Ocean wave energy can be used for electricity supply to ocean data acquisition buoys. A heaving buoy wave energy converter is designed and the damping plate and taut line system are used to provide the mooring stability for better operating conditions. The potential flow assumption is employed for wave generation and fluid structure interactions, which are processed by the commercial software AQWA. Effects of damping plate diameter and taut line linking style with clump and seabed weights on reduction of displacements in 6 degrees of freedom are numerically studied under different operating wave conditions. Tensile forces on taut lines of optimized mooring system are tested to satisfy the national code for wire rope utilization.
The resource of fossil fuel on land has been reducing significantly and rapidly because of the huge demand and consumption of energy in the economy development. Ocean contains abundant energies such as wave, tidal stream, and thermal energy. For instance, wave energy resource for technical exploitation is up to 0.1 to 1 TW·h/year, which is of the same order of magnitude of world electricity consumption. Wave energy has become one of the most popular research areas, which is also quite different from traditional ocean engineering [
Originally, the mooring system of floating marine structures was designed and investigated for drilling platforms and offshore wind turbines. A new hybrid mooring system was designed to reduce the tension on the lines and is widely used in various water depths [
The catenary and vertical tensioned mooring lines are then numerically studied for the mooring control of tri-floater support structures for wind turbines [
For the studies of mooring system for wave energy converters, the field sea trials and physical model tests can provide valuable information and validation for the numerical models. An approach is proposed to calculate and predict the fatigue damage of the mooring system [
Within the development of the computation capability and numerical models, the mathematical models for analysis of mooring system and stability characteristics become popular and useful in the wave energy field. A method to include the influence of mooring cables in the frequency domain analysis of wave energy converters was proposed to be applied to a generic wave energy device based on a truncated vertical cylinder of 100 ton displacement [
Most previous published researches focused on the mooring system of large ocean engineering structures such as oilrig platforms, wind turbines, and high installed capacity wave energy converters. The present paper deals with the small heaving body wave energy converter (WEC) within 1 kW level electricity generation, which is supposed to be used for long-term energy supply for offshore ocean environmental monitoring devices, such as the ocean buoys. The design of WEC mainly includes the energy converting and mooring systems. The station-keeping capability and low costs demands are considered together. Numerical model based on the commercial software Ansys-AQWA is applied for the fluid structure interaction analysis. Effects of the damping plate and taut line system on stability are studied and engineering application of the optimized design is scheduled as the sea trial proofs.
Long-term independent electricity supply of offshore ocean data acquisition buoys has proposed the demands for in situ power take-off, which can be satisfied by wave energy converters within suitable electricity cable connection approaches. Since the electricity request is not high, 1 kW installed capacity is enough for everyday and long-term supply. On the other hand, the wave energy converter is considered to be operated around nearshore sea area in China, where the flux density of wave energy is significantly smaller than that in the Atlantic. This ideal was initially supported by the Special Fund Project for Ocean Renewable Energy, which was granted by State Oceanic Administration of Chinese center government.
Following the above conditions and demands, the design principle of the small wave energy converter for ocean buoys electricity supply, located in Qingdao, China, should be the following: 1 kW installed capacity with high reliability energy converting mechanism (project evaluating indicator). Away from coastline: High stability of mooring system: heave less than 0.1 m, surge and sway less than 0.2 m, and pitch, roll, and yaw less than 10° under operating wave conditions (project admissible values). Low costs on manufacturing, transportation, and deployment. Easy access to repairing and maintenance.
The 1 kW heaving body wave energy converter is illustrated in Figure
Schematic of 1 kW heaving body wave energy converter.
Linear wave is considered based on the assumption of homogeneous, incompressible, inviscid fluid and irrotational flow. In addition, the wave amplitude is assumed to be small compared to the wave length and water depth; hence, the linear free surface condition is used. In the Cartesian coordinate system, the velocity potential, velocity, and free surface elevation can be expressed as
By accounting for wave radiation and diffraction, the fluid structure interaction behavior is described by the set of equations
The velocity potential could be expressed by using superposition principle as follows:
Assuming that the body motion is small around the still water surface, the velocity potential
In order to derive the motion of the system motion in six degrees of freedom, the motion equation of the floating body in the time domain should be considered and expressed as follows [
First-order wave force can be resolved from the convolution relationship between the wave force on the frequency and time domains proposed by Cummins. The equation is expressed as
The calculation of second-order wave force could be conducted using the method proposed by Newman. Based on the indirect time domain method, after the Fourier transform, the delay function can be expressed as
Added mass in the time domain can be expressed as
Ansys-AQWA is the commercial computational fluid dynamics software based on the governing equations described in Section
All the structures and grids will be generated in Ansys Mechanical APDL software and then transferred as the AQWA executive files. In the present paper, the scheme in the numerical model is slightly simplified where the crane piles are cancelled and the buoy is fixed on the guide rod without any relative motions. Some corresponding parameters are shown in Figure
Numerical model setup of WEC with mooring system.
