Aerodynamic design and numerical investigation of a new radial bi-directional turbine for wave energy conversion

Transcription

1 10 th European Wave and Tidal Energy Conference, Aalborg, DK, - 5 Sept. Aerodynamic design and numerical investigation of a new radial bi-directional turbine for wave energy conversion C. Moisel #1, R. Starzmann # # Institut für Fluid und Thermodynamik, University of Siegen Siegen, Germany 1 christoph.moisel@uni-siegen.de, ralf.starzmann@uni-siegen.de Abstract Over the last decades different types of bidirectional turbines for use in oscillating water column (OWC) wave energy converters have been investigated extensively. A turbine concept which has never been investigated in detail is a bi-directional radial turbine as suggested by KENTFIELD (1983). This paper presents an analytical design method for a bi-directional radial lift-based (BiRLi) OWC turbine. The blade cascade design is based on a blade element momentum (BEM) method combined with WEINIG S cascade correction. Employing the design method, a full BiRLi turbine layout, including the blade cascade, a set of guide vanes and the meridional contour is designed. Three dimensional steady state RANS simulations of the BiRLi turbine from no-load to near stall are carried out to show the performance and flow characteristics as well as to validate the BEM design of the turbine. It is shown that the performance of a first investigated BiRLi turbine design is promising to be an alternative to the turbine concepts presently in place. Keywords Wave Power, Oscillating Water Column, Wells Turbine, Radial Turbine NOMENCLATURE C coefficient [-] D diameter [m] F force [N] L chord length [m] Ma Mach number [-] P power [W] V volume flow rate [m 3 /s] b radial blade width [m] c absolute velocity [m/s] n rotational speed [rps, rpm] p pressure [Pa] r radius [m] t angular spacing u circumferential velocity [m/s] w relative velocity [m/s] z number of blades [-] p pressure drop [Pa] lift/drag ratio [-] flow rate coefficient [-] pressure coefficient[-] power coefficient [-] efficiency [-] density [kg/m 3 ] solidity [-] aspect ratio [-] SUBSCRIPTS 0 design 1 upstream downstream BE blade element CV control volume GV guide vane L lift ba bladed annulus hyd hydraulic leak leakage m merdian r radial sl secondary loss ts total to static tt total to total u circumferential vol volumetric ABBREVIATIONS BiRLi CFD OWC BEM RANS Bidirectional Radial Lift-based Computational Fluid Dynamics Oscillating Water Column Blade Element Momentum Reynolds-averaged Navier-Stokes equations I. INTRODUCTION Over the last decades oscillating water column (OWC) wave energy converter systems have been under examination and a continuous development to increase reliability and

2 efficiency from wave to wire had been taken place [1-3]. One main issue to improve the nowadays critical economical feasibility of the OWC technology is to improve the energy output of the air turbine. Different turbine concepts have been presented capable to equip an OWC wave power plant over the last decades [4-6]. Mainly two basic turbine concepts prevailed up to now. These are the lift-based axial Wells turbine [7-9] and different types of axial and radial impulse turbines [10-16]. The main drawback of impulse turbines was a small peak efficiency because of high losses in the downstream set of guide vanes. Especially recent developments of new impulse turbines by GATO et al. [17] and NATANZI et al. [18] improved the achievable aerodynamic efficiency considerably compared to earlier impulse turbine concepts. The axial (lift-based) Wells turbine has been mainly used as power conversion system in existing OWC power plants (e.g. LIMPET, PICO, Mutriku, see [19-1]). However, due to the non-staggered blade cascade, strong secondary flow effects on the blades suction side result in a limited operating range [8, -4]. This technology seems to be at the end of it s development stage with less potential for further improvement [8]. In the 1980ies another lift-based turbine with a radial cascade of non-staggered blades has been proposed by KENTFIELD [5]. The flow either enters the rotor axially or leaves it in radial direction (centrifugal flow direction) or vice versa (centripetal flow direction), Fig. 1a. a) b) Fig. 1 Bidirectional radial lift-based turbine; a) sectional view (schematically): 1) rotor, ) radial ducting, 3) axial ducting, 4) small hub cone, 5) inner radial guide vane (optional), 6) outer radial guide vane (optional); b) 3D model Fig. 1b pictures a 3D model of the radial turbine with the turbine blades shown in red and optional guide vanes in blue. A hub cone assists the centrifugal flow turning from axial into radial direction of the rotor blades. In contrast to an axial blade, each segment of a radial rotor blade is located on the same radius, i.e. it moves with the same circumferential velocity. This clearly avoids any needs for blade