energies Article

Computational Fluid Dynamics Modelling and Simulation of an Inclined Horizontal Axis Hydrokinetic Turbine Leidy Tatiana Contreras 1 , Omar Dario Lopez 2 1 2

*

and Santiago Lain 1, *

PAI+ Group, Energetics & Mechanics Department, Faculty of Engineering, Universidad Autónoma de Occidente, 760030 Cali, Colombia; [email protected] Computational Mechanics Research Group, Mechanical Engineering Department, Faculty of Engineering, Universidad de los Andes, 111711 Bogotá, Colombia; [email protected] Correspondence: [email protected]; Tel.: +57-2-318-8000 (ext. 11882)

Received: 2 August 2018; Accepted: 30 October 2018; Published: 14 November 2018

Abstract: In this contribution, unsteady three-dimensional numerical simulations of the water flow through a horizontal axis hydrokinetic turbine (HAHT) of the Garman type are performed. This study was conducted in order to estimate the influence of turbine inclination with respect to the incoming flow on turbine performance and forces acting on the rotor, which is studied using a time-accurate Reynolds-averaged Navier-Stokes (RANS) commercial solver. Changes of the flow in time are described by a physical transient model based on two domains, one rotating and the other stationary, combined with a sliding mesh technique. Flow turbulence is described by the well-established Shear Stress Transport (SST) model using its standard and transitional versions. Three inclined operation conditions have been analyzed for the turbine regarding the main stream: 0◦ (SP configuration, shaft parallel to incoming velocity), 15◦ (SI15 configuration), and 30◦ (SI30 configuration). It was found that the hydrodynamic efficiency of the turbine decreases with increasing inclination angles. Besides, it was obtained that in the inclined configurations, the thrust and drag forces acting on rotor were lower than in the SP configuration, although in the former cases, blades experience alternating loads that may induce failure due to fatigue in the long term. Moreover, if the boundary layer transitional effects are included in the computations, a slight increase in the power coefficient is computed for all inclination configurations. Keywords: computational fluid dynamics; three-dimensional unsteady flow; inclined axis hydrokinetic turbine; turbulent flow

1. Introduction Climate change, associated with negative impacts resulting from overexploitation and the use of fossil fuels, has not only induced environmental problems of great magnitude but has also generated an awakening in the scientific community and governments. All interested actors agree today that an alternative solution to the increasing energy deficit is the use of renewable energies [1]. Therefore, using hydrokinetic energy as a renewable source for generating electricity is nowadays one of the most active fields of research [2]. Water currents such as oceans and rivers constitute a wide and almost unexploited source for renewable energy generation. According to Reference [3], a representative electricity generation can be obtained by the ocean energy industry and the forecast for the year 2025 is to reach up to 200 GW of installed generation capacity. On the other hand, many developing countries are crossed by rivers which carry significant volumetric water flow along the year. This fact could be a revolutionary scenario for remote populations which could use this energy source if effective and low-cost energy harnessing mechanisms are developed [3]. Around the world there are more than 300 hydrokinetic Energies 2018, 11, 3151; doi:10.3390/en11113151

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projects already in process, divided into four main types of technologies: ocean wave, tidal stream, ocean current and river hydrokinetic [3]; many of the applications in marine environments are for the large-scale, while, the river and channels applications are for the small-scale [4]. Because of its predictability, the large density of energy, and the low environmental impact (scarce visual impact, no emissions, no noise), the kinetic energy present in water streams (oceans, rivers, or tidal channels) has received considerable attention in recent years [3–5]. Such kinetic energy can be extracted through properly designed immersed turbines [6] without the need of large facilities as reservoirs or dams. As it generates no emissions, the environmental impact is minimal. Compared to other hydraulic technologies, the site selection is much less restrictive and because it does not require significant infrastructure, the implementation time is short and the initial costs are reduced. Moreover, the modular character of hydraulic power enables scalable output energy, allowing for a reduction of the energy cost per kW. Another advantage is related with the continuous flow of water in oceans and rivers which eliminates the need for storing the energy, which is a crucial benefit for remote communities and very convenient in public services [6]. From the technical point of view, the conversion of kinetic energy present in large rivers, tides, and ocean currents involves two processes. The first process implies that the energy available on tidal, ocean or river currents must be extracted and converted into mechanical energy at the rotor axis, and the second process deals with converting such mechanical energy into electricity using a generator [7]. However, despite all the performed research and experiments, the study of hydrokinetic turbines (concentrated mainly in the primary process), is still in an incipient state due to the complexity and cost that represents a suitable testing bench to operate this kind of rotors. That is, the reason why the main part of its design is based on the analogy with wind turbines. Moreover, the majority of the developed innovations have been the result of empirical studies conducted in order to deal with anchoring systems, channels, debris protection, and maintenance [8]. Flow dynamics in the horizontal axis hydrokinetic turbines (HAHT) is complex and has attracted the interest of the scientific community during the last years, specifically aimed to understand their performance and to improve efficiencies. To reach such objectives, a deep understanding of the involved hydrodynamics is required. In that sense, since a few years ago, Computational Fluid Dynamics (CFD) has become an essential approach for describing the fluid flow behavior around hydro turbines. CFD numerically solves the governing equations of Fluid Mechanics (i.e., mass, momentum, and energy conservation) in complex geometries in a general framework. Due to its advantages over other simplified methods [9], it has been the approach adopted in the present study and, in the following analysis, several recent studies that employ CFD to investigate different aspects of the design, development, and operation of HAHT’s are described. Kang et al. [10] conducted a numerical study with two kinds of geometry composed of a rectangular box and a rotating domain; in the first case they only analyzed the rotor, while in the second case the complete structure (rotor and mounting) was analyzed to determine the effect of the support in the turbine hydrodynamic efficiency. The results of these authors illustrated the flow complexity and showed that the extracted power of the full turbine mainly depends on the rotor geometry and the TSR (Tip Speed Ratio), as they were not very affected by the mounting components of the turbine and the channel bed. The authors carried out an experimental analysis used to validate the CFD results; they found that the refined grid presented a discrepancy at the power coefficient less than 5%, which is considered quite satisfactory taking into account that measurements were carried out for the complete turbine geometry including an ambient turbulence in the site. In Reference [11], the authors wanted to identify the main design parameters affecting the performance of a Horizontal Axis Water Turbine by presenting numerical results in comparison with experimental measurements. In such work, it was demonstrated that, when the other parameters were kept constant, the numerical output power of the turbine was roughly proportional to the square of the blade span and to the cube of the incoming velocity. Regarding the blade number, the authors found that the optimum number was three and that an increase beyond that caused a decrease in power production. Again,

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the authors validated the simulation with experimental data obtaining a difference of power coefficient between experimental and numerical results lower than 15%; the discrepancy could be attributed to the generator losses and possible measuring errors. Guo et al. [12] used a three-dimensional CFD simulation to analyze the turbulent flow characteristics in the velocity field up and downstream of the turbine and the effects of a discrete number of blades. Motivated by its use in BEM (Blade Element Momentum theory), the authors derived the flow induction factors (axial and tangential) at several locations downstream of the rotor from their CFD results. It was concluded that the main induced velocity component by the vortices was the axial component. Additionally, the computations showed that vortices developed at the tip of each blade induced a down-wash velocity near the rotor and generated an azimuthal variation of velocity components; these are responsible for the appearance of flow non-uniformities upstream and downstream the rotor. The authors concluded that the calculation model used provided an acceptable accuracy because the differences between the numerical results and experimental values of power and thrust coefficients were lower than 5%. With the objective of reducing the computational effort of CFD, some authors have coupled BEM and CFD. In this context, BEM, using the hydrofoil characteristics in two dimensions, can be employed to predict the hydrodynamic performance of a hydrokinetic turbine, while the CFD coupled with BEM take into account three dimensions using an actuator disc which in addition to predicting the performance also allows us to predict wake features of the turbine; however, these estimations do not include the rotating blades and are not able to predict some details of the flow field. For instance, Reference [13] present a usable tool which was applied to predict the behavior of tidal stream turbines in typical offshore conditions. The obtained results were satisfactory because the comparison of the power coefficient estimation by BEM-CFD with experimental data showed a difference between 0.3% and 8.8%. As another example of the coupling BEM-CFD, Reference [14] concludes that the BEM-CFD results of the hydrokinetic turbine were able to accurately predict the thrust; however, the power was overestimated. This behavior was present at lower values of TSR. In particular, the BEM-CFD calculations provided a fairly good approximation to the near rotor circumferentially averaged fluid velocity with the exception of the tip vortices [14]. In Reference [15] the authors reviewed and compared results from various models of horizontal axis water turbines at different spatial resolutions; the aim of the study was to investigate the effect of small variations in lift and drag characteristics of the hydrofoils employed in the blade design on the turbine performance. They found that from a practical perspective, relatively small changes on the blade aerodynamic properties are improbable to cause a significant decrease in the performance. However, such modifications had the effect of altering the value of the optimum power coefficient as well as the tip speed ratio at which it is achieved. Understanding the behavior of turbine wakes is crucial if turbines are to be deployed in arrays; for such reason, a comparison between BEM-CFD and full CFD method was focused on determination of velocity deficit in the turbine wake. When comparing with experimental data, Reference [15] found that both models captured reasonably well the wake dynamics, although there was around a 5% difference between both predictions. Reference [16] presented comparisons between experiments and CFD numerical computations focused on the velocity profiles in the wake region of a HAHT. The agreement between them was very reasonable, showing the same predicted wake recovery trend. Moreover, the turbine closeness to the water surface promoted the flow modification around the turbine which affected the wake development downstream the rotor. Finally, supported by the presented results, Zhang et al. [16] claimed that CFD is an appropriate tool to simulate the performance of tidal turbines and that the turbine proximity to the water surface influences the wake recovery. In a HAHT, the lowest pressure near the blade tip is due to the high revolution speed around these sections. Therefore, the accurate description of the flow field near the blade tip becomes important for two reasons: to analyze the turbine power performance and because cavitation is prone to occur in these areas, which of course alters turbine efficiency [17]. Following Reference [4] in order to design a high-performance rotor, the cavitation and pressure coefficient should be as low as possible while

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the lift to drag ratio should be kept high. In particular, Lee et al. [17] introduced a new blade design 4 of 23 included a raked tip shape aimed to noise reduction and cavitation inception delay. The concept was evaluated by numerical CFD simulations showing positive results in cavitation inceptionwithout delay. The concept evaluated by numerical CFD simulations showing delaying cavitation degrading thewas turbine efficiency. positive in contribution delaying cavitation without degrading theestimation turbine efficiency. Theresults present deals with the performance of small HAHT’s of Garman The present contribution deals with the performance estimation of small HAHT’s Garman type using CFD. The arrangement of such turbines can be appreciated in Figure 1b: theofturbine is type using CFD. The arrangement turbines canoperating be appreciated Figure 1b: the turbinethe is assembled in a floating structure onofa such channel or river with itsinaxis inclined regarding assembled in a floating structure on a channel oruse river its axisisinclined regarding the flow direction. As it was mentioned, the main ofoperating this kind with of turbines to provide electricity flow direction. As it was mentioned, the main use of this kind of turbines is to provide electricity to to isolated communities so their design has been essentially empirical and only a few experimental isolated communities their design has been essentially and only a fewonexperimental studies have appearedso [18,19]. For instance, Al Mamun [18]empirical performed experiments a laboratory ◦ studies have appeared [18,19]. For instance, Al Mamun [18] performed experiments on a laboratory Garman turbine with three blades operating with an inclination of 45 with respect to the main channel Garman turbineExperiments with three were blades operating inclination of and 45° with respect angles to the aimed main flow direction. conducted forwith threean incoming speeds two pitching channel flow Experimentsversus were tip conducted for three incoming speeds and twoofpitching to analyze thedirection. turbine performance speed ratio. As a result, a power coefficient around angles aimed to analyze thenoturbine versus tipofspeed ratio. As a have result,been a power 30% was reached. However, reports performance about the CFD analysis inclined HAHT’s found coefficient of around 30% was However, theknowledge, CFD analysis in the literature. Therefore, the reached. authors believe that,notoreports the bestabout of their thisofisinclined the first HAHT’s have been found in the literature. Therefore, thebehavior authors of believe that,which to theoperates best of their time in which the CFD simulation of the hydrodynamic a HAHT with knowledge, this is the first time in which the CFD simulation of the hydrodynamic behavior of a an inclined axis respect to the main stream is attempted. HAHT which operates with an inclined axis respect to the main stream is attempted. Energies 2018, 11, x water FOR PEER REVIEW for horizontal rotors that

(a)

(b)

Figure 1. The Theschematics schematicsof of inclined hydrokinetic turbine showing its components (a) and Figure 1. thethe inclined hydrokinetic turbine showing its components (a) and isometric isometric view of the geometrical model (b). view of the geometrical model (b).

