Surge Motion Research Articles

Aerodynamic damping of a semi-submersible floating wind turbine: An analytical, numerical and experimental study

Aerodynamic damping of floating wind turbines (FWTs) plays a dominant role in suppressing the vibration of the tower and blades and the platform motions. Although much effort has been paid to investigating the aerodynamic damping of FWTs, their characteristics and influential factors have not been studied thoroughly. In the present study, the aerodynamic damping of a semi-submersible FWT is investigated by a frequency-domain analytical method and a fully coupled decay-based time-domain method, which are validated against the wave basin model tests. Effects of controller dynamics are discussed, and then the dynamic characteristics of aerodynamic damping in surge and pitch motion are addressed. It is found that the proposed analytical method can predict the aerodynamic damping with enough accuracy and extremely high efficiency compared to the time-domain numerical method. The effects of controller dynamics should be considered in the over-rated wind speed region, especially pitch motion. Controller gains can significantly affect the aerodynamic damping in pitch motion in the over-rated wind speed region. In contrast, the initial offset and wind turbulence may not be the main influential factors. The outcomes of the present study can provide insight into the aerodynamic damping and the controller design of FWTs.

Numerical modelling of wave run-up heights and loads on multi-degree-of-freedom buoy wave energy converters

With the development of wave energy converters (WECs), multi-degree-of-freedom (multi-DOF) buoy has become popular. The effect of nonlinear phenomena, such as wave run-up and wave impact, on an oscillating buoy WEC, may decrease its efficiency and even lead to overturning, plastic deformation, and fatigue failure. This study used a Fortran code for the custom development of Flow-3D software to apply independent power take-off (PTO) damping to each DOF. A hydrodynamic simulation model of the interaction between a wave and cylindrical buoy under six types of motions was developed and verified through model tests of the motion response of the buoy and wave run-up on it. Wave run-up heights and maximum wave loads on buoys with different motions and PTO combinations were investigated and compared. The numerical results show that coupled motion can lead to a less intense wave field distribution than a single motion and reduce the risk of overtopping. In addition, the bottom pressure of the buoy for the pitch–surge motion increased by a maximum of 101.6 % compared to the initial pressure. For independent linear PTO damping, heave damping has the most significant influence on the maximum wave load on the coupled motion buoys, followed by surge damping, while pitch damping has no significant effect. The results of this study can guide the designing of safe and reliable multi-DOF buoy WECs.

Station keeping of a subsea shuttle tanker system under extreme current during offloading

ABSTRACT This paper presents the station keeping challenge of the subsea shuttle tanker (SST) design during underwater loading and offloading at a subsea well under an extreme current environment. The paper investigates the movement of the SST during offloading with extreme current speeds, i.e. above 1.6 m/s, in the surge, heave and pitch motions, respectively. A linear quadratic regulator (LQR) is used for SST motion control. The LQR’s primary focus is to achieve the target for the SST during the offloading process. Then, the average exceedance rate method is used to predict the maximum and minimum potential depth excursion. This extreme value prediction result will serve as a basis for obtaining a cost-efficient design of the subsea shuttle tanker and provide recommendations for the decision-makers upon SST operation.

Nonlinear inviscid aerodynamics of a wind turbine rotor in surge, sway, and yaw motions using a free-wake panel method

Abstract. We investigate the aerodynamics of a surging, heaving, and yawing wind turbine with numerical simulations based on a free-wake panel method. We focus on the UNAFLOW (UNsteady Aerodynamics of FLOating Wind turbines) case: a surging wind turbine which was modeled experimentally and with various numerical methods. Good agreement with experimental data is observed for amplitude and phase of the thrust with surge motion. We achieve numerical results of a wind turbine wake that accurately reproduce experimentally verified effects of surging motion. We then extend our simulations beyond the frequency range of the UNAFLOW experiments and reach results that do not follow a quasi-steady response for surge. Finally, simulations are done with the turbine in yaw and heave motion, and the impact of the wake motion on the blade thrust is examined. Our work seeks to contribute a different method to the pool of results for the UNAFLOW case while extending the analysis to conditions that have not been simulated before and providing insights into nonlinear aerodynamic effects of wind turbine motion.

