Theoretical and experimental analysis of a dual chamber floating oscillating water column device for efficient power absorption in Greek waters

1 Introduction

Numerous studies, both past and ongoing, on floating oscillating water column (OWC) devices emphasize this wave energy conversion method due to its straightforward operation, structural durability, ease of maintenance, and versatility. The OWC converter captures wave energy by utilizing the movement of the water’s free surface as a piston, which generates an air flow that drives an air turbine coupled to a generator.

OWCs confer several notable advantages over other wave energy conversion devices (WECs). Primarily, they are characterized by a minimal number of moving components, notably the air turbine and electrical generator, which are typically situated above the water surface in conventional configurations (Rosati et al., 2022). These systems are capable of operating efficiently even under low wave frequencies, approximately 0.1 Hz (Evans and Porter, 1995). Additionally, OWCs attain the highest rotational speeds of the Power-Take-Off (PTO) system among WECs, thereby resulting in reduced torque levels and associated mechanical stresses. A further advantage lies in their capacity to regulate or dissipate surplus energy by modulating the torque exerted on the air turbine through the use of bypass or series valves (Garrido et al., 2017). The presence of air compressibility within the chamber imparts a spring-like effect, which serves to diminish structural stresses and prolong the fatigue life of the device (Falcao and Henriques, 2018; Portillo et al., 2023). Nonetheless, the principal drawback of OWCs pertains to their relatively high structural costs in comparison to their wave energy absorption efficiency, thereby elevating the Levelized Cost of Energy (LCOE). This financial burden tends to escalate from nearshore to deep-water sites, as well as from regions with mild wave conditions to those experiencing extreme wave activities. Moreover, the commercialization of ocean energy technology continues to face significant challenges, partly due to the limited availability of suitable locations and space, particularly within heavily contested coastal zones where increasing competition for utilization further constrains deployment options.

The earliest documented hydrodynamic analysis of a floating oscillating water column (OWC) was conducted by McCormick (1976), who provided a theoretical examination of a pneumatic-type wave energy buoy, operating under the assumption that the buoy’s heave motion was independent of the water column’s oscillations within the chamber. Since that initial study, numerous investigations have explored various geometric configurations of OWCs with the aim of maximizing their efficiency. Over the past decade, dual-chamber OWCs have gained considerable prominence. This design permits enhanced energy capture by amplifying the oscillations of the water column, thereby improving the pneumatic efficiency of the system. Additionally, the dual-chamber arrangement facilitates a more stable and uniform airflow to the turbines, which substantially enhances the overall energy conversion process.

Ning et al. (2018) employed an analytical methodology to simulate a floating dual-chamber OWC, demonstrating that the incorporation of an outer-chamber shell improves both the peak hydrodynamic efficiency and the effective frequency bandwidth. Ning et al. (2019) utilized a higher-order Boundary Element Method (BEM) to evaluate the hydrodynamic efficiency of a two-dimensional onshore dual-chamber OWC, concluding that its performance near resonance was superior to that of single-chamber alternatives. Shalby et al. (2019) performed three-dimensional Computational Fluid Dynamics (CFD) simulations using STAR-CCM + on a small-scale fixed multi-chamber OWC, with results in good agreement with experimental measurements regarding air pressure, free surface elevation, and airflow rate. Wang et al. (2019) adopted a two-dimensional numerical CFD model in OpenFOAM to estimate wave power extraction from a dual OWC system. Wang et al. (2021) developed a theoretical analysis of a dual-chamber oscillating water column featuring a pitching front lip, achieving more efficient wave power extraction across a broader wave frequency spectrum compared to OWCs with stationary lips. Wang and Zhang (2021) examined a dual-chamber OWC comprising separate units, analyzing how the chamber’s breadth, lip-wall drafts, and gap length influence efficiency. Gadelho and Guedes Soares (2022) simulated a dual-chamber OWC using OpenFOAM, reporting enhanced efficiency at high wave heights for moving OWCs in comparison to restrained configurations. More recently, Rezanejad et al. (2025) experimentally examined an improved floating dual-chamber OWC design, reporting a substantial increase in hydrodynamic efficiency over earlier flexibly moored configurations, while Zhou et al. (2025) numerically investigated a multi-chamber OWC array over complex bathymetry, further confirming the efficiency and bandwidth benefits of multi-chamber arrangements.

Building upon prior research, it is evident that the hydrodynamic performance of OWCs can be markedly improved through the optimization of their geometric features. While considerable attention has been directed toward refining the geometry of single-chamber OWCs to enhance their efficiency, dual-chamber configurations are demonstrated to be more effective and to offer a wider operational bandwidth. Nonetheless, most existing studies focus on bottom-fixed, near-shore devices (e.g., Rezanejad et al., 2015; 2019; Gadelho et al., 2024; Palmer et al., 2023; Mandev et al., 2024) or employ two-dimensional (2-D) modeling approaches (e.g., Wang et al., 2019; 2022a; 2022b; Trivedi et al., 2022; Wang et al., 2020; Elhanafi et al., 2018). There remains limited research dedicated specifically to floating dual-chamber OWCs, with most existing work emphasizing experimental investigations on rectangular converters, whether fixed in response to wave impacts (Ning et al., 2019; Kim et al., 2023) or moored using flexible systems (Xu et al., 2020; 2022; Gadelho et al., 2021).

In contrast, the present study investigates an integrated offshore floating dual-chamber OWC system specifically developed for realistic deployment conditions in the Aegean Sea. The proposed OWC concept combines a coaxial cylindrical dual-chamber configuration with a tension-leg platform (TLP) mooring system and includes coupled hydro-aero-dynamic analysis, site-selection methodology, metocean extreme-value assessment, and experimental validation through scaled model testing. Unlike previous dual-chamber OWC studies, which have largely relied on two-dimensional or CFD-based hydrodynamic modelling of fixed or restrained rectangular geometries (Ning et al., 2018; Ning et al., 2019; Wang et al., 2019; 2022a; Wang and Zhang, 2021; Gadelho and Guedes Soares, 2022) or on experimental investigations of flexibly moored rectangular converters (Xu et al., 2020; 2022; Gadelho et al., 2021; Kim et al., 2023), the present work introduces a fully three-dimensional, axisymmetric coaxial cylindrical dual-chamber geometry coupled with a TLP mooring system, which to the authors knowledge have not previously been examined for dual-chamber OWC devices. Moreover, the analysis is grounded in site-specific metocean conditions for the Aegean Sea and is validated directly against dedicated scaled-model wave-tank experiments, providing an integrated theoretical-experimental verification. Specifically, this paper presents a design-oriented semi-analytical approach for addressing linearized diffraction and radiation issues related to a dual-chamber, surface-piercing cylindrical OWC with a vertical symmetry axis. Additionally, it includes a framework for experimental design and the selection of measurement instruments for scaled-down model tests. The focus is on the ETHOS (Novel Type Offshore Floating Wave Energy Converter for Efficient Power Absorption) OWC converter which has been described in Konispoliatis (2025); Konispoliatis and Mavrakos (2025) works. The ETHOS floating system consists of two coaxial hollow cylindrical shapes. The space between the vertical walls of these cylinders allows for oscillations of the water column inside (see Figures 1, 2). Wave action causes the water column to move up and down like a piston, resulting in the compression and decompression of air. This movement creates an air flow that travels back and forth through an air turbine connected to an electric generator.