This This paper paperisisstructured structured in inthe thefollowing followingway. way. After Afterthe theintroduction, introduction,the theconsidered consideredgeometrical geometrical configurations andthethe meshing process are described in 1.Section 1. The simulation numericalmethodology simulation configurations and meshing process are described in Section The numerical methodology and the key parameters the operation HAHT’s are Section and the key parameters governing the governing operation of HAHT’s are of summarized insummarized Section 2. Theinobtained 2. The obtained results for the non-dimensional turbine coefficients presented in are Section 3 which results for the non-dimensional turbine coefficients are presented in are Section 3 which organized in are organized in several theirabehavior along a turbine revolution described and several subsections: theirsubsections: behavior along turbine revolution is described first is and later thefirst analysis later the analysis is extended to build the versus respective curvesratio; versus tip speed moreover, the is extended to build the respective curves tip speed moreover, theratio; effects of including effects of including the modeling of theoftransitional behavior the boundary layerareondiscussed turbine the modeling of the transitional behavior the boundary layer onofturbine performance performance discussed in 4.3. Comparison ofwith the computed CFD results with available in Section 4.3.are Comparison of Section the computed CFD results available experimental data and those experimental data and those obtained with more simplified models is performed in Section 4; also, obtained with more simplified models is performed in Section 4; also, in this section, a comparison of in this section, a comparison additionaldata CFDin results the experimental dataisin another additional CFD results with the of experimental anotherwith horizontal axis tidal turbine performed. horizontal tidal turbine Finally,and theperspectives. last section draws the main conclusions and Finally, theaxis last section draws is theperformed. main conclusions perspectives. 2. Geometrical Configuration and Mesh Generation 2. Geometrical Configuration Mesh Generation The numerically evaluatedand horizontal axis hydrokinetic turbine in this study has been an existing machine Aquavatio. Such ahorizontal HAHT wasaxis empirically built, adopting Garman turbine The called numerically evaluated hydrokinetic turbine ina previous this study has been an design. machine Such a machine was operating situ” on the Cauca River (Colombia) doing feasibility existing called Aquavatio. Such“in a HAHT was empirically built, adopting for a previous Garman studies during years 2010–2011, a careful“in experimental characterization was never performed. turbine design. the Such a machine wasbut operating situ” on the Cauca River (Colombia) for doing feasibility studies during the years 2010–2011, but a careful experimental characterization was never performed. Aquavatio consists of a three-bladed rotor, with a diameter D = 1.8 m and a truncated conical hub connects the blades to the shaft (see Figure 1a). The blade design was adopted from an existing wind turbine IT-PE-100 [20] which has nearly the same rotor size as Aquavatio; this design is based on the NACA 4412 airfoil with pitch angle and chord distributions lineal from root to tip.

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Aquavatio consists of a three-bladed rotor, with a diameter D = 1.8 m and a truncated conical hub connects the blades to the shaft (see Figure 1a). The blade design was adopted from an existing wind turbine IT-PE-100 [20] which has nearly the same rotor size as Aquavatio; this design is based on the Energies 11, x with FOR PEER REVIEW 5 of 23 the NACA 44122018, airfoil pitch angle and chord distributions lineal from root to tip. Figure 1a shows geometry of the HAHT schematically and illustrates its real operation configuration while Figure 1b Figure 1a shows the geometry of the HAHT schematically and illustrates its real operation presents the generated modelthe ofgenerated the turbine in isometric view; here, the stream direction configuration while geometrical Figure 1b presents geometrical model of the turbine in isometric follows the ‘z’ direction, ‘y’ represents the vertical and ‘x’ the lateral coordinate. view; here, the stream direction follows the ‘z’ direction, ‘y’ represents the vertical and ‘x’ the lateral In the present study, three configurations have been analyzed: a first assembly where the rotor coordinate. the present study, threeincoming configurations have so been analyzed: a first assembly where the is placedInperpendicular to the velocity that the turbine axis is parallel to rotor the flow is placed perpendicular toand thetwo incoming velocity so that thewhere turbine parallelantoangle the flow direction (SP configuration), inclined arrangements theaxis axisismakes γ of 15◦ (SP configuration), and two inclined arrangements the axis respectively makes an angle γ of 15° 2b). (SI15 direction configuration) and 30◦ (SI30 configuration) regarding thewhere free surface, (see Figure (SI15 configuration) and 30° (SI30 configuration) regarding the free surface, respectively (see Figure Obviously, the two last cases mimic the conditions in which the real HAHT operates. The three 2b). Obviously, the two last cases mimic the conditions in which the real HAHT operates. The three configurations considered allowing for a quantitative estimation of the influence of the inclination configurations considered allowing for a quantitative estimation of the influence of the inclination angle on machine performance as well as on the forces acting on the turbine. angle on machine performance as well as on the forces acting on the turbine.

(a)

(b) Figure 2. The front view and sideview view(b) (b) of of the the geometry the inclined HAHT. The The employed Figure 2. The front view (a)(a) and side geometryfor for the inclined HAHT. employed boundary conditions are also shown. boundary conditions are also shown.

considered computational domain has the following dimensions, which are expressed in The The considered computational domain has the following dimensions, which are expressed in terms of the rotor diameter D: length, 20D height, 4D and width, 6D. With such dimensions, the terms of the rotor diameter D: length, 20D height, 4D and width, 6D. With such dimensions, the turbine turbine operates in almost isolated conditions, as the resulting blockage ratio is lower than 5%. operates in almost isolated conditions, as the resulting blockage ratio is lower than 5%. Moreover, Moreover, the computational domain is divided into two sub-domains: an inner rotating domain of the computational domain dividedthe into two sub-domains: anhub), innerand rotating domain cylindrical cylindrical shape, whichisincludes turbine rotor (blades and an outer steadyofdomain shape, which includes the turbine rotor (blades and hub), and an outer steady domain encompassing encompassing the water environment. In the cases of inclined configurations, the shaft was included the water In the cases of inclined therepresent shaft was included this domain, in thisenvironment. domain, but not in the parallel to flowconfigurations, configuration. To the physicalin rotational motion of parallel the blades, the cylindrical domainTorotates with the a prescribed velocity withofrespect but not in the to flow configuration. represent physicalangular rotational motion the blades, to the steady domain,rotates which with numerically is realized by a sliding mesh technique in domain, the the cylindrical domain a prescribed angular velocity with respectimplemented to the steady commercial software employed, (Fluent v. 14.0, ANSYS, Inc., Canonsburg, PA, USA). which numerically is realized by a sliding mesh technique implemented in the commercial software employed boundary conditions can be appreciated in Figure 2a,b. As indicated in Figure 2b, employedThe (Fluent v. 14.0, ANSYS, Inc., Canonsburg, PA, USA). the left side is specified as a velocity inlet with a constant velocity (equal to 1.0 m/s in this study), the The employed boundary conditions can be appreciated in Figure 2a,b. As indicated in Figure 2b, right face is set as a pressure outlet (0 Pa), the bottom boundary (channel bed) consists on a steady the left side is specified as a velocity inlet with a constant velocity (equal to 1.0 m/s in this study), non-slip wall) whereas the top border, representing the free surface, was established as a zero stress the right facewall is settranslating as a pressure (0 Pa), the bottom consists on aas steady moving with outlet the same velocity as that boundary imposed at(channel the inlet.bed) The lateral walls, shown in Figure 2a, are defined to be non-slip walls. Inside the rotating subdomain is the rotor, this

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non-slip wall) whereas the top border, representing the free surface, was established as a zero stress moving wall translating with the same velocity as that imposed at the inlet. The lateral walls, as shown in Figure 2a, are defined to be non-slip walls. Inside the rotating subdomain is the rotor, this cylinder is Energies 2018, 11, x FOR PEER REVIEW 6 of 23 connected with the outer domain though interfaces specified as the sliding mesh boundary condition. cylinder is connected with the outer domain though interfaces specified as the sliding mesh boundary Moreover, because the turbulence levels at the inlet were not known, it was decided to work with condition. Moreover, because the turbulence levels at the inlet were not known, it was decided to a moderate turbulence intensity equal to 5%. work with a moderate turbulence intensity equal to 5%. The computational domain has been discretized by means of a non-structured mesh created with The computational domain has been discretized by means of a non-structured mesh created with the ANSYS ICEM-CFD software (v. 14.0, ANSYS, Inc., Canonsburg, PA, USA). Figure 3a presents the ANSYS ICEM-CFD software (v. 14.0, ANSYS, Inc., Canonsburg, PA, USA). Figure 3a presents a a perspective of the employed mesh where the darkest area corresponds to the rotating sub-domain. perspective of the employed mesh where the darkest area corresponds to the rotating sub-domain. To adequately describe thethe boundary thegrid grid closest to the blades be fine To adequately describe boundarylayer layerdevelopment, development, the closest to the blades mustmust be fine enough; as an Figure surfacemesh meshemployed employed in the blades the hub, enough; as illustration, an illustration, Figure3b 3bshows shows the the surface in the blades and and the hub, which is pretty uniform. Consequently, the mesh around the blade has an O-grid topology which is pretty uniform. Consequently, the mesh around the blade has an O-grid topology with with twelve prism layers. Outside the tetrasbased basednon-structured non-structured constructed, twelve prism layers. Outside theprisms prismsregion, region, a tetras gridgrid waswas constructed, taking their aspect ratioisissimilar similar to prisms with the the purpose of guaranteeing a taking carecare thatthat their aspect ratio to that thatofofthe the prisms with purpose of guaranteeing smooth transitionbetween betweenboth both mesh mesh regions. density is higher downstream than than a smooth transition regions.Finally, Finally,the thegrid grid density is higher downstream upstream the rotor to the complexityof ofthe the flow flow in TheThe quality parameters of of upstream the rotor duedue to the complexity in the theturbine turbinewake. wake. quality parameters the meshes have been checked with the tools available in ANSYS ICEM-CFD and are listed in Table the meshes have been checked with the tools available in ANSYS ICEM-CFD and are listed in Table 1. 1.

