fails to predict forces on variable diameter piles accurately. In contrast, the extended Morison equation, incorporating nonlinear effects and variable cross-sections, provides significantly more accurate force predictions, particularly in the diffraction zone compared to the numerical simulations. This study emphasizes the critical importance of accounting for geometric variations, such as linearly varying pile diameters, under separate waves and currents loadings in hydrodynamic force calculations. These considerations support the development of enhanced design methods and optimization strategies, leading to safer and more efficient offshore structures. [ABSTRACT FROM AUTHOR]

Currently, divers face significant safety risks when cleaning marine organisms from the steel structures of offshore underwater platform jackets. Consequently, utilizing robots instead of divers to carry out underwater biofouling removal operations will be an important development direction for the underwater maintenance of offshore platforms in the future. In this study, a wall-climbing robot was designed to clean marine organisms from the underwater surface of a platform jacket leg. The overall structure of the underwater cleaning wall-climbing robot is introduced, including the cleaning actuator and the variable curvature-adapted connecting rod mechanism. The corresponding relationship between the variable curvature-adapted connecting rod mechanism and the jacket leg is analyzed in detail. The variable curvature-adapted connecting rod mechanism was optimized using a genetic algorithm to ensure that the underwater cleaning wall-climbing robot can adapt to a minimum diameter of 1 m for the jacket leg. By drawing on Airy wave theory and random wave theory, the Airy wave parameters for waves were analyzed under different sea conditions, considering practical application scenarios. By using Fluent software 2022, a 2D numerical wave tank was constructed to simulate waves under various sea conditions, and the wave surface shapes for different sea states were determined. By building on the Morison equation, a method for calculating the horizontal wave forces on the underwater cleaning wall-climbing robot using the equivalent area and equivalent volume is proposed. By using the two aforementioned methods, the horizontal wave forces on the underwater cleaning wall-climbing robot under specific sea states were determined. The horizontal wave forces of the underwater cleaning wall-climbing robot under different sea conditions were analyzed and simulated in a 3D numerical wave tank. By comparing the theoretical analysis results with the numerical simulation results, where the maximum difference at the extreme points is approximately 11%, the feasibility of the proposed horizontal wave force estimation method was verified. [ABSTRACT FROM AUTHOR]

Accurately simulating the deployment process of coupled systems in deep-sea environments remains a significant challenge. This study employs the Absolute Nodal Coordinate Formulation (ANCF) to dynamically model and analyze multi-body systems based on the Pendant Installation Method (PIM). Utilizing the principle of energy conversion, this study calculates the stiffness, generalized elastic forces, mass matrices, and Morison equation, formulating a motion equation for the dynamic coupling of nonlinear time-domain forces in cables during pendulum deployment, which is numerically solved using the implicit generalized-α method. By comparing the simulation results of this model with those from the catenary theory model, the advanced modeling capabilities of this model are validated. Lastly, the sensitivity of the multi-body system under various boundary conditions is analyzed. The results indicate that deployment operations are more effective in environments with strong ocean currents. Furthermore, upon comparing the impacts of structural mass and deployment depth on the system, it was found that deployment depth has a more significant effect. Consequently, the findings of this study provide a scientific basis for formulating subsequent optimization strategies. [ABSTRACT FROM AUTHOR]

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 discrepancies 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. [ABSTRACT FROM AUTHOR]

Abstract Background This study introduces a numerical model designed to simulate interactions occurring between a wind turbine's tower and the surrounding soil, as well as between the nacelle, blades, and the surrounding environment. This simulation accounts for both fore–aft and side-to-side movements. To describe these interactions, the model leverages the Euler–Lagrange equations. It calculates wave loads utilizing the Morison equation, with wave data generated based on the JONSWAP spectrum. Furthermore, aerodynamic loads are determined using the blade element moment theory, and the wind spectrum is generated using the Von Karman turbulence model. The tower is represented as a variable cross-sectional beam, employing a two-noded Euler beam element with two degrees of freedom: transverse displacement and rotation, and utilizing Hermite polynomial shape functions. Results In a comparative analysis against experimental data, this modified model demonstrates significant enhancements in accurately reproducing the dynamic behavior of wind turbines with variable cross-sectional towers, outperforming models that approximate the tower with a constant cross section. Our findings reveal that the modified model achieves a remarkable improvement of 15% in replicating the tower's dynamic response when compared to the constant cross-sectional models. As a case study, a 5 MW monopile wind turbine with a flexible foundation, specifically the one provided by the National Renewable Energy Laboratory (NREL), is employed to simulate its dynamic response. Conclusions This research presents a robust numerical model for simulating wind turbine behavior in various environmental conditions. The incorporation of variable cross-sectional tower representation significantly improves the model's accuracy, making it a valuable tool for assessing wind turbine dynamics. The study's findings highlight the importance of considering tower flexibility in wind turbine simulations to enhance their real-world applicability.