twisting and hence has the potential of increased peak efficiency, extended stall free operating range and less noise emission due to partial flow separation. Until now, not much research has been reported for this type of turbine. KENTFIELD in 1983 [5] proposed a radial lift-based turbine with freely-hinged blades. SUGIHARA et al. [6] launched a patent application on several configurations of a lift-based radial turbine for reciprocating flow. He also introduced blade curvature aiming at zero lift of the airfoils placed on a circumference. Additionally KANEKO et al. [7] submitted a patent for a radial turbine based on the same working principle with the intention to overcome the high axial forces of a Wells turbine rotor. LEWIS [8] proposed a variable width rotor for control purposes and guide vanes close to the design in Fig. 1. Objective of this study is introducing a blade element momentum (BEM) design method for a radial bi-directional blade cascade based on a set of predefined input parameters related to given aerodynamic and geometric design requirements. The BiRLi turbine design includes a set of axial guide vanes and the layout of the turbines ducting. Steady state numerical RANS simulation from no load to near stall are carried out to predict the performance characteristics, analyse the flow behaviour in the BiRLi turbine and enabling a first validation of the BEM turbine design. II. RADIAL TURBINE DESIGN A. Blade cascade design 1) Blade element momentum model (BEM) The fundamental blade cascade design method employed, is based on a blade element momentum (BEM) model combined with Weinig s cascade correction as in [9], necessarily taken into account as for Wells turbines [30]. For a given 'load' at a distinct design point of operation, the model yields under respect of some aerodynamic and geometric constraints dimensionless coefficients (pressure drop, flow rate and power coefficient) and the blade cascade geometry. Note that within the cascade design process we estimate the shape of the radial blade cascade to be a standard unstaggered cascade as known for Wells turbines analogue to [31]. We start by establishing analytical estimates of turbine design points (index 0 ) which theoretically correspond to flow conditions in the turbine with minimal losses. In terms of dimensionless turbine coefficients; these are the flow rate coefficient 3 0 V 0 D n (1) 4 and the total to total pressure (or head) coefficient tt,0 ptt,0 D n. () We assume that the variation of the fluid density in the turbine is small, hence = const. The total pressure drop (or head) across the turbine rotor from station 1 to (Fig. 3a) is p tt = p t,1 - p t, = p tt,ba - p tt,loss, with p tt,ba being the theoretical pressure drop in the bladed annulus and p tt,loss the airfoil or cascade and secondary flow losses. The hydraulic losses may be expressed in terms of a hydraulic efficiency in a way that p p. (3) tt,ba hyd tt

3 The volume flow rate through the turbine is the sum of the volume flow rate through the bladed annulus (index ba ) and the leakage flow rate through the tip clearance. A volumetric efficiency is defined such that V ba volv (4) eventually the power available at the turbine shaft becomes Ps V baptt,ba volhydv ptt, Ps 0. (5) Fundamentally the blade element (BE) (Fig. 3b ) analysis is employed. That means ptt,be ptt,ba ucu (6) (Euler s equation of turbo machinery) and V ba cm1 cm cm. (7) Db The local flow rate coefficient at the BE (Fig. 4) and cm BE (8) u the overall design flow rate coefficient becomes 1 4b 0 BE. (9) D vol Similarly, in terms of the local pressure coefficient BE cu BE, (1) u the overall total to total pressure coefficient becomes 1 tt,0 BE. (13) hyd Here the circumferential velocity is replaced by u D n. From this one easily can obtain the overall total to static pressure coefficient 1 1 ts,0 tt,0 vol 0 hyd tt, (14) r a) Fig. 4 Turbine BE with control volume, velocity triangles and exerted angular force F u b) Fig. 3 Radial turbine; a) Sketch of loss analysis, b) blade with blade element (BE) With the aspect ratio v r, the abbreviation for the relationship of blade width b to rotor diameter D b r (10) D we finally get Now we seek estimates for those values of BE and BE that can be achieved by the cascade of unstaggered blades. Conservation of angular momentum analysis on a control volume around one blade element BE (Fig. 4) yields Fu cucmt b. (15) t is the angular spacing between two blades, b the extension of the BE. Alternatively this can be expressed in terms of lift and drag/lift ratio, the circumferential flow induced force on an isolated airfoil (Fig. 5) is Fu L1 sin tan (16) w CL lb1 sin. tan Equating the right hand sides of eqs. (15) and (16) yields the solidity of the blade cascade L (17) t CL with the abbreviation r BE vol. (11)