(a)

(b)

Figure 3. The overview meshused usedat atthe the steady steady domain and thethe surface mesh on the Figure 3. The overview of of thethe mesh domain(a)(a) and surface mesh onturbine the turbine blades and hub (b). blades and hub (b). 1. The parameters describingthe thequality quality of the different turbine configurations. TableTable 1. The parameters describing the mesh meshfor forthe the different turbine configurations. Parameter SP Configuration SP Configuration Aspect ratio (average) 0.95 Aspect ratio (average) 0.95 Equiangle skewness (average) 0.52 Equiangle skewness (average) 0.52 Determinant (average) 0.93 Determinant (average) 0.93 Expansion factor 1.20

Parameter

Expansion factor

1.20

SI15 Configuration SI30 Configuration SI15 Configuration SI30 Configuration 0.96 0.95 0.96 0.46 0.45 0.95 0.46 0.91 0.91 0.45 0.91 1.20 1.20 0.91

1.20

1.20

3. Numerical Simulation Methodology

3. Numerical Simulation The transient flow Methodology around the HAHT was computed with the help of the transient rotor-stator framework, realized by the sliding mesh approach. In that model, the turbine hub and blades rotate

The transient flow around the HAHT was computed with the help of the transient rotor-stator counterclockwise (see Figure 4) with a prescribed angular velocity; in this way, the development of framework, realized by the sliding mesh approach. In that model, the turbine hub and blades rotate the flow field at each time step is described. The interface position between the rotating inner and counterclockwise (see Figure 4) with a prescribed angular velocity; way, theflux development steady outer sub-domains is actualized every time step allowing forina this conservative interchangeof the flow between field at each step is described. The interface between the rotating innerfeatures and steady them.time The Shear Stress Transport (SST) model position was adopted to describe the turbulent outerofsub-domains is actualized every time stepofallowing for[21,22] a conservative interchange between the flow. In this study the standard version such model was mainlyflux employed, however, them.the The Shear Stress Transport (SST) model was adopted to describe the turbulent features of the flow. transition version [23] was also tested. It is well known that the SST model improves the predictions other two-equation turbulence flow configurations where strongthe adverse In this study theof standard version of such modelmodels [21,22]in was mainly employed, however, transition pressure gradients occur, such those happening around HAHT,improves and it has the beenpredictions widely usedofinother version [23] was also tested. It is as well known that the SSTamodel the simulation of hydraulic turbines [24–33], where it has become a sort of standard. two-equation turbulence models in flow configurations where strong adverse pressure gradients occur, Regarding the employed discretization schemes, all the results converged at each time step using second order schemes in space, upwind for the convective and centered for the diffusive terms,

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such as those happening around a HAHT, and it has been widely used in the simulation of hydraulic turbines [24–33], where it has become a sort of standard. Regarding the employed discretization schemes, all the results converged at each time step using second order schemes in space, upwind for the convective and centered for the diffusive terms, respectively, and the second order in time for all the variables. Pressure-velocity coupling is dealt with Energies 2018, 11, x FOR PEER REVIEW 7 of 23 the SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) approach. Computations were performed for anand incident velocity V0in=time 1 m/s angular velocities, coupling depending on the tip respectively, the second order for with all thedifferent variables. Pressure-velocity is dealt speed ratio (see Equation (1) below). Theforemployed time step corresponds to a Computations turbine rotation of with theλSIMPLE (Semi-Implicit Method Pressure-Linked Equations) approach. around , was chosen after a sensitivity which a trade-off between computational were1◦performed for an incident velocityanalysis 𝑉 = 1 m/s with represents different angular velocities, depending on speed ratio 𝜆 (see Equation (1) below). The of employed time step corresponds to each a turbine cost the andtipaccuracy. Moreover, a maximum number 200 iterations was specified at time step −5 . rotation of around 1°, was chosen after analysis which represents a trade-off between using a residual convergence criterion of a10sensitivity computational cost and accuracy. Moreover, a maximum number of 200 iterations specified Simulations are started by computing the flow around the HAHT using thewas steady MFRatmodel each time step using a residual convergence criterion of 10−5. of ANSYS-Fluent software (v. 14.0, ANSYS, Inc., Canonsburg, PA, USA), which is used as an initial Simulations are started by computing the flow around the HAHT using the steady MFR model condition for the transient computation. The unsteady computation is launched, initially using schemes of ANSYS-Fluent software (v. 14.0, ANSYS, Inc., Canonsburg, PA, USA), which is used as an initial of the first order during approximately ten turbine revolutions to get the flow developed. When the condition for the transient computation. The unsteady computation is launched, initially using torque has settled down, i.e., the torque curve shows a quasi-periodic the discretization schemes of the first order during approximately ten turbine revolutions to behavior, get the flow developed. schemes of the advective terms are changed to second order, firstly for the continuity and momentum When the torque has settled down, i.e., the torque curve shows a quasi-periodic behavior, the equations and later also for the turbulent variables equations. Finally, the simulation was run until the discretization schemes of advective terms are changed to second order, firstly for the continuity and momentum equationsbetween and later also the turbulent variables equations. simulation averaged torque difference twofor successive turns was below 0.2%Finally, [24]. Inthe the present study, was run until thecase, averaged torque difference between two have successive was below 0.2% [24]. In for each computed at least twenty rotor revolutions been turns simulated. the presentverification study, for each computed case, at least rotor revolutions beentosimulated. A spatial study was performed for twenty the rotor with the shaft have parallel the flow direction A spatial verification study was performed for the rotor with the shaft parallel to the flow (SP configuration). The evaluated operating point was the nominal condition of the wind rotor IT-PE-100 direction (SP configuration). The evaluated operating point was the nominal condition of the wind because the same blade design was used for both machines and it corresponds to a tip speed ratio λ = 5.7 rotor IT-PE-100 because the same blade design was used for both machines and it corresponds to a (see tip Equation (1) below) using a rotor angular velocity of 60 rpm. For this grid independence study, speed ratio λ = 5.7 (see Equation (1) below) using a rotor angular velocity of 60 rpm. For this grid the sampled variable was to be the power coefficient Equation (3) C below). According to P (see independence study, thechosen sampled variable was chosen to be C the power coefficient P (see Equation the usual procedure, three meshes with an increasing number of cells were considered: a coarse (3) below). According to the usual procedure, three meshes with an increasing number of cells were 6 6 gridconsidered: with 5.2 ×a10 elements, an5.2 intermediate mesh with 8.2 × 10 , elements refined grid coarse grid with 10 elements, an intermediate mesh with 8.2 and 10 a, elements and with grid with 10.5 10 elements. obtained averaged power have 0.2383 been the 10.5 a×refined 106 elements. The obtained averagedThe power coefficients have beencoefficients the following: (coarse), following: 0.2383 (coarse), 0.2430 (intermediate) and 0.2410 (refined). As the difference in 𝐶 is 0.8% 0.2430 (intermediate) and 0.2410 (refined). As the difference in C p is 0.8% between the medium and fine between the medium and the in intermediate grid was employed the computations meshes, the intermediate gridfine wasmeshes, employed the computations allowing us in to maintain an affordable allowing us to maintain an affordable computational time. Based on this result, representing a computational time. Based on this result, representing a compromise between the computational cost compromise between the computational cost and accuracy, it was decided to mesh the inclined and accuracy, it was decided to mesh the inclined configurations with a similar distribution and number configurations with a similar distribution and number of elements than the SP case. In those cases, of elements than the SP case. In those cases, the employed number of elements in the meshes has been the employed number of elements in the meshes has been 8.2 10 elements (SI15 configuration) 8.2 ×and 1067.9 elements (SI15 configuration) and 7.9 × 106 elements (SI30 configuration). 10 elements (SI30 configuration).

Figure Therotor rotor view the blades’ position and the and employed coordinate system. Blades Figure 4. 4.The viewillustrating illustrating the blades’ position the employed coordinate system. rotate counterclockwise. Blades rotate counterclockwise.

The following non-dimensional parameters govern the behavior of the HAHT: the tip speed ratio or TSR (𝜆) is the non-dimensional angular velocity regarding the incoming velocity, 𝑉 :

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The following non-dimensional parameters govern the behavior of the HAHT: the tip speed ratio or TSR (λ) is the non-dimensional angular velocity regarding the incoming velocity, V0 : ωD 2V0

λ=

(1)

where ω is the rotor angular velocity and D its diameter. The torque coefficient Cm relates to the total torque M, the density of the fluid ρ, and the area swept by the rotor, Sre f = πD2 /4; it is written as: Cm =

M

(2)

1 2D 2 ρV0 2 Sre f

The turbine efficiency, or performance, is expressed by the power coefficient Cp , which is the non-dimensional variable associated with the power produced by the turbine, P: Cp =

P 1 3 2 ρV0 Sre f

= Cm λ

(3)

Cp is obtained as the product of the torque coefficient Cm and the tip speed ratio λ. Therefore, the operating point of the turbine is defined by the pair (λ, CP ). The total hydrodynamic force F acting on each blade is projected on the directions perpendicular to the rotation plane, or normal force Fn , and parallel to it, or tangential force Ft . The tangential force is connected with the torque transmitted by the fluid to the blade while the normal force is responsible for the cyclic loading and fatigue on the blades. In the last case, each blade contribution can be added to compute the normal force acting on the whole rotor—the thrust—which is characterized by the thrust coefficient Cn . Fn Cn = 1 (4) 2 2 ρV0 Sre f Moreover, on the whole rotor, as an object immersed in a moving fluid, the total hydrodynamic force can be decomposed in a component parallel to the incoming flow velocity, which constitutes the drag, D, and in a component in the vertical plane perpendicular to such velocity which constitutes the lift force, L. Coefficients associated with such forces are written as: CD =

D 1 2 2 ρV0 Sre f

; CL =

L 1 2 2 ρV0 Sre f

(5)

4. Results 4.1. The Behavior of Non-Dimensional Coefficients Along A Turbine Revolution In this subsection, the behavior of the power and force coefficients along a cycle is discussed depending on the rotor inclination, and for a TSR λ = 5.7. For this operating point, the inflow velocity was 1 m/s and the angular velocity 60 rpm. As indicated previously, the employed turbulence model was k-ω SST [22]. Figure 5 presents the values obtained for the power coefficient C p in the three considered configurations, SP, SI15 and SI30. This figure illustrates the behavior during a turbine revolution of C p with the azimuthal angle, defined by Figure 4. Figure 5b shows the contribution of one blade to the power coefficient for the three configurations. In the SP case, the delivered power for one blade depends only very slightly on the azimuthal position, but in the case of the inclined turbines, it shows a clear dependence on such an angle. Therefore, the power coefficient curve consists on a fairly constant curve for SP configuration and on a periodic function with a maximum and a minimum in configurations SI15 and SI30. This fact is associated with differences in the relative velocity experienced