Currently, divers face significant safety risks when cleaning marine organisms from the steel structures of offshore underwater platform jackets. Consequently, utilizing robots instead of divers to carry out underwater biofouling removal operations will be an important development direction for the underwater maintenance of offshore platforms in the future. In this study, a wall-climbing robot was designed to clean marine organisms from the underwater surface of a platform jacket leg. The overall structure of the underwater cleaning wall-climbing robot is introduced, including the cleaning actuator and the variable curvature-adapted connecting rod mechanism. The corresponding relationship between the variable curvature-adapted connecting rod mechanism and the jacket leg is analyzed in detail. The variable curvature-adapted connecting rod mechanism was optimized using a genetic algorithm to ensure that the underwater cleaning wall-climbing robot can adapt to a minimum diameter of 1 m for the jacket leg. By drawing on Airy wave theory and random wave theory, the Airy wave parameters for waves were analyzed under different sea conditions, considering practical application scenarios. By using Fluent software 2022, a 2D numerical wave tank was constructed to simulate waves under various sea conditions, and the wave surface shapes for different sea states were determined. By building on the Morison equation, a method for calculating the horizontal wave forces on the underwater cleaning wall-climbing robot using the equivalent area and equivalent volume is proposed. By using the two aforementioned methods, the horizontal wave forces on the underwater cleaning wall-climbing robot under specific sea states were determined. The horizontal wave forces of the underwater cleaning wall-climbing robot under different sea conditions were analyzed and simulated in a 3D numerical wave tank. By comparing the theoretical analysis results with the numerical simulation results, where the maximum difference at the extreme points is approximately 11%, the feasibility of the proposed horizontal wave force estimation method was verified.

Accurately simulating the deployment process of coupled systems in deep-sea environments remains a significant challenge. This study employs the Absolute Nodal Coordinate Formulation (ANCF) to dynamically model and analyze multi-body systems based on the Pendant Installation Method (PIM). Utilizing the principle of energy conversion, this study calculates the stiffness, generalized elastic forces, mass matrices, and Morison equation, formulating a motion equation for the dynamic coupling of nonlinear time-domain forces in cables during pendulum deployment, which is numerically solved using the implicit generalized-α method. By comparing the simulation results of this model with those from the catenary theory model, the advanced modeling capabilities of this model are validated. Lastly, the sensitivity of the multi-body system under various boundary conditions is analyzed. The results indicate that deployment operations are more effective in environments with strong ocean currents. Furthermore, upon comparing the impacts of structural mass and deployment depth on the system, it was found that deployment depth has a more significant effect. Consequently, the findings of this study provide a scientific basis for formulating subsequent optimization strategies.

In offshore engineering, a compliant offshore structure accommodates dynamic forces by flexibility rather than rigidly withstanding load effects. As an alternative to conventional fixed platforms for loading/mooring in deep waters, articulated offshore towers are highly appealing because of their reduced structural weight. This study presents the results of a probabilistic random wave with and without current force on a 500 m high articulated tower with two hinges. By using the Lagrangian approach, governing nonlinear equations of motion are derived. The motion equation has been resolved in the time domain with the Houbolt approach. Based on Stokes fifth order nonlinear wave theory, wave forces have been assessed. Hydrodynamic forces are determined using a modified Morison equation with stretching modifications developed by Chakrabarti. The study examined two marine states, i.e., 10 m/10 s and 15 m/15 s. The current intensity of 2 m/sec has been taken into account. The salient statistical parameters such as maximum, minimum, mean, and standard deviation are presented under both the ocean environments. The proposed model is feasible for both the sea states. When comparing sea states, those with a greater wave height and period and those with a smaller wave height and period have more energy in their PSDs for all responses. [ABSTRACT FROM AUTHOR]

Background: This study introduces a numerical model designed to simulate interactions occurring between a wind turbine's tower and the surrounding soil, as well as between the nacelle, blades, and the surrounding environment. This simulation accounts for both fore–aft and side-to-side movements. To describe these interactions, the model leverages the Euler–Lagrange equations. It calculates wave loads utilizing the Morison equation, with wave data generated based on the JONSWAP spectrum. Furthermore, aerodynamic loads are determined using the blade element moment theory, and the wind spectrum is generated using the Von Karman turbulence model. The tower is represented as a variable cross-sectional beam, employing a two-noded Euler beam element with two degrees of freedom: transverse displacement and rotation, and utilizing Hermite polynomial shape functions. Results: In a comparative analysis against experimental data, this modified model demonstrates significant enhancements in accurately reproducing the dynamic behavior of wind turbines with variable cross-sectional towers, outperforming models that approximate the tower with a constant cross section. Our findings reveal that the modified model achieves a remarkable improvement of 15% in replicating the tower's dynamic response when compared to the constant cross-sectional models. As a case study, a 5 MW monopile wind turbine with a flexible foundation, specifically the one provided by the National Renewable Energy Laboratory (NREL), is employed to simulate its dynamic response. Conclusions: This research presents a robust numerical model for simulating wind turbine behavior in various environmental conditions. The incorporation of variable cross-sectional tower representation significantly improves the model's accuracy, making it a valuable tool for assessing wind turbine dynamics. The study's findings highlight the importance of considering tower flexibility in wind turbine simulations to enhance their real-world applicability. [ABSTRACT FROM AUTHOR]