4 p tt,ba (18) wu1 tan the aspired radial turbine cascade cannot be considered as a number of isolated airfoils. Their mutual interference effects must be taken into account. For the ideal case, i.e. assuming no drag, the lift force on a cascade of unstaggered airfoils is 1 k tan (19) times larger as compared with the isolated airfoil case (WEINIG [3]). Assuming that this holds true also for the case of drag being present we replace eq. (17) by kc L. (0) Note that as approaches zero k becomes 1 (isolated airfoil limit) and for 1 (the airfoils touch each other, a purely academic limit) k. Inserting k, eq. (19), into eq. (0) yields atan. CL (1) With vector-mean flow angle and velocity (see Fig. 4) cm BE tan () u c 1 u 1 BE 4 and 1 w u cu 4cm (3) we finally get 1 BE 1 BE tan 4 (4) and atan BE 1. 1 CL BE 1tan 1 tan (5) Eqs. (4, 5) are the two key equations for the unknowns BE and BE. Note that the only parameters involved are:, associated with the envisaged design point ( V 0, p tt,0 for a chosen u the properties of the selected airfoils C L and for = and the chosen solidity. By contrast r is required not until we determine the overall design coefficients 0 and ts,0 from eqs. (11) and (14). A strategy to deduce optimum design parameters from this analysis is as follows: Assume a maximum being equivalent to the angle of airfoil attack which corresponds to good airfoil performance; identify C L and from polars of the airfoil used for the blade design. Select a solidity (must be smaller than 1 to avoid intersection of BE s). Solve eq. (5) by iteration and obtain the local pressure coefficient BE. Find the local flow rate coefficient BE eq. (4). Estimate volumetric and hydraulic efficiencies and compute overall design coefficients 0, tt,0. Fig. 5 Definition of vector-mean flow velocity w and flow direction ) Conformal mapping of radial blades As for a bidirectional axial cascade the blades in the radial cascade also have to be non-staggered and - crucial for equal performance for centrifugal and centripetal flow symmetric. A first attempt is a simple geometrical mapping of the blades mean line on the circumference. This can be achieved by conformal mapping. Conformal mapping methods can be traced back to potential flow analysis where they are applied to transfer known flow behaviour around a simple geometry to more complex geometries [33]. Here the inverse method is applied to transfer a symmetric airfoil under rectilinear flow conditions to a curved flow situation present in a radial cascade. Assuming only the circumferential velocity due to the rotational speed being relevant (i.e. neglecting any inflow velocity and the difference in velocity magnitude between the airfoil surfaces), a simple complex transformation of the symmetrical airfoil coordinates (expressed in the ratio of chord length to rotor radius L/r) from Cartesian into the Polar coordinate system is carried out [34]. B. Design of the meridional contour and peripheral parts Numerical investigations prior to this study showed that some remarkable modifications of the meridional contour (as e.g. proposed in the open literature) are necessary to achieve efficient and nearly symmetric performance behaviour of the turbine under reciprocating flow. This comprises two aspects, mainly relevant for the centripetal flow direction. Firstly, the width b of the radial meridional contour in the vicinity of the blades has to be shaped divergent inwards of the blade mainline to achieve an acceptable performance behaviour of

5 the blade cascade [34]. The second main issue is the shaping of the axial meridional contour. The swirl impaired flow downstream of the blades entering the axial cascade leads to a strongly developing dead water zone in the axial contour, Fig. 6. Fig. 7 Bidirectional radial lift-based turbine; 1a) rotor with variable radial width b, ) radial ducting, 3a) modified axial ducting, 4a) outstretched hub body, 5a) axial guide vanes Fig. 6 Dead water in radial turbine under centripetal flow To repress this phenomena the theories of MELDAU [35] and STRSCHELETZKY [36] can be adopted. Accordingly the diameter r d of the dead water zone in an outstretched ducting V is a function of that depends because of V c m on (rc u )R the ratio of meridian- and circumferential velocity component c m /c u, see [37]. Considering the swirled flow commonly applied as a rotating rigid body with c u r = const. there are two possible methods to repress the dead water zones. One is to increase r by placing an outstretched body designed by the STRSCHELETZKY criteria into the axial contour. The other is to reduce or eliminate the circumferential flow component c u by the use of guide vanes before the flow enters the axial contour. Because of the findings out of an earlier numerical study and rotor-stator interaction noise studies in [8], a combination of both methods is applied subsequently. An outstretched hub body is placed into the axial contour. Additionally a set of swirl reducing axial guide vanes is positioned downstream