Nonlinear Analysis of an Oscillating Water Column Wave Energy Device in Frequency Domain via Statistical Linearization

2019 ◽  
Author(s):  
Leandro S. P. da Silva ◽  
Celso P. Pesce ◽  
Helio M. Morishita ◽  
Rodolfo T. Gonçalves
Keyword(s):  
System Dynamics ◽  
Frequency Domain ◽  
Water Column ◽  
Wave Energy ◽  
Time Domain ◽  
Computational Cost ◽  
Operating Conditions ◽  
Statistical Linearization ◽  
Large Displacements ◽  
Oscillating Water Column

Abstract Wave energy converters (WECs) are often subject to large displacements during operating conditions. Hence, nonlinearities present in numerical methods to estimate the performance of WECs must be considered for realistic predictions. These large displacements occur when the device operates on resonant conditions, which results in maximum energy conversion. The system dynamics are usually simulated via time domain models in order to being able to capture nonlinearities. However, a high computational cost is associated with those simulations. Alternatively, the present work treats the nonlinearities in the frequency domain via Statistical Linearization (SL). The SL results are compared to the Power Spectrum Density (PSD) of time domain simulations to verify the reliability of the proposed method. In this regard, the work initiates with the derivation of the governing equations of the air-chamber and the Oscillating Water Column (OWC). Then, the SL technique is presented and applied. The SL results show a satisfactory agreement for the system dynamics, mean surface elevation, mean pressure, and mean power compared to time domain simulations. Also, the SL technique produces a rapid estimation of the response, which is an effective approach for the evaluation of numerous environmental conditions and design, and further optimization procedures.

Nonlinear Analysis of an Oscillating Wave Surge Converter in Frequency Domain via Statistical Linearization

2020 ◽  
Author(s):  
Leandro S. P. da Silva ◽  
Nataliia Y. Sergiienko ◽  
Benjamin S. Cazzolato ◽  
Boyin Ding ◽  
Celso P. Pesce ◽  
...  
Keyword(s):  
Nonlinear Analysis ◽  
Frequency Domain ◽  
Wave Energy ◽  
Numerical Models ◽  
Computational Cost ◽  
Viscous Drag ◽  
Design Parameters ◽  
Statistical Linearization ◽  
Mean Power ◽  
Energy Devices

Abstract Wave energy devices operate in resonant conditions to optimize power absorption, which leads to large displacements. As a result, nonlinearities play an important role in the system dynamics and must be accounted for in the numerical models for realistic prediction of the power generated. In general, time domain (TD) simulations are employed to capture the effects of the nonlinearities. However, the computational cost associated with these simulations is considerably higher compared to linear frequency domain (FD) methods. In this regard, the following work deals with the nonlinear analysis of an oscillating wave surge converter (OWSC) in the FD via the statistical linearization (SL) technique. Four nonlinearities for the proposed device are addressed: Coulomb-like torque regulated by the direction of motion, viscous drag torque, nonlinear buoyant net torque, and parametric excitation torque modulated by the flap angle. The reliability of the SL technique is compared with nonlinear TD simulations in terms of response probability distribution and power spectrum density (PSD) of the response and torque; and mean power produced. The results have demonstrated a good agreement between TD simulations and SL, while the computation time of the SL model is approximately 3 orders of magnitude faster. As a result, SL is a valuable tool to assess the OWSC performance under various wave scenarios over a range of design parameters, and can assist the development of such wave energy converters (WECs).

A Multiple Harmonic Open-Loop Controller for Hydro/Aerodynamic Force Measurements in Rotating Machinery Using Magnetic Bearings

2002 ◽  
Vol 124 (4) ◽  
pp. 827-834 ◽  
Author(s):  
D. O. Baun ◽  
E. H. Maslen ◽  
C. R. Knospe ◽  
R. D. Flack
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Open Loop ◽  
Rotating Machinery ◽  
Operating Conditions ◽  
Rotor Vibration ◽  
Aerodynamic Forces ◽  
Analog Input ◽  
Input And Output ◽  
The Time Domain

Inherent in the construction of many experimental apparatus designed to measure the hydro/aerodynamic forces of rotating machinery are features that contribute undesirable parasitic forces to the measured or test forces. Typically, these parasitic forces are due to seals, drive couplings, and hydraulic and/or inertial unbalance. To obtain accurate and sensitive measurement of the hydro/aerodynamic forces in these situations, it is necessary to subtract the parasitic forces from the test forces. In general, both the test forces and the parasitic forces will be dependent on the system operating conditions including the specific motion of the rotor. Therefore, to properly remove the parasitic forces the vibration orbits and operating conditions must be the same in tests for determining the hydro/aerodynamic forces and tests for determining the parasitic forces. This, in turn, necessitates a means by which the test rotor’s motion can be accurately controlled to an arbitrarily defined trajectory. Here in, an interrupt-driven multiple harmonic open-loop controller was developed and implemented on a laboratory centrifugal pump rotor supported in magnetic bearings (active load cells) for this purpose. This allowed the simultaneous control of subharmonic, synchronous, and superharmonic rotor vibration frequencies with each frequency independently forced to some user defined orbital path. The open-loop controller was implemented on a standard PC using commercially available analog input and output cards. All analog input and output functions, transformation of the position signals from the time domain to the frequency domain, and transformation of the open-loop control signals from the frequency domain to the time domain were performed in an interrupt service routine. Rotor vibration was attenuated to the noise floor, vibration amplitude ≈0.2 μm, or forced to a user specified orbital trajectory. Between the whirl frequencies of 14 and 2 times running speed, the orbit semi-major and semi-minor axis magnitudes were controlled to within 0.5% of the requested axis magnitudes. The ellipse angles and amplitude phase angles of the imposed orbits were within 0.3 deg and 1.0 deg, respectively, of their requested counterparts.

