Heave Modes Research Articles

A study into the correlation between single array-hull configurations and wave spectrum for floating solar photovoltaic systems

Floating photovoltaic (FPV) systems offer a viable renewable energy solution due to easy installation and cost-effectiveness compared to other renewable energy generation methods. On the other hand, land-based solar photovoltaics face challenges such as space scarcity and environmental impacts. Shifting to nearshore locations unlocks vast ocean space potential, though waves expose significant challenges to FPV systems. Several novel FPV system designs are proposed, inspired by high-speed vessel multihulls, including catamaran, trimaran, quadrimaran, and pentamaran configurations, as floating supports for solar panels. Simulations were conducted to determine Response Amplitude Operators (RAOs) under various irregular wave spectrum conditions in a free-floating initial state. The FPV motion problem was solved using linear potential-flow theory with the Boundary Element Method (BEM) with Green-Function approach. Superposition of wave spectral energy and motion RAOs was used to obtain spectral structural responses. Motion in heave, roll, and pitch modes was evaluated across wave spectrum types. Results show that adding hulls reduces the significant amplitude response in all motion modes. In summary, valuable insights into floater designs and the hydrodynamic evaluation of FPV systems are presented.

Resonant response of a flexible semi-submersible floating structure: experimental analysis and second-order modelling

The dynamics and nonlinear wave forcing of a flexible floating structure are investigated experimentally and numerically. The floater was designed to match sub-harmonic rigid-body natural frequencies of typical floating wind turbine substructures, with the addition of a flexible bending mode. Experiments were carried out for three sea states with phase-shifted input signals to allow harmonic separation of the measured response. We find for the weakest sea states that sub-harmonic rigid-body motion is driven by even-harmonic difference frequency forcing, and by linear forcing for the strongest sea state. The flexible mode was tested in a soft, linearly forced layout, and a stiff layout, forced by second-, third- and fourth-harmonic frequency content, for increasing severity of the sea state. Further insight is gained by analysis of the amplitude scaling of the resonant response. A new simplified approach is proposed and compared with the recent method of Orszaghova et al. (J. Fluid Mech., vol. 929, 2021, A32). We find that resonant surge and pitch motions are dominated by even-harmonic potential-flow forcing and that odd-harmonic response is mainly potential-flow driven in surge and mainly drag driven in pitch. The measured responses are reproduced numerically with second-order forcing and quadratic drag loads, using a recent and computationally efficient calculation method, extended here for the heave, pitch and flexible motions. We are able to reproduce the response statistics and power spectra for the measurements, including the subharmonic pitch and heave modes and the flexible mode. Deeper analysis reveals that inaccuracies in the even-harmonic forcing content can be compensated by the odd-harmonic loads.

Hydrodynamic responses and layout optimization of wave energy converter arrays consisting of five-degree-of-freedom truncated cylinders in front of a vertical wall

The hydrodynamic responses and layout optimization of a group of cylindrical wave energy conversion devices (WEC) in front of a fully reflecting vertical wall are investigated. Each truncated floating cylinder can oscillate with five degrees of freedom, i.e., surge, sway, heave, roll, and pitch. Based on the linear water wave theory, an analytical solution is developed for the hydrodynamic problem. The results of specific parameter studies suggest that the wall reflection effect significantly improves the energy extraction performance of the WEC array with the appropriate parameter conditions. A multi-level optimization method based on a genetic algorithm is developed. This paper investigates the optimal layout of the six WEC arrays, composed of 2–7 buoys, respectively. Additionally, the impact of other degrees of freedom (DOFs), besides the heave mode, on the hydrodynamic performance of the array is investigated. For β ≤ π/12, there is no need to consider the impact of other DOFs on the energy extraction in heave mode. The dimensionless amplitudes of other DOFs gradually decrease as the equivalent constraint stiffness increases. For k0a > 1.0, the heave amplitude and energy capture performance of the WEC array are significantly smaller. However, the amplitudes of other DOFs still have considerable magnitudes for k0a > 1.0. Therefore, for the sea area with high-frequency incident waves (k0a > 1.0), setting up a power takeoff system on other DOFs of each buoy to extract energy is a feasible solution to improve the performance of the WEC array.

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.