of the radial-axial bend. The new bidirectional radial lift-based (BiRLi) turbine layout with an aerodynamically beneficial cross-flow section is shown schematically in Fig. 7. By use of this turbine layout the flow is guided trough the redirection with minimum losses. This includes the swirl reduction by the axial guide vanes before decelerating the flow in the axial diffuser. The axial diffuser consists of a diverging axial ducting, Fig. 7 (3a), and the converging hub body, Fig. 7 (4a). Focussing on the turbine s meridional contour under centrifugal flow it had been ascertained, that guide vanes in the radial contour outside of the rotor are not essentially needed and furthermore do not improve the performance of the turbine significantly fur the current setup investigated. C. BiRLi turbine design code The full design process for a BiRLi turbine layout is implemented into MATLAB. This includes the BEM design code described, including the use of the software XFOIL [38] which yields accurately the BE airfoil lift and drag coefficients as a function of the chosen airfoil contour, angle of attack, Reynolds and Mach number. The design of the meridional contour is based on the STRSCHELETZKY [36] design method for the axial hub, the layout of the meridional cross sections is based on IDELCHIK [39] as well as geometrical dependencies and surface ratios determined during extensive numerical studies. The well-known WEINIG guide vane design method [3], as described in BOMMES [40], is employed to obtain a circular-arc profile axial guide vane design. Note that because of the complex centripetal flow behaviour downstream of the radial-axial bend a straight forward analytical guide vane design process based on analytical design inflow angle prediction is not applicable. The guide vane design angles have to be optimized iteratively by numerical investigations. To identify a optimal ratio of rotor and guide vane blades a method proposed by TYLER and SOFRIN [41] is applied to reduce evanescent acoustic waves in the turbine casing at blade passing frequencies and hence reduce the sound emitted by the turbine. Finally the design routine yields estimates of the turbines performance characteristics as dimensionful and dimensionless coefficients at the design point and the full turbine geometry as parameter set and point clouds ready for CAD and CFD. D. BiRLi turbine design To validate the full turbine design process an exemplary turbine layout is designed to be investigated by stationary numerical RANS simulations. The main input and output parameter for the design process of a model scale turbine BiRLi-1 design are listed in Tab. 1. The volume flow-rate V 0 and pressure drop p tt,0 define the aerodynamic design point of the turbine. Estimates for the number of blades z, the relationship of radial width of the turbine blade to diameter r

6 and circumferential Mach-number Ma u = u/c s are found during previous CFD studies. The local blade design flow rate coefficient BE,0 equating to a local flow angle of BE,0 4.6 which is in a range where XFOIL is able to predict realistic values of lift and drag in the design process. The hydraulic efficiency used in the design process is the product of hyd = drag x sl whereupon the airfoil drag drag is predicted by XFOIL and the estimate efficiency for secondary losses sl 0.95 based on previous CFD studies. rotor with annular rotating discs in- / outlet interface periodic Tab. 1 Main Parameter of the investigated turbine Input BiRLi-1 Output BiRLi-1 z [-] 9 z GV [-] 5 r [-] 0.14 D [m] 0.48 Ma u [-] 0.4 n rpm [rpm] 375 BE,0 [-] V 0 [m 3 /s] [-] p tt,0 [Pa] 1468 tt,0 [-] 0.44 vol [%] 100 Airfoil NACA 0015 III. NUMERICAL SETUP The flow in the BiRLi turbine is simulated using the commercial 3D Navier-Stokes code ANSYS CFX with the standard SST-turbulence-model [4] and the high resolution advection scheme [43]. In the composite computational domain (Fig. 7) the steady, incompressible, three-dimensional Reynolds-averaged Navier-Stokes (RANS) equations are solved in a rotating reference frame (in the section where the rotor is placed) and in a stationary reference frame (where the guide vane) is placed. The block-structured numerical grid, prepared using ANSYS TurboGrid consists of about million nodes. Common grid quality criteria were considered; for instance the grid angles are all above 34. The maximum value of y + max for the first node adjacent to the blade surface (of rotor and stator) was set in TurboGrid to y + < 1 at a Reynolds Number Re = 4e5, a suitable mesh resolution out of a mesh refinement study. The rotating reference frame of the rotor section and the stationary reference frame of the guide vane section are linked by the common so called stage interface. At this connection only the averaged fluxes are transformed from the upstream reference frame through the interface. Steady state solutions are then obtained in each