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Energies 2018, 11, xblades FOR PEER 9 ofclearly 23 by the turbine at REVIEW different angular positions in the inclined turbine cases. As it can be seen in Figure 5b, the oscillation amplitude in CP increases with the inclination angle (γ), keeping its can be clearly seen in Figure 5b, the oscillation amplitude in 𝐶 increases with the inclination angle maximum to very similar values slightly above 0.08 for all cases; however, the minimum value reduces (γ), keeping its maximum to very similar values slightly above 0.08 for all cases; however, the if angle γ increases. Interestingly, the maximum CP for the SI15 case is slightly higher than the value minimum value reduces if angle γ increases. Interestingly, the maximum 𝐶 for the SI15 case is computed for the SPthe configuration as it for canthe be SP appreciated in Figure 5b.beSuch a maximum value is slightly higher than value computed configuration as it can appreciated in Figure ◦ ◦ attained the blade azimuthal angle of −45 315 (see Figure 5b)or whilst 5b. Such when a maximum valueisisaround attainedthe when the blade is around the or azimuthal angle of −45° 315° the ◦ . This fact means that the angular distance between the maximum and minimum is reached around 150 (see Figure 5b) whilst the minimum is reached around 150°. This fact means that the angular distance ◦ ), implying that minimum is longer (aboutand 195◦minimum ) than between the minimum and than maximum (about between the maximum is longer (about 195°) between the165 minimum and the oscillation behavior is not fully Thebehavior turbine is CPnot can be harmonic. observed in 5a: maximum (about 165°), implying thatharmonic. the oscillation fully TheFigure turbine 𝐶 as it iscan clearly seen, the contributions to the power coefficient of each blade combine to produce a fairly be observed in Figure 5a: as it is clearly seen, the contributions to the power coefficient of each constant value for all the azimuthal positions. Only the azimuthal SI30 case can a gentle ripple curve blade combine to produce a fairly constant value for for all the positions. Only for in thethe SI30 case can a gentle Regarding ripple in thethe curve be appreciated. Regarding effect of inclination it was be appreciated. effect of inclination angle, itthe was found that in theangle, inclined cases, found thatcoefficient in the inclined cases, by the13% power coefficient decreases by30% 13%(SI30 (SI15configuration) configuration) compared and 30% to the power decreases (SI15 configuration) and (SI30 configuration) compared to the parallel configuration. necessary to mention that the SP the parallel configuration. It is necessary to mention that the ItSPisconfiguration presented a small value configuration presented smallattributed value in the efficiency, around 25%, the shape. hub geometry, in the efficiency, around a25%, to the hub geometry, of a attributed truncated to cone Such a hub of a truncatedproduces cone shape. Such wake a hub which configuration produces a wide wake which increases the drag configuration a wide increases the drag on the turbine. on the turbine.

(a)

(b)

◦ ) and Figure 5. 5. The The power the three studied configurations, SP, SP, SI15SI15 (15°)(15 and SI30 SI30 Figure powercoefficient coefficientatatλλ= =5.7 5.7forfor the three studied configurations, ◦ ) inclined (30°) inclined with one blade; (b)(b) complete turbine. (30 with respect respectto tothe theflow flowdirection: direction:(a)(a) one blade; complete turbine.

In Figure Figure 6, 6, the the behavior behavior of Equation (4))(4)) versus azimuthal angle In of the thethrust thrustcoefficient coefficient𝐶 C(see Equation versus azimuthal angle n (see along a rotor revolution for one blade (Figure 6b) and the complete turbine (Figure 6a) is illustrated. along a rotor revolution for one blade (Figure 6b) and the complete turbine (Figure 6a) is illustrated. On the the SP SP configuration, configuration, the constant along the the turn, which also also On thethrust thruston oneach eachblade bladeis isroughly roughly constant along turn, which implies that the thrust of the turbine does not vary with the angular position (Figure 6a). However, implies that the thrust of the turbine does not vary with the angular position (Figure 6a). However, for the inclined configurations, the normal force on the rotor does vary with the azimuthal angle, for the inclined configurations, the normal force on the rotor does vary with the azimuthal angle, which generates alternating loads that could induce material fatigue in the long term. The maximum which generates alternating loads that could induce material fatigue in the long term. The maximum value of the thrust is experienced by a single blade between the −45° and 0° angles, whereas the value of the thrust is experienced by a single blade between the −45◦ and 0◦ angles, whereas the minimum appears around 150°. The difference between both thrust values also increases with the minimum appears around 150◦ . The difference between both thrust values also increases with the inclination angle γ. For instance, in Figure 6b, it can be appreciated that for the SI15, the maximum inclination angle γ. For instance, in Figure 6b, it can be appreciated that for the SI15, the maximum thrust on the blade overcomes the respective value for the SP turbine. When the total thrust on the thrust blade overcomes value for the SP turbine. smaller When the total thrust on the turbineonisthe computed (Figure 6a),the therespective inclined configurations experience loads than the SP turbine is computed (Figure 6a), the inclined configurations experience smaller loads than the SP case, around 4.1% and 10.9% for the SI15 and SI30 cases, respectively. Moreover, the thrust on thecase, around andconstant 10.9% for the SI15 SI30 cases, theathrust the for turbine turbine4.1% is pretty along withand a revolution forrespectively. all the cases, Moreover, showing only small on ripple an is pretty constant with a revolution for all the cases, showing only a small ripple for an azimuthal azimuthal anglealong of 30°. angle of 30◦ .

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(a) (b) (a) (b) Figure Figure 6. 6. The The thrust thrust coefficient coefficient at at λλ == 5.7 5.7 for for the the three three studied studied configurations, configurations, SP, SP, SI15 SI15 (15°) (15◦ ) and and SI30 SI30 Figure 6. The thrust coefficient at λ = 5.7 for the three studied configurations, SP, SI15 (15°) and SI30 ◦ (30°) (30 ) inclined inclined with with respect respect to to the the flow flow direction: direction: (a) (a) one one blade; blade; (b) (b) complete complete turbine. turbine. (30°) inclined with respect to the flow direction: (a) one blade; (b) complete turbine.

According to to Figure 7, as the γ given by by According γ inclination angle angle increases, increases, the the drag drag coefficient coefficient C 𝐶D given According to Figure 7, as the γ inclination angle increases, the drag coefficient 𝐶 given by Equation (5) decreases. thethe one blade andand thethe fullfull turbine coefficient. Consistent with Equation decreases.This Thisisistrue truefor forboth both one blade turbine coefficient. Consistent Equation (5) decreases. This is true for both the one blade and the full turbine coefficient. Consistent the previous results,results, it can be that the that inclined (SI15 and (SI15 SI30) present drag coefficients with the previous it noticed can be noticed the cases inclined cases and SI30) present drag with the previous results, it can be noticed that the inclined cases (SI15 and SI30) present drag smaller thansmaller that ofthan the parallel around 14% around and 20%, respectively. The main reason coefficients that of configuration, the parallel configuration, 14% and 20%, respectively. The coefficients smaller than that of the parallel configuration, around 14% and 20%, respectively. The for that behavior is behavior that, as the inclination angle grows, thegrows, rotor transversal area facing the flow main reason for that is that, as the inclination angle the rotor transversal area facing main reason for that behavior is that, as the inclination angle grows, the rotor transversal area facing decreases, reducingreducing the widththe of the wake results in aresults lower in value of thevalue pressure component the flow decreases, width of which the wake which a lower of the pressure the flow decreases, reducing the width of the wake which results in a lower value of the pressure of the drag force. SP configuration, the CD of one a roughly value along component of the For dragthe force. For the SP configuration, theblade 𝐶 ofkeeps one blade keepsconstant a roughly constant component of the drag force. For the SP configuration, the 𝐶 of one blade keeps a roughly constant the whole revolution, the inclined a maximum andaa maximum minimum. and In the value along the wholebutrevolution, butconfigurations the inclined present configurations present a value along the whole revolution, but the inclined configurations present a maximum and a◦ SI15 case, two minima similar at an azimuthal angle 90◦ and 150of, minimum. In the SI15 of case, two values minimaare ofobserved similar values are observed at of anaround azimuthal angle minimum. In the SI15 case, two minima of similar values are observed at an azimuthal angle of◦ whereas90° theand maximum is located around 300 ; for theatSI30 case,300°; the minimum is case, placed around 150 around 150°, whereas theat maximum is ◦located around for the SI30 the minimum around 90° and 150°, whereas the maximum is located at around 300°; for the SI30 case, the minimum ◦ and the maximum beyond curves beyond do not show particular For any the full turbine, is placed around 150° and310 the. Both maximum 310°.any Both curves symmetry. do not show particular is placed around 150° and the maximum beyond 310°. Both curves do not show any particular the drag coefficient curves exhibit approximately constant valueanwith a fairly small ripple for the symmetry. For the full turbine, thean drag coefficient curves exhibit approximately constant value symmetry. For the full turbine, the drag coefficient curves exhibit an approximately constant value SI30 configuration. with a fairly small ripple for the SI30 configuration. with a fairly small ripple for the SI30 configuration.

(a) (b) (a) (b) Figure 7. The drag coefficient at λ = 5.7 for the three studied configurations, SP, SI15 (15°), and SI30 Figure 7. drag coefficient at for studied configurations, SP, Figure 7. The Thewith dragrespect coefficient at λ λ ==5.7 5.7 for the the three three studied SP, SI15 SI15 (15°), (15◦ ), and and SI30 SI30 (30°) inclined to the flow direction: (a) one blade; configurations, (b) complete turbine. (30°) (30◦ )inclined inclinedwith withrespect respect to tothe the flow flow direction: direction: (a) (a) one one blade; blade; (b) (b) complete complete turbine. turbine.

From Figure 8a, it can be noticed that the inclined rotors experience a net upward lift force which From can be be noticed thatthat the inclined rotors experience a net upward lift force FromFigure Figure8a, 8a,it it can noticed the inclined rotors experience a net upward liftwhich force is absent in the parallel configuration. The lift coefficient 𝐶 is computed by Equation (5) and in the is absent in the parallel configuration. The liftThe coefficient 𝐶 is computed by Equation (5) and(5) in and the which is absent in the parallel configuration. lift coefficient C is computed by Equation SP case, each blade experiences a small lift force component whichLis positive or negative depending SP each blade experiences a small lift force component which is positive negative or depending in case, the SP case, each blade experiences a small lift force component which or is positive negative on its azimuthal position. In that case, the contributions of the three blades compensate among them on its azimuthalitsposition. In that case, the contributions of the three blades them depending azimuthal position. In that the contributions thecompensate three bladesamong to produce aon zero net lift coefficient (Figure 8a)case, for the turbine at eachofposition. This fact compensate is expected, to produce a zero net lift acoefficient (Figure 8a) for the turbine each position. This fact is expected, among to produce net lift coefficient (Figure 8a) foratthe turbine at each owing tothem the symmetry of zero the geometrical configuration. As the inclination angle γposition. increases,This the fact lift owing to the symmetry of the geometrical configuration. As the inclination angle γ increases, the lift coefficient turns positive and augments with it (Figure 8b). It can be observed that in a cycle, the coefficient turns positive and augments with it (Figure 8b). It can be observed that in a cycle, the

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is expected, owing to the symmetry of the geometrical configuration. As the inclination angle γ 11 of 23 increases, the lift coefficient turns positive and augments with it (Figure 8b). It can be observed that inEnergies a cycle, lift experienced by one blade is located at the azimuthal angle of 11 0◦ofand 2018,the 11, xmaximum FOR PEER REVIEW 23 maximum lift experienced◦ by one blade is located at the azimuthal angle of 0° and the minimum the minimum around 210 for the inclined configurations. Again, the contributions to the lift of the around 210° for the inclined configurations. Again, the contributions to the lift of the three blades maximum experienced by one blade is located the azimuthal 0° and the minimum three bladeslift compensate providing a fairly constantatvalue of the lift angle along of with a revolution for all compensate providing a fairly constant value of the the contributions lift along with a revolution for blades all the around 210° for the inclined configurations. Again, to the lift of the three the configurations. configurations. compensate providing a fairly constant value of the lift along with a revolution for all the configurations. Energies 2018, 11, x FOR PEER REVIEW

(a)

(b)

(a) (b) Figure Figure8. 8.The Thelift liftcoefficient coefficientat atλλ==5.7 5.7for forthe thethree threestudied studiedconfigurations, configurations,SP, SP, SI15 SI15 (15°) (15◦ )and andSI30 SI30(30°) (30◦ ) inclined with to (a) one blade; complete Figure 8. Therespect lift coefficient at λ =direction: 5.7 for the three configurations, SP, SI15 (15°) and SI30 (30°) inclined with respect to the the flow flow direction: (a) onestudied blade; (b) (b) complete turbine. turbine. inclined with respect to the flow direction: (a) one blade; (b) complete turbine.