Coupled dynamic analysis of a floating offshore wind turbine (FOWT) is predicted with in-house ITU-WAVE computational tool. The hydrodynamic parameters are approximated with time marching of boundary integral equation whilst aerodynamic parameters are solved with unsteady blade element momentum method. In addition, forces on FOWT due to mooring lines are predicted with quasi-static analysis whilst hydrodynamic viscous effects are included with Morison equation. FOWT's blades are considered as an elastic structure whilst tower is considered as a rigid structure. The effects of steady wind speed on surge motion spectrum decrease the spectrum amplitude over wave frequency ranges, but this effect is not significant. The duration of time domain simulation plays significant role in the region of surge and pitch resonant frequencies. The numerical results of in-house ITU-WAVE computational code for eigenfrequencies of blades, aerodynamics and hydrodynamics parameters are validated against other numerical results which shows satisfactory agreements. [ABSTRACT FROM AUTHOR]

It is essential to give the applicable range of nonlinear theories of the internal solitary wave in different classification conditions and water depth. The nonlinear theories used to describe the ISW, including KdV, eKdV and MCC theories were compared with experimental results. The characteristic parameters of ISW (waveform, phase speed, and wave frequency) and its load on slender body were chosen to provide a quantitatively applicable range of three nonlinear theories at different water depths. In general, the optimal theories are KdV, eKdV and MCC in turns for most conditions. However, for the description of phase speed, both the eKdV and MCC theories can describe it well, where the KdV theory has a large error in describing phase speed at large ISW amplitude. For the vertical force, the KdV and eKdV theories can describe it well in turns, while the MCC theory has a large error in calculating the vertical force. A diagram of the applicable range under different classification conditions and at different water depths is proposed for choosing a better theory in different fields. [ABSTRACT FROM AUTHOR]

Hydrodynamic pressure on hydraulic structure is produced by water during earthquake. How to consider hydrodynamic pressure conveniently and efficiently is the basis of dynamic response analysis of intake tower. Morison equation, which is widely used to calculate wave forces on piers in deep water, was introduced into intake tower structure, and Morison equation was extended to make it applicable to tower intake with rectangular section. The results show that the hydrodynamic pressure inside and outside the tower is transformed into additional mass, and its distribution is directly related to the cross-section shape of the tower body, and has nothing to do with the height of the water body. The extended Morison equation was compared with the added mass formula of intake tower, and the applicability of the proposed method was evaluated by the obtained hydrodynamic pressure. It proves that the extended Morison equation can provide a new way to solve the hydrodynamic pressure of intake tower. [ABSTRACT FROM AUTHOR]

Copyright of Engineering Mechanics / Gongcheng Lixue is the property of Engineering Mechanics Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Comparative hydrodynamic loads caused by a focused wave acting on differently sized slender vertical cylinders placed in a wave canal were predicted at model scale using an unsteady Reynolds-averaged Navier–Stokes (URANS) solver and the Morison equation. This paper focused, first, on wake effects that need to be considered for the structural design of tripod configurations and, second, on the influence of these wake effects on wave-induced loads. For the Morison approach, flow velocities were gathered at incremental representative locations along the length of the cylinders, whereby the use of a central differencing approach obtained the associated flow accelerations. A first scenario dealt with a small- and a large-diameter cylinder, implemented individually at two immersion depths. A second scenario considered medium- and large-diameter cylinders arranged in a tripod configuration, where the upstream and downstream cylinders had the same diameter. For the single cylinder, impact loads obtained by both methods compared favorably to experimental measurements. For the tripod configuration, however, impact loads obtained by both methods differed due to the influence of wake effects. Thus, it was necessary to determine the influence of wake effects to assess the structural integrity of tripod configurations. [ABSTRACT FROM AUTHOR]

