Scale eﬀects in physical modelling of a generalized OWC

Physical modelling is extensively applied in the study of Oscillating Water Column (OWC) devices since it furnishes a reliable evaluation of nonlinear eﬀects, as those induced by the interaction between surface waves and air inside the pneumatic chamber. In this paper, a small scale generalized device is compared to a similar large scale model under random waves, in order to evaluate the main scaling issues on (i) hydrodynamics of the water column, (ii) wave reﬂection and (iii) loadings at the outer front wall. The small scale model tested allowed to investigate the eﬀects of air compressibility to be investigated as well. loadings on the front wall can be underestimated by the small scale but safe conditions are always achieved for the high-chamber model.

On the basis of such a scale factor between lengths, the ratios between areas 151 and between volumes can be obviously obtained geometrically as ε 2 and ε 3 , 152 respectively.

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Once the geometrical similarity is chosen, the physical phenomenon must

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The interaction between surface waves and OWC device involves the dy- allowing an adequate modelling of the turbine, which is usually substituted 166 by an orifice or by a layer of porous media.

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The application of the dimensional analysis approach to continuity and where U is a characteristic speed of the fluid, L is a characteristic length 172 of the system, g is the acceleration of gravity, ρ and µ are the density and 173 the viscosity, respectively. For water motion under waves, the characteristic 174 speed U can be defined by employing the maximum water particle velocity 175 from small-amplitude water wave theory (Dean and Dalrymple, 1991): where A w is the amplitude and ω is the angular frequency of the incoming 177 waves (ω = 2π/T with T the period on waves).

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For the two dimensionless groupings introduced above, the physical mean- respectively. The volume variation inside the chamber can be seen as the 197 flow rate q of the water inside the OWC.

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The density variation is due to the presence of air compression, which 199 can be well represented inside the OWC chamber by means of the pressure-200 density relationship for a perfect gas: where p is the relative pressure inside the chamber, p at is the absolute pressure 202 out of the OWC, ρ at is the outer density, k is the polytropic exponent which is 203 related to the turbine efficiency, as obtained in Falcao and Henriques (2014).

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The latter exponent assumes the maximum value 1.4 if the turbine is perfectly 205 efficient and the flow is isoentropic. On the contrary, k = 1 for a turbine 206 which has null efficiency, since no work is done and the process is isothermal.

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On the basis of the eq. (5), it is possible to compare the air mass variability 208 inside the OWC due to density and volume variation, thus obtaining the 209 following dimensionless group: Falcao and Henriques (2014) suggest that such a dimensionless group must

Modelling setup
Physical modelling of an OWC system is a complex task since it involves 239 at the same time wave-structure interaction, air compressibility and PTO 240 dynamics. A simplified approach is here followed, in which the PTO is sub-241 stituted by an orifice.

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The reference modelling setup, shown in Figure 1, is a generalized OWC  orifice. The slope of the ramp (s = 1:6) is the same in the two models.

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The system adopted in CT-experiments allows to vary the top of the   output signal is given in voltage with a sensitivity 5.0 mbar/V.

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All the tests were carried out with random waves having JONSWAP 297 spectrum and peak enhancement factor γ = 3.3. Nine wave conditions have 298 been tested in both GWK and CT models, which are summarized in Table 2.

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Small scale CT incident wave conditions are chosen in order to follow the 300 Froude similarity of GWK tests: (i) significant wave heights H m0,i are scaled 301 with ε; (ii) peak wave periods T p are scaled with ε 0.5 .

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Dimensionless parameters are also introduced in Table 2, which are the by the width of chamber B, so obtaining: All the dimensionless groups defined above allow a direct comparison   The flow inside the chamber is related both to the OWC geometry and 331 to the incident wave conditions. In particular, the volume of air inside the 332  where σ is the standard deviation.
In order to compare data measured at different scales, H m0 is made di-    to the air volume. In the so called small-scale models, the ratio between the 505 two values of h a (and of air volume) tested was 4.75.

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The increase in chamber height affects the air water dynamics inside the 507 device by means of the increase of both the natural period and the significant 508 wave height measured inside the chamber, as shown in the Figures 5 and 6 509 respectively.

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The natural period is increased weakly (lower than 10%) but quite uni- in the small scale models, also for the high-chamber configuration.

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It is important to stress that the adopted geometrical scaling procedure