The present work serves as a follow-up to the study by Konispoliatis (2025), in which advanced numerical simulations were conducted to predict the geometrical characteristics of the ETHOS floating system under wave loading conditions. Key parameters examined included the oscillating chamber’s geometry (draft and thickness) as well as the number and type of oscillating chambers. Furthermore, Konispoliatis and Mavrakos (2025) performed a comprehensive theoretical analysis to assess the influence of various mooring systems on the energy conversion efficiency of the ETHOS wave energy converter. Their comparative study demonstrated the superior performance of the tension-leg platform (TLP) mooring system over a catenary mooring configuration across a wider range of wave frequencies.

Consequently, the primary objective of this manuscript is to systematically present a frequency-domain analysis of the ETHOS system, accounting for prevailing environmental conditions at selected locations along the Greek coastline. Advanced numerical simulations are performed to model the coupled hydro-aero-dynamic behavior of the system, incorporating hydrodynamic interactions on the ETHOS floater, air turbine characteristics, and mooring system properties. These simulations aim to evaluate the wave energy conversion efficiency of the ETHOS device at the proposed installation sites. Additionally, this work includes the design of wave tank experiments and the selection of appropriate measurement instrumentation for scaled-down model tests, enabling a direct comparison between experimental and numerical results.

The manuscript is structured as follows. Section 2 outlines the key characteristics of the ETHOS floating structure, while Section 3 presents a climate analysis for potential installation sites along the Greek coastline. Section 4 details the hydrodynamic analysis of the ETHOS system, conducted in the frequency domain under regular wave conditions. This section includes the hydrodynamic modeling of the floater using an analytical approach, along with the coupled hydro-aero-dynamic solution integrating the floater, air turbine, and mooring system. In Section 5 numerical results regarding the wave power efficiency of the ETHOS system are presented. Section 6 provides a comprehensive presentation of wave tank experiments performed on a scaled dual-chamber OWC model. Section 7 discusses the validation of experimental results against numerical predictions, and finally, Section 8 summarizes the key findings and conclusions of the study.

2 Description of the ETHOS floating WEC system

The ETHOS floating WEC system comprises two coaxial, free-surface-piercing toroidal cylinders with vertical symmetry axes, positioned in a water domain of constant depth, d (see Figure 2). In the present study, the water depth is set to d = 130 m. Based on the analysis conducted by Konispoliatis (2025), the inner toroidal body has a radius of a 2 = 9 m, while the radius of the internal water surface is a 1 = 6.083 m. The vertical distance between the bottom of the inner body and the seabed is h 1 = 124.5 m. Similarly, the outer toroidal body has a radius of a 4 = 13 m, with its bottom positioned at h 2 = 116 m, from the seabed. The annulus water region between the two bodies has a radius of a 3 = 12 m . The center of gravity of the ETHOS system is assumed to be located approximately 1.4 m above the waterline. A summary of the primary geometric parameters of the OWC under consideration is provided in Table 1.

TABLE 1. Floating cylindrical body geometry.

The dual-chamber OWC device incorporates a TLP mooring system comprising four symmetrically arranged steel spiral rope tethers (Class 1,640), as illustrated in Figure 2. The fairleads–defined as the body-fixed connection points between the mooring lines and the floater–are positioned at the base of the inner pontoon at a depth of 5.5 m below the SWS (refer to Figure 3). Each mooring line has an unstretched length of 124.5 m. The technical specifications of the TLP mooring configuration are comprehensively detailed in Konispoliatis and Mavrakos (2025), with key parameters summarized in Table 2.

TABLE 2. TLP mooring properties.

The implemented TLP configuration enhances the system’s vertical stiffness, resulting in a significant reduction of the heave natural period. This mechanical response characteristic enables the system’s heave period to be tuned outside the predominant energy range of the wave spectrum, thereby optimizing the device’s operational performance in typical sea states.

3 Environmental conditions and design values

3.1 Site selection and data

The optimum location for the ETHOS OWC operation depends on multiple factors, yet demanding specific principles. The four main criteria that were taken into consideration are the wave regime, bathymetry, marine protected areas and territorial waters. However, subsea grid, marine traffic, access to big ports and tourism development areas were also accounted for in the site selection process. The aforementioned standards are discussed along with the respective utilized data.

3.1.1 Wave regime

As far as wave energy converters are concerned, due to their operation principles, an intense wave climate is of utmost importance for generating the highest possible energy. It is therefore fundamental to install such structures in areas with high wave energy potential. In this context, the wave regime is evaluated based on the wave power density P in W/m (also known as wave energy flux per unit length of wave front) that is defined in the following Equation 1:where ρ is the density of seawater that is considered constant and equal to 1,025 kg/m³, g is the gravitational acceleration equal to 9.8066 m/s², H s is the significant wave height in m, and T e is the wave energy period in s.

P = ρ g 64 π H s 2 T e (1)

The above metric requires a reliable dataset for the adequate extraction of inferences. Produced by the European Centre for Medium-Range Weather Forecasts (ECMWF), the ERA5 reanalysis dataset was utilized, which combines vast amounts of historical observations into global estimates using advanced modeling and data assimilation systems (Hersbach et al., 2020). Moreover, it provides hourly estimates of a large number of atmospheric, land and oceanic climate variables, covering the Earth on a ≈30 km grid and resolving the atmosphere using 137 levels from the surface up to a height of 80 km. The data can be freely accessed from the Copernicus Climate Data Store (https://cds.climate.copernicus.eu/), as well as from the European Centre for Medium-Range Weather Forecasts (https://www.ecmwf.int) (Hersbach et al., 2020; 2023). In the present work, 20 years (1 January 2000–31 December 2019) of available wave data were utilized for the Greek Seas (defined by a rectangle with the top left corner at 42° N, 19° E and bottom right corner at 33° N, 30° E). For the significant wave height and the wave energy period, the data are provided on a 0.50° × 0.50° spatial grid (Hersbach et al., 2023).

The spatial distributions of the mean annual wave power potential of the Greek seas are presented in Figure 4. Wave energy flux appears higher in areas characterized by large fetch lengths that lead to larger wind waves and swells. Although the Aegean Sea is an area characterized by strong winds, the presence of many islands limits the wind fetch blocking swells from being developed (Kardakaris et al., 2021). Consequently, wave power density values are relatively low (3–5 kW/m), while in northeast of Skyros Isl. and west and northeast areas of Crete Isl., it ranges between 5–7 kW/m.

3.1.2 Bathymetry

The Aegean Sea is known for its deep waters and steep seabed slopes. Considering the fact that floating structures, such as ETHOS OWC, demand depth limitations for financial feasibility due to increased costs and complexity of their mooring systems, the representative installation locations should be advantageous both in terms of wave power production and bathymetric conditions. The bathymetry data of the examined region were derived from the European Marine Observation and Data Network (EMODnet Bathymetry). The investigated marine territories were limited offshore to water depths between 50 and 200 m, as presented in Figure 4 (brown areas).

At this stage, three possible locations for installing ETHOS OWC are presented (Figure 4) considering the two main discussed criteria. To fulfill both, all sites are located in the range of 100–200 m water depth with significant wave energy potential. Furthermore, requirements that are further elaborated herein were accounted for during the selection process. Locations 1 (L1) and 2 (L2) are in the northern part of the Aegean Sea and more specifically south of Ag. Efstratios Isl. [39.40° N, 24.95° E] (at ≈130 m water depth) and north of Skyros Isl. [39.10° N, 24.51° E] (at ≈200 m water depth), respectively. Location 3 (L3) is located in the southern part of the Aegean Sea, northwest of Kasos Isl. and Karpathos Isl. [35.90° N, 26.51° E] (at ≈150 m water depth).

