1D simulation of oscillating water column wave energy converter with multiple inclination and change of cross-sectional area

Title: Influence of Water Column Geometry on Natural Period in Oscillating Water Column Wave Energy Converters Abstract: The primary energy conversion in Oscillating Water Column (OWC) wave energy converters involves transforming wave energy into pneumatic energy. Due to the utilization of water column oscillations, energy conversion efficiency peaks when the natural frequency of the water column resonates with the incident wave frequency, decreasing significantly outside this resonance range. Therefore, in the initial design phase, it is crucial to ensure that the natural frequency, estimated based on the water column's geometry, aligns closely with the expected wave periods. For a basic vertical OWC, the natural period can be calculated using the ratio of gravitational acceleration to water column depth. However, in practical engineering, the water column depth often matches the wave height due to structural constraints and the desire to harness energy from near-surface waves, making precise natural period adjustments uncommon. Previous studies have shown that modifying the water column into a U-shape or introducing an inclination allows for adjustments in both the effective length and gravitational effects, with U-shaped OWCs already implemented in breakwater structures. This study investigates how fundamental geometric parameters, such as water column length, inclination, and cross-sectional area, influence the natural period. We derived the natural period and the equations of motion for one-dimensional (1D) simulations using the unsteady Bernoulli equation for eight different configurations: varying inclination angles in two stages and cross-sectional area changes along the column. The experimental setup featured simple cylindrical columns submerged in water, allowing wave transmission and fixing the columns in place—idealized conditions focused on principle verification rather than practical application. The equations of motion resemble traditional single-degree-of-freedom oscillation models; however, our derivation revealed that changes in cross-sectional area introduce effects analogous to mechanical speed increasers or torque converters, significantly impacting the natural period. The derived equation is validated against experimental results across the eight geometric configurations. Model parameters were identified through free oscillation experiments, and the water column's dynamic response under wave excitation in wave tank experiments closely matched the theoretical predictions, particularly concerning the natural period. These findings highlight the critical role in determining basic geometric shape of OWC device, providing foundational insights for future engineering applications.