In In order order to to determine determine the the loads loads on on the the configurations configurations studied, studied, the the total total force force acting acting on on the the rotor rotor In order toSuch determine loads on force acting aaon therelated rotor was aa force is for the inclined than parallel turbine, fact was computed. computed. Such forcethe is smaller smaller forthe theconfigurations inclined cases casesstudied, than for forthe thetotal parallel turbine, fact related wasthe computed. Suchin a force iscase smaller for the inclined cases than for thethe parallel turbine, a fact related with wider the (which has the of pressure component of with the wider wake wake in the SP SP case (which has the effect effect of increasing increasing the pressure component of the the withforce). the wider wake the SP case has effect of pressure increasing the skin pressure component of the drag This fact in(which Figure 9, where thethe pressure andand skin friction coefficients on the drag force). This factisin isillustrated illustrated in Figure 9,the where friction coefficients on drag force). This fact is illustrated in Figure 9, where the pressure and skin friction coefficients on the blades pressure sideside are shown. The The top row of Figure 9 presents the the pressure coefficient for the SP the blades pressure are shown. top row of Figure 9 presents pressure coefficient for the blades pressure side shown. The top rowthe of Figure 9row presents thefigure pressure coefficient for friction the SP (a), SI1 SI1 (b) andand SI2 (c)are configurations while bottom exhibits the SP (a), (b) SI2 (c) configurations while the bottom rowofofthat that figure exhibits theskin skin friction ◦ (e) ◦ (f) (a), SI1 (b)for and (c) configurations: configurations axis while the bottom row of 15° that figure exhibits the skinthe friction coefficient the same parallel (d), inclined and main coefficient theSI2 same configurations: 15 (e) and 30° 30 (f)regarding regarding the main coefficient for the same configurations: axis parallel (d), inclined 15° (e) and 30° (f) regarding the main flow. flow. From From Figure Figure 9a–c 9a–c itit is is obvious obvious that that pressure pressure acting acting on on the the blades blades decreases decreases with with increasing increasing axis axis flow. Fromthis Figure it is obvious that pressurein acting onof the blades with increasing axis inclination; fact is well observed the the three blades. 9d–f inclination; this fact9a–c is particularly particularly well observed in the tip tip of the threedecreases blades. Figure Figure 9d–f illustrates illustrates inclination; this fact is particularly well observed in the tipangle; of the in three 9d–f illustrates the behavior skin friction with case, slight of the behavior of of the the skin friction coefficient coefficient with inclination inclination angle; in this thisblades. case, aaFigure slightincrease increase of such such the behavior of the skin friction coefficient with inclination angle; in this case, a slight increase of such coefficient coefficient is is found found by by increasing increasing the the operation operation slant slant angle, angle, mainly mainly visible visible at at the the blade’s blade’s mid-span mid-span coefficient is found by increasing the operation slant angle, mainly visible at the blade’s mid-span where aa transition between the and light color is However, is where transition between the dark dark and light blue blue color is appreciated. appreciated. However, is the the considered considered where a transition between theof and blue over colorthe is appreciated. However, is the the considered cases, the pressure the prevails friction and cases, the pressure component component ofdark the force forcelight prevails over the friction component component and the net net result result is is cases, the pressure component of the force prevails over the friction component and the net result that that the the slanted slanted configurations configurations experience experience smaller hydrodynamic forces than the SP configuration.is that the slanted configurations experience smaller hydrodynamic forces than the SP configuration. (b) (b)

(a) (a)

Figure 9. Cont.

(c) (c)

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(d) (d)

SP configuration SP configuration

(e) (e)

SI1 configuration SI1 configuration

(f) (f)

SI2 configuration SI2 configuration

Figure9.9. The Thepressure pressurecoefficient coefficient(a–c) (a–c)and andskin skinfriction frictioncoefficient coefficient(d–f) (d–f)atatthe theblade’s blade’spressure pressureside sidein Figure Figure 9. The pressure coefficient (a–c) and skin friction coefficient (d–f) at the blade’s pressure side in the three considered inclinations. the three considered inclinations. in the three considered inclinations.

Figure10 10presents presents aa vorticity vorticity iso-surface of value 1.5 Hz Figure Hz at at the thetip tipspeed speedratio ratio𝜆λ==5.7 5.7illustrating illustrating Figure 10 presents a vorticity iso-surface of value 1.5 Hz at the tip speed ratio 𝜆 = 5.7 illustrating thedifferences differences in in the the trailing trailing vortices between the between the the cases cases of of the the parallel paralleland andinclined inclinedturbines. turbines.Here, Here, the differences in the trailing vorticesdetached between from the cases of the parallel and inclinedby turbines. Here, besides the trailing thethe blades, the the wakes generated besides the trailing and andshed shedvortices vortices detached from blades, wakes generatedthe byhub theand hub besides thecan trailing and shed vortices detached from the the wakes generated bythat the induces hub and the shaft also observed. The hub wake onblades, a quasi-steady toroidal vortex and the shaft can be also be observed. The hubconsists wake consists on a quasi-steady toroidal vortex that the shaft canand alsolow be observed. wake consists on a quasi-steady toroidal vortex that induces a backflow pressure inThe thathub zone. As zone. a consequence, the drag force, as well as as the thrust, is induces a backflow and low pressure in that As a consequence, the drag force, well as the aincreased backflow on andthe lowrotor, pressure in that zone. As a consequence, the drag force, as well as the thrust, the efficiency of the of turbine. From From FigureFigure 10, it10, is it possible tois thrust, is increased on thereducing rotor, reducing the efficiency the turbine. is possible increased on the rotor, reducing the efficiency of the turbine. From Figure 10, it is possible to appreciate that the to appreciate that thehub hubwake wakeininthe theSP SPconfiguration configurationisissignificantly significantlywider widerthan thanininthe theinclined inclined appreciate that moreover, the hub wake in theofSP significantly wider than in the inclined configurations; thelength length theconfiguration tip vortices vortices is is is also larger configurations; moreover, the of the tip also larger in in the the SP SP case. case. configurations; moreover, the length of the tip vortices is also larger in the SP case. (a) (a)

(b) (b)

(c) (c)

Figure 10. The vorticity isosurface of 1.5 Hz showing the detached boundary layer for the SP (a), SI15 (b), and SI30 (c) configurations from the turbine axis and the blades.boundary The bladelayer tip layer vortices clearly Figure 10. The vorticity isosurface of of 1.51.5 Hz showing the the detached for the SP Figure 10. The vorticity isosurface Hz showing detached boundary forare the(a), SPSI15 (a), visible. (b), and SI30 (c) configurations from the turbine axis and the blades. The blade tip vortices are clearly SI15 (b), and SI30 (c) configurations from the turbine axis and the blades. The blade tip vortices are

visible. clearly visible.

4.2. Variation of Non-Dimensional Coefficients with the Tip Speed Ratio 4.2. Variation of of Non-Dimensional Non-Dimensional Coefficients Coefficients with with the the Tip Tip Speed Ratio 4.2. Variation Speed Ratio versus 𝜆 is discussed depending In this section, the behavior of the non-dimensional coefficients In this this section, the behavior behavior ofcase, the non-dimensional non-dimensional coefficients versus 𝜆λequal is discussed discussed depending on the turbine inclination. In this the inflow velocity is kept constant, to 1 m/s, and the In section, the of the coefficients versus is depending turbine angular velocity is varied in the range 40–70 rpm to build the curves. on the turbine inclination. In this case, the inflow velocity is kept constant, equal to 1 m/s, and the the on the turbine inclination. In this case, the inflow velocity is kept constant, equal to m/s, and Previously to discuss performance curve CP-λ, it isto comment that computing the turbine angular velocity velocity is the varied in the the range range 40–70 rpm tonecessary build the turbine angular is varied in 40–70 rpm build thetocurves. curves. power coefficient using Equation (5) is somehow unfair with the inclined configurations as Previously to discuss the performance curve C -λ, it is necessary to turbine comment that computing P Previously to discuss the performance curve CP-λ, it is necessary to comment that computing the in such cases the rotor area faced to the incoming flow is reduced by a factor cos 𝛾 regarding the SP the power coefficient using Equation (5) is somehow unfair with the inclined turbine configurations power coefficient using Equation (5) is somehow unfair with the inclined turbine configurations as configuration. Because the extracted power is proportional the by area transversal flow,the it the is as in such cases the rotor area faced to the incoming flow isto reduced by a factor γthe regarding in such cases the rotor area faced to the incoming flow is reduced a factor coscos 𝛾 to regarding SP customary to redefine the power coefficient taking into account this effect. Therefore, a corrected SP configuration. Because the extracted power is proportional to the area transversal to the flow, it is configuration. Because the extracted power is proportional to the area transversal to the flow, it is power coefficient, 𝐶 , is defined by Equation (6), where 𝐶 is the power coefficient given by Equation , the power coefficient taking into account this effect. Therefore, a corrected customary to redefine (3): coefficient, 𝐶 , is defined by Equation (6), where 𝐶 is the power coefficient given by Equation power ,

(3):

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customary to redefine the power coefficient taking into account this effect. Therefore, a corrected power Energies 2018, 11, x FOR PEER REVIEW 13 of 23 coefficient, CP,c , is defined by Equation (6), where CP is the power coefficient given by Equation (3): CP,c C P , c==

CPP cos cos γ γ

(6) (6)

Figure 11 shows ofof thethe studied configurations. Additionally, for Figure shows the theperformance performancecurves curvesfor foreach each studied configurations. Additionally, the the inclined configurations, thethe corrected that for inclined configurations, correctedpower powercoefficient coefficientisisshown shown in in comparison comparison with that computed using using Equation Equation (3). (3). As Ascos cosγ𝛾 ≤ ≤ 1, 1, C 𝐶 P,c the SP SP computed ≥ 𝐶CPand andthe thecorrected corrected values values are are closer to the , ≥ values. In In all all the the cases, cases, the the maximum maximum of of the the curve curve isisobtained obtainedfor forλ𝜆 = = 4.8 4.8 with with an an approximate approximate value value values. of 0.3 0.3 for forthe theSP SPconfiguration configurationand andsome someconsistent consistentlower lowervalues values the inclined turbines. For higher of forfor the inclined turbines. For higher λ 𝜆 values, angle of attack experienced theisblade is reduced, with the subsequent effect of values, thethe angle of attack experienced by theby blade reduced, with the subsequent effect of decreasing decreasing thelift generated and coefficient. the power coefficient. Onhand, the other hand,TSR for lower TSR the generated and the lift power On the other for lower values, thevalues, anglesthe of anglesofofthe attack of the flow approaching the blades increase, eventuallythe overcoming the attack relative flowrelative approaching the blades increase, eventually overcoming dynamic stall dynamic stall anglesaugmenting of the profiles, augmenting and decreasing which reduces the angles of the profiles, drag and decreasingdrag lift, which reduces the lift, transmitted torque from transmitted torque fromFigure the fluid to the blades. Figure 11highest demonstrates that theishighest performance the fluid to the blades. 11 demonstrates that the performance obtained for the SP is obtained forwhich, the SPregarding configuration which, regarding the corrected power coefficient, on average configuration to the corrected powertocoefficient, is on average 6.5% andis25% higher 6.5%that andfor 25% higher thanSI30 thatconfigurations, for the SI15 andrespectively. SI30 configurations, respectively. than the SI15 and

Figure 11. 11. The power coefficient coefficient versus versus tip tip speed speed ratio ratio for for the the different differentconfigurations. configurations. Figure

Figure Figure 12 12 illustrates illustrates the the behavior behavior of of the the force force coefficients coefficients versus versus tip tip speed speed ratio ratio for for the the three three turbine turbine configurations. configurations. Figure Figure 12a 12a shows shows the the variation variation of of the the thrust thrustcoefficient coefficientwith withλ. 𝜆. It It is is seen seen that that in all the cases it grows monotonically with the tip speed ratio and, according to the results found in all the cases it grows monotonically with the tip speed ratio and, according to the results found previously, previously,ititisishigher higherfor forthe theSP SPconfiguration configurationthan thanfor for the theinclined inclined turbines. turbines. As As mentioned mentioned before, this smaller width width of of the thehub hubwake wakefor forthe theinclined inclinedcases, cases,resulting resultinginina this phenomenon phenomenon is related to the smaller alower lowerpressure pressuredrag. drag.However, However,ininspite spiteof ofthe the lower lower thrust, thrust, the the blades of the inclined inclined turbines turbines are are exposed exposed to to alternating alternating loads loads that that can caninduce inducematerial materialfatigue fatiguein inthe thelong longterm. term.