3.1.3 Marine protected areas

Environmental goals globally, focus on expanding the protected area network for biodiversity loss interception. The European Union’s Natura 2000 network covers a high percentage of the terrestrial area of Greece (27.3%), one of the highest in Europe (Spiliopoulou et al., 2021). When siting infrastructure works, a major factor for decision making is to comply with the framework of protected areas. Although such environmental studies are formed in great detail as an independent part of a project, it is vital to locate the unavailable territories in the preliminary design. In this context, selected sites are outside of marine protected areas (shown with green hatch in Figure 5) described by the Natura 2000 network (Natura 2000 protected areas network).

3.1.4 Territorial waters

The concept of an exclusive economic zone (EEZ) was adopted through the 1982 United Nations Convention on the Law of the Sea (1982). The installation of ETHOS OWC is chosen not to exceed the territorial waters over which Greece has full sovereignty and have been established to the breadth of a six nautical mile zone. In this respect, although potential installation areas were limited significantly, Figure 5 shows that the three selected locations cover these requirements. It is noted that the purple line indicates the six nautical mile zone limit.

In addition to the above hard constraints for selecting a proper location for the ETHOS OWC installation, the below criteria were also accounted for in the site selection process for a more realistic approach.

3.1.5 Subsea grid

In order for anchoring problems to not arise, selected sites are not located above submarine cable routes. However, it is beneficial for the respective areas to facilitate subsea grid in a relevant close distance not only for easier connection and power transfer, but also for a potential installation of an offshore substation. Figure 6a depicts the aforementioned locations with the present subsea cables of the Aegean Sea, confirming the capability of a direct connection to the nearest available shore.

3.1.6 Access to big ports

The installation of an offshore facility demands access to big ports with a proper industrial zone where onshore works can be completed efficiently. Regarding the selected sites, the nearest ports for supporting installation and maintenance operations are.

• Port of Thessaloniki: ≈265 km from L1 and ≈250 km from L2
• Port of Volos: ≈220 km from L1 and ≈165 km from L2
• Port of Heraklion: ≈140 km from L3

More detailed analysis on transportation costs as well as adequate port facilities, skilled labor force and crane capacity are not examined in this work.

3.1.7 Marine traffic

An offshore power plant should operate in territories where no marine traffic occurs or ship traffic density is relatively low. Navigational safety, as well as vessel traffic risk analysis, has to be taken into account otherwise. In the discussed process, major ship routes were avoided and minor ones were accounted for during the site selection process (Figure 6b).

3.1.8 Tourism

Tourism development areas were also considered in the current methodology (Figure 7). Although their small footprint and volume above sea level, the presence of such offshore energy systems may downgrade the areas aesthetically and visual disturbance may rise to visitors; thus, the respective territories were avoided, or the system is considered for installation far away from areas with significant levels of visits.

For a holistic approach of the ETHOS OWC installation phase, further details on marine spatial planning (Theodora, 2019) should be investigated along with a comprehensive environmental impact study. At the current stage, the data from the three selected locations will be further analyzed to extract the design values that refer to critical environmental conditions determining the robustness of the floating structure and its mooring system.

3.2 Design values

In this subsection, an extreme value analysis (EVA) is performed on wave parameters.

3.2.1 Peaks-over-threshold (POT) method and model diagnostics

As far as EVA methods are concerned, the most widely used are the Block Maxima (BM) and the Peaks-Over Threshold (POT). The latter is chosen amongst the two, since the available sample size of annual maxima is rather poor (20 years) (Soukissian and Tsalis, 2015; 2018). More applications regarding the estimation of metocean extremes can be found in (Soukissian and Kalantzi, 2006; Sartini et al., 2015; Park et al., 2020; Devis-Morales et al., 2017; Ferreira and Guedes Soares, 1998; Caires and Sterl, 2005; Méndez et al., 2006; Dissanayake et al., 2021). For the current data analysis of the extremes, the Peaks-Over-Threshold (POT) method is utilized. A detailed description of the method can be found in Coles (2001).

Using the POT method presupposes the selection of a threshold above which all values are considered extreme. The main challenge, however, is to choose a threshold u that balances bias and variance. Too low a threshold is likely to violate the asymptotic basis of the model, leading to bias, whereas too high a threshold will generate few excesses with which the model can be estimated, leading to high variance. In this context, two approaches are available for threshold selection. One is an exploratory technique carried out prior to model estimation; the other is an assessment of the stability of parameter estimates, based on the fitting of models across a range of different thresholds (Lemos et al., 2020). Regarding the first approach, above a threshold u 0 at which the generalized Pareto distribution provides a valid approximation to the excess distribution, the mean residual life (MRL) plot should be approximately linear in u. The MRL plot consists of the pairs as shown in Equation 2:where x 1 , …, x n u consist of the n u observations that exceed u, and x max is the largest of the x i. In the second approach, the aim is to estimate the model at a range of thresholds and to look for stability of parameter estimates. This argument suggests plotting both σ * = σ u − ξ u (modified scale) and ξ (shape) estimates of the generalized Pareto distribution against u, together with confidence intervals for each of these quantities, and selecting u 0 as the lowest value of u for which the estimates remain near-constant. The parameters of the generalized Pareto distribution can be estimated by the Maximum Likelihood (ML) method.

u , 1 n u ∑ i = 1 n u x i − u : u < x max (2)

The quality of the fitted generalized Pareto model can be assessed by probability (PP) and quantile (QQ) plots. For a threshold u, threshold excesses y 1 ≤…≤ y n and an estimated model H ^, the probability plot consists of the pairs as shown in Equation 3:wherewhile the quantile plot constitutes the locus of points of Equation 5:whereprovided that ξ ^ ≠0. If ξ ^ = 0 the Equations 4, 6 are modified, accordingly, as follows in Equations 7, 8:

i k + 1 , H ^ y i ; i = 1 , … , k (3)

H ^ y = 1 − 1 + ξ ^ y σ ^ − 1 / ξ ^ (4)

H ^ − 1 i k + 1 , y i ; i = 1 , … , k (5)

H ^ − 1 y = u + σ ^ ξ ^ y − ξ ^ − 1 (6)

H ^ y = 1 − exp − y σ ^ , y > 0 , (7)

H ^ − 1 y = u − σ ^ log y , y > 0 (8)

Provided that both plots depict a very close relation between theoretical and sample quantities, the model diagnostics are completed, and the model is adequately identified.

In offshore engineering applications, the concept of return period and design value is applied to adequately cover the ultimate limit state scenarios. The formal definition of the return period implies that the n −year design value is expected to be exceeded on average once during the next n years. The period of n years is called the return period, associated with the design value (Coles, 2001). Denoting ζ u as the exceedance probability or the proportion of data above a threshold u, and n y the exceedance observations per year, the N-year return level z N is estimated in Equation 9:

z N = u + σ ξ Ν n y ζ u ξ − 1 i f ξ ^ ≠ 0 u + σ ⁡ log Ν n y ζ u i f ξ ^ = 0 (9)

3.2.2 Results

Having concluded to the three representative locations in the Aegean Sea for installing the ETHOS OWC, both time series of significant wave height and wave energy period are analyzed using the peaks-over-threshold (POT) method, modelling the extremes and resulting in 100-year return levels.

