Effects of Inclination and Cross-Sectional Variations on Resonance Characteristics of Oscillating Water Columns

Abstract

The oscillating water column (OWC) wave energy converter (WEC) is one of the most reliable methods for wave power generation. OWCs typically have low energy conversion efficiency for waves outside their resonance period. Therefore, it is crucial to align the OWC's resonance period with the prevalent frequencies of the incoming waves. Traditional OWCs utilize a vertical motion, with their resonance period determined by the water column's depth. However, previous research has shown that the resonance period can be adjusted by other methods, such as by using an inclined OWC or increasing the water column's mass to form a U-shaped OWC, without altering its depth. Nevertheless, few studies have systematically investigated the effects of the water column's length and angle on the resonance period. This study aims to understand the resonance characteristics of OWCs in which the inclination angle and cross-sectional area change midway along the column, systematically formulating the resonance period.

The target OWCs have a circular cross-section, with changes in inclination angle and cross-sectional area occurring midway under the water. These OWCs operate under offshore conditions, where waves are transmitted, and the air chambers remain fixed.

Prior to conducting simulations and experiments with specific OWC shapes, we derived the equation of motion for the OWC model using the unsteady Bernoulli equation for the target shape. This equation allowed us to formulate the undamped natural frequency, which is known to closely approximate the resonance period, using geometrical parameters such as depth, cross-sectional area, and inclination angle.

For the simulations and experiments, we used OWCs with inclined cylindrical shapes. The basic geometry of these cylinders includes an inclined cylindrical air chamber with an inner diameter of 10 cm, inclined at 90°, 45°, and 30° from the horizontal. To examine the effects of changes in cross-sectional area, models with a four times larger under water cross-sectional area than the water surface cross-sectional area were tested .Additionally, to understand the effects of changes in inclination angle, more 30° inclined cylinders were added to the basic shapes underwater.

In the numerical analysis, the potential flow around the OWCs was solved using Ansys AQWA. The simulation confirmed that the Response Amplitude Operator (RAO) peaked near the natural frequency period estimated by the unsteady Bernoulli equation.

In the water tank experiment, free-damped oscillation measurements were initially taken to validate the equation estimating the undamped natural period. Subsequent wave-making experiments utilized regular waves with a height of 5 cm and periods ranging from 0.8 s to 2.5 s to assess energy conversion efficiency. It was confirmed that larger area ratios and smaller inclination angles extended the resonance period and the resonance period does not change much with the same underwater length of the OWC.