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(a)

(b)

(c) Figure 12. The force coefficient versus tip speed ratio for the different configurations: (a) thrust Figure 12. The force coefficient versus tip speed ratio for the different configurations: (a) thrust coefficient; (b) drag coefficient; (c) lift coefficient. coefficient; (b) drag coefficient; (c) lift coefficient.

By thinking thinking of of the the turbine turbine as as aa whole whole object object immersed immersed in in aa moving moving fluid, fluid, itit is is interesting interesting to to look look By to the behavior of the drag and lift forces through its coefficients because such forces have some to the behavior of the drag and lift forces through its coefficients because such forces have some effects effects on the turbine operation that should be considered the design process. Figure 12b presents on the turbine operation that should be considered in thein design process. Figure 12b presents the the variation of the drag coefficient in terms of the tip speed ratio for the studied configurations. In variation of the drag coefficient in terms of the tip speed ratio for the studied configurations. In the the same way, as happened for the thrust coefficient, the drag coefficient increases monotonically same way, as happened for the thrust coefficient, the drag coefficient increases monotonically with and decreases withturbine the turbine inclination, approximately and 23.2% forSI15 the and SI15SI30 and λwith and𝜆decreases with the inclination, approximately 7.5% 7.5% and 23.2% for the SI30 cases, respectively, regarding the SP configuration. Figure 12c shows the change of the lift coefficient with 𝜆 for the three turbine cases. Of course, 𝐶 for the SP configuration, owing to the

geometrical symmetry, is very close to zero for all tip speed ratios. For the inclined configurations, on the other hand, it grows monotonically with 𝜆 and also increases with the inclination angle γ. Such a positive lift tends to effectively push up the turbine and eventually could produce vertical oscillations during Energies 2018, 11, 3151 the turbine’s operation. 15 of 23 Summarizing the results for the performance and force coefficients curves, the inclined configurations have a lower power coefficient than the SP configuration but also experience lower cases, respectively, regarding the SP configuration. Figure 12c shows the change of the lift coefficient loads. In particular, the rotor drag and thrust decrease with the increasing inclination angle γ and the with λ for the three turbine cases. Of course, CL for the SP configuration, owing to the geometrical counterpart of the amplitude of the experienced alternating stresses grows with it. This fact may symmetry, is very close to zero for all tip speed ratios. For the inclined configurations, on the other cause material fatigue in the blades after long periods of operation. Additionally, the fluid forces hand, it grows monotonically with λ and also increases with the inclination angle γ. Such a positive acting on the blades increase with tip speed ratio for all the studied turbine configurations. lift tends to effectively push up the turbine and eventually could produce vertical oscillations during As a final comment, the actuator disc theory can be extended to consider situations where the the turbine’s operation. incident flow makes an angle γ with the direction perpendicular to the rotor [25]. In that case, the Summarizing the results for the performance and force coefficients curves, the inclined maximum power coefficient is given by Equation (7): configurations have a lower power coefficient than the SP configuration but also experience lower 16 with loads. In particular, the rotor drag and thrust the cos 3 γ the increasing inclination angle γ and (7) C Pdecrease max = 27 counterpart of the amplitude of the experienced alternating stresses grows with it. This fact may cause material fatigue aincommon the blades after long periods operation.the Additionally, theoffluid acting on Therefore, practical approach forofestimating performance windforces turbines when the blades increase with tip speed ratio for all the studied turbine configurations. the flow is not perpendicular to the rotor is to multiply the power coefficient by the cube of the cosine Asangle a final comment, the actuator disc theory be revolution extended to consider situationsiswhere of the between the incoming velocity and thecan rotor axis. This procedure knownthe as incident flow makes an angle γ with the direction perpendicular to the rotor [25]. In that case, the cos 𝛾 correlation. In this study, the comparison was made using Equation (8), which is an the maximum power coefficient (7): extension of Equation (7) whereis𝐶givenisby theEquation power coefficient obtained for the SP configuration at ,

each considered TSR and 𝛾 is the inclination angle16of the rotor. This value was compared with that CPmax = cos3 γ (7) obtained in the simulation, which is given by Equation 27 (3). See the lines (solid for SI1 and dashed for SI2) in Figure 13. Therefore, a common practical approach for estimating3 the performance of wind turbines when ) = CP , SP (the λ) cos γ coefficient by the cube of the cosine(8) P (λ the flow is not perpendicular to the rotor isCto multiply power of the angle between the incoming velocity and the rotor revolution axis. Thiswith procedure is known Figure 13 presents the comparison of applying such a correlation the CFD results as in the the 3 γ correlation. In this study, the comparison was made using Equation (8), which is an extension of cos inclined configurations. As it can be clearly noticed, for the SI15 case, the correlation works pretty Equation (7) where CP,SP is the power coefficient for thethe SPtwo configuration at each well for the four tip speed ratios computed. In obtained the SI30 case, central values forconsidered λ are well TSR and γ is the inclination angle of the rotor. This value was compared with that obtained in the approximated but for the extreme values, noticeable differences appear: for λ = 3.8 the CFD result is simulation, which is given by Equation (3). See the lines (solid for SI1 and dashed for SI2) in Figure 13. underpredicted by the correlation (about 12%) and for λ = 6.7 it is overpredicted (about 21%). Nevertheless, owing to the simplicity of the correlation, the3results are approximate enough from an CP (λ) = CP,SP (λ) cos γ (8) engineering point of view.

Figure 13. 13.The The evaluation the correlation cos 𝛾 , Equation for turbine the inclined turbine Figure evaluation of theofcorrelation cos3 γ, Equation (8), for the (8), inclined configurations. ◦ configurations. Lines indicate 15 the inclination: correlation: solid 15° inclination: solid line; dashed 30° inclination: dashed line. Lines indicate the correlation: line; 30◦ inclination: line.

Figure 13 presents the comparison of applying such a correlation with the CFD results in the inclined configurations. As it can be clearly noticed, for the SI15 case, the correlation works pretty well for the four tip speed ratios computed. In the SI30 case, the two central values for λ are well approximated but for the extreme values, noticeable differences appear: for λ = 3.8 the CFD result

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is underpredicted by the correlation (about 12%) and for λ = 6.7 it is overpredicted (about 21%). Nevertheless, owing to the simplicity of the correlation, the results are approximate enough from Energies 2018, 11, xpoint FOR PEER REVIEW 16 of 23 an engineering of view.

4.3. Comparison Comparisonofofthe theResults Resultswith withTransitional TransitionalTurbulence TurbulenceModeling Modeling 4.3. Tostudy studythe thesensitivity sensitivityof ofthe theresults resultsto tothe themodeling modelingof ofthe thetransitional transitionaleffects effectson onthe theboundary boundary To layer, in addition to the k-ω SST model (SST Standard), the SST Transitional version has beenbeen also layer, in to the k-ω SST model (SST Standard), the SST Transitional version has employed. The Transition SST model includes two additional equations that describe the laminar– also employed. The Transition SST model includes two additional equations that describe the turbulent boundary layer transition: the first one for the intermittency factor (the time fraction in laminar–turbulent boundary layer transition: the first one for the intermittency factor (the time which the flow in point boundary layer is turbulent) and aand second equation for for the fraction in which theaflow in inside a pointthe inside the boundary layer is turbulent) a second equation transition momentum thickness Reynolds transition the transition momentum thickness Reynoldsnumber number[9,26]. [9,26].The Thereason reasonbehind behind employing aa transition model is is that that in the hydrokinetic and in model hydrokinetic turbine turbine the the blade bladeReynolds Reynoldsnumber numberchanges changesalong alongitsitsspan span and time, soso phenomena such as as laminar separation, thethe transition to turbulence, flowflow reattachment, and in time, phenomena such laminar separation, transition to turbulence, reattachment, turbulent separation take take placeplace in theinboundary layer. layer. These phenomena cannot cannot be captured by fully and turbulent separation the boundary These phenomena be captured turbulent models,models, even though the turbulent kinetic energy production could be be limited by fully turbulent even though the turbulent kinetic energy production could limitedbybya adamping dampingfunction. function. The performance curvefor forthe theSP SPand and SI30 SI30 configurations configurationsobtained obtainedwith withboth bothturbulence turbulencemodels models The performance curve areshown shownin inFigure Figure14. 14.For For the the SP SP and and the the SI30 SI30 inclined inclined configurations, configurations,the theaverage averagepower powercoefficient coefficient are estimatedwith withthe theSST SSTTransition Transitionmodel modelwas wasincremented incrementedregarding regardingthe theSST SSTstandard. standard.The Thesame samefact fact estimated was found previously in the case of vertical axis water turbines [26,27]. However, for the SP turbine, was found previously in the case of vertical axis water turbines [26,27]. However, for the SP turbine, thedifference differencebetween betweenthe thepredictions predictionsof ofboth bothturbulence turbulencemodels modelsincrease increaseas asthe thetip tipspeed speedratio ratiogrows grows the and,for forthe thelargest largestvalue valueconsidered considered = 6.7), it about is about 40%. This behavior found previously and, (λ(λ = 6.7), it is 40%. This behavior waswas found previously by by Reference [27] in a vertical axis tidal turbine with even larger differences in the 𝐶 values obtained Reference [27] in a vertical axis tidal turbine with even larger differences in the CP values obtained with withturbulence both turbulence the SP2 configuration, on hand, the other hand, the in differences in both models.models. For the For SP2 configuration, on the other the differences predictions predictions between both turbulent models decrease as the tip speed ratio increases, with the highest between both turbulent models decrease as the tip speed ratio increases, with the highest difference difference about 15% being aboutbeing 15% obtained forobtained λ = 3.8. for λ = 3.8.

Figure The power power coefficient coefficientversus versustip tipspeed speedratio ratiofor forthe the two evaluated turbulence models. Figure 14. 14. The two evaluated turbulence models. SP SP and SI30 configurations. and SI30 configurations.