More specifically, the ERA5 reanalysis dataset was spatially co-located with the selected locations via the nearby grid point values by using a simple form of inverse squared distance weighting interpolation function based on the values of the four nearest grid points (Figure 8). Denoting by x 1, x 2, x 3 and x 4 the respective variables at the four grid points surrounding the selected location, and r 1, r 2, r 3 and r 4 the corresponding distances from that location, the requested data for each variable at the installation sites can be estimated in Equation 10:

x = ∑ i = 1 4 x i r i 2 ∑ i = 1 4 1 r i 2 (10)

The proper threshold selection for each parameter is based on the aforementioned methodology. Nevertheless, higher thresholds than the ones obtained from the two previous approaches are accepted, if enough excesses are considered and proper diagnostic plots are attained. Besides, such approach is in favor of safety when designing a project, since EVA results are utilized for robustness in extreme scenarios. Tables 3–5 describe the wave climate (i.e., significant wave height H s and wave energy period T e) of locations L1, L2, L3, respectively. Table 6 presents the thresholds for both examined variables of the three selected installation sites along with the amount of each analyzed dataset. Indicatively for the significant wave height of the third location and noting that enough excesses were considered, diagnostic plots show a fair agreement of fit (Figure 9), although MRL and stability plots may suggest lower values of u (Figure 10). None of the plots gives any real cause for concern about the quality of the fitted model, which supports the bias-variance trade-off, suggesting that extremes can be adequately modelled.

TABLE 3. Occurrence table for location 1.

TABLE 4. Occurrence table for location 2.

TABLE 5. Occurrence table for location 3.

TABLE 6. Thresholds and excesses dataset length for every examined parameter and location.

As far as design values are concerned, Figure 11 depicts the return levels, where the well fitted model is also justified by the narrow confidence bands. Respective inferences as the aforementioned ones can result for the rest examined variables. In some cases, the 50-year return level is applied for covering the structural integrity criteria in the design process. However, the 100-year return level is mostly used in such projects to determine the final specifications of a robust structure. Table 7 presents the design values with a return period of 100 years, which will be considered as the main input for further analysis of ETHOS OWC and its mooring system.

TABLE 7. 100-year return values and 95% confidence intervals of H s (m) referring to the three presented locations.

4 Coupled hydro-aero-dynamic analysis

4.1 Diffraction and radiation boundary value problem

The comprehensive potential flow theory governing the hydrodynamic analysis of both single and dual-chamber cylindrical OWC converters has been extensively documented in the works of Konispoliatis and Mavrakos (2016), Konispoliatis and Mavrakos (2019), Konispoliatis et al. (2016), and Konispoliatis (2025). The following presents a succinct overview of the fundamental principles underlying this hydrodynamic problem.

The dual-chamber OWC device is subjected to monochromatic incident waves characterized by frequency ω and linear wave amplitude H / 2. A right-handed cylindrical coordinate system, r , θ , z is adopted, with its origin fixed at the seabed and the z-axis aligned vertically upward with the converter’s axis of symmetry. The analysis employs the following key assumptions: (1) fluid viscosity is neglected, (2) the fluid is incompressible, and (3) both the OWC structure and fluid motions are sufficiently small to justify the application of linear diffraction and radiation theory.

The solution of the diffraction and radiation problems is achieved through the method of matched axisymmetric eigenfunction expansions. The fluid domain surrounding the converter is partitioned into five distinct coaxial ring-shaped regions, designated as I through V (see Figure 2). Within each region, the velocity potential is expressed through appropriate series expansions that satisfy the governing hydrodynamic equations and boundary conditions.

Under regular wave excitation, the dual-chamber OWC device exhibits three degrees of freedom: two translational motions (surge ξ 1, heave ξ 3) and one rotational motion (pitch ξ 5). The corresponding velocity potential Φ r , θ , z ; t = Re φ r , θ , z e − i ω t is formulated as:

φ r , θ , z = φ D r , θ , z + p i n 0 φ p r , θ , z + ∑ j = 1 , 3 , 5 ξ ˙ j 0 φ j r , θ , z (11)

In Equation 11, φ D corresponds to the diffraction potential of the fixed OWC device under wave excitation, where the air duct atop the oscillating columns remains open to the atmosphere, ensuring that the chamber pressure equals atmospheric pressure. The diffraction potential is expressed as φ D = φ 0 + φ 7, with φ 0 denoting the undisturbed incident wave velocity potential and φ 7 representing the scattered potential induced by the presence of the OWC structure. Furthermore, φ p signifies the pressure-radiation potential generated by an oscillating air pressure head P i n = R e p i n 0 e − i ω t, within the chambers which are otherwise stationary. The term φ j describes the motion-radiation potential arising from the forced oscillation of the converter in the j th mode with unit velocity amplitude, while the air duct remains open to atmospheric conditions. The complex velocity amplitude of the converter’s motion in the j th direction is given by ξ ˙ j 0.

The velocity potentials governing the wave-structure interaction problem - comprising the undisturbed incident wave potential φ 0, diffraction potential φ D, and motion-pressure- radiation potentials φ j , φ p are expressed in Equations 12–15 (Konispoliatis and Mavrakos, 2016): where ε m represents the Neumann symbol (ε 0 = 1 ; ε m = 2 for m > 0). The term J m denotes the m th order Bessel function of the first kind, and k is the wavenumber determined from the dispersion relation ω 2 = k g ⁡ tanh k d. Additionally, Z 0 describes the vertical eigenfunction (Equation 6), with Z 0 ′ d being its derivative evaluated at z = d. Also, ρ indicates the water density. The vertical eigenfunction is given by Equation 16:

φ 0 r , θ , z = − i ω H 2 Z 0 z Z 0 ′ d ∑ m = 0 ∞ ε m i m J m k r cos m θ (12)

φ D r , θ , z = − i ω H 2 ∑ m = 0 ∞ ε m i m Ψ D m l r , z cos m θ (13)

φ j r , θ , z = ∑ m = 0 ∞ Ψ j m l r , z cos m θ , j = 1 , 3 , 5 (14)

φ p r , θ , z = 1 i ω ρ ∑ m = 0 ∞ Ψ p m l r , z cos m θ (15)

Z 0 z = 1 2 1 + sinh 2 k d 2 k d − 1 2 ⁡ cosh k z (16)

The functions Ψ D m l, Ψ j m l and Ψ p m l constitute the fundamental unknowns of the boundary value problem. The subscript notation follows: (1) first subscript identifies the boundary problem type (i.e., D: diffraction, j: motion radiation, p: pressure radiation), (2) second subscript indicates the azimuthal mode m, (3) superscript l designates the corresponding fluid region (i.e., I, I I, I I I, I V, and V) surrounding the converter structure.

The velocity potentials φ l (where l = D , j , p) must satisfy the Laplace equation throughout the fluid domain while adhering to the following boundary conditions (Konispoliatis and Mavrakos, 2016; Konispoliatis, 2025):

Outer and inner free surface conditions (z = d):

ω 2 φ l − g ∂ φ l ∂ z = 0 for r ≥ a 4 ; l = D , j , p 0 for a 2 ≤ r ≤ a 3 ; l = D , j − i ω ρ for a 2 ≤ r ≤ a 3 ; l = p 0 for 0 ≤ r ≤ a 1 ; l = D , j − i ω ρ for 0 ≤ r ≤ a 1 ; l = p (17)

Here g is the acceleration due to gravity.

Seabed condition (z = 0):

∂ φ l ∂ z = 0 for l = 0 , j , p (18)

Kinematic conditions of the mean converter’s wetted surface of the converter:

∂ φ l ∂ n → = 0 for l = D , p n j for l = j on S (19)

Radiation condition at infinity (r → ∞) (Kokkinowrachos et al., 1986):

lim r → ∞ k r ∂ φ l ∂ r − i k φ l = 0 for l = j , p (20)

In Equation 19, n → represents the outward unit normal vector to the mean wetted surface S with normal components n j defined as:

n → = n 1 , n 2 , n 3 , r → × n → = n 4 , n 5 , n 6 (21)

In Equation 21, r → denotes the position vector relative to the converter’s reference point. Moreover, the unknown functions Ψ l m l , l = D , j , p and their derivatives ∂ Ψ l m l ∂ r , l = D , j , p must maintain continuity across vertical boundaries between adjacent fluid regions.