Experimental and Numerical Studies on Motion Response of Side-by-Side Two Floating Vessels in Waves

In the world of oil and gas, there will definitely be a structure for either the production process, exploration and so on. The structure consists of three types, namely the fixed structure, the floating structure and the moored structure. Floating structures can be the best option in terms of cost and time. Things that can interfere with floating structure when operating are environmental loads. One example of its operation is offloading, it can be offloading side by side or tandem configurations. The main focus of this study is the motion response both when single body and side by side configuration. The result of experimental studies obtained the maximum RAO (Response Amplitude Operator) for heave, surge, and pitch motion modes occurred when the model was configured side by side with a distance of 0.5 from the width. For numerical studies, the maximum RAO of heave motion when single body is 0.69 cm/cm, the maximum RAO of surge motion occurs when side by side configuration with a gap of 10 cm which is 0.71 cm/cm, and the maximum RAO of pitch motion occurs when the model is configured side by side with a gap of 10 cm which is 1.54 rad/rad.

Nonlinear dynamic characteristics analysis of the surge motion of a tender-assisted drilling operation system

ABSTRACT In this study, a numerical analysis is carried out to investigate the coupled behaviour of a TLP (tension leg platform) -TAD (tender-assisted drilling) system under a series of regular waves in surge direction. The numerical model is established in the time domain considering the nonlinear characteristics of the mooring systems and the hydrodynamic interference. After the case validations, the effects of the wave periods and amplitudes on the nonlinear dynamic characteristics of the surge motions are investigated in detail. Then, the observed nonlinear dynamic characteristics are interpreted in detail through the existing theory of phase dynamics. The surge motions of the coupled system can show multiperiod nonlinear characteristics under regular waves in certain wave periods. Three forms of phase dynamic characteristics: phase locking, phase trapping, and phase drifting and slipping are observed in the surge motions of the tender-assisted drilling operation system.

Numerical investigation of the aerodynamic and wake characteristics of a floating twin-rotor wind turbine under surge motion

To elevate the power capacity of floating wind turbines and cut costs, development towards large-scale systems is underway. However, this requires solving the problem of fatigue loading on large, flexible blades, as well as corresponding improvements to production and installation technology. As an alternative to larger turbines, twin-rotor floating wind turbines have been proposed. The aerodynamic and wake interference characteristics of this twin-rotor are not yet well understood. In this study, we have investigated the power and wake characteristics of a twin-rotor floating wind turbine based on unsteady Reynolds-averaged Navier-Stokes turbulence model for a comprehensive analysis. Specifically, the power and wake recovery of a twin-rotor floating horizontal-axis wind turbine (FHAWT) under surge motion are compared in detail with those of a single floating wind turbine and bottom-fixed case, while both the effects of the three wind directions (β = 0°, 45°, 90°) and spacing ratios (S/D = 1.2, 1.375, 1.5) are considered. The results suggest that the mean power of the twin-rotor is enhanced by a maximum of 13% under surge motion compared to the single rotor, the small spacing ratio promotes the power gain. Surge motion plays a significant role in wake interaction between the twin-rotor and facilitates wake recovery. As compared to the baseline case, both power and wake recovery performance of the twin-rotor are boosted at β = 45°, with an increase in power of 12.7% as opposed to the single rotor. The modified Jensen wake model is proposed for the far-wake region and a modified Gaussian wake model is also suggested for different cases. This study can provide affiliated guidance for the application of the twin-rotor floating wind turbine.