Mathematical modelling of a floating Clam-type wave energy converter

In this paper, wave power extraction from a floating Clam-type wave energy converter is investigated. The device is mainly composed of a Clam, which is formed from two pieces of floating flaps hinged at a submerged body. The Clam is closed by a flexible impermeable bag with the two hinged floating flaps kept apart by a Power Take-Off system. As waves propagate through the device, the Clam motion of the device is excited, which can be used to drive the Power Take-Off system to capture wave power. To evaluate the response and also the wave power absorption of the device, a mathematical model is developed based on the linear potential flow theory, in which a generalised mode method is adopted to model the Clam action. Theoretical expressions of the maximum wave power absorption and the corresponding optimised Power Take-Off system and mooring parameters are derived. Good agreement between the present numerical results of the device response and the physical observations is obtained. The validated model is then applied to do a series of case studies. It is revealed that the optimised Power Take-Off stiffness and mooring stiffness are independent of the Power Take-Off damping. The maximum wave power absorption can be achieved when the device is fixed in heave mode or free-floating without any constraints from the mooring system.

A new floor heave mechanism considering the influences of the in-situ stress lateral coefficient and rock tensile strength

Floor heave is a disaster that is frequently encountered in tunnel engineering. Existing explanations of floor heave mechanisms have many limitations, and the most important of which is that the stress concentration, release and transfer phenomena and the influences of the in-situ stress lateral coefficient and tensile strength are ignored. Therefore, the combined finite-discrete element method (FDEM) is used to study the failure process of floor rock masses and propose a new mechanical mechanism of floor heave that can consider the influences of the in-situ stress lateral coefficient and tensile strength. The type I fracture energy corresponding to different tensile strengths is calibrated using a direct tensile simulation test. Then, the floor heave mechanism is investigated under different lateral coefficients and tensile strengths, and five different floor heave modes are proposed under different in-situ stress lateral coefficients and tensile strengths. The floor heave modes controlled by the various in-situ stress lateral coefficients and tensile strengths are different, but they can all be explained by the maximum concentrated tangential stress.

Experimentalna analiza ispitivanja i mjerne nesigurnosti referentnog modela broda na pravilnim pramčanim i valovima u bok

Confidence levels of the seakeeping experiment results can be assessed through uncertainty analysis. The seakeeping experiments with a free-running model system were carried out in the manoeuvring and ocean engineering basin (MOB) at the Indonesian Hydrodynamic Laboratory (IHL) using uncertainty techniques to improve the experiment quality. The method used is the International Organization for Standardization, Guide for Uncertainty of Measurements (ISO-GUM), type A and B uncertainty, which is the foundation for the uncertainty analysis for seakeeping experiment recommendations released by the International Towing Tank Conference (ITTC). This research aims to determine the combined uncertainty value of the seakeeping experiment on a benchmark ship model with a scale of 1:62, representing the full scale of 186 meters. Seakeeping testing is carried out under head and beam waves, each with regular waves at one wave height (Hs) with three different wave periods (Tw). The experimental seakeeping result, generally, has the same tendency in each heave, pitch, and roll motion mode. The expanded uncertainty with 95% confidence level of the RAO-Heave uncertainty in all period conditions is always less than 3%, RAO-Pitch uncertainty in all period conditions is always less than 1%, and RAO-Roll uncertainty in all period conditions is always less than 1.2%. These uncertainties are quite small.

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.

Experimental investigation on an OWC wave energy converter integrated into a floating offshore wind turbine

A multi-functional floating foundation integrating an Oscillating Water Column (OWC) Wave Energy Converter (WEC) with a Floating Offshore Wind Turbine (FOWT) is a promising design for achieving cost reduction, adaptability and stability improvements. Yet, such a multi-functional integration is still in a demonstration phase and additional investigations are required to reach industrial maturity. This work assesses the hydrodynamic performance of such a design by carrying out a series of carefully instrumented scaled model tests. Two distinct sets of experimental models were designed accordingly, i.e., a pure FOWT without the OWC device, and the FOWT incorporating the OWC device. The multi-functional foundation is either fixed or allowed to move in heave mode along four vertical sliding rails. The introduction of the OWC device enhances the stability of the FOWT in heave, with a maximum motion reduction rate of 54.1%. The chamber air orifice size and the foundation geometries were optimized. The OWC with an air chamber opening ratio of 3.0% produces the maximum relative capture width. A larger chamber draft and breadth lead to a lower chamber resonance frequency. The main objective of this paper is to guide the design and application of the OWC device integrated into a floating offshore wind turbine.