The analysis employs separation of variables, yielding eigenfunction expansions for Ψ l m l , l = D , j , p ; l = I , … , V, within each fluid region. These expansions are constructed to satisfy: (1) the kinetic boundary condition on horizontal surfaces (Equation 19), (2) the seabed impermeability condition (Equation 18), (3) the linearized free surface condition (Equation 17), and (4) the far field radiation condition (Equation 20).

4.2 Air volume flow

The oscillatory motion of water within the chambers drives the displacement of dry air above the free surface through a Wells-type turbine. The volumetric flow rate resulting from the oscillating internal water surface is characterized by Q t = Re q e − i ω t), where:

q = ∬ S u z d S i = ∬ S ∂ φ ∂ z r d r d θ (22)

In Equation 22, u z represents the vertical velocity of the water free surface within the ETHOS device, φ denotes the velocity potential, and r , θ , z are cylindrical coordinates (Konispoliatis and Mavrakos, 2016).

Following the decomposition approach for spatial functions established in (Zhou et al., 2018), the volumetric flow q can be similarly decomposed into three components corresponding to diffraction, motion-dependent radiation, and pressure-dependent radiation problems, expressed as:

q = q D + q R + ∑ p = 1 N p i n 0 q p (23)

The complex quantity q p is herein referred to as the radiation admittance, a concept originally introduced by Evans (1982).

The motion-dependent radiation component of the volumetric flow rate can be expressed in terms of the relative vertical displacement between the internal free surface elevation and device motion, following (Falnes and McIver, 1985):where q 3 , j represents the chamber inflow due to motion-dependent radiation resulting from device oscillation in the j th direction. These complex coefficients quantify the hydrodynamic coupling between the oscillating OWC device and pressure distributions (Falnes and McIver, 1985). As demonstrated for isolated single-chamber OWC devices, only vertical displacement contributes significantly to the volumetric flow (Mavrakos and Konispoliatis, 2012).

q R = ∑ j = 1 6 ξ ˙ j 0 q 3 , j − ξ ˙ 30 S i (24)

The system incorporates a Wells-type turbine in the duct connecting the chambers to the atmosphere, which maintains unidirectional rotation independent of airflow direction, which stands for the Power Take off System. For modeling purposes, the turbine is represented through a pneumatic complex admittance Κ. The total volumetric flow q relates to chamber pressure as established in Equation 25:

q = K p i n 0 (25)

Under isentropic conditions, where air density and pressure variations maintain proportionality c a i r 2 = d p i n / d ρ a i r , with c a i r being the speed of sound in air, the pneumatic complex admittance Κ is defined as follows (Sarmento and Falcao, 1985):

K = Λ D N ρ a i r − i ω V 0 c a i r 2 ρ a i r (26)

In Equation 26, N denotes turbine rotational speed, D represents turbine rotor diameter, ρ a i r is the static air density, and V 0 is the chamber air volume. The empirical coefficient Λ depends on the design, configuration, and the number of turbines involved.

The real component of K corresponds to turbine pressure drop, while the imaginary component reflects air compressibility effects within the chamber. While compressibility effects are typically negligible, studies (Sarmento and Falcao, 1985; Martins-Rivas and Mei, 2009a; Martins-Rivas and Mei, 2009b) demonstrate their potential significance for OWC power extraction and the introduction of phase lag between flow and pressure variations. The current analysis neglects compressibility effects, treating K as a real quantity equal to the optimal coefficient K o p t for an isolated, restrained OWC device as derived in (Evans and Porter, 1996), which maximizes power absorption. This modeling approach maintains sufficient accuracy while enabling practical performance evaluation under operational conditions. Future research may incorporate compressibility effects to further elucidate OWC device dynamics and efficiency. The presented framework provides a comprehensive understanding of the coupled mechanical-hydraulic interactions in OWC systems, advancing the development of efficient wave energy conversion technologies.

4.3 Hydrodynamic forces

The hydrodynamic forces acting upon the OWC device may be systematically classified into three fundamental components: diffraction-induced forces, motion-dependent forces, and pressure-driven radiation effects. These force components are mathematically expressed as follows:

Diffraction-Induced Excitation Forces: The wave excitation forces and moments derived from diffraction analysis are given by:

f j e x c = i ω ρ ∫ S φ D n j d A , j = 1 , … , 6 (27)

Motion-Dependent Hydrodynamic Reactions: The hydrodynamic reaction forces and moments in the i-th direction, resulting from forced oscillations in the j th direction, are expressed as

f i , j h y d = − i ω ρ ξ ˙ j 0 ∫ S φ j n j d A = ω 2 a i j + i ω b i j ξ j 0 , i , j = 1 , … , 6 (28)

Pressure-Induced Hydrodynamic Forces: The hydrodynamic forces generated by oscillating chamber pressures are described by:

f j p r e = i ω ρ p 0 ∫ S φ p n j d A , j = 3 (29)

In Equations 27–29, n j represents the j th component of the generalized unit normal vector directed outward into the fluid domain, and S refers to the wetted surface of the converter. Also, In Equation 28 a i j , b i j are the added mass and damping coefficients, respectively. The damping acting on the floating structure comprises only the frequency-dependent hydrodynamic radiation damping coefficients b i j obtained from the matched eigenfunction expansion solution (Equation 28); viscous roll/drag damping and mooring-line damping are not explicitly modeled, consistent with the linear potential-flow assumptions adopted herein.

4.4 Coupled motion equation

The coupled equations of motion governing this multi-degree-of-freedom system in the frequency domain are expressed as:where m k j and c k j denote the structural mass and stiffness matrix elements, respectively, while a k j , b k j represent the hydrodynamic added mass and radiation damping coefficients (refer to Equation 28). The excitation forces and moments are given by f k e x c (refer to Equation 27) and f j p r e corresponds to the hydrodynamic pressure forces acting on the OWC (refer to Equation 29). The mooring system’s contribution is incorporated through the stiffness components c k j m (see Konispoliatis and Mavrakos, 2025). The Kronecker delta δ k , 3 (where δ k , 3 = 0 , k ≠ 3 ;; δ k , 3 = 1 , k = 3) ensures selective application of pressure-dependent terms in the heave direction. The force f k m p resulting from internal air pressure acting on the chamber’s horizontal wall, is defined in Equation 31:with S i representing the cross-sectional area of the inner water surface.

∑ j = 1 , 3 , 5 m k j + a k j ξ ¨ j 0 + b k j ξ ˙ j 0 + c k j ξ j 0 + c k j m ξ j 0 = f k e x c + δ k , 3 f k p r e + δ k , 3 f k m p , k = 1 , 3 , 5 (30)

f k m p = S i p 0 , k = 3 (31)

The coupled system is completed by the volume flow continuity equation:where q D , q R , q p are as detailed in Equations 23, 24, and the term S i ξ ˙ 30 accounts for the relative motion between the internal free surface and the device. The simultaneous solution of Equations 30, 32 yields the complete dynamic response of the OWC system, including motion components and internal pressure head distribution. The hydrodynamic (structural motion) and pneumatic (chamber pressure) sub-problems are coupled linearly in the frequency domain through the radiation admittances q R and q p (Equations 23, 24). This coupling is solved simultaneously with the equations of motion (Equation 30) and the volume-flow continuity equation (Equation 32). This formulation rigorously captures the coupled hydro-aero-dynamic interactions, incorporating hydrodynamic effects, mooring system influences, and pneumatic chamber behavior through a comprehensive set of governing equations.

q D = K − q p p 0 − q R ξ ˙ 30 + S i ξ ˙ 30 (32)

4.5 Absorbed power

The time-averaged power absorbed by the device from the waves, P o u t, is obtained from (Martins-Rivas and Mei, 2009b):

P o u t = 1 2 Re K p 0 2 (33)

Where K is the turbine’s admittance and p 0 the inner air pressure.