Investigation of higher-harmonic wave loads and low-frequency resonance response of floating offshore wind turbine under extreme wave groups

When floating offshore wind turbines (FOWT) encounter extreme waves in operation, it is a highly nonlinear system involving floater motion and extreme wave–structure interactions. The behavior is crucial for floating offshore wind turbine safety. With the aid of a high-fidelity CFD solver, a harmonic separation method through a ‘Stokes-like’ formulation was adopted to obtain the parameters for each harmonic response. The present study focuses on analyzing higher harmonic load, dynamic motion response, and tension load of the mooring line the DeepCwind semi-submersible FOWT. The results show that the higher-harmonic wave load cannot be ignored in the extreme marine environment, the second harmonic can be over 16% of the linear wave load, and the third harmonic can be over 10% of the linear wave load with large wave steepness. The duration of a focused wave crest interaction with the platform is a short process of only 1.4 s in model scale, corresponding to about 10 s for the prototype. The wave runup at the upstream column is larger than the other columns, and the flow velocity is double that of the wave without the floater in presence. The dynamic response of the floater contains two phases, ’forced oscillations’ is identified to be drag-driven from odd harmonics, and ’free decay’ mainly comes from second-order difference-frequency influence from even harmonics. The properly normalized wave forces of surge and heave motion are not influenced by steepness kpAlinear. For surge motion, the total motion mainly comes from the nonlinear low frequency component. For pitch motion, the linear response is dominant in small kpAlinear. When the steepness kpAlinear increases gradually, the second-order low-frequency response of pitch motion will increase rapidly and dominate the total response.

Dynamic response analysis of a floating vertical axis wind turbine with helical blades based on the model test

The helical type floating wind turbine can be a promising choice to harvest offshore wind energy because it has the merits of straight blade floating VAWTs and could reduce the aerodynamic torque fluctuations. In this study, the wave basin model tests for a 5 MW helical type floating wind turbine were carried out, and the dynamic response behaviors are specifically discussed. In general, the motions of the floating foundation obey the regularity that aerodynamic loads mainly affect the average value while hydrodynamic loads affect the standard deviation. For the mooring system, the tensile forces are dominated by the floating foundation motions as well as the stiffness behavior of the mooring lines. Furthermore, the comparative study is conducted with the numerical results of a floating HAWT. It is found that the standard deviations of heave and pitch motions of the helical type floating wind turbine are slightly smaller than those of floating HAWT, while the standard deviations of surge and yaw motions are larger. As to the mooring system, the tensile force of mooring line 1 of helical type floating wind turbine is smaller than that of floating HAWT, while the tensile forces of mooring lines 2 and 3 are larger.

Adaptive Backstepping Axial Position Tracking Control of Autonomous Undersea Vehicles with Deferred Output Constraint

In this paper, an adaptive backstepping control scheme is proposed to solve the the surge motion tracking control problem of an autonomous undersea vehicle (AUV) with system constraint. First, an initial rectification reference signal is constructed for the subsequent implementation of deferred output constraint and making the control input smaller and smoother in the early stage of system operation. Second, a barrier Lyapunov function is adopted for developing an output-constrained state feedback adaptive controller. Then, on the basis of coordinate transformation and estimating the derivative of surge displacement by a linear and nonlinear combined differentiator, we develop an output feedback adaptive backstepping control scheme for AUVs whose velocity signals are unmeasurable. We also carried out a comparative numerical simulation with traditional adaptive control to verify the feasibility of the proposed control strategy.

Application of simple harmonic motion theory to the prediction of floating wind turbine first order motions

An alternative solution for achieving a high stability floating foundation for supporting large horizontal axis wind turbines is compared against current floating offshore wind solutions. The testing of a 1:36th scale model of the solution, called Starfloat, in the wind/wave basin of the Cantabria Coastal and Ocean Basin, Santander and the design of this physical model, including scaling issues, is discussed. A method for calculating the added mass of entrained water in heave and surge and the added mass moment of inertia in pitch for semi-submerged cylindrical columns is presented and the computed natural periods of motion are compared against physical trial measurements obtained from motion decay tests. The wave forces exciting the simple harmonic motion are calculated and the resultant approximate solution for the uncoupled floating platform motions in heave, pitch and surge are compared against response amplitude operator curves obtained from the physical model trials, showing reasonable correlation. The importance of depth correction for wave particle velocities and accelerations is very evident and emphasises the need for physical models to be exposed to the correct orbital particle motions over the water column if measured pitch and surge motions are to be a realistic representation of full scale performance.

Coupled dynamic analysis of horizontal axis floating offshore wind turbines with a spar buoy floater

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.

