Pitch Response Amplitude Operators Research Articles

Numerical study for nonlinear hydrodynamic coefficients of an asymmetric wave energy converter

In this study, the nonlinear dynamic behavior of an asymmetric Wave Energy Converter (WEC) was studied on a 1/11-scale model based on a numerical and experimental method in a regular wave field. The numerical analysis involved both frequency-domain and time-domain solutions. The frequency-domain solution was based on linear potential flow theory using the WAMIT® model whereas the time-domain solution was based on the Reynolds-Averaged Navier-Stokes (RANS) equation using the OpenFOAM® model. The pitch response amplitude operators obtained from the numerical results were compared with experimental data. Additionally, the nonlinear dynamic behavior of the asymmetric WEC due to various wave heights and periods obtained through the experiments were compared with the OpenFOAM results. Wave excitation moments and hydrodynamic coefficients based on the linear solution approach were separately obtained for the fixed asymmetric WEC induced by waves and the forced oscillating motion with OpenFOAM. Moreover, frequency-domain solutions based on linear potential flow theory were obtained in order to ascertain the nonlinear effects observed in the OpenFOAM results. It was found that a higher motion amplitude could be attributed to nonlinear hydrodynamic coefficients on the asymmetric WEC calculated by the forced oscillation motion of the RANS-based solution.

Verification and Validation of Computational Fluid Dynamic Simulations of a FOWT Semi-Submersible Under Bichromatic and Random Waves

AbstractIn the present work, an extensive verification and validation study is performed to evaluate the accuracy and credibility for computational fluid dynamic (CFD) simulations of the hydrodynamic responses of a semi-submersible floating offshore wind turbine (FOWT) platform under bichromatic waves and random waves. A dynamic mooring model is coupled with the CFD code to accurately simulate the mooring system. For the bichromatic wave cases, the surge, heave, and pitch response amplitude operators (RAOs) at wave frequencies, mean surge offset and mean surge force of the semi-submersible platform are investigated. The numerical uncertainties of the above metrics are quantified, which are primarily sourced from the discretization uncertainty. For the random wave cases, the surge, heave, and pitch power spectral density (PSD) sums in wave frequency range and low frequency range are validated against the experimental results. The numerical uncertainty derived from the bichromatic wave cases is applied in the validation of the random wave cases. The PSD sums in wave frequency range have achieved the validation within the validation uncertainty. Though the PSD sums in low-frequency range are under-predicted, the results with the utilization of the CFD code agree more with the experimental value than the results from mid-fidelity tools.

Unlocking the Wave's Potential: Dynamic Numeric Simulation Response of Hexagon Buoy and Ring Heave Plate in a Shared Wave Environment

Wave electricity extraction technology in advanced international locations holds to advance. One of the strategies used is a point absorber, which extracts electricity from the response of its system. The essential machine includes a floating buoy and a response management tool referred to as a heave plate. This look discusses the impact of the heave plate's floor location variant at the hydrodynamic parameters of a hexagonal-fashioned buoy (heave and pitch Response Amplitude Operator (RAO), brought mass, and radiation damping). The evaluation changed into performed the usage of the industrial software program ANSYS AQWA. The effects of the evaluation display that the presence of the heave plate at the buoy version affects the RAO values, mainly for the heave and pitch modes. Increasing the ratio of the heave plate's floor location results in a growth withinside the RAO heave price however decreases the RAO pitch price. Additionally, the presence of the heave plate influences the values of brought mass and radiation damping. The maximum ratio of heave plate location effects withinside the maximum brought mass price. This price gradually decreases because the ratio of the heave plate location decreases, and the buoy without a heave plate has the bottom price. This is reversed for the radiation damping price, wherein the best heave plate ratio corresponds to the bottom damping price. The damping price will gradually increase because the heave plate ratio decreases, with the buoy without a heave plate having the best price. The presence of the heave plate in the buoy model influences the RAO values, particularly in the observed motion modes of heave and pitch.