Copyright of Engineering Mechanics / Gongcheng Lixue is the property of Engineering Mechanics Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In order to ensure the safety of the cooling water source of coastal nuclear power plants (NPP), trash-blocking nets (TBNs) are usually installed at the entrance of the penstock to prevent marine sewage and organisms flowing into the front pool of the pump house of the nuclear power plant. The safety evaluation of these trash-blocking nets is of paramount importance for the stable operation of a nuclear power plant. However, there is no reliable analysis method for improving the design of trash-blocking nets and mooring systems. In this study, a numerical model of in-current trash-blocking nets based on the lumped mass method was developed to calculate the tension force on the trash-blocking nets and mooring system. A comparison with the experimental data indicates that the present numerical model is appropriate for calculating the in-current hydrodynamic loads on the trash-blocking nets. In addition, the effects of the width of trash-blocking nets, hanging ratio, water depth, and net solidity are discussed in detail, and the damage process of trash-blocking nets was also investigated. The results indicate that the maximum tension force on the trash-blocking net linearly increases with the increasing width of trash-blocking nets, and it is greatly decreased with the increase in the horizontal hanging ratio of trash-blocking nets. It can be increased by 200% when the net solidity is increased from 0.16 to 0.6. Two damage modes for mooring lines can be observed, which are determined by the strength of mooring lines. [ABSTRACT FROM AUTHOR]

Hydrodynamic loads acting on a pump tower inside a liquefied natural gas (LNG) tank were numerically investigated by considering the hydroelasticity of the tower's flexible structural components. Nine tank motion scenarios were considered, including regular motions of the tank in sway and roll and irregular motions likely to occur for an LNG carrier at zero speed in a long-crested beam seaway. The investigated filling level was 50% with water and air as fluids. Two-way fluid-structure interaction (FSI) simulations coupled the finite element method (FEM), idealizing the tower structure, with the finite volume method (FVM), modeling the flow of water inside the tank. Unsteady Reynolds-averaged Navier-Stokes equations (URANS), using the volume of fluid (VoF) method, modeled the sloshing-induced free surface flow. Hydrodynamic loads were calculated on the tower's emergency pipe and on its two discharge pipes with FSI simulations and compared to loads obtained from calculations with Morison's equation. Generally, forces based on Morison's equation compared favorably to URANS simulated forces acting on the tower's main members. The tower's response loads were filtered to quantify the influence of its hydroelasticity, which was notable for regular and minor for irregular tank motions. Prevailing hydroelastic effects demonstrated the necessity of FSI simulations. • Notable influence of tower's hydroelasticity on the tower's response loads for regular sway motions of LNG tanks. • Less notable influence of tower's hydroelasticity on the tower's response loads for regular roll motions of LNG tanks. • Minor influence of tower's hydroelasticity on the tower's response loads for irregular motions of LNG tanks. • Morison's equation provided initial estimates of sloshing-induced loads on the tower's main pipes. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Monopiles are commonly adopted in marine structures and subject to combined loading from waves and currents. The nature of superposition of wave and current loads needs to be known during the design stage. In the present paper, combined hydrodynamic loading induced by nonlinear waves and uniform currents on a cylinder is experimentally investigated. The current is represented by towing the cylinder along the flume. By this, nonlinear wave–current interactions are excluded physically, but the loading of a proportional current following or opposing a wave group is captured and analyzed. It is argued that towing makes provision for analyzing the nature of superposition of wave and current loads using Morison theory (which is not applicable to true combined wave–current fields) and also facilitates experimentation of a wide range of nonlinear wave and uniform current loading combinations onto the structure. Accordingly, regular, steep non-breaking and breaking focused waves interacting with the cylinder towed along and in opposition to the wave-field at different speeds have been investigated. The non-breaking wave–structure interactions have been analyzed within the framework of Morison theory using Fully Nonlinear Potential Theory (FNPT) based kinematics. Breaking wave–cylinder interactions have been analyzed through a spectral approach. The experiments demonstrate that wave and locally-acting current loads on the structure can be linearly superimposed, irrespective of the nature of waves and towing speed. Hence, provided wave–current interactions are excluded, steep breaking wave and uniform current loads can be linearly superimposed, despite focused wave generation itself being inherently nonlinear. • Experimental study on combined nonlinear waves and uniform current load on monopile. • Applicability of Morison theory for nonlinear wave–current interactions load. • New experiments on regular, focused and breaking waves with cylinder towed along and in opposition to waves. • Non-breaking wave–local current loads linearly superpose as per Morison theory. • Linear superposition of breaking wave–current loads at impact demonstrated from experiments. [ABSTRACT FROM AUTHOR]

The Morison equation is widely used to estimate the loads by surface waves on cylinders. The formulation and coefficients determination method of the original work by Morison et al. are revisited, it is found that there exist some issues yet to be explained, e.g., the larger uncertainties in drag coefficient and the underestimated maximum moments. Numerical simulation with a similar configuration is used to reproduce these issues and the results help discover the reason and mechanism for these phenomena. The analysis shows that the larger uncertainties in drag coefficient are caused by the introduction of linear wave theory, which is used to derive the velocity and acceleration at cylinder location as direct measurements are not available. The results also show that the underestimation of maximum moments is induced by the wave run-up process, which is neglected in the Morison equation. The scale of wave run-up is approximately the length of cylinder diameter. The results indicate although most recent studies are focusing on the high-frequency loads on cylinders by nonlinear waves, there still exist some issues to be resolved in the linear wave regime. Further studies are required to parameterize the additional loads by wave run-up to strengthen the robustness of the Morison equation. [ABSTRACT FROM AUTHOR]

