Hydrodynamic coefficients and pressure loads on heave plates for semi-submersible floating offshore wind turbines: A comparative analysis using large scale models
Introduction
Floating offshore wind turbines (FOWT) are a promising mean for harvesting electric power from a renewable source. Within the three main FOWT concepts [1], the semi-submersible one is receiving significant attention due to several advantages [2]. Namely:
- 1.
these types of platforms can be fully assembled onshore and towed ready-to-use to their final destinations;
- 2.
the available mooring systems are well-known and cost competitive;
- 3.
if properly designed, downtime in operational sea states, due to excessive platform motion, is low.
Most semi-submersible FOWT platforms consist of three cylindrical columns linked together with a set of braces [3]. In order to minimize heave motions and accelerations, and to shift heave resonance periods out of the first-order wave energy range, heave plates are attached to the column base [4]. The hydrodynamic performance of such plates has received some attention in the literature: Tao and Dray [5] performed experiments with solid and porous plates in deep water conditions and Ref. [6] used a porous square plate, performing experiments and numerical analysis with varying depth. Philip et al. [7] and Nallayarasu and Bairathi [8] numerically and experimentally assessed the effects of including a heave plate in a spar type floater. Wadhwa and Thiagarajan [9] and Wadhwa et al. [10] analyzed the dependence of the hydrodynamic response with the motion amplitude for a fixed oscillation frequency, finding a critical value above which response stops increasing. This analysis was done both close to the free surface and close to the seabed. For the latter, their results were numerically confirmed by Refs. [11], [12].
Tao and Thiagarajan [13] performed a detailed numerical analysis of the vortex shedding mechanisms, responsible for the main part of induced damping in heave plates. Tao and Thiagarajan [14] analyzed, in a column with a heave plate the relationship between damping, plate thickness and motion amplitude, for a fixed motion frequency. They provided rationale for an accurate extrapolation of the results. Takaki and Lee [15] computed, with a moving grid Navier–Stokes solver, the added mass and damping of an oscillating plate close to the free surface. They found and provided experimental validation, that, under these circumstances, radiation is the main damping factor. Koh and Cho [16] performed a similar analysis using AQWA and a multimodal type (MEEM) potential method. On the other hand, Ref. [4] found that radiation damping is a small fraction of the viscous damping when the heave plate depth is large.
It is relevant to mention that, in a seakeeping analysis, having an accurate estimation of viscous damping is crucial when predicting the platform behavior in survival conditions with time domain simulations, often coupled with the aeroelastic code FAST (see e.g. Refs. [17], [18]).
It is also important to highlight that, in practice, the heave plates require some structural reinforcements that may alter their hydrodynamic performance. In the present research, a plain solid heave plate an a reinforced version, to be built at full scale, with a vertical flap at its edge, have been considered. While the influence of the plate edge sharpness in the hydrodynamic response has received some attention in the literature [19], [20], to the authors' knowledge, flaps influence has not been investigated.
In addition, in order to dimension the plate thickness and the previously mentioned reinforcements, knowing the pressure difference during the heave motion between the bottom and top sides, becomes very important. With this aim, the present experimental campaign has also included the direct measurement of dynamic pressure on the heave plates, which is a fundamental magnitude for the structural design. The cost of the floater is a major component of the initial investment [21] and therefore, cost reductions due to an optimized structural design are crucial in order to attain a competitive alternative. Such an optimized structural design may assist in reducing other high-cost factors such as transport, disposal, etc. Ref. [22]. Since electricity is a commodity, being a competitive technology mostly means being cost competitive for the final user, something very challenging for floating offshore wind turbines considering the many different well-established available electrical power sources. Therefore, having an optimized design with minimum cost, that can be replicated for large farms [23], becomes a crucial design goal.
This paper is organized as follows: the case study characteristics are first described. Experimental procedure and numerical solvers are discussed next. Test matrix and results are then presented and compared with literature. The prototype reinforced configuration results are then discussed. Finally, some conclusions and future work threads are summarized.
Section snippets
Prototype
The heave plates under study belong to the semi-submersible platform whose second order surge motions were analyzed by Ref. [24]. The structure of the floater consists of three vertical columns linked by trusses. A circular heave plate is added to the bottom of each column, as a mean to increase the natural heave period and, as a consequence, to prevent resonant motions in both operational and survival sea states.
The main dimensions of the platform are given in Table 1 and a schematic view of
Hydrodynamic model
The phenomenon to analyze is the forced harmonic heave motion of the leg (column plus heave plate-disc), considered a rigid body. The reference system is shown in Fig. 5.
The hydrodynamic force time history, , from one sample experiment can be seen in Fig. 6. This time history is presented in non-dimensional form as a force coefficient:where is the heave plate surface, A is the amplitude of the oscillation, ω its frequency and ρ the fluid density.
is
General
For comparative reasons, numerical simulations have been conducted, following common industry standards, both with a widely used frequency domain commercial panel method – to compute added masses – and a commercial RANS CFD – to compute viscous damping. The aim is to briefly discuss the accuracy, when used with standard computational power and widely used commercial software, of these types of computations, by directly comparing their outcomes to experimental data. We believe this discussion
Test matrix
Vertical oscillations were performed with different amplitudes (0.05; 0.1, 0.14 m) and periods (1–4 s). For each period, the maximum feasible amplitude depended on the actuator power, leading to smaller motion amplitudes for the highest oscillation frequencies. The test matrix is presented in Table 2, with being the Reynolds number and m and p sub-indexes referring to model and prototype scales respectively. Reynolds number is defined as:
It is easy to check that .
From the
Prototype geometry
Analyzing the plain disc configuration without any structural reinforcements is relevant for academic and comparison purposes, along with numerical model calibration. However, from a structural standpoint, a plain disc configuration is not viable in a practical application. At full scale, a diaphanous plate would require a steel thickness that would make it unaffordable. Therefore, in practice, the disc has to be radially and circularly reinforced. The proposed configuration to be built is
Conclusions
Hydrodynamics of a heave plate design for a semi-submersible offshore wind turbine has been discussed in the present paper. The considered platform is composed of three cylindrical legs linked together by a set of structural braces. The cylinders provide floatability and restoring forces and moments. Large circular heave plates have been attached to their bases. A large scale model of the leg has been built. The final dimensions of the specimen (1 m diameter discs) make it, to the authors'
Acknowledgments
The authors gratefully acknowledge the financial support from CDTI (center for development the development of industrial technology) CEN-20101009 through CENIT Program (AZIMUT project), which made this work possible. Moreover, the use of the FP7 project HiPrwind geometry for the tests is gratefully accredited. Finally, authors are thankful to the data access provided by ACCIONA Energia and in particular to Raul Manzanas for the support on this investigation. The authors thank Mr. Elkin
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