A control technique for hybrid floating offshore wind turbines using oscillating water columns for generated power fluctuation reduction

Abstract The inherent oscillating dynamics of floating offshore wind turbines (FOWTs) might result in undesirable oscillatory behavior in both the system states and the generated power outputs, leading to unwanted effects on critical, extreme, and fatigue loads, and finally to a premature failure of the facility. Therefore, this kind of system should be capable of lessening such undesired effects. In this article, four oscillating water columns (OWC) have been installed within a FOWT barge-type platform. A novel switching control technique has been developed in order to reduce oscillations of the system created by both wind and wave, as well as the fluctuations in the generated power, by adequately regulating the airflow control valves. While the impact of the coupled wind-wave loads has been considered, a set of representative case studies have been taken into account for a range of regular waves and wind speeds. The study relies on the use of response amplitude operators (RAO) that have been pre-processed and evaluated in order to apply the switching control technique. In this sense, the starting time of the switching for below-rated, rated, and above-rated wind speeds have been calculated using the platform’s corresponding pitch RAO. Additionally, the blades’ pitch and generator torque have also been regulated by means of a constant torque variable speed controller to capture maximum energy for below-rated wind speed conditions and to match the rated generator power for rated and above-rated wind speed conditions, respectively. In order to peruse the feasibility and performance of the proposed strategy, a comparison has been carried out between the uncontrolled traditional barge-type platform and the controlled OWCs-based barge FOWT. The results demonstrate that the proposed control approach can effectively and successfully decrease both the oscillations in the system’s modes and the fluctuations in the generated power.

Numerical and experimental study on the influence of a moonpool on motion performance and stability of a drillship

The existence of a moonpool may affect motion characteristics and stability of a drillship. This paper presents numerical and experimental study on the influence of the configuration of a moonpool on the motion performance and stability of a drillship under the condition of a constant displacement. Ship hydrostatics and three-dimensional (3D) potential flow theory are employed to calculate the static stability curves (GZ curves) and motion response amplitude operators (RAOs) of the drillship with conjoined double moonpools, separated double moonpools and single rectangular moonpools, respectively. Numerical model is validated by sea-keeping model tests of the drillship with a conjoined double moonpool carried out in towing tank. It is found that there is a critical heeling angle for the static stability curve of the drillship. The variation of the opening size of the moonpool is found to merely have significant effect on the heave RAOs of the drillship near the piston mode resonance period, while slightly influence on the pitch RAOs near the sloshing mode resonance period. It is demonstrated that smaller or larger openings of the moonpool under a constant displacement can reduce dramatically roll RAOs of the drillship around the natural roll period under bow quartering waves and beam waves, respectively. The coupling effect of roll and heave leading to the heave RAOs decreasing around the natural roll period in beam waves, as well as coupling effect in heave, pitch and roll motion RAOs around the natural roll period in bow quartering waves are observed in the experimental results. The results presented in this study can provide references to the design of the moonpool of a drillship.

Power production of the hybrid Wavestar point absorber mounted around the Hywind spar platform and its dynamic response

This article presents the novel hybrid Wavestar–Hywind concept that combines a floating wind turbine with a number of Wavestar point-absorbers on a shared OC3-Hywind spar platform. The effect of increasing Wavestar number on the wave power production and platform motions has been investigated using both time and frequency domains. Simulations were carried out with the boundary element method using the three-dimensional diffraction/radiation theory, which is employed by the ANSYS AQWA software. Regular Airy wave under different wave periods from 4 to 16 s and constant wave height (1.2 m) was considered as an environmental condition. The results of the response amplitude operator (RAO) motions of the platform show that increasing wave periods cause an increase on the surge, heave, and pitch RAO. Moreover, in higher periods as Wavestar numbers increase, the heave motion decreases, while it does not significantly affect the surge and pitch motions. Due to Wavestar resonance, the maximum capture width ratio occurs in wave periods 5 and 6 s for all case studies, that means higher Wavestar power and lower platform motion due to increasing radiation damping force. Furthermore, the result shows that the angle between Wavestar arm and wave direction and its location are two main factors that influence the power production. The maximum power absorbed by Wavestar occurs in the wave periods 6 s and makes 46, 103, 160, and 210 kW power for 3, 6, 9, and 12 WS, respectively.

Effects of damping plate position on heave and pitch responses of spar platform with single and double damping plates under regular waves

Damping plates are generally used to reduce the response of floating platform by increasing the added mass and damping. Heave and pitch responses of spar platform with single and double damping plates under regular waves are discussed in this paper. Regular wave experiments are conducted on 1:50 scale spar hull with damping plate. Heave and pitch response amplitude operators (RAOs) are obtained numerically using Boundary Element Method (BEM) based software ANSYS-AQWA and compared with the model test results. Parameters of scaling ratio, damping plate diameter to spar diameter ratio, damping plate position to spar draft ratio and spacing between the double damping plates to spar draft ratio are considered for the numerical analysis. It is found that the heave and pitch RAOs reduce with an increase in scaling ratio. Diameter ratios of 1.2–1.4, position to spar draft ratio of 0.16 and spacing to spar draft ratio of 0.16 are suggested for reducing the heave response. Similarly, diameter ratios of 1.2–1.4, position to spar draft ratio of 0.12 and spacing to spar draft ratio of 0.2 are recommended for pitch response reduction.