A prediction method, based on the Morison equation as well as Froude-Krylov formula, is presented to simulate the loads acting on the columns and caissons of the semi-submersible platform induced by Internal Solitary Wave (ISW) respectively. Combined with the experimental results, empirical formulas of the drag and inertia coefficients in Morison equation can be determined as a function of the Keulegan–Carpenter (KC) number, Reynolds number (Re) and upper layer depth h1/h respectively. The experimental and calculated results are compared. And a good agreement is observed, which proves that the present prediction method can be used for analyzing the ISW-forces on the semi-submersible platform. Moreover, the results also demonstrate the layer thickness ratio has a significant effect upon the maximum horizontal forces on the columns and caissons, but both minimum horizontal and vertical forces are scarcely affected. In addition, the incoming wave directions may also contribute greatly to the values of horizontal forces exerted on the caissons, which can be ignored in the vertical force analysis.

This paper presents a comparative numerical study on liquefied natural gas (LNG) pump tower loads, while focusing on two aspects. First, are impact loads relevant for the structural design of LNG pump towers and, second, in which way does fluid-structure interaction influence these loads? Numerical simulations of the multiphase problem were conducted using viscous field methods. First, unsteady Reynolds-averaged Navier-Stokes (URANS) equations, extended by the volume of fluid (VoF) approach, were used to simulate, at model scale, the flow inside a three-dimensional LNG tank without the tower structure. Then, these results were used to validate the numerical method against model test measurements. Afterward, motion periods and amplitudes were systematically varied in the flow simulations. Flow velocities and accelerations along the positions of the main structural members of the pump tower were extracted and used as input data for load approximations based on the Morison equation. Finally, these load approximations were compared with loads determined from solving the delayed detached eddy simulation (DDES). Time histories as well as statistical measures of global loads acting on the entire and the simplified tower structure were of the same order of magnitude. However, their time evolution differed, especially at their peaks, and this was considered significant for structural design. [ABSTRACT FROM AUTHOR]

Copyright of Experimental Technology & Management is the property of Experimental Technology & Management Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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 different k — ω turbulence 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 — ω turbulence model and Shear-Stress Transport (SST) k — ω turbulence 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 k — ω turbulence model performs better in predicting wave run-up for water depth 0.42 m, while the laminar model and standard k — ω model perform better at water depth 0.52 m and 0.62 m, respectively. [ABSTRACT FROM AUTHOR]

The article presents the results of the research conducted within the framework of the project entitled WIND-TU-PLA (ERA-NET, MARTEC II), the general aim of which was to design and analyse supporting structures for wind turbines intended for operation on the South Baltic area. The research part described in the article aimed at developing a preliminary design for a jack-up platform which can operate on water areas with depth of 40 m. The main task was to determine optimal dimensions of platform legs and the radius of their spacing. Two jack-up platform concepts differing by spacing radius and hull dimensions were designed with the intention to be used as a supporting structure for a 6-MW offshore wind turbine. For each concept, the parametric analysis was performed to determine optimal dimensions of platform legs (diameter Dleg and plating thickness tleg). Relevant calculations were performed to assess the movements of the platform with parameters given in Table 1 in conditions simulating the action of the most violent storm in recent 50 years. The obtained results, having the form of amplitudes of selected physical quantities, are shown in comprehensive charts in Fig. 6 and 7. Based on the critical stress values (corresponding to the yield stress), the area was defined in which the impact strength conditions are satisfied (Fig. 14).

Comparative hydrodynamic loads caused by a focused wave acting on differently sized slender vertical cylinders placed in a wave canal were predicted at model scale using an unsteady Reynolds-averaged Navier–Stokes (URANS) solver and the Morison equation. This paper focused, first, on wake effects that need to be considered for the structural design of tripod configurations and, second, on the influence of these wake effects on wave-induced loads. For the Morison approach, flow velocities were gathered at incremental representative locations along the length of the cylinders, whereby the use of a central differencing approach obtained the associated flow accelerations. A first scenario dealt with a small- and a large-diameter cylinder, implemented individually at two immersion depths. A second scenario considered medium- and large-diameter cylinders arranged in a tripod configuration, where the upstream and downstream cylinders had the same diameter. For the single cylinder, impact loads obtained by both methods compared favorably to experimental measurements. For the tripod configuration, however, impact loads obtained by both methods differed due to the influence of wake effects. Thus, it was necessary to determine the influence of wake effects to assess the structural integrity of tripod configurations.