Although coefficients with thethe turbulence model is similar to Althoughnot notshown, shown,the thebehavior behaviorofofthe theforce force coefficients with turbulence model is similar that of the power coefficients: the transitional version provides higher values than the standard SST. to that of the power coefficients: the transitional version provides higher values than the standard Therefore, it can it becan concluded that thethat transitional formulation predictspredicts that thethat transfer of energy SST. Therefore, be concluded the transitional formulation the transfer of from thefrom fluidthe to the blades improved regardingregarding the standard formulation, at least inatthe range of energy fluid to theisblades is improved the standard formulation, least in the TSRs in the present rangeconsidered of TSRs considered in thestudy. present study.

As an example to highlight the transitional behavior of the boundary layer computed with the SST Transition turbulence model, Figure 15 shows the intermittency contours on a section of the first blade (at mid-span) in the SP, SI15 and SI30 configurations at the 0° azimuthal position. In Figure 15, values close to zero (black color) indicate the laminar regime whereas values close to 1 (white color) indicate the mean turbulent boundary layer. In the contour plots flow proceeds from bottom to top.

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As an example to highlight the transitional behavior of the boundary layer computed with the SST Transition turbulence model, Figure 15 shows the intermittency contours on a section of the first blade (at mid-span) in the SP, SI15 and SI30 configurations at the 0◦ azimuthal position. In Figure 15, values close to zero (black color) indicate the laminar regime whereas values close to 1 (white color) indicate turbulent boundary layer. In the contour plots flow proceeds from bottom to 17 top. Energies the 2018,mean 11, x FOR PEER REVIEW of 23 As it is readily observed, the contour plots present noticeable differences. In the SP configuration (Figure 15a), the the intrados boundary layer develops entirelyentirely in the laminar in the extrados (Figure 15a), intrados boundary layer develops in the regime, laminarwhile regime, while in the layer, laminar-turbulent transition phenomena (the contours evolve from black to white along to extrados layer, laminar-turbulent transition happen phenomena happen (the contours evolve from black thewhite extrados surface); besides,surface); around the profile,around a laminar envelope is clearly visible (variable grey along the extrados besides, theflow profile, a laminar flow envelope is clearly intensity). Such an envelope is also present around the profile for the SI15 configuration (Figure 15b), visible (variable grey intensity). Such an envelope is also present around the profile for the SI15 butconfiguration here the boundary layer experiences laminar to turbulent transition in both surfaces (intrados and (Figure 15b), but here the boundary layer experiences laminar to turbulent transition extrados). However,(intrados for the SI30 (Figure 15c), suchSI30 a laminar flow envelope in both surfaces andconfiguration extrados). However, for the configuration (Figuredisappears, 15c), such a being turbulent the major part of thebeing flow around thefor profile; also, the transition between laminar and laminar flow for envelope disappears, turbulent the major part of the flow around the profile; turbulent is very clear for intrados and extrados.regimes Finally,isalthough not for shown, such and transitional also, theregimes transition between laminar and turbulent very clear intrados extrados. behavior changes along the blade span, a fact that illustrates the water flow complexity in the vicinity Finally, although not shown, such transitional behavior changes along the blade span, a fact that of illustrates the turbinethe blades offlow the HAHT. water complexity in the vicinity of the turbine blades of the HAHT.

(a) SP Configuration

(b) SI15 Configuration

(c) SI30 configuration

Figure The intermittency contours around first blade mid-span plane: SI15 (b), Figure 15.15. The intermittency contours around thethe first blade at at thethe mid-span plane: SPSP (a),(a), SI15 (b), and SI30 (c) configurations. The black color indicates the laminar flow. Flow progresses from bottom and SI30 (c) configurations. The black color indicates the laminar flow. Flow progresses from bottom top. to to top.

5. 5. Comparison ofof CFD Simulations with Other Sources Comparison CFD Simulations with Other Sources AsAs previously commented; the the evaluated turbine was empirically designed and tested in situ only previously commented; evaluated turbine was empirically designed and tested in situ foronly feasibility purposes, on the Cauca river in the southwest of Colombia. However, the prototype wasthe for feasibility purposes, on the Cauca river in the southwest of Colombia. However, never adequately characterized. Therefore, data on the extracted power in terms of prototype was experimentally never adequately experimentally characterized. Therefore, data on the extracted incident flow velocity or turbine angular velocity are not available. Consequently, some alternative for power in terms of incident flow velocity or turbine angular velocity are not available. Consequently, comparing the obtained CFD results to be CFD devised. some alternative for comparing thehave obtained results have to be devised. AsAs a first step, thethe CFD computations have to to bebe validated versus thethe experimental results in in thethe a first step, CFD computations have validated versus experimental results HAHT configuration. For that purpose, the experimental measurements reported in Reference [34] HAHT configuration. For that purpose, the experimental measurements reported in Reference [34] have been considered. Such experiments have been employed byby several authors to to validate different have been considered. Such experiments have been employed several authors validate different types of numerical computations, from BEM to CFD [11,34]; therefore, they constitute an appropriate types of numerical computations, from BEM to CFD [11,34]; therefore, they constitute an appropriate source forfor validating thethe CFD computations. In In thethe experiments of of Reference [34], thethe model turbine source validating CFD computations. experiments Reference [34], model turbine rotor is placed perpendicularly to to thethe main flow direction, so so itsits inclination angle γ is zero; thethe rotor rotor is placed perpendicularly main flow direction, inclination angle γ is zero; rotor diameter was 800 mm with blades based on the profile NACA 63-8XX. The considered experiments for diameter was 800 mm with blades based on the profile NACA 63-8XX. The considered experiments comparison are those to a pitch angle 0◦ and with anwith inflow of 1.4 m/s. for comparison are corresponding those corresponding to aset pitch setof angle of 0° and an velocity inflow velocity of 1.4 The additional CFD simulations consider a grid arrangement similar to that of the case of the m/s. inclinedThe rotor: the computational domain has the same dimensionssimilar as those shown in Figure additional CFD simulations consider a grid arrangement to that of the case of 2. the The boundary conditions are also the same andhas the the gridsame size isdimensions similar to that for the Aquavatio inclined rotor: the computational domain as employed those shown in Figure 2. The model comprising around million elements, also using prisms to resolvefor thethe flow in the boundary conditions areeight also the same and the grid size is12 similar to layers that employed Aquavatio boundary layer. Threearound tip speed ratios close to the pointalso of the maximum efficiency been simulated. model comprising eight million elements, using 12 prisms layershave to resolve the flow in

the boundary layer. Three tip speed ratios close to the point of the maximum efficiency have been simulated. The obtained results for the power coefficient are presented in Figure 16. In that figure, the crosses correspond to the experimental points and some other numerical simulations are also included for the purpose of comparison: the results of the commercial software GH-tidal (based on BEM) presented by Bahaj et al. [34] and the CFD results of Wu et al. [11]. Regarding the experimental

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The obtained results for the power coefficient are presented in Figure 16. In that figure, the crosses correspond to the experimental points and some other numerical simulations are also included for the purpose of comparison: the results of the commercial software GH-tidal (based on BEM) presented by Bahaj et al. [34] and the CFD results of Wu et al. [11]. Regarding the experimental data, the BEM results slightly over-predict them, while the CFD predictions of Reference [11] (based on the standard k-ε turbulence areREVIEW below the experiments, except for λ = 6. The present CFD computations Energies 2018, 11, xmodel) FOR PEER 18 of 23 based on the SST model of turbulence, provide values that are fairly close to the measurements, at least in the threeatcomputed TSR, a fact that is attributed the is better performance of theperformance SST model measurements, least in the three computed TSR, a facttothat attributed to the better regarding k-ε model in these of rotating machines The results presented Figure 15 of the SSTthemodel regarding thekinds k-ε model in these kinds[27]. of rotating machines [27].inThe results show that the employed CFD simulations are appropriate enough to be used in the computations of presented in Figure 15 show that the employed CFD simulations are appropriate enough to be used HAHTs. References [35–37] present additional examples in other Engineering applications where CFD in the computations of HAHTs. References [35–37] present additional examples in other Engineering techniques have beenCFD found to perform adequately. applications where techniques have been found to perform adequately.

Figure16. 16.The Thecomparison comparisonof ofthe theexperimental experimentalmeasurements measurementsand andCFD CFDcomputations computationsperformed performedin in Figure thiswork workon onthe theturbine turbineofofBahaj Bahajetetal. al.(2007) (2007)[34]. [34]. this

Another the results resultsobtained obtainedininthis thiswork workisisprovided provided wind turbine Another option option to to compare compare the byby thethe wind turbine ITIT-PE-100 developed by the company ITDG [20,28] because the blade design was adopted by the PE-100 developed by the company ITDG [20,28] because the blade design was adopted by the computed turbine Aquavatio. However, the hub is very different both machines; computedhydrokinetic hydrokinetic turbine Aquavatio. However, thedesign hub design is very in different in both in the river in turbine, theturbine, hub hasthe a shape of aatruncated (see Figure 1a) motivated structural machines; the river hub has shape of acone truncated cone (see Figure 1a) for motivated for reasons. This hub geometry, as already shown in Figure 10, generates a wide wake that affects the structural reasons. This hub geometry, as already shown in Figure 10, generates a wide wake that performance of the turbine. affects the performance of the turbine. The experimental power-velocity curve of the rotorrotor IT-PE-100 is available [28]. Nominal values The experimental power-velocity curve of wind the wind IT-PE-100 is available [28]. Nominal of incident velocity and angular velocity are 6.5 m/s and 420 rpm, respectively, giving a nominal tip speeda values of incident velocity and angular velocity are 6.5 m/s and 420 rpm, respectively, giving ratio of λ =tip 5.75, for the nominal m; this TSR is veryofclose to the initially nominal speed ratio of λ = diameter 5.75, for of the1.7 nominal diameter 1.7 m; thisvalue TSR considered is very close to the in this work for the hydrokinetic turbine, λ = 5.7. With the previous data, the performance curve for value considered initially in this work for the hydrokinetic turbine, λ = 5.7. With the previous data, turbine IT-PE-100 can be constructed. C vs. λ curves for both turbines are shown in Figure 17. It can be P the performance curve for turbine IT-PE-100 can be constructed. 𝐶 vs. λ curves for both turbines are seen thatinthe performance ofbe both is roughly same for λof = 5.75, is around 25% (SP configuration). shown Figure 17. It can seen that the the performance bothwhich is roughly the same for λ = 5.75, which The wind turbine presents a fairly flat C curve for the considered range of tip speed ratios, while the P is around 25% (SP configuration). The wind turbine presents a fairly flat 𝐶 curve for the considered hydrokinetic presents a clear at λturbine = 4.8 and decreasing formaximum larger and at lower values, range of tip turbine speed ratios, while the maximum hydrokinetic presents a clear λ = 4.8 and as discussed in Section 4.2. In Figure 17, the performance curves for the inclined turbines are also included decreasing for larger and lower values, as discussed in Section 4.2. In Figure 17, the performance just for comparison. From that figure, it can be seen just that,for forcomparison. the SP configuration, efficiency is curves for the inclined turbines are also included From thatthe figure, it cancurve be seen displaced towards lower values the of λefficiency than that of the IT-PE-100 rotor, which lower is obviously consequence that, for the SP configuration, curve is displaced towards valuesaof λ than thatof of the different operating conditions. However, the maximum C of both turbines is totally comparable, P the IT-PE-100 rotor, which is obviously a consequence of the different operating conditions. However, about 25–30%. Therefore, although conditions ofabout both machines their performance the maximum 𝐶 of both turbinesthe isworking totally comparable, 25–30%. differ, Therefore, although the curves areconditions similar because they share thediffer, bladetheir design and have very similar working of both machines performance curves are dimensions. similar because they share

the blade design and have very similar dimensions.