Experimental study on the motions of a dual chamber floating oscillating water column device

The hydrodynamics and the motions of a novel dual chamber floating oscillating water column device are studied experimentally. This novel wave energy converter consists of the combination of two already known concepts into a single floating structure: An oscillating water column and a backward bend duct buoy. The surge, heave, and pitch response amplitude operators of the floating device are determined and the impact of the chambers damping conditions on the model motions is evaluated. The results show that in surge motion, the natural frequency is much lower than the generated waves and in some cases the device travels towards the incident wave (initial negative drift) due to negative drift forces. The free surface elevations and air pressures inside the chambers are studied and their correlation with the motion of the device has been explored. Results of the amplitude of the free surface elevations inside the chambers show that the device can amplify it up to 2 times the incident wave height. The experimental data presented here can be used on the verification and validation of numerical models that deal with similar floating devices.

Influence of Viscosity and Non-Linearities in Predicting Motions of a Wind Energy Offshore Platform in Regular Waves

AbstractMotion predictions of floating bodies in extreme waves represent a challenging problem in naval hydrodynamics. The solution of the seakeeping problem involves the study of complex non-linear wave-body interactions that require large computational costs. For this reason, over the years, many seakeeping models have been formulated in order to predict ship motions using simplified flow theories, usually based on potential flow theories. Neglecting viscous effects in the wave-induced forces might largely underestimate the energy dissipated by the system. This problem is particularly relevant for unconventional floating bodies at resonance. In these operating conditions, the linear assumption is no longer valid, and conventional boundary element methods, based on potential flow, might predict unrealistic large responses if not corrected with empirical viscous damping coefficients. The application considered in this study is an offshore platform to be operated in a wind farm requiring operability even in extreme meteorological conditions. In this paper, we compare heave and pitch response amplitude operators predicted for an offshore platform using three different seakeeping models of increasing complexity, namely, a frequency-domain boundary element method (BEM), a partly nonlinear time domain BEM, and a non-linear viscous model based on the solution of the unsteady Reynolds-averaged Navier–Stokes (URANS) equations. Results are critically compared in terms of accuracy, applicability, and computational costs.

Study on capture power of the sealed-buoy wave energy converter in low energy flow density area

In order to achieve the conversion of the wave energy into electrical energy in low energy flow density sea areas in this paper, the capture power of the sealed-buoy wave energy converter (SBWEC) was investigated by dynamics methods of rigid bodies based on the hydrology data of Shandong Peninsula. The effect of buoy diameter on the response amplitude operator (RAO) was studied using frequency domain analysis method. The effect of buoy diameter on the instantaneous capture power and the effect of mooring angle on the pitch time domain response were studied using time domain analysis method. Results show that the pitch RAO is increased by 10.5 times from 8°/m to 93°/m with the decrease in buoy diameter. The maximum pitch time domain response and capture power are obtained in the SBWEC with the diameter 15m, mooring angle 45° and the slider mass 40 Kg. It is derived that the average capture power and wave energy conversion efficiency are 44.1 KW and 54.44% for the SBWEC in low energy flow density sea areas. Then, the relevant research results provide some reference for the design and utilization of wave energy converter in low energy flow density sea areas.

Influencing Factors of Motion Responses for Large-Diameter Tripod Bucket Foundation

Large-diameter multi-bucket foundation is well suited for offshore wind turbines at deeper water than 20 m. Air floating transportation is one of the key technologies for the cost-effective development of bucket foundation. To predict the dynamic behavior of large-diameter tripod bucket foundation (LDTBF) supported by an air cushion and a water plug inside every bucket in waves, three 1/25-scale physical model tests with different bucket spacing were conducted in waves; detailed prototype foundation models were established using a hydrodynamic software MOSES with a draft of 4.0 m, 4.5 m, and 5.0 m and with a water depth of 10.0 m, 11.25 m, and 12.5 m. The numerical and experimental results are consistent for heaving motion, while exhibiting favorable agreement for pitching motion. The results show that the resonant periods for heaving motion increased with increasing draft and water depth. The maximum amplitude for heaving motion first decreased and then increased with the increase of water depth and spacing between the buckets. The maximum amplitude for pitching motion first decreased and then increased with increasing water depth but decreased with increasing spacing between the buckets. The wider the spacing between the bucket foundations, the larger the heave response amplitude operators (RAOs). Simply improving the pitch RAOs by increasing the spacing between bucket foundations is limited and negatively affects motion performance during the transportation of LDTBF.

