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Fundamental formulae for wave-energy conversion
Johannes Falnes1, Adi Kurniawan2
1Department of Physics , Norwegian University of Science and Technology (NTNU) , 7491 Trondheim, Norway.
Royal Society Open Science
|June 12, 2015
Summary
This study compares three mathematical expressions for wave power absorbed by wave energy converters (WECs). It finds that while all yield correct average power, only one quantifies instantaneous absorbed power and reactive power.
Area of Science:
- Ocean Engineering
- Renewable Energy Systems
- Wave Mechanics
Background:
- Wave energy conversion (WEC) devices, including oscillating bodies and oscillating water columns (OWCs), are crucial for harnessing ocean energy.
- Accurate mathematical modeling of absorbed wave power is essential for optimizing WEC performance and design.
- Recent discussions have highlighted the need for clarity on different methods for calculating time-average absorbed wave power.
Purpose of the Study:
- To derive, compare, and discuss three distinct mathematical expressions for time-average absorbed wave power by WEC units or arrays.
- To identify the expression suitable for quantifying instantaneous absorbed wave power and reactive power.
- To introduce new formulae for reactive radiation parameters and simplify calculations for maximum absorbed wave power.
Main Methods:
- Mathematical derivation and comparison of three expressions for time-average absorbed wave power.
- Development of new formulae relating added-mass and reactive radiation-parameter matrices to surrounding fluid energy.
- Introduction of a complex collective oscillation amplitude for simplified power absorption calculations.
- Extension of existing results for direction-average maximum absorbed wave power.
Main Results:
- All three derived expressions accurately calculate the time-average absorbed wave power.
- Only the expression based on complex oscillation amplitudes can quantify instantaneous absorbed wave power and associated reactive power.
- New formulae were developed for reactive radiation parameters, linking them to kinetic and potential energy differences.
- A simplified algebraic method using a complex collective oscillation amplitude was presented for maximum absorbed wave power.
Conclusions:
- The choice of mathematical expression for absorbed wave power depends on whether instantaneous or time-average values are required.
- The new formulations provide deeper insights into the reactive aspects of WEC hydrodynamics.
- The study offers a simplified approach to calculating maximum wave power absorption for WEC arrays, including complex configurations.
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