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Figure Figure 17. The of the CFD results inthe the present study versus the efficiency 17.comparison The comparison of the CFD resultsobtained obtained in present study versus the efficiency curve curve of the IT-PE-100 turbine. of the IT-PE-100 windwind turbine. The comparison third comparison carriedout outversus versus the by the software [29] The third waswas carried theresults resultsprovided provided by Qblade the Qblade software [29] which Figure is available online at www.q-blade.org. Qblade in is the a general purpose software for wind turbine 17. The comparison of the CFD results obtained present study versus the efficiency curve which is available online at www.q-blade.org. Qblade is a general purpose software for wind turbine evaluation, andturbine. vertical. It employs well established simplified methods such as the BEM of the horizontal IT-PE-100 wind evaluation, horizontal and vertical. It employs well established simplified methods such as the BEM (Blade Element Momentum) model and other vortex based models such as LLFVW (Lifting Line Free (Blade Element Momentum) model and other vortex based such as Qblade LLFVW (Lifting thirdand comparison was carried out such versus resultsmodels provided by the software [29]Line VortexThe Wake) includes extra features asthe structural and aeroelastic modules. In spite of Free whichand is available online at a general purpose software for wind turbine Vortex Wake) includes extra features such asitQblade structural and aeroelastic modules. In spite of Qblade Qblade being developed forwww.q-blade.org. wind turbines, allowsisus to modify the physical properties of the evaluation, horizontal and vertical. It employs well established simplified methods such theworking BEM working fluid so it is applicable to evaluate hydrokinetic turbines. Here, properties the results obtained by the fluid being developed for wind turbines, it allows us to modify the physical of as the (Blade Momentum) and other based models as configuration LLFVW (Lifting Line Free BEM andElement LLFVW methods aremodel compared withvortex the Here, CFD results for such the obtained SP Figure 18.LLFVW so it is applicable to evaluate hydrokinetic turbines. the results by the in BEM and Vortex Wake) and includes extra features such as structural and aeroelastic modules. In spite of From Figure 18 it is obvious that the simplified models provide substantially higher power methodsQblade are compared with the results forit the SP us configuration Figureproperties 18. being forCFD wind allows modify thein physical of the coefficients thandeveloped those obtained with turbines, CFD. This assertion isto true for both methods, BEM and LLFVW, From Figure 18 it is obvious that the simplified models provide substantially higher working fluid so it is applicable to evaluate hydrokinetic turbines. Here, the results obtained by the power even including the Prandtl tip and root losses. It is interesting to remark that the LLFVW method, BEM and LLFVW methods are compared with the CFD results for the SP configuration in Figure 18. LLFVW, coefficients those with CFD. This assertion is true for both methods, BEM results and whichthan is one of theobtained most sophisticated techniques among the simplified approaches, provides From Figure 18 it is obvious that the simplified models provide substantially higher power even including Prandtl tipBEM. andThe root losses. Itbetween is interesting to remark LLFVW method, very close the to those of the differences such predictions andthat thosethe obtained with coefficients than those obtained with CFD. This assertion is true for both methods, BEM and LLFVW, CFD as follows: ontechniques the one hand, it is known that BEM tends to overestimate the results which is onecan of be theexplained most sophisticated among the simplified approaches, provides even including the Prandtl tip and root losses. It is interesting to remark that the LLFVW method, power coefficient, specifically high solidity turbines and,predictions on the otherand hand, in the simplified very close to those BEM.sophisticated Thefor differences between those obtained with CFD which is oneof ofthe the most techniques amongsuch the simplified approaches, provides results methods the hub is not taken into account in the computation. It has been already remarked that the can be explained follows: onBEM. the one hand, it isbetween knownsuch thatpredictions BEM tends overestimate the power very close as to those of the The differences andto those obtained with truncated cone shape of the hub produces a broad wake responsible for augmenting the thrust and CFD can be explained as follows: onturbines the one hand, is known thathand, BEM tends to simplified overestimatemethods the coefficient, specifically for high solidity and,iton the other in the the drag forces on the rotor, consequently reducing the turbine performance. power coefficient, specifically for high solidity turbines and, on the other hand, in the simplified hub is not taken into account in the computation. It has been already remarked that the truncated cone methods the hub is not taken into account in the computation. It has been already remarked that the shape of the hub produces a broad wake responsible for augmenting the thrust and drag forces on the truncated cone shape of the hub produces a broad wake responsible for augmenting the thrust and rotor, consequently the turbine reducing performance. drag forces onreducing the rotor, consequently the turbine performance.

Figure 18. The comparison of the CFD results obtained in the present work versus those provided by BEM and LLFVM implemented in the Qblade software. The results computed by the SST Transition turbulence model are also included for reference.

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Figure 18. The comparison of the CFD results obtained in the present work versus those provided by BEM and LLFVM implemented in the Qblade software. The results computed by the SST Transition Energies 2018, 11, 3151 20 of 23 turbulence model are also included for reference.

Additionally, as as aa reference, reference, Figure Figure 18 18 includes includes the the results results computed computed with with the the SST SST Transition Transition Additionally, turbulence model, model, which which are are also also well well below below the the simplified simplifiedmethod’s method’spredictions. predictions. turbulence As aa final final comparison, comparison, the the experimental experimental results results of of Reference Reference[18] [18]have havebeen beenconsidered. considered. Al Al As Mamun [18] [18]conducted conducted an experimental of the performance a small three-bladed Mamun an experimental study study of the performance of a small of three-bladed hydrokinetic hydrokinetic turbine in aworking water channel with an γ inclination anglediameter γ = 45. The turbine in a water channel with anworking inclination angle = 45. The rotor wasrotor small,diameter 0.223 m, was small, 0.223 m, and the blade was based on the NACA 4412 profile. The rotation angular velocity and the blade was based on the NACA 4412 profile. The rotation angular velocity was about 120 rpm. wasexperimental about 120 rpm. The are experimental results are summarized in Appendix of Reference [18] and The results summarized in Appendix G of Reference [18] andGthose corresponding to those corresponding to an incident velocity of 0.65 m/s are presented in Figure 19 compared with the an incident velocity of 0.65 m/s are presented in Figure 19 compared with the CFD computations of the CFD computations of the present study. present study.

Figure Figure 19. 19. The comparison of the CFD CFD computation computation of the the present present study study versus versus the the experimental experimental ◦ measurements measurements of of Reference Reference[19] [19]in inaa45 45° inclined inclined rotor rotor with with the the incident incident flow flowvelocity velocityof of0.65 0.65m/s. m/s.

Although Although the the tip tip speed speed ratio ratio ranges ranges between between both both turbines turbines are are different, different, the the maximum maximum values values of of the areare comparable for the 0 (seeof Figure 19).Figure For λ

Computational Fluid Dynamics Modelling and Simulation of an Inclined Horizontal Axis Hydrokinetic Turbine Leidy Tatiana Contreras 1 , Omar Dario Lopez 2 1 2

*

and Santiago Lain 1, *

PAI+ Group, Energetics & Mechanics Department, Faculty of Engineering, Universidad Autónoma de Occidente, 760030 Cali, Colombia; [email protected] Computational Mechanics Research Group, Mechanical Engineering Department, Faculty of Engineering, Universidad de los Andes, 111711 Bogotá, Colombia; [email protected] Correspondence: [email protected]; Tel.: +57-2-318-8000 (ext. 11882)

Received: 2 August 2018; Accepted: 30 October 2018; Published: 14 November 2018

Abstract: In this contribution, unsteady three-dimensional numerical simulations of the water flow through a horizontal axis hydrokinetic turbine (HAHT) of the Garman type are performed. This study was conducted in order to estimate the influence of turbine inclination with respect to the incoming flow on turbine performance and forces acting on the rotor, which is studied using a time-accurate Reynolds-averaged Navier-Stokes (RANS) commercial solver. Changes of the flow in time are described by a physical transient model based on two domains, one rotating and the other stationary, combined with a sliding mesh technique. Flow turbulence is described by the well-established Shear Stress Transport (SST) model using its standard and transitional versions. Three inclined operation conditions have been analyzed for the turbine regarding the main stream: 0◦ (SP configuration, shaft parallel to incoming velocity), 15◦ (SI15 configuration), and 30◦ (SI30 configuration). It was found that the hydrodynamic efficiency of the turbine decreases with increasing inclination angles. Besides, it was obtained that in the inclined configurations, the thrust and drag forces acting on rotor were lower than in the SP configuration, although in the former cases, blades experience alternating loads that may induce failure due to fatigue in the long term. Moreover, if the boundary layer transitional effects are included in the computations, a slight increase in the power coefficient is computed for all inclination configurations. Keywords: computational fluid dynamics; three-dimensional unsteady flow; inclined axis hydrokinetic turbine; turbulent flow

1. Introduction Climate change, associated with negative impacts resulting from overexploitation and the use of fossil fuels, has not only induced environmental problems of great magnitude but has also generated an awakening in the scientific community and governments. All interested actors agree today that an alternative solution to the increasing energy deficit is the use of renewable energies [1]. Therefore, using hydrokinetic energy as a renewable source for generating electricity is nowadays one of the most active fields of research [2]. Water currents such as oceans and rivers constitute a wide and almost unexploited source for renewable energy generation. According to Reference [3], a representative electricity generation can be obtained by the ocean energy industry and the forecast for the year 2025 is to reach up to 200 GW of installed generation capacity. On the other hand, many developing countries are crossed by rivers which carry significant volumetric water flow along the year. This fact could be a revolutionary scenario for remote populations which could use this energy source if effective and low-cost energy harnessing mechanisms are developed [3]. Around the world there are more than 300 hydrokinetic Energies 2018, 11, 3151; doi:10.3390/en11113151

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projects already in process, divided into four main types of technologies: ocean wave, tidal stream, ocean current and river hydrokinetic [3]; many of the applications in marine environments are for the large-scale, while, the river and channels applications are for the small-scale [4]. Because of its predictability, the large density of energy, and the low environmental impact (scarce visual impact, no emissions, no noise), the kinetic energy present in water streams (oceans, rivers, or tidal channels) has received considerable attention in recent years [3–5]. Such kinetic energy can be extracted through properly designed immersed turbines [6] without the need of large facilities as reservoirs or dams. As it generates no emissions, the environmental impact is minimal. Compared to other hydraulic technologies, the site selection is much less restrictive and because it does not require significant infrastructure, the implementation time is short and the initial costs are reduced. Moreover, the modular character of hydraulic power enables scalable output energy, allowing for a reduction of the energy cost per kW. Another advantage is related with the continuous flow of water in oceans and rivers which eliminates the need for storing the energy, which is a crucial benefit for remote communities and very convenient in public services [6]. From the technical point of view, the conversion of kinetic energy present in large rivers, tides, and ocean currents involves two processes. The first process implies that the energy available on tidal, ocean or river currents must be extracted and converted into mechanical energy at the rotor axis, and the second process deals with converting such mechanical energy into electricity using a generator [7]. However, despite all the performed research and experiments, the study of hydrokinetic turbines (concentrated mainly in the primary process), is still in an incipient state due to the complexity and cost that represents a suitable testing bench to operate this kind of rotors. That is, the reason why the main part of its design is based on the analogy with wind turbines. Moreover, the majority of the developed