Nonlinear dynamics of an aquaculture cage array induced by wave-structure interactions

Computer simulations were conducted to understand the nonlinear dynamics of the cage array to establish an offshore fish farm capable of surviving the severe conditions. To that end, a large fish farm containing 16 net cages in a 2 × 8 configuration was modeled based on the lumped mass model. This numerical model was verified against the physical model tests regarding a single net cage and a net cage array. In particular, three different equivalent mesh groups were compared to each other to balance the numerical accuracy and the computational efficiency. Then, the candidate equivalent mesh group was used to separately model the rigid and the flexible cage arrays subjected to severe conditions. The results show that most trajectory patterns of mooring lines are not as elliptical as the water particle trajectories. This provides evidence to justify the perturbations about the equilibrium of the mooring grid for the full-scale aquaculture cage array system. Alongside this, flexible cages with lower bending stiffness have greater tension forces on the weather side. The bending stiffness has a predominant effect on the surge motion and is also the leading contributor to the nonlinearity of cage motion. The flexible cage with lower bending stiffness is appropriate for more exposed, open ocean fish farming applications, but the increased mooring tension should be taken into account for future design consideration.

Experimental Study on Vortex-Induced Vibration of Tension Leg and Riser for Full Depth Mooring Tension Leg Platform

According to the geometric parameters of the tension leg platform, the test model was made with a scale ratio of 1:61. The model was used to conduct the full-depth simulation test of uniform flow and wave current combination in the test pool. The model test results showed that when the reduced speed was between 5.5 and 8.5, and the lateral motion response of the platform was the most significant. In the interval of the reduced speed, the response frequency of transverse vortex-induced motion was close to the natural transverse frequency of the platform, and resonance occurred. The amplitude of surge motion increased with the increase of reduced speed. Due to the pull of the floating body, the tension of tension legs and risers increased with the flow rate but did not increase significantly in the floating body lock zone. The mooring tension had a certain limiting effect on the floating body sway. The displacement modes of tension legs and risers were greatly affected by the flow velocity. With the flow velocity increasing, the mode order increased. In addition, the increase in tension caused by the large displacement of the floating body had a certain impact on the displacement amplitude. The wave could reduce the sway of the floating body and strengthen the surge. Therefore, under the combined action of wave and current, the tension amplitude of the tension leg and riser was increased compared with that under the uniform flow. The conclusions obtained in this paper could be used for reference in the engineering design of tension legs and risers.

Analysis of a Moored and Articulated Multibody Offshore System in Steep Waves

Abstract Wave-induced motions and loads on a moored and articulated multibody offshore structure are numerically analyzed, where a coupled mooring–joint–viscous flow solver is used to count for mooring dynamics, joint restrictions, nonlinear rigid body motions, and viscous flow effects. The considered concepts consist of two modular floating structures (MFSs) connected by two types of connections, namely, a rigid joint and a flexible joint, and positioned by four symmetrical catenary mooring lines. The analyzed responses comprised multibody motions as well as associated forces acting in the hinged joints and the mooring lines. Results indicate that surge motions of articulated bodies are almost identical to each other, whereas the effects of the joint on heave motions are not pronounced. However, highly dynamic pitch motions between two hinged MFSs are observed. Apart from motion responses, forces acting on the hinged joint and the mooring lines are estimated. The importance of wave nonlinearity and higher order components is identified by studying waves with different steepness. The coupled mooring–joint–viscous flow solver demonstrates its capability to predict wave-induced motions and loads on a moored multibody offshore structure articulated by various types of joints.

Nonlinear dynamic analysis of aquaculture platforms in irregular waves based on Hilbert–Huang​ transform

This study aimed to examine the nonlinear dynamics of aquaculture platforms using the Hilbert–Huang transform (HHT). First, a numerical model that couples the boundary element method and lumped-mass model was used to simulate the dynamic behavior of a multi-body floating aquaculture platform in irregular waves. Second, a time–frequency analysis method based on the HHT was used to analyze the dynamic responses, including motion and mooring force responses. The results highlight that the surge motion of the net cage is dominated by the low-frequency components, whereas the heave and pitch motions are dominated by the wave-frequency components. The pitch response of the net cage has an obvious energy concentration near the peak frequency region of the incident wave. The surge motion of the net cage in the middle of the platform has a greater response to wave components with lower frequencies than that of the other two cages. The inherent characteristic vibration form of the mooring force response is affected by both the low-frequency characteristic of surge motion and the wave-frequency characteristic of motions in the vertical plane. The amplitudes of the wave-frequency components of the mooring force are much larger than those of the low-frequency components, which is like the characteristics of heave and pitch motions. The gravity periods of the wave-frequency mode components of the mooring force response were very close to the gravity period of the surge motion.