Analytical stress solution for cold region tunnels with unequal ground stress and support delay under different frost heave conditions of surrounding rock

Stress response analysis of tunnels under the frost heave state is a crucial problem in cold region tunnel construction. Hence, in this study, an analytical stress solution for cold region tunnels with unequal ground stress and support delay under different frost heave conditions is presented. The solution simultaneously considers the unequal ground stress along the horizontal and vertical directions, the rock displacement occurring before support installation, and the different frost heave modes of surrounding rock. To resolve the unequal ground stress boundary condition, the complex function method is utilized, and the stress solution is directly acquired by the method under isotropic frost heave (IFH) condition, whereas the solution under transversely isotropic frost heave (TIFH) condition is acquired through combination with the superposition method. In addition, a displacement release coefficient is adopted to depict the support delay. The solution is validated by existing solutions in degenerate cases. Finally, the stress distributions and the influence of key factors for cold region tunnels are discussed with a case study. In the lining, the radial stress increases with the radius and decreases from 0° to 90°, and the maximum of tangential stress occurs at the inner edge. Moreover, the normal contact stress between the lining and surrounding rock is much greater under TIFH condition; however, the tangential contact stress is identical under the two different frost heave modes. The lateral pressure coefficient shows greater impact on the stress in the lining along the vertical direction, whereas the displacement release coefficient exhibits greater effect on the stress along the horizontal direction. The stress in the lining under TIFH condition is much greater than that under IFH condition, and increases significantly as the degree of anisotropy increases, which implies that the TIFH condition is a much severer state.

Hydrodynamic interactions among wave energy converter array and a hierarchical genetic algorithm for layout optimization

This paper focuses on the layout optimization and hydrodynamic investigation of wave energy converter (WEC) array. For hydrodynamic analysis, each buoy is modeled as a truncated floating cylinder that can move with five degrees of freedom. The hydrodynamic response of such an array is analyzed by a semi-analytical method. Then, the power extraction by the array is used as the objective function for layout optimization. To improve efficiency, especially for an array with a large number of WECs, a novel hierarchical optimization method based on matrix coded genetic algorithm is proposed. Within this method, a large-scale array is firstly divided into several levels of small-scale arrays which are easy to handle, then, the genetic algorithm developed in this paper is used to optimize the small array of each level. An example of two-level optimization is given in this paper and compared with the result by conventional optimization routine. Finally, we investigate the influence of introducing other degrees of freedom, besides the heave mode, on the performance of arrays. Results show that as the constraints get weaker in non-heave directions, the effect of other degrees of freedom on the WEC array interaction factor becomes more and more obvious.

Design considerations for a three-tethered point absorber wave energy converter with nonlinear coupling between hydrodynamic modes

Multi-mode Wave Energy Converters (WECs) are designed to harvest energy simultaneously from multiple hydrodynamic modes, thereby maximising power absorption. The behaviour of each mode must be carefully considered, given that hydrodynamic and geometric coupling between modes can lead to severe reductions in power if improperly designed. This study aims to investigate how the design of a planar three-tethered WEC can be used to tune the surge, heave and pitch hydrodynamic modes to achieve maximum power absorption. The effect of various tether arrangement and mass distribution design parameters on the performance of a WEC subjected to both geometric and hydrodynamic nonlinearities was investigated. Results indicated that, to absorb the most power in regular waves, the tether configuration should be adjusted such that the surge and heave dominant rigid body modes are resonant with the incident wave. Geometric nonlinearities associated with the tether arrangement were found to cause sub-harmonic excitations which severely compromised device performance, with further reductions in power when nonlinear hydrodynamics were considered. In irregular waves, the optimal design became more strongly driven by performance in surge. Overall, maximum power was achieved when all three tethers were attached close to one another on the bottom of the buoy.

Linear and quadratic damping coefficients of a single module of a very large floating structure over variable bathymetry: Physical and numerical free-decay experiments

The linearity assumption is widely used when acquiring the hydrodynamic coefficients of a floating structure. However, the linear damping is frequently underestimated, especially for the natural frequency. To investigate the sloping seafloor effects on the damping terms of a single module of a semi-submersible Very Large Floating Structure (VLFS), this paper revisits the conventional formulation and further proposes the direct integration method for obtaining the linear and quadratic damping coefficients from free-decay tests. Numerical free-decay simulations of the single module over variable bathymetry are carried out by the CFD numerical tank. Corresponding model tests are also implemented to verify and validate against the numerical solutions. The effects of the sloping seafloor, as well as the water depth, on the hydrodynamic coefficients are investigated based on the validated CFD modeling. Both numerical and experimental results indicate that the acquisition of the linear and quadratic damping coefficients is sensitive to the data-processing and identification approaches. For the case studied in present paper, the identification errors introduced by the conventional method are 1.5% while they are 0.5% using the direct integration method. The quadratic damping coefficient for heave mode decreases about 10.4% when the sloping angle increases from 0 to 6 deg.