reference frame [43]. Due to the turbine symmetry, only one blade annulus was modelled and 1:1 periodic boundary conditions were imposed in the circumferential direction. An inlet normal velocity was imposed on the respective upstream boundary for each flow direction; an area averaged static pressure at the corresponding downstream boundary. Note that within this study there is no tip or duct clearance modelled in the computational domain. Fig. 7 BiRLi turbine numerical domain Results of the numerical RANS simulation are presented in terms of dimensionless characteristic curves for both flow directions in the turbine. Besides the formerly defined dimensionless coefficients we use the power coefficient Ps Dtipn, (9) 8 the total to total pressure coefficient tt ptt D n (30) and the total to static efficiency ts Ps V p ts. (31) Convergence was evaluated by monitoring the integral performance parameters, e.g. blade torque. For pre-stall points a mean deviation range of the blade torque monitor point below 1.5 % had been achieved. Note that stall prediction is vague with a RANS approach, because of the unsteady flow behaviour and therefore the poor convergence in the turbine s overload operating regime. These post-stall operating points showed torque fluctuations exceeding 0%. IV. RESULTS guide vanes in- / outlet A. Characteristic curves Fig. 8 shows steady state characteristic curves, determined by numerical RANS simulations for the BiRLi-1 turbine. The volume flow-rate power coefficient and the total to static efficiency ts are plotted over the total to total pressure drop tt for the centripetal (cpt) and centrifugal (cfg) flow direction. Obviously the / characteristics of the BiRLi turbine are nearly linear, as well-known for the Wells turbine, Fig. 8a. Furthermore the characteristic of the centrifugal flow direction differs from the centripetal; see also Fig. 8b. This can be explained by the upstream swirl entering the radial blade cascade for the centrifugal direction caused by the axial guide vanes placed upstream of the cascade.

7 a) BiRLi-1 cfg BiRLi-1 cpt Design B. Flow field To investigate detailed flow characteristics in the BiRLi-1 turbine, the absolute flow velocity is plotted in a meridional view at the periodic interface for centrifugal (Fig. 9a) and centripetal flow (Fig. 9b) at a volume flow rate of = a) 0.04 rotor 0.0 guide vane b) b) c) ts [-] tt [-] Fig. 8 Characteristic curves of the BiRLi-1 turbine Also the different upstream meridional contour, dependent on the flow direction, can affect the flow behaviour around the blades and therefore the blade performance. This can also lead to different stall behaviour for both flow directions. It can be concluded that the tendency of an earlier stall of the centripetal flow direction as discussed in [34] is also visible in the characteristic curves of the full turbine setup. The BEM design point Fig. 8a matches the numerical results of the full BiRLi turbine reasonably well. The turbines total to static efficiency, plotted in Fig. 8c is remarkably higher for the centrifugal compared to the centripetal flow direction. One reason van be the pre-swirl generated by the guide vanes under centrifugal flow which is known to improve the blade cascade efficiency [8]. Note by observing the efficiency curves that within this first numerical study no gaps are included in the investigated numerical model and therefore no volumetric losses are considered. Fig. 9 Streamlines in the BiRLi-1 turbine at = 0.095; a) centrifugal flow direction, b) centripetal flow direction The thin black lines indicate absolute velocity streamlines at the sections surface. Observing the centrifugal flow direction, the flow field in the axial ducting is smooth up to the point where the flow enters the axial-radial bend. A vortex can be identified, caused by the inhomogeneous flow around the bend. This leads to an axial deflection of the flow entering the radial blade cascade and hence a deflected flow field in the radial cascade, causing a developing vortex in the radial ducting. It is not yet clear how much the axial deflected flow effects the blade performance and stall mechanism because the effect of the pre-swirl generated by the upstream guide vanes leads to a different performance and stall mechanism compared to the performance behaviour out of the radial cascade study [34], where no pre-swirl and axial flow deflection is considered. For the centripetal direction in Fig.9b it can be observed, that the flow is guided smoothly through the radial ducting and the radial-axial bend. In the hub region downstream of the axial guide vanes deflections of the streamlines, caused by slip in the vanes flow redirection are visible and reduce the overall efficiency for this operation direction. Fig. 10 visualizes the 3-dimensional flow phenomena in the turbine. The coloured streamlines indicate the local absolute flow velocity in the turbine.