Stabilization of the Wind Turbine Floating Platform using Mooring Actuation

In this study, a wind turbine spar-buoy floating platform is modeled in the Control-oriented, Reconfigurable, and Acausal Floating Turbine Simulator (CRAFTS), a comprehensive wind turbine simulation tool being developed by the authors, to investigate mooring actuation for stabilizing the surge and pitch motions. The model is validated against the industrial-standard simulator OpenFAST. A reduced-order model of the platform is developed using a mass-spring-damper system (M-K-C system), and the system parameters are estimated. Optimal LQR control gains are obtained for the reduced-order model, and the required actuation forces are calculated using these gains. A control allocation matrix is used to represent the relation between the necessary cable tensions and the required actuation forces from the control system. The performance of the mooring actuation is tested under various load cases: initial perturbations and different sea state conditions with irregular waves. Simulation results demonstrate that surge motion is significantly reduced with moderate changes in cable lengths in both load cases while controlling pitch motion requires higher changes in cable length and is challenging to control under irregular wave conditions.

Initial-Rectification Neuroadaptive Finite-Time Surge Motion Tracking Control of Autonomous Underwater Vehicle With Input Saturation

Initial-Rectification Neuroadaptive Finite-Time Surge Motion Tracking Control of Autonomous Underwater Vehicle With Input Saturation

Motion-inhibition control of a multi-robot mooring system using an actuating force fuzzy control method

The multi-robot mooring system (MRMS) composed of robots and a moored ship has characteristics of strong fluid-structure coupling, high nonlinear, complex disturbance, and difficulty in establishing models accurately. Thus, the conventional model-based control method is difficult to be implemented for motion-inhibition control. In the paper, the displacement gain coefficient and velocity gain coefficient of the local feedback PD control law are defined as the actuating restoring force (ARF) coefficient and the actuating damping force (ADF) coefficient, respectively, and a local feedback PD motion-inhibition control law is given. Then a mapping relationship from moored-ship motions to the ARF and ADF coefficients is developed using a maximum normalized deviation index and fuzzy reasoning logic, and an actuating force fuzzy control (AFFC) method is proposed. An optimization approach is proposed to solve the problem that too many fuzzy control parameters are not easy to adjust. An MRMS composed of a ship model (266000 m3 LNG ship of 1:60 scale) and a dual parallel elastic underactuated mooring robot is used to conduct experiments in terms of different motion-inhibition control methods. The results show that the proposed method can effectively inhibit the surge, sway, and yaw motions of the ship under different wave directions.

Analytical modelling of ship bottom grounding considering combined surge and heave motions

This paper provides a new contribution to the analytical treatment of ship grounding accidents. New formulations are proposed to assess the resisting force of outer/inner bottom plating and transverse floors when the vessel undergoes combined surge and heave motions during the grounding event. Considering shallow and sharp rocks described by parabolic functions, analytical solutions are derived from plastic limit analysis and validated by comparison to non-linear finite element simulations. A failure criterion is also proposed to trigger the rupture of the bottom plating and all the derived closed-form expressions are implemented into an in-house solver. The solver is then coupled to a 6-DOFs external dynamics program, which allows to account for the action of the surrounding water. Resulting tool is first validated on a full scale cruise ship by comparison to finite element results. It appears than although some discrepancies arise, especially in the response of transverse floors after rupture, the bottom damage distribution seems to be well predicted. Finally, the developed tool is used to quickly predict the grounding response of different types of ships and the influence of their mass and hydrodynamic properties on the damage extent is investigated.