Analytical and Numerical Study of Piston-Type Active Wave Absorbers with Different Draft Ratios

For active wave absorbers in force-control mode, the optimal feedback (control) force provided by the control system depends on the hydrodynamic forces. This work investigates a piston-type wave absorber with different draft-to-water depth ratios, focusing on the frequency-dependent hydrodynamic coefficients, wave absorption efficiency, wave absorber displacement and velocity, and control force. Analytical results were derived based on potential flow theory, confirming that regular incident waves can be fully absorbed by the piston-type active wave absorber at any draft ratio by optimizing the control force. The results for the wave tank with a typical water depth of 3 m were studied in detail. The draft ratio has a strong influence on the hydrodynamic coefficients. At the maximum wave absorption efficiency, the displacement and velocity amplitudes are sensitive to the draft ratio in the low-frequency region, increase with decreasing draft ratio, and are independent of the mass of the wave absorber. The control force required can be extremely large for a draft ratio greater than 1/3. The control force increases significantly as the draft ratio increases. The mass of the wave absorber has a weak influence on the control force. A time-domain numerical method based on the boundary element method was developed to verify the analytical solutions. Perfect agreements between the analytical solutions and the numerical results were obtained.