On the importance of nonlinear hydrodynamics and resonance frequencies on power production in multi-mode WECs

Multi-mode Wave Energy Converters (WECs) are able to harvest energy from multiple Degrees-of-Freedom (DOFs) simultaneously, which increases the power that can be absorbed from the incident wave compared to single-DOF WECs. However, nonlinear coupling between hydrodynamic modes, which occurs when the WEC oscillates simultaneously in multiple directions, means that simply applying the typical control strategies used for single-DOF WECs can lead to sub-optimal performance. This study investigates the multi-DOF dynamic control of a submerged, flat cylindrical WEC subjected to hydrodynamic coupling effects modelled under the weakly nonlinear potential flow theory based on the weak-scatterer approximation. Results show that, at low incident wave frequencies, tuning the surge, heave and pitch modes of the WEC to the same natural frequency can result in power losses of up to 30% in the weakly nonlinear model compared to results obtained from a fully linear model. These discrepancies are attributed to the pitching motions of the WEC, which changes the projected surface area of the device relative to the equilibrium position and hence violates the assumptions of the linear theory. From these findings, a suggested design strategy where the surge, heave and pitch DOFs were all decoupled and tuned to different natural frequencies was therefore proposed. In the presence of weakly nonlinear hydrodynamic coupling, it was found that this design may result in significant improvements in power absorbed for the multi-mode WEC, compared to a case where all DOFs are simply tuned to match the peak frequency of a given sea state.

Opening the air‐chamber of an oscillating water column spar buoy wave energy converter to avoid parametric resonance

The oscillating-water-column (OWC) spar-buoy is a type of wave energy converter that may exhibit undesirable large roll and pitch amplitudes caused by a dynamic instability induced by parametric resonance. The occurrence of this phenomenon not only reduces the power extraction but significantly increases the structural loads on the buoy, the turbine rotor and on the mooring system. The paper compares the parametric resonance behaviour of two configurations of an OWC spar-buoy using experimental data obtained in a wave flume at a scale of 1:100. The configurations investigated were: (1) closed and (2) fully open-air chamber. The experimental tests covered a wide range of regular and irregular waves, as well as in free decay experiments. Results showed that opening the air chamber reduces the coupling between the buoy and the OWC within, thus shifting the damped natural heave frequency of the system in comparison with the closed chamber configuration. This effect changes parametric resonance characteristics of the two configurations due to the coupling between roll/pitch and heave modes. Moreover, for specific wave frequencies, the occurrence of parametric resonance observed when the chamber is closed do not occur while the air chamber is fully open. These results suggest the possibility of controlling a pressure relief valve installed on top of the device to reduce parametric resonance whenever this dynamic instability is detected.

Numerical study on the improvement design of the oscillating buoy wave energy converter

The oscillating buoy wave energy converter (OBWEC) is a popular and widely used wave energy converter (WEC) due to the simplicity of its structure and its strong adaptability. In this paper, the “Haiyuan No. 1″ OBWEC is taken as the research object, in which the buoys adopt heave mode of motion. In order to further enhance the hydrodynamic performance of the buoys, an improved scheme with longitudinal swing motion is proposed through theoretical analysis for the buoy. A 2D numerical wave tank (NWT) model based on the RANS equation is established by using CFD software. The numerical model is applied to compare and analyze the hydrodynamic performance differences of the buoy under two different motion forms: heaving and longitudinal swing, and the consistency of the numerical results is validated by the experimental data under regular waves. Finally, the irregular wave data obtained during the sea trial of the “Haiyuan No. 1″ OBWEC is used to numerically simulate the two buoys. The results show that the buoy with longitudinal swing motion is more effective in improving the hydrodynamic performance compared to the buoy with heave motion, in both regular and irregular waves. The conclusions of this paper can serve as a guide to improve the design of the hydrodynamic performance of the buoy.

Driving Safety Improved with Control of Magnetorheological Dampers in Vehicle Suspension