Parameters of WEC
Structure and grids in the numerical model (snapshot from the software)
The grid structures in the numerical model are shown in Figure
In order to validate the capability of the present numerical model on floating body motion under wave excitation, experimental data of the oscillating motion of the buoy are used for the validation. The buoy is restricted to move in one degree of freedom along the guide rod without any damping plates, which is fixed to the tank bottom. All the physical model tests were carried out in the wave tank of Shandong Provincial Key Laboratory of Ocean Engineering, Ocean University of China [
Comparisons between the numerical and experimental results of the buoy heaving amplitudes are shown in Figure
Comparison between experimental and numerical heaving amplitudes of the buoy.
For the mooring system of heaving type point absorber wave energy converter, it is very important to keep the whole facility in stationary state, which will provide a better operating condition for the buoy to oscillate along the guide rod. Hence, the displacements in the six degrees of freedom will be treated as the evaluating indexes in the present paper. The damping plate and the taut line system are designed and tested to reduce the movements in 6 DOF. Time histories of the mooring system displacements and tensile forces of taut lines are demonstrated first. Effects of damping plate diameter, taut line number, and mooring types are then studied. Based on the above investigation results, tension loads under the extreme wave conditions are calculated to verify the safety of wire ropes as taut lines.
A typical case of the mooring system is used for time domain results demonstration. The incident waves come from left side. The diameter of damp plate is
Time histories of mooring system motions and forces (
Translation displacement
Rotation displacement
Tension forces on various taut lines
It can be seen in Figure
The variations of tensions on four taut lines are illustrated in Figure
Damping plate is used to compete against the motion caused by the incident waves in order to give the appropriate stability of the mooring system. The diameter
Effects of damping plate diameters on mooring stability are shown in Figure
Effects of damping plate diameters on mooring system stability.
Surge
Heave
Effects of
Surge
Heave
Effects of incident wave direction on mooring system stability.
Incident angles of oblique waves
Surge
Sway
Heave
Considering the performance of single CWL on the mooring system stability, two CWLs are proposed with twin seabed weights. The opening level of CWLs is represented by ratio
In Figure
In order to deal with the paradoxical effects of
Since the layout of taut lines is designed to be parallel to the incident wave direction, it is necessary to study the operating performance of the mooring system under oblique waves. Two angles are employed as 45° and 90° in Figure
In Figure
Tensile forces on the taut lines are calculated under extreme wave conditions (
Tension forces on taut lines under extreme wave conditions.
A small oscillating wave energy converter has been designed for electricity supply of nearshore ocean buoys. The mooring system utilizes wire ropes as taut lines to connect the damping plate and clump weight with seabed weights, which are investigated numerically to provide stationary state for heaving buoy operation. Ansys-AQWA was used to deal with the potential flow, waves, and fluid structure interactions in the time domain.
It has been found that the damping plate could provide a good station-keeping for the energy converting compartment. Under the current design parameters, the diameter
All the above results show that the mooring system utilized and optimized here is feasible and reliable. In the future, more detailed design is to be carried out for the prototype machine manufacture. Through rough calculations, the costs of the present mooring system are about 40% lower than those of the traditional 4 or 5 points mooring system. Sea trials will be conducted in order to test the station-keeping capability of the present mooring system.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The authors are grateful to the financial support provided by National Natural Science Foundation of China (41376100), National High Technology Research and Development Program of China (863 Project, 2012AA052601), Special Fund for Ocean Renewable Energy of SOA (QDME2011GD02), Shandong Natural Science Funds for Distinguished Young Scholar (JQ201314), Qingdao Municipal Science & Technology Program (13-4-1-38-hy), and the Program of Introducing Talents of Discipline to Universities (111 Project, B14028).