Nonlinear 2D analysis of the efficiency of fixed Oscillating Water Column wave energy converters

2014 ◽  
Vol 64 ◽  
pp. 255-265 ◽  
Author(s):  
Yongyao Luo ◽  
Jean-Roch Nader ◽  
Paul Cooper ◽  
Song-Ping Zhu
Keyword(s):  
Water Column ◽  
Wave Energy ◽  
Oscillating Water Column ◽  
Wave Energy Converters ◽  
Energy Converters

Scale and Configuration Effects of an Airchamber on PTO of Oscillating Water Column Type Wave Energy Converters

2021 ◽  
Author(s):  
Tomoki Ikoma ◽  
Shota Hirai ◽  
Yasuhiro Aida ◽  
Koichi Masuda
Keyword(s):  
Water Column ◽  
Wave Energy ◽  
Water Surface ◽  
Air Pressure ◽  
Scale Model ◽  
Linear Potential ◽  
Oscillating Water Column ◽  
Wave Energy Converters ◽  
Air Chamber ◽  
Energy Converters

Abstract Wave energy converters (WECs) have been extensively researched. The behaviour of the oscillating water column (OWC) in OWC WECs is extremely complex due to the interaction of waves, air, and turbines. Several problems must be overcome before such WECs can be put to practical use. One problem is that the effect of the difference in scale between a small-scale experimental model and a full-scale model is unclear. In this study, several OWC models with different scales and geometries were used in forced oscillation tests. The wave tank was 7.0 m wide, 24.0 m long, and 1.0 m deep. In the static water experiment, we measured the air pressure and water surface fluctuations in an air chamber. For the experiments, models with a box shape with an open bottom, a manifold shape with an open bottom, and a box shape with a front opening, respectively, were fabricated. Furthermore, 1/1, 1/2, and 1/4 scale models were fabricated for each shape to investigate the effects of scale and shape on the air chamber characteristics. Numerical calculations were carried out by applying linear potential theory and the results were compared with the experimental values. The results confirmed that the air chamber shape and scale affect the air pressure fluctuation and water surface fluctuation inside the OWC system.

Evaluation of 3-D Computational Model of Oscillating Water Column Converter with Constructal Design with Three Degrees of Freedom and Limited Chimney Height

2021 ◽  
Vol 407 ◽  
pp. 128-137
Author(s):  
Vinícius Bloss ◽  
Camila Fernandes Cardozo ◽  
Flávia Schwarz Franceschini Zinani ◽  
Luiz Alberto Oliveira Rocha
Keyword(s):  
Water Column ◽  
Wave Energy ◽  
Degrees Of Freedom ◽  
Numerical Study ◽  
Mechanical Energy ◽  
Ocean Waves ◽  
Response Surfaces ◽  
Oscillating Water Column ◽  
Promising Source ◽  
Three Degrees Of Freedom

Theoretically, ocean waves contain enough mechanical energy to supply the entire world’s demand and, as of late, are seen as a promising source of renewable energy. To this end, several different technologies of Wave Energy Converters (WEC) have been developed such as Oscillating Water Column (OWC) devices. OWCs are characterized by a chamber in which water oscillates inside and out in a movement similar to that of a piston. This movement directs air to a chimney where a turbine is attached to convert mechanical energy. The analysis conducted was based on the Constructive Design Method, in which a numerical study was carried out to obtain the geometric configuration that maximized the conversion of wave energy into mechanical energy. Three degrees of freedom were used: the ratio of height to length of the hydropneumatic chamber (H1/L), the ratio of the height of the chimney to its diameter (H2/d) and the ratio of the width of the hydropneumatic chamber to the width of the wave tank (W/Z). A Design of Experiments (DoE) technique coupled with Central Composite Design (CCD) allowed the simulation of different combinations of degrees of freedom. This allowed the construction of Response Surfaces and correlations for the efficiency of the system depending on the degrees of freedom (width and height of the chamber), as well as the optimization of the system based on the Response Surfaces.

scholarly journals Wave power extraction from a bottom-mounted oscillating water column converter with a V-shaped channel

2014 ◽  
Vol 470 (2167) ◽  
pp. 20140074 ◽  
Author(s):  
Zhengzhi Deng ◽  
Zhenhua Huang ◽  
Adrian W. K. Law
Keyword(s):  
Water Column ◽  
Water Depth ◽  
Wave Energy ◽  
High Efficiency ◽  
Expansion Method ◽  
Opening Angle ◽  
Energy Extraction ◽  
Oscillating Water Column ◽  
Wave Direction ◽  
Power Extraction

An analytical theory is developed for an oscillating water column (OWC) with a V-shaped channel to improve the pneumatic efficiency of wave energy extraction. An eigenfunction expansion method is used in a cylindrical coordinate system to investigate wave interaction with the OWC converter system. Auxiliary functions are introduced to capture the singular behaviours in the velocity field near the salient corners and cusped edges. Effects of the OWC dimensions, the opening angle and length of the V-shaped channel, as well as the incident wave direction, on the pneumatic efficiency of wave energy extraction are examined. Compared with a system without the V-shaped channel, our results show that the V-shaped channel can significantly increase the conversion efficiency and widen the range of wave frequency over which the OWC system can operate at a high efficiency. For typical coastal water depths, the OWC converter system can perform efficiently when the diameter of the OWC chamber is in the range of 1 5 – 1 2 times the water depth, the opening angle of the V-shaped channel is in the range of [ π /2, 3 π /4] and the length of the V-shaped channel is in the range of 1–1.5 times the water depth.

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