Validation of a 750 kW semi-submersible floating offshore wind turbine numerical model with model test data, part II: Model-II

Floating Offshore Wind Turbines (FOWT) installed in the deep sea regions where stable and strong wind flows are abundant would have significantly improved energy production capacity. When designing FOWT, it is essential to understand the stability and motion performance of the floater. Water tank model tests are required to evaluate these aspects of performance. This paper describes a model test and numerical simulation for a 750-kW semi-submersible platform wind turbine model-II. In the previous model test, the 750-kW FOWT model-I suffered slamming phenomena from extreme wave conditions. Because of that, the platform freeboard of model-II was increased to mitigate the slamming load on the platform deck structure in extreme conditions. Also, the model-I pitch Response Amplitude Operators (RAO) of simulation had strong responses to the natural frequency region. Thus, the hub height of model-II was decreased to reduce the pitch resonance responses from the low-frequency response of the system. Like the model-I, 750-kW FOWT model-II was built with a 1/40 scale ratio. Furthermore, the experiments to evaluate the performance characteristics of the model-II wind turbine were executed at the same location and in the same environment conditions as were those of model-I. These tests included a free decay test, and tests of regular and irregular wave conditions. Both the experimental and simulation conditions considered the blade rotating effect due to the wind. The results of the model tests were compared with the numerical simulations of the FOWT using FAST (Fatigue, Aerodynamics, Structures, and Turbulence) code from the National Renewable Energy Laboratory (NREL).

Study on force and wave energy conversion efficiency of buoys in low wave energy density seas

The performance of wave energy converters is significantly affected by buoys. This research studied the force and conversion efficiency of buoys in low wave energy density seas and involved the selection of a cylindrical buoy and a hemispherical buoy, which were applied in a sealed-buoy wave energy converter (SBWEC). The underwater equivalent area was utilized as the variable to investigate the force, pitch response amplitude operator (RAO), and conversion efficiency of the buoys in irregular waves. The results show that the common responses occurred both in the cylindrical and hemispherical buoys. The force of the buoys in a resonance state was distributed in a concentric ring shape and gradually decreased from the inner to the outer areas. The force, pitch RAOs, and conversion efficiency increased with a corresponding increase in the underwater equivalent area. Results determined that owing to the difference in the underwater equivalent area and shape, the force of the cylindrical buoy with a diameter 2 m and 4 m was 194–1455% larger than that of the hemispherical buoy with the same diameter. The pitch RAOs of the cylindrical buoy were 0.6–52.59% larger than that of the hemispherical buoy because of the difference in force. In turn, the average conversion efficiency of the cylindrical buoy was 1.31% greater than that of the hemispherical buoy. The novel SBWEC made the wave energy conversion efficiency of the buoys in low wave energy density seas 0.6–1.4% less than that in high wave energy density seas. The utilization of the underwater equivalent area provides a new method for researching the force and conversion efficiency of buoys.

Study on hydrodynamic performance of the sealed-buoy wave energy converter

For investigating the wave energy converter working in low-energy flow density sea area, a novel sealed-buoy wave energy converter (SBWEC) was analysed by using the fluid simulation software ANSYS and AQWA according to Shandong Peninsula marine environment in this paper. For the SBWEC in the range of 5-20 m buoy diameter, the effect of mass on the response amplitude operator (RAO) and the motion response were analysed based on the frequency domain method and the time domain method. The wavelength range with higher wave energy was also investigated. Within the mass range of 8-12 t, the study found that the mass did not has a significant impact on the roll, yaw and pitch RAO and the pitch motion response except for the SBWEC with 5 m buoy diameter. The wavelength range with higher wave energy in Shandong Peninsula is 10-40 m, which is more suitable for operation of the SBWEC. These results can provide a reference for the design of related wave energy converters.

OpenFOAM을 이용한 부유식 구조물의 운동해석

In this study, the numerical simulation with OpenFOAM, an open source library in Computational Fluid Dynamics(CFD), to analyze a dynamic behavior of a floating structure in wave field is carried out. The two-dimensional numerical wave tank with a simple rectangular floating body constrained in two degree of freedom(heave and pitch) is modelled. “interDyMFoam” which solves the Reynolds-Averaged Navier-Stokes(RANS) for two incompressible phase using Volume Of Fluid(VOF) technique and dynamic mesh method for the floating body is used. Comparisons of free decay tests and heave and pitch Response Amplitude Operators (RAOs) have been made using existing experimental data performed with two dimensional wave flume in Jeju National University. Moreover, velocity field and vorticity near the floating body show how viscous damping is affected on the dynamic behavior. The results shows that the numerical wave tank with OpenFOAM can be used for the behavior analysis of the floating structure.