In order to ensure the safety of the cooling water source of coastal nuclear power plants (NPP), trash-blocking nets (TBNs) are usually installed at the entrance of the penstock to prevent marine sewage and organisms flowing into the front pool of the pump house of the nuclear power plant. The safety evaluation of these trash-blocking nets is of paramount importance for the stable operation of a nuclear power plant. However, there is no reliable analysis method for improving the design of trash-blocking nets and mooring systems. In this study, a numerical model of in-current trash-blocking nets based on the lumped mass method was developed to calculate the tension force on the trash-blocking nets and mooring system. A comparison with the experimental data indicates that the present numerical model is appropriate for calculating the in-current hydrodynamic loads on the trash-blocking nets. In addition, the effects of the width of trash-blocking nets, hanging ratio, water depth, and net solidity are discussed in detail, and the damage process of trash-blocking nets was also investigated. The results indicate that the maximum tension force on the trash-blocking net linearly increases with the increasing width of trash-blocking nets, and it is greatly decreased with the increase in the horizontal hanging ratio of trash-blocking nets. It can be increased by 200% when the net solidity is increased from 0.16 to 0.6. Two damage modes for mooring lines can be observed, which are determined by the strength of mooring lines.

The Morison equation is widely used to estimate the loads by surface waves on cylinders. The formulation and coefficients determination method of the original work by Morison et al. are revisited, it is found that there exist some issues yet to be explained, e.g., the larger uncertainties in drag coefficient and the underestimated maximum moments. Numerical simulation with a similar configuration is used to reproduce these issues and the results help discover the reason and mechanism for these phenomena. The analysis shows that the larger uncertainties in drag coefficient are caused by the introduction of linear wave theory, which is used to derive the velocity and acceleration at cylinder location as direct measurements are not available. The results also show that the underestimation of maximum moments is induced by the wave run-up process, which is neglected in the Morison equation. The scale of wave run-up is approximately the length of cylinder diameter. The results indicate although most recent studies are focusing on the high-frequency loads on cylinders by nonlinear waves, there still exist some issues to be resolved in the linear wave regime. Further studies are required to parameterize the additional loads by wave run-up to strengthen the robustness of the Morison equation.

In this article, a numerical model based on the Morison equation and lump-mass method is developed to simulate the failure of an aquaculture net cage system, by changing an upstream anchor from a fixed node to a free node. Current-only and wave-current conditions are employed to investigate the mooring line tension and volume reduction coefficient of a net cage after a failure. The results show that both mooring line tension and volume reduction coefficient increase after a failure. The failure causes the cage system to drift downstream and move aside. Remaining mooring lines twist to rotate and deform the net cage. The maximum mooring line tension for the current-only cases increases with the current speed. However, the tension ratio only increases up to some certain value, i.e., 1.91 instead of 2. Beyond this, the cage system is completely collapsed resulting in a smaller minimum volume reduction coefficient compared to its counterpart under the normal state. When examined under wave-current conditions, the cage system exhibits oscillatory motion, and a large excitation of the mooring line tension is induced. The corresponding minimum volume reduction coefficient is larger than under the normal state, due to the twisting deformation of the net cage. Different instances of failure time are also examined. It is found that the results at later times (steady-state region), including the mooring line tension, the volume reduction coefficient, and the body motion of the floating collar, are not affected by the failure time. Different wave heights, wave periods, and current speeds are also simulated. The results show that the tension ratio increases with the wave height and the current speed but it decreases with the wave period. [ABSTRACT FROM AUTHOR]

Copyright of Engineering Mechanics / Gongcheng Lixue is the property of Engineering Mechanics Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Offshore structures such as jacket platforms have anodes fitted on their steel structural members to prevent corrosion. The anodes are projections on the surface of a tubular structural member and they increase the hydrodynamic forces and hydrodynamic coefficients of the tubular member. The effect of anodes on hydrodynamic forces and coefficients depends on several factors. The industrial practice to account for this effect is to multiply the total hydrodynamic force by a global factor, which may be conservative and uneconomical. The objective of this particular study is to determine the effect of location and orientation of anodes on wave loads and hydrodynamic coefficients of a cylinder, which have not been studied extensively to the authors' best knowledge. The hydrodynamic forces and coefficients on a bare cylinder and a cylinder fitted with anodes were studied for regular waves of Keulegan-Carpenter (KC) number ranging from 0.42 to 1.91 in this experimental investigation. [ABSTRACT FROM AUTHOR]

Under the action of earthquake, the dynamic interaction between the bridge pier and the surrounding water has a great impact on the dynamic response of the bridge structure. With a continuous sea-crossing beam bridge as an example, this paper studied the stochastic optimization of the parameters of nonlinear viscous damper and its damping performance under the fluid-solid coupling effect of waves and piers. In this study, a 2-degree-offreedom bridge analysis model considering the fluid-solid coupling effect was constructed, and a nonlinear viscous damper was set in the model and subject to equivalent linearization according to the equivalent energy consumption criterion. Then on this basis, with minimizing the variance of the displacement of pier top as the target, this study applied the Lyapunov method to optimize the parameters of the damper, and explored its impact on the seismic response of the bridge and the damping performance considering the fluid-solid coupling effect. The research results showed that the fluid-solid coupling effect changed the dynamic characteristics of the bridge and increased its seismic response, and the viscous damper can effectively reduce the seismic response of the sea-crossing bridge and improve its damping performance. [ABSTRACT FROM AUTHOR]