Based on the absorbed wave power defined in Equation 33, the relative capture width (or device efficiency), denoted as E f can be expressed as follows (Cruz, 2011):

E f = P o u t 2 α 4 P w (34)

In Equation 34, P o u t corresponds to the mean absorbed wave power per unit length of the wave crest for a monochromatic harmonic wave with an amplitude of H / 2 and frequency ω. Also a 4 is the radius of the outer toroidal solid i.e., 13 m. The incident wave power per unit crest length P w, is given by Equation 35:where C g is the group velocity.

P w = 1 2 ρ g H 2 2 C g (35)

To estimate the actual power generation at the designated locations, the JONSWAP spectrum (DNVGL-RP-C205, 2010) is employed to characterize short-term sea states. This formulation facilitates the computation of generated power over a 20-year period. The spectral density function is expressed as:In Equation 36:and the parameters are defined as follows.

S ω = A γ 5 16 ω p 4 · H s 2 ω 5 e − 5 4 ω p 4 ω 4 γ a (36)

a = e − ω − ω p 2 2 ω p 2 σ 2 (37)

• ω: Wave frequency (rad/s)
• ω _*p*: Peak wave frequency (rad/s)
• H s: Significant wave height (m)
• A γ = 1–0.287ln(γ)
• γ: Dimensionless peak enhancement factor, given by Equation 38:

γ = 5 if Tp Hs ≤ 3.6 exp 5.75 − 1.15 T p H s if 3.6 < Tp Hs < 5 1 if Tp Hs ≥ 5 (38)

• σ: Spectral width parameter which is defined in Equation 39:

σ = 0.07 if ω < ω p 0.09 if ω > ω p (39)

The spectral shape corresponding to Η s , T p = 0 − 1 m , 4 − 5 s sea state is depicted in Figure 12.

The absorbed wave power for each combination of significant wave height Η s and peak period T p, as tabulated in Tables 3–5, is computed using the integral relationship (Cruz, 2011):where P o u t denotes the time-averaged power absorbed by the device (see Equation 33).

P = ∫ 2 P o u t S ω d ω (40)

The numerical implementation proceeds as follows: First, the integral in Equation 40 is evaluated for each significant wave height and peak period combination listed in Tables 3–5 using Simpson’s rule of numerical integration. Each integration yields the instantaneous absorbed power for the corresponding sea state. As the input wave data represent hourly sea state estimates, the resulting power values require temporal scaling. Each integrated result is multiplied by a factor of 1 h to convert the power values to energy quantities expressed in watt-hours. This conversion accounts for the hourly resolution of the input wave parameters. Following the energy calculation for all sea states, the individual energy contributions are summed to obtain the total absorbed energy over the 20-year period. To determine the average annual energy production, this 20-year cumulative energy is divided by twenty. This normalization provides the mean annual absorbed wave power, representing the long-term average energy capture of the device. Results of this procedure are presented in the following chapter 5.

5 Numerical results

The theoretical analysis presented in Section 4 enables the evaluation of power absorption by the ETHOS wave energy converter through the application of Equation 33. Figure 13 illustrates the relationship between the absorbed power, P o u t, and wave frequency, demonstrating the converter’s performance characteristics across the operational frequency spectrum.

Based on the wave condition frequency distributions presented in Tables 3–5 for the three installation sites (L1, L2, and L3), the total absorbed power by the ETHOS converter was computed for each (H s, T e) cell using Equation 40, along with Equation 41 below assuming a standard JONSWAP spectrum with a peak enhancement γ = 3.3 (Guillou, 2020), in order to incorporate in the calculations the difference of the two wave periods (peak wave period T p and wave energy period T e).

T e = 0.9 T p (41)

The results are summarized in Table 8. The contribution of each wave condition to the total absorbed power was then determined through the following procedure: First, the element-wise product of Tables 3–5 with Table 8 was calculated. These products were subsequently normalized by dividing by the total number of observations (175,320). The resulting distributions, representing the relative power absorption across wave conditions for each location, are presented in Tables 9–11 for sites L1, L2, and L3, respectively.

TABLE 8. Total absorbed power of ETHOS converter [kW].

TABLE 9. Absorbed power [kWh/year] for Location 1 (in bold the cell with the largest value).

TABLE 10. Absorbed power [kWh/year] for Location 2 (in bold the cell with the largest value).

TABLE 11. Absorbed power [kWh/year] for Location 3 (in bold the cell with the largest value).

Tables 3–5 demonstrate that the most frequently occurring wave conditions (H s, T e) or locations L1, L2, and L3 are (0–1 m; 3–4 s), (0–1 m; 3–4 s), and (0–1 m; 4–5 s), respectively. However, Tables 9–11 reveal that the wave conditions contributing the highest percentage of total absorbed power differ significantly, being (4–5 m; 7–8 s) for L1, (4–5 m; 7–8 s) for L2, and (2–3 m; 6–7 s) for L3.

Table 12 presents a consolidated summary of these findings, quantifying the annual absorbed power in kilowatt-hours (kWh) and the annual capture width ratio (CWR) for each location. The comparative analysis clearly indicates that Location 2 demonstrates superior performance in wave energy extraction, with the ETHOS converter achieving significantly higher annual power absorption and CWR compared to Locations 1 and 3.

TABLE 12. Absorbed power [kWh/year] and annual capture width ratio (CWR) for each installation location (in bold the cell with the largest value).

6 Experimental setup and measurements

6.1 Model instrumentation

A comprehensive experimental investigation was conducted to evaluate the performance of the wave energy conversion system using a 1:20 scaled model of the ETHOS converter (Figure 14). The tests were carried out in the towing tank of the Laboratory for Ship and Marine Hydrodynamics (LSMH) of the National Technical University of Athens (NTUA) (Figure 15), which measures 100 m in length, 4.56 m in width, and offers a maximum water depth of 3 m. The facility is equipped with a carriage capable of operating across a wide velocity range, from 0.01 m/s in manual mode up to 5.5 m/s (10.50 knots). Wave generation is achieved through a unidirectional flap-type wave maker that produces head waves with frequencies ranging from 0.3 to 1.2 Hz and maximum amplitudes of 35 cm. To ensure proper wave energy dissipation and minimize reflections, the tank features an inclined beach structure at the opposite end of the wave maker. For this experimental campaign, testing was exclusively conducted under head sea conditions to maintain consistent wave-structure interaction parameters.

The experimental setup employed a comprehensive array of measurement systems to monitor the wave-structure interactions. Wave amplitudes were recorded using three non-intrusive acoustic probes, with one positioned near the wave maker and two others monitoring the water surface at the converter location. A dedicated wave probe was installed within the toroidal air chamber of the OWC device to measure internal water surface fluctuations (Figure 16). These measurements enabled calculation of the air volume flux through temporal differentiation of the water surface elevation, accounting for the OWC’s net cross-sectional area. An additional probe was positioned 3 cm ahead of the external cylinder to record incident wave characteristics.