An Experimental Investigation of Ride Control Algorithms for High-Speed Catamarans Part 1: Reduction of Ship Motions

Ride control systems are essential for comfort and operability of high-speed ships, but it remains an open question what is the optimum ride control method. To investigate the motions of a 112-m high-speed catamaran fitted with a ride control system, a 2.5-m model was tested in a towing tank. The model active control system comprised two transom stern tabs and a central T-Foil beneath the bow. Six ideal motion control feedback algorithms were used to activate the model scale ride control system and surfaces in a closed-loop control system: heave control, local motion control, and pitch control, each in a linear and nonlinear version. The responses were compared with the responses with inactive control surfaces and with no control surfaces fitted. The model was tested in head seas at different wave heights and frequencies and the heave and pitch response amplitude operators (RAOs), response phase operators, and acceleration response were measured. It was found that the passive ride control system reduced the peak heave and pitch motions only slightly. The heave and pitch motions were more strongly reduced by their respective control feedback. This was most evident with nonlinear pitch control, which reduced the maximum pitch RAO by around 50% and the vertical acceleration near the bow by about 40% in 60-mm waves (2.69 m at full scale). These reductions were influenced favorably by phase shifts in the model scale system, which effectively contributed both stiffness and damping in the control action.

An Experimental Investigation of Ride Control Algorithms for High-Speed Catamarans Part 1: Reduction of Ship Motions

Ride control systems are essential for comfort and operability of high-speed ships, but it remains an open question what is the optimum ride control method. To investigate the motions of a 112-m high-speed catamaran fitted with a ride control system, a 2.5-m model was tested in a towing tank. The model active control system comprised two transom stern tabs and a central T-Foil beneath the bow. Six ideal motion control feedback algorithms were used to activate the model scale ride control system and surfaces in a closed-loop control system: heave control, local motion control, and pitch control, each in a linear and nonlinear version. The responses were compared with the responses with inactive control surfaces and with no control surfaces fitted. The model was tested in head seas at different wave heights and frequencies and the heave and pitch response amplitude operators (RAOs), response phase operators, and acceleration response were measured. It was found that the passive ride control system reduced the peak heave and pitch motions only slightly. The heave and pitch motions were more strongly reduced by their respective control feedback. This was most evident with nonlinear pitch control, which reduced the maximum pitch RAO by around 50% and the vertical acceleration near the bow by about 40% in 60-mm waves (2.69 m at full scale). These reductions were influenced favorably by phase shifts in the model scale system, which effectively contributed both stiffness and damping in the control action.

Optimization of Spacing for Oscillating Wave Surge Converter Arrays Using Genetic Algorithm

AbstractThe oscillating wave surge converter (OWSC) is a type of ocean wave power device typically consisting of a flap, or arm, hinged at the bottom to allow forward and backward movement by surging waves, and is efficient in generating electricity from waves due to its capability in operating at a wide range of wave spectra. The power generated from the OWSC could be further maximized by arranging the devices in an array at their optimal spacing. This paper addresses the optimization of device configuration within an array by using the genetic algorithm (GA) scheme, for which the spacings between devices are taken as the optimization variables, and the maximum q-factor is chosen as the objective function. The q-factor is a performance assessment parameter that quantifies the average total power produced by an array compared to an individual device. Three array layouts—namely, the single-, double-, and triple-array, each comprising 12 OWSCs—were considered. The pitch response amplitude operator (RAO) of ...

Measurement of Response Amplitude Operators for an 86 m High-Speed Catamaran

Radar observations of encountered wave profile and measurements of vessel motions have been used to derive motion response amplitude operators, and the results are compared with predicted motion responses. Data were collected from an INCAT Tasmania built ferry while on delivery between Australia and England. It has been found that the predicted motions using a time domain method are consistent with those observed with respect to the increase of response with vessel speed and the decrease of response for seas encountered from the beam directions. Peak heave and pitch response amplitude operators were measured and computed at up to 2.5 and 1.8, respectively, at high speed in head seas. Conventional low-speed frequency domain motion analysis was found to give smaller predicted responses at somewhat higher frequency than the high-speed time-domain motion analysis. Significantly larger rolling motions were measured than predicted, and it appears that the action of the steering system may contribute substantially to in-service rolling.