The article is dedicated to the control of magnetorheological dampers (MR) included in a semi-active suspension of an all-terrain vehicle moving along a rough road profile. The simulation results of a half-car model and selected feedback vibration control algorithms are presented and analysed with respect to the improvement of driving safety features, such as road holding and vehicle handling. Constant control currents correspond to the passive suspension of different damping parameters. Independent Skyhook control of suspension parts represents the robust and widely used semi-active algorithm. Furthermore, its extension allows for the control of vehicle body heave and pitch vibration modes. Tests of the algorithms are carried out for a vehicle model that is synthesised with particular emphasis on mapping different phenomena occurring in a moving vehicle. The coupling of the vehicle to the road and environment is described by non-linear tire-road friction, rolling resistance, and aerodynamic drag. The pitching behaviour of the vehicle body, as well as the deflection of the suspension, is described by a suspension sub-model that exhibits four degrees of freedom. Further, three degrees of freedom of the complete model describe longitudinal movement of the vehicle and angular motion of its wheels. The MR damper model that is based on hyperbolic tangent function is favoured for describing the key phenomena of the MR damper behaviour, including non-linear shape and force saturation that are represented by force-velocity characteristics. The applied simulation environment is used for the evaluation of different semi-active control algorithms supported by an inverse MR damper model. The vehicle model is subjected to vibration excitation that is induced by road irregularities and road manoeuvres, such as accelerating and braking. The implemented control algorithms and different configurations of passive suspension are compared while using driving-safety-related quality indices.

Frost heave and freezing processes of saturated rock with an open crack under different freezing conditions

Frost heave experiments on saturated sandstone and tuff with an open crack are conducted under uniform and unidirectional freezing conditions. Frost heave of crack in sandstone with high permeability is more significant under uniform freezing condition than that under unidirectional freezing condition. However, frost heave of crack in tuff with low permeability is more significant under unidirectional freezing condition. To illustrate the reasons for this phenomenon, a numerical model on the freezing processes of saturated rock with an open crack considering the latent heat of pore water and water in crack is proposed and confirmed to be reliable. Numerical results show that a frozen shell that blocks the migration of water in crack to rock develops first in the outer part of the rock before the freezing of water in crack under uniform freezing condition. However, the migration path of water in crack to the unfrozen rock under freezing front exists under unidirectional freezing condition. The freezing process and permeability of rock together determine the migration of water in crack and lead to the different frost heave modes of crack for various permeable rocks under different freezing conditions. The frost heave modes of crack in rock with low or high permeability are similar under uniform freezing condition because water migration is blocked by a frozen shell and is irrelevant to rock permeability. For high permeability rock, the frost heave of crack will be weakened due to water migration under unidirectional freezing condition; however, the frost heave of crack would be more significant for low permeability rock because water migration is blocked under unidirectional freezing condition. Therefore, the freezing condition and rock permeability determine the frost heave of rock with crack together, and this should be concerned in cold regions engineering applications.

Experimental investigation on hybrid mooring systems for wave energy converters

Abstract This study presents a comprehensive experimental assessment of three hybrid mooring systems for a heaving-buoy wave energy converter. Free decay model tests are conducted to study the natural periods in heave, pitch and surge modes of the buoy when it is moored with different mooring configurations. A series of regular and irregular wave model tests are carried out to investigate the hydrodynamic responses of the point absorber as well as mooring dynamics. The effects of wave period, incident wave height and mooring configuration are evaluated. Besides, the influence of mooring configuration on buoy motion is discussed. To study the short term extreme dynamic tension, the traditional Weibull distribution, Weibull distribution based on tail data and peaks-over-threshold method are applied. The results showed that the Weibull distribution failed to present accurate extreme dynamic tension prediction when the snap events occur frequently, while the other two methods showed good performance despite of number of snap events. Based on the results of energy production performance and extreme dynamic tension, a novel mooring line design is suggested, which helps to reduce mooring dynamic tension.

HYDRODYNAMIC ASSESMENT ON MOTION PERFORMANCE CHARACTERISTICS OF GENERIC WAVE ENERGY POINT ABSORBERS

This work condenses various modeling techniques for different Point Absorber configurations. An alternating frequency - time domain model is implemented in MatlabFORTRAN in order to compute the displacement, velocities and the power absorbed in the heave mode for both single and multiple body configurations. Coupling of different degrees of freedom are merely contemplated with regard to a single buoy motion. NEMOH and BEMIO solvers are applied in the solution of Newtons second law according to the Boundary Element Methodology. Initially, this Wave-to-Wire model is validated through comparison with previous experimental results for a floating cone cylinder shape (Buldra-FO3). A single, generic, vertical floating cylinder is contemplated then, that responds to the action of the passing regular waves excitation. Later, two equally sized vertical floating cylinders aligned with the incident wave direction are modeled for a variable distance between the bodies. In deep water, we approximate the convolutive radiation force function term through the Prony method. Using for instance triangular or diamond shaped arrays of three and four bodies respectively, the study delves into the interaction effects for regular waves. The results highlight the most efficient layout for maximizing the energy production whilst providing important insights into their performance, revealing displacement amplification-, capture width-ratios and the commonly known park effect.