The converter’s dynamic response was quantified using an optical motion capture system comprising four high-speed digital cameras (Figure 17). This system tracked retro-reflective markers mounted on the model’s deck (Figure 18), acquiring two-dimensional positional data at 50 Hz sampling rate with high spatial resolution. The Qualisys Track Manager (QTM) software reconstructed the three-dimensional marker positions and derived the six-degree-of-freedom motions (Figure 19), including translational (surge, sway, heave) and rotational (roll, pitch, yaw) components. Post-processing of these data yielded corresponding velocity and acceleration time histories (Grigoropoulos et al., 2011).

The dynamics of the mooring system were monitored through four underwater load cells installed near a weighted base at the tanks bottom capturing both static pretension and dynamic tension with minimum interference with the model’s leg motions. The mooring system employed 3 mm stainless steel wires connecting the inner cylinder to a carriage-mounted adjustable configuration through the bottom base via pulleys (Figure 20). Length adjusting screws and slow carriage speeds were utilized to achieve the desired draft and guarantee perfectly equal tension across all four mooring tethers.

The experimental infrastructure included a weighted base assembly installed at the tank bottom to anchor the tension-leg platform mooring system (Figure 21). This configuration was amenable to fine tuning adjustments, allowing for dynamic response measurements under controlled wave conditions.

For turbine simulation, perforated carpets were implemented as filter plugs at the top of OWC chambers. These were specifically calibrated to reproduce the linear pressure-air flux relationship characteristic of Wells turbines, with comparative testing of single-layer and three-layer configurations, in order to simulate two different PTO values. Pressure differentials across the OWC dome were measured using precision differential pressure gauges. All instrumentation signals, except the optical motion system, were sampled at 100 Hz and processed through digital filtering protocols. At Figure 22, the model and sensors position as well as the experimental setup are illustrated.

6.2 Model scale

The scaled down model was composed of: (a) two chambers OWC converter; (b) the OWC air chamber conic dome; (c) TLP tendons; and (d) a bottom base for the tension leg connections. The design of the two oscillating chambers and the conic air chamber is shown in the following Figure 23. Also, Table 13 presents a summary of the principal geometric characteristics of the OWC under consideration in full scale and scaled down.

TABLE 13. Floating cylindrical body geometry.

The scaled model was fabricated using composite materials, with a primary structure consisting of plywood and foam components. This manufacturing process resulted in a lightweight construction, enabling testing at different drafts and weight distributions. To enhance structural integrity, metal reinforcing rods were strategically positioned both within and between the internal chambers. The assembly was subsequently encapsulated with a fiberglass-resin composite layer to ensure complete watertight integrity. Afterwards, the model underwent surface finishing processes including polishing and painting in preparation for hydrodynamic testing at the predetermined draft condition.

The vertical center of gravity (VCG) was determined experimentally through a series of suspension tests conducted from multiple vertical reference points (Figure 24). Ballast weights were systematically distributed, with primary concentrations at both the conical section and base of the model, to achieve the target displacement while maintaining even keel conditions. Through iterative adjustment of these weights, the final center of gravity was positioned 7.6 cm above the designed waterline, satisfying the required hydrostatic properties for experimental validation.

The model’s mass moment of inertia was experimentally measured by bifilar suspension method. The buoy was suspended in the air by two parallel beams, allowing horizontal oscillation (refer to Figure 25).

Then, by measuring the natural period of oscillation the moment of inertia was calculated be the following Equation 42:where m is the mass of the structure; g denotes the acceleration due to gravity; α is the distance between the center of gravity (CG) and each suspension point; T is the oscillating period (2.46 s); and L is the suspension length. Using the above equation, the mass moment of inertia in air was calculated to be 4.51 k g m 2.

I a i r = m g α 2 Τ 2 16 π 2 L (42)

6.3 Test conditions

The model was tested at a draft of 70 cm (draft without the pretension was about 40 cm), at nine regular waves from 0.4 rad/s to 1.55 rad/s with different amplitudes and a realistic sea state condition with significant wave height of H s = 5 cm and model period T p = 1.35 s. Table 14 summarizes the examined experimental wave frequencies. To achieve the specific draft a pretension of 153 kg was applied to the model.

TABLE 14. Examined experimental wave frequencies.

A series of preliminary tests were conducted without the installed model to properly calibrate the wave generation system, which demonstrated linear behavior within specific ranges of wave heights and frequencies. Attention was paid to the temporal characteristics of wave reflections from the inclined beach, where the reflection arrival time exhibited an inverse relationship with wavelength. To ensure measurement integrity, all data acquisition was carefully timed to occur during the interval between the initial wave passage and subsequent reflection arrival at the model position.

The experimental investigation employed regular wave conditions to evaluate the hydrodynamic behavior of the converter and to establish the transfer functions (Response Amplitude Operators, RAOs). The testing matrix corresponded to a range of full-scale frequencies from 5 to 15 in 1 s increments. This approach enabled both the identification of potential resonance phenomena within the operational spectrum, and the accurate determination of the system’s transfer functions across the complete frequency range of interest.

7 Validation of the numerical models with the experimental results

In this section the numerical predictions are validated via the experimental measurements for the dual-chamber OWC converter, focusing on three key: structural motions, internal air pressure dynamics, and wave surface elevation. The analysis presents the responses non-dimensionalized by the wave amplitude normalized as H/2, to facilitate direct comparison between numerical and experimental datasets.

The surge response RAOs, presented in Figure 26, demonstrate excellent agreement between numerical predictions and experimental measurements across the entire investigated frequency range (0.4–1.55 rad/s), with a root-mean-square error (RMSE) of 0.199 between the two datasets. The extended frequency representation (up to 1.5 rad/s) provides complete characterization of the floater’s dynamic response within this operational regime.

Figures 27, 28 present the internal pressure head and air volume flow characteristics respectively, both showing strong correlation between numerical and experimental results. The numerical model successfully captures the characteristic pressure reduction observed experimentally above 0.75 rad/s, as well as the corresponding decrease in air volume flow at higher frequencies, with an RMSE of 35.6 m 3 s · m between the numerical and experimental air volume flow results. These results were obtained using a three-layer perforated carpet configuration, representing a full-scale turbine coefficient of 150 m⁵/(kN·s).

The first-order surge forces are examined in Figure 29 which compares theoretical and experimental results. The close agreement between numerical predictions and measured responses validates the coupled hydrodynamic-structural interaction modeling approach.

Figure 30 illustrates the free surface elevation for both the interior and exterior of the oscillating chambers at a frequency of ω = 0.421 rad/s for a system incorporating a three-layer perforated carpet. The objective of this analysis is the experimental validation of the wave profile in these two regions. The results show an excellent agreement between theoretical predictions and experimental data for the exterior region of the converter. In contrast, a discrepancy is observed for the free surface elevation inside the oscillating chamber. This deviation is attributed to a measured air pressure head within the chamber that is lower than the theoretically predicted value, as previously indicated in Figure 27.

Further validation is provided in Figures 31, 32, which present results for a single-layer permeable carpet configuration (equivalent to a full-scale turbine coefficient of 290 m5/(kN·s)). Comparative analysis with the three-layer configuration (Figure 27 vs. Figure 31) reveals that the single-layer arrangement produces reduced internal air pressures while maintaining excellent correlation between numerical and experimental results, with an RMSE of 23.83 m 3 s · m for the air volume flow comparison. This agreement is further demonstrated in Figure 33, which illustrates the wave profile comparisons inside and outside the ETHOS system. A comparison between Figures 30, 33 shows that the theoretical and experimental results for the outer fluid domain are in good agreement. Moreover, the internal theoretical wave profile aligns more closely with experimental measurements. This improved correlation is attributable to the fact that the measured internal air pressure (Figure 31) is in better agreement to the theoretical prediction.