Utilizing a numerical simulation method to investigate the hydrodynamic response of the semi-submersible aquaculture platform in waves provides guidance for the design and optimization to ensure the stability and structural safety of the aquaculture platform in the open sea. Combining diffraction theory and Morison equation, the present study focuses on the semi-submersible aquaculture platforms to investigate the influence of draught, wave period and linear elasticity coefficient on the hydrodynamic response of semi-submersible aquaculture platforms in regular waves. The findings indicate that the combined effect of draught and wave period causes two or three peaks in the mooring force and motion response of the aquaculture platform, and a valley occurs in large draught and short period conditions. Additionally, increasing the draught can effectively mitigate the mooring force and motion response of the semi-submersible aquaculture platform in large wave height conditions. As for the mooring elastic coefficient, increasing the elastic coefficient does not significantly weaken the mooring force and motion response of the aquaculture platform. Conversely, the semi-submersible aquaculture platform reaches a peak in a high elastic coefficient and minor draught, and attains a valley value in large draught conditions. Taking into account the combined impact of the two factors of draught and wave period, wave height and elastic coefficient on the dynamic response of the aquaculture platform can more comprehensively reflect the changing of the mooring force and motion response of the aquaculture platform, and provide a reference for site selection and structural optimization, which has great practical engineering significance. • Diffraction theory and Morison equation are applied to study dynamic of aquaculture platform in waves. • The influence of draught on the dynamic response of semi-submersible platform has been thoroughly studied. • Considering the draught and wave period can better reflect the hydrodynamic of aquaculture platform. [ABSTRACT FROM AUTHOR]

Flexible single-link underwater manipulator (FSLUM) can be installed in autonomous underwater vehicles, it can carry out underwater tasks such as offshore oil and gas exploration, underwater cable maintenance as well as fishery farming and fishing. The design and development of the FSLUM are of great significance for ocean exploration and development. The FSLUM is affected by the underwater interference torque during underwater tasks in the flowing water environment, which will greatly affect the operational accuracy. In addition, many nonlinear factors such as the flexibility of the transmission system and the two-dimensional deformation of flexible links will aggravate the control difficulty of the FSLUM. An improved sliding mode control (SMC) strategy based on neural network identification is proposed to enhance the FSLUM's control accuracy. Neural networks are proposed to identify uncertain components including underwater interference and flexible nonlinear terms, so as to advance the control law design accuracy. Firstly, the FSLUM dynamic equations coupled with underwater interference torque considering multiple nonlinear factors are established according to the assumed mode method (AMM). A modified Morison equation is proposed to abbreviate the underwater interference torque in flowing water environments. Next, the control law of improved neural network sliding mode control (NNSMC) strategies are proposed according to the Lyapunov stability theorem, so as to ensure closed-loop stability of the FSLUM. Finally, the results of simulation and prototype tracking control experiments show that the improved NNSMC strategy has high tracking accuracy. • A modified Morison equation is proposed to accurately calculate underwater torque. • The dynamic modeling considers transmission flexibility, two-dimensional deformation and flowing underwater torque. • The RBF neural network is suggested to accurately compensate for underwater torque in varying water flows. • The NNSMC strategy control law is enhanced by replacing the step function with a hyperbolic tangent function. [ABSTRACT FROM AUTHOR]

Under the action of earthquakes, the dynamic responses of cross-sea bridges are greatly influenced by the dynamic interaction between each pier and the surrounding water. Based on Morison equation, this paper mainly explores the responses of a continuous girder cross-sea bridge in uncontrolled and semi-active control modes, under the combined effect of earthquake and hydrodynamic pressure. First, a simplified two-degree-of-freedom (2DOF) analysis model was constructed for the bridge: the combined stiffness was proposed to reflect the effects of the bending and shear deformation features of the pier; the pier mass was aggregated on the top of the pier as the additional pier mass, using the shape function of linear deformation; the hydrodynamic pressure distributed on the pier was calculated by the Morison equation, converted into the equivalent node load on the top of the pier, and further transformed into the additional hydrodynamic mass. Then, a magnetorheological (MR) damper was added between the pier and the girder. The semi-active algorithm of the MR damper was designed based on the clipped-optimal control algorithm. The control force of the MR damper was optimized by the H2/LQG active control method. The results show that the hydrodynamic pressure changes the dynamic features of the bridge and increases the seismic responses of the bridge, calling for a stronger control force for semi-active control; the impact of hydrodynamic pressure must be considered in the seismic design of cross-sea bridges; the MR semi-active control can effectively suppress the dynamic responses of cross-sea bridges, enhancing the seismic safety of the bridge. The research results provide new insights into the vibration control of cross-sea bridges. [ABSTRACT FROM AUTHOR]