8 a) experimental results are available. The numerical results indicate that the BiRLi turbine with total to static efficiencies in the main operation range in between 70 and 80 % is promising to be an alternative to the turbine concepts presently in place. Nevertheless experimental investigations are essentially needed to indicate the potential of the turbine including realistic volumetric losses and a validation of the vague stall prediction of the RANS simulation. These will allow comparing the BiRLi turbine with other bidirectional air turbines under realistic conditions. Furthermore detailed analysis has to show the potential of improvement achievable in efficiency and operation range due to meridional contour and blade optimization. b) VI. ACKNOWLEDGMENTS This work is sponsored by the German Federal Ministry for the Environment, Nature Conservation and Nuclear Safety with the support code Fig. 10 Absolute velocity streamlines in the BiRLi-1 turbine; a) centrifugal flow direction; b) centripetal flow direction In Fig. 10a where the flow enters axial and leaves the turbine in radial direction especially the flow acceleration and swirl generation in and downstream of the guide vanes can be identified. The upstream swirl seen by the blades leads together with the increasing radius (keeping in mind rc u =const.) to a nearly swirl free outflow. But again visible is the flow deflection in the radial ducting caused by the slip in the axial-radial flow redirection. In Fig. 10b the highly swirl impaired flow downstream of the blades, getting straightened by the axial guide vanes, is visible. Note that the swirl is removed only to a certain amount to allow beneficial flow deceleration in the axial diffuser contour. V. CONCLUSIONS A blade element momentum (BEM) design method for radial bidirectional lift-based (BiRLi) turbine cascades has been introduced and applied to generate a first turbine layout, including the design of a new meridional contour and axial guide vanes. Numerical steady state RANS simulations are carried out and the performance characteristics shown. The BEM design point is matched reasonably well by the numerical results but the efficiencies involved in the BEM design process have to be determined in more detail when REFERENCES [1] A. F. d. O. Falcão, "Wave energy utilization: A review of the technologies," Renewable and Sustainable Energy Reviews, vol. 14, pp , 010. [] J. Cruz, Ocean Wave Energy: Current Status and Future Perspectives Berlin: Springer-Verlag, 008. [3] A. F. D. Falcao, "The history of and progress in wave energy conversion devices " presented at the 9th World Renewable Energy Conference, Florence, Italy, 006. [4] A. F. O. Falcão and L. M. C. Gato, "Air Turbines," in Comprehensive Renewable Energy. vol. 8, A. Sayigh, Ed., ed Oxford: Elsevier, 01, pp [5] T. Setoguchi and M. Takao, "Current status of self rectifying air turbines for wave energy conversion," Energy Conversion and Management, vol. 47, pp , 006. [6] R. Curran and M. Folley, "Air turbine design for OWC s," in Ocean Wave Energy: Current Status and Future Perspectives, J. Cruz, Ed., ed Berlin: Springer-Verlag, 008. [7] A. A. Wells, "Fluid driven rotary transducer," British Patent Spec No , [8] R. Starzmann, Aero-Acoustic Analysis of Wells Turbines for Ocean Wave Energy Conversion vol. 7. Duesseldorf: VDI, 01. [9] S. Raghunathan, "The Wells air turbine for wave energyconversion," Progress in Aerospace Sciences, vol. 31, pp , [10] T. Setoguchi, S. Santhakumar, H. Maeda, M. Takao, and K. Kaneko, "A review of impulse turbines for wave energy conversion," Renewable Energy, vol. 3, pp. 61-9, 001. [11] B. Pereiras, F. Castro, A. e. Marjani, and M. A. Rodríguez, "An improved radial impulse turbine for OWC," Renewable Energy, vol. 36, pp , 011. [1] B. Pereiras, D. Montoya, F. Castro, A. de la Villa, A. El Marjani, and M. A. Rodriguez, "Conception of a radial impulse turbine for an oscillating water column (OWC)," presented at the 3rd International Conference on Ocean Energy, Bilbao, Spain, 010. [13] Y. Shpolyanski, I. N. Usachev, B. Istorik, and V. Sobolev, "The new orthogonal turbine for tidal, wave and low-head hydro power plants," Supplement to International Journal on Hydropower (Marine Energy), vol. 6, pp , 009. [14] M. E. McCormick, J. G. Rehak, and B. D. Williams, "An experimental study of a bidirectional radial turbine for pneumatic wave energy conversion," in Mastering Ocean through Technology, Newport, Rhode Island, 199, pp [15] T. Setoguchi, S. Santhakumar, M. Takao, T. H. Kim, and K. Kaneko, "A performance study of a radial turbine for wave energy

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