The consistent agreement observed across all response parameters confirms the validity of the numerical models and demonstrates the reliability of the computational tools developed within the ETHOS project framework. This comprehensive validation establishes confidence in the predictive capabilities of the numerical methodology for engineering analysis and design optimization of OWC systems.

8 Conclusion

The study presents a comprehensive theoretical and experimental analysis of the ETHOS dual-chamber floating OWC device, demonstrating its potential for efficient wave energy conversion in Greek waters. The hydrodynamic performance of the device was evaluated through advanced numerical simulations and scaled-down experiments, with results showing strong agreement between theoretical predictions and experimental measurements. The dual-chamber design, combined with a TLP mooring system, proved effective in enhancing energy capture and operational stability across a broad range of wave frequencies. The validation of the numerical models against experimental data underscores the reliability of the applied methodologies for future design optimizations and real-world deployments.

The environmental analysis identified three optimal deployment sites in the Aegean Sea, with Location 2 exhibiting the highest annual energy absorption potential. Extreme value analysis using the POT method provided critical design values for robust structural and mooring system performance under extreme wave conditions. The study highlighted the importance of site-specific wave climate assessments, as the most frequent wave conditions did not always correlate with the highest energy contributions. This insight is crucial for maximizing the efficiency and economic viability of wave energy projects in regions with complex wave regimes.

Experimental testing of the 1:20 scale model in a wave tank facility validated the device’s hydrodynamic behavior, including motion responses, internal pressure dynamics, and free surface elevation. The use of perforated carpets to simulate turbine behavior further confirmed the device’s adaptability to varying operational conditions. The close alignment between numerical and experimental results reinforces the effectiveness of the coupled hydro-aero-dynamic modeling approach, providing a solid foundation for scaling up the technology for commercial applications.

It should be noted that the present numerical formulation is based on linear potential flow theory and therefore neglects viscous dissipation, vortex shedding effects, nonlinear free-surface deformation, and nonlinear air compressibility phenomena inside the oscillating chambers. These assumptions are commonly adopted in frequency-domain analyses of oscillating water column devices and are considered appropriate for preliminary design and performance assessment under moderate operational wave conditions. Nevertheless, such simplifications may affect the predicted hydrodynamic and pneumatic response, particularly near resonance conditions where nonlinear effects become more pronounced. In these regions, viscous damping and nonlinear air-flow behavior may reduce the oscillation amplitude and energy absorption efficiency compared to idealized linear predictions. Despite these limitations, the comparison between numerical predictions and scaled experimental measurements demonstrated satisfactory agreement regarding the dominant response characteristics of the ETHOS system, supporting the applicability of the adopted modeling approach for preliminary offshore design studies. Future work will focus on incorporating higher-fidelity aero-hydrodynamic and viscous-flow models to further investigate nonlinear effects and quantify their influence on the converter’s performance under extreme and strongly resonant sea states.

It should be also noted that although the ETHOS OWC device offers several advantages, including structural durability, and efficient energy extraction even at low wave frequencies, challenges such as high structural costs and competition for coastal space remain barriers to widespread adoption. Future research should also focus on the reduction of the Levelized Cost of Energy (LCOE) and enhance its competitiveness in the renewable energy market. Additionally, long-term environmental impact assessments and pilot-scale deployments will be essential to validate the device’s performance in real-world conditions.

While the present study establishes the hydrodynamic feasibility and wave power absorption performance of the ETHOS system, a full assessment of its practical implementation remains an important direction for future work. This includes a detailed economic feasibility analysis, long-term structural survivability under cyclic and extreme loading, maintenance and inspection strategy, air-turbine efficiency and control under realistic operational spectra, and the logistical challenges associated with offshore installation and grid integration. These aspects fall outside the hydrodynamic and mooring-performance scope of the present work but are essential steps toward the commercial deployment of the ETHOS converter.

In conclusion, this study advances the understanding of dual-chamber OWC systems and their potential for sustainable wave energy harvesting. The integration of theoretical, numerical, and experimental approaches provides a robust framework for designing and optimizing floating OWC devices. With continued innovation and site-specific adaptations, the ETHOS system could play a significant role in Greece’s renewable energy portfolio, contributing to global efforts to transition toward cleaner and more sustainable energy sources.

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Glossary

d Constant water depth a 1 Radius of the internal water surface a 2 Radius of the inner toroidal body a 3 Radius of the annulus water area between the two solids a 4 Radius of the outer toroidal body h 1 Distance from the bottom of the inner body to the seabed h 2 Distance from the bottom of the outer body to the seabed ω Incident wave frequency P Wave power density ρ Water density g Gravity acceleration x n u n u Observations that exceed u x max Largest value of the x i σ * Modified scale estimates of the generalized Pareto distribution ξ Shape estimates of the generalized Pareto distribution ζ u Exceedance probability or the proportion of data above a threshold u n y Exceedance observations per year z N N-year return level x i Respective variables at the four grid points surrounding the selected location, i = 1 , 2 , 3 , 4 r i Respective variables indicating the distances from the selected location, i = 1 , 2 , 3 , 4 H s Significant wave height T e Wave energy period H / 2 Wave amplitude k Wave number r , θ , z Cylindrical coordinates I , I I , I I I , I V , V Coaxial ring-shaped fluid regions ξ 1 Surge motion of the converter ξ 3 Heave motion of the converter ξ 5 Pitch rotation of the converter φ 0 Undisturbed incident wave velocity potential φ 7 Scattered velocity potential φ D Diffraction velocity potential φ p Pressure-radiation velocity potential φ j Motion-radiation velocity potential p i n 0 Complex Air-pressure amplitude inside the chambers ξ ˙ j 0 Complex velocity amplitude of the converter’s motion in the j th direction ε m Neumann’s symbol J m m th order Bessel function of first kind Z 0 Orthonormal equation n → Outward unit normal vector to the mean wetted surface r → Position vector of a point on the converter’s wetted surface with respect to its reference point of motion n j Generalized normal components of n → q Total air volume flow inside the oscillating chambers q D Diffraction volume flow q R Motion-radiation volume flow q p Pressure-radiation volume flow u z Vertical velocity of the water surface inside the chambers S i Cross-sectional area of the water surface inside the oscillating chambers K Turbine’s pneumatic complex admittance N Turbine’s rotational speed D Turbine’s rotor diameter ρ a i r Static air density V 0 Chamber air volume Λ Turbine’s empirical coefficient f j e x c Exciting forces/moments f i , j h y d r Hydrodynamic reaction forces/moments f j p r e Hydrodynamic forces due to the air pressure inside the oscillating chambers m k j Structural mass coefficient c k j Stiffness coefficient a k j Hydrodynamic added mass coefficients b k j Radiation damping coefficients δ k , 3 Kronecker delta f k m p Internal air pressure force P o u t Time-averaged power absorbed by the device E f Relative capture width P w Incident wave power per unit crest length S ω JONSWAP spectrum *γ Dimensionless peak enhancement factor σ* Spectral width parameter

Footnotes

Edited by: Paula B. Garcia-Rosa, SINTEF Energy Research, Norway

Reviewed by: Carlos Pérez-Collazo, University of Vigo, Spain

Ravi Manjul, Ramchandra Chandravansi Institute of Technology, India