This paper presents the effect of mooring diameters, fairlead slopes and pretensions on the dynamic responses of a truss spar platform in intact and damaged line conditions. The platform is modelled as a rigid body with three degrees-of-freedom and its motions are analysed in time-domain using the implicit Newmark Beta technique. The mooring restoring force-excursion relationship is evaluated using quasi-static approach. MATLAB codes DATSpar and QSAML, are developed to compute the dynamic responses of truss spar platform and to determine the mooring system stiffness. To eliminate the conventional trial and error approach in the mooring system design, a numerical tool is also developed and described in this paper for optimising the mooring configuration. It has a graphical user interface and includes regrouping particle swarm optimisation technique combined with DATSpar and QSAML. A case study of truss spar platform with ten mooring lines is analysed using this numerical tool. The results show that optimum mooring system design benefits the oil and gas industry to economise the project cost in terms of material, weight, structural load onto the platform as well as manpower requirements. This tool is useful especially for the preliminary design of truss spar platforms and its mooring system. [ABSTRACT FROM AUTHOR]

The substructure of cross-sea bridge has its unique structural form, the calculation of drag force is related to working, designing, constructing and maintaining of the bridge in the marine environment. So in order to guarantee the construction and use safely, accurate and convenient calculation method of drag force is necessary. The calculation method of drag force theory is studied in this paper, with using shear stress transport model to set up eddy viscosity model, which is adopted to establish the numerical water tank and analysis the whole process of eddy generation and shedding in the wake area. Considering the features of cross-sea bridge substructure, the effect of the flow velocity, the depth of water and the section form of pier on the drag force is researched. The difference between the superposition method and integral calculation method, which are used for calculating the drag force of group pile cap composite structure, is studied. The results show that the water flow velocity is square relation with the drag force, and the depth of water is linear relation with the drag force. The drag coefficient CD of round-ended pier is 1.35, which is between the values of circular pier and rectangular pier. Due to the shield and interference with each component, the drag force calculated by integral method is less than the other one, and the lift force can be considered in the integral method. [ABSTRACT FROM AUTHOR]

Copyright of China Petroleum Machinery is the property of China Petroleum Machinery Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The support structure being the object of the analysis presented in the article is Tripod. According to the adopted assumptions, it is a foundation gravitationally set in the water region of 60 m in depth, not fixed to the seabed, which can be used for installing a 7MW wind turbine. Due to the lack of substantial information on designing and strength calculations of such types of structures in the world literature, authors have made an attempt to solve this problem within the framework of the abovementioned project. In the performed calculations all basic loads acting on the structure were taken into account, including: the self mass of the structure, the masses of the ballast, the tower and the turbine, as well as hydrostatic forces, and aero- and hydrodynamic forces acting on the entire object in extreme operating conditions.

A concrete gravity base structure may not be suitable for offshore weak soil because of its heavy weight. Therefore, a conceptual model for a concrete offshore wind turbine structure suitable for weak soils is proposed. The proposed model is composed of a prestressed concrete (PSC) supported by a pile foundation. For a three-dimensional analysis of the large concrete structure, wave pressures based on the diffraction wave theory are developed using a three-dimensional solid finite element method. Static and dynamic analyses were performed to achieve the conceptual model of a PSC structure subjected to ocean environmental loads and a 5-MW turbine load on southwest coast in Korea. From the analysis, the maximum displacement and stresses of the proposed model did not exceed the allowable values from design standard, and the first mode of natural frequency of the structure was in a safe range to avoid resonance. The proposed model has enough structural stability to withstand external loads, and it is expected to be used in locations suitable for concrete gravity structures. [ABSTRACT FROM AUTHOR]

Motivated by the design of a protective anti-shark cable net enclosure located in heavy surf on La Réunion, France, this paper presents a modeling technique for underwater cable structures subject to breaking wave action. Such modeling capability is not offered in leading commercial software. Forces on underwater cable structures are frequently modeled using the well-established Morison equation. These forces are functions of the fluid velocity and acceleration, which are normally calculated using an appropriate wave theory. Such an approach works well in many applications, but it does not permit the modeling the effects of breaking waves. However, considering the absence of wave impact loads on submerged structures, the Morison equation is still valid provided that a suitable hydrodynamic time history is available. In the presented work, the Morison equation is coupled with a high-resolution breaking wave simulation obtained by solving the full air-water Navier-Stokes equations, creating a time-domain analysis approach suitable for studying underwater cable structures subject to breaking waves. The hydrodynamic model is validated using the software package ProteusDS, and the presented model is used to characterize the mechanical response of a moored cable net. This research is of relevance to the analysis and design of submerged cable structures. [ABSTRACT FROM AUTHOR]