Geometrical Optimization of U-Oscillating Water Columns in Random Waves

Abstract

This paper deals with the problem of designing an optimal U - Oscillating Water Column (U-OWC) device equipped with a Wells turbine. Specifically, the paper proposes the implementation of a genetic algorithm for designing a U-OWC exposed to the typical sea states available in the Mediterranean Sea. The first challenge encountered in this problem is the efficient calculation of the U-OWC hydrodynamic parameters. The second challenge relates to the fact that the U-OWC dynamics is governed by two coupled nonlinear ordinary differential equations with no closed-form solution. For reducing the computational cost, the genetic algorithm is combined with a semi-analytical approach used for determining the U-OWC hydrodynamic parameters and with a statistical linearization based approximate solution of the equations governing the U-OWC dynamics. Such a procedure allows estimating efficiently, albeit approximately, the power output of the system. Numerical results compare a design based on a conventional “design sea state” vis-à-vis a design based on a “design wave climate”. For this purpose, the case study of the Roccella Jonica marina (Reggio Calabria, Italy) is considered, as relevant wave data are available to characterize the most energetic seas as well as depicting the global wave climate available at that location. The numerical results highlight the fact that an optimization conducted on the basis of a design sea state does not lead to an optimal design in a wave climate.

Stochastic response determination of U-OWC energy harvesters: a statistical linearization solution treatment accounting for intermittent wave excitation

“…[10], where it was shown that the U-OWC configuration exhibited enhanced hydrodynamic performance compared to the traditional OWC, or to the L-shaped OWC. Moreover, the performance of the U-OWC is strongly dependent on its geometrical characteristics [11,12], such as the length and the width of the U-duct, the position of its opening below the mean water level, and the width and height of the inner chamber. Further, the optimal selection and control of the Power Take-Off (PTO) system is critical for maximizing the amount of converted energy [13].…”

“…Furthermore, statistical linearization has been employed for stochastic response determination and optimization of diverse wave energy harvesting devices [26], including point-absorbers [27], OWCs [28], and arrays of OWCs and U-OWCs [29]. Also, the methodology has found practical applications pertaining, indicatively, to the case study of the U-OWC in the Civitavecchia harbor (Rome, Italy) [30], and to the design of a U-OWC wave power plant to be installed in the Mediterranean Sea [11]. Although statistical linearization has exhibited a high degree of reliability in determining both OWC and U-OWC statistics, note that the horizontal opening of the U-duct is closer to the free surface compared to the traditional OWCs.…”

“…In this regard, considering time domain response analyses within the context of a MC solution treatment of the problem, the above phenomenon can be readily taken into account by examining at a given time instant whether the water surface is below, or not, the U-duct opening. Nevertheless, referring to earlier efforts considering a statistical linearization solution treatment of the problem, the inlet uncovering effect was either neglected [29,30], or accounted for in a rather heuristic manner [11]. In both cases, it is clear that the degree of the involved approximations is quite high, especially in cases of severe seas where inlet uncovering can be a frequent event.…”

Nonlinear stochastic analysis of wave energy converters via statistical linearization.

“…However, despite the advantages of the technique, a limited number of papers has applied the SL for WECs [21][22][23][24][25][26][27]. This technique is a valuable tool for estimating the nonlinear response of the system, especially for optimizing a system with a large number of parameters [28] and several sea states [29].…”

“…In addition, the mean power is calculated to compare the difference between the traditional FD results with those using SL. In this regard, the linearized form of Equations (5.21) and (5.22) are derived: The response matrix is computed as: 28) where S F (ω) denotes the power spectrum of the excitation, and ( ) T is the transpose conjugate of a matrix. As the wave excites the water column, the power spectrum of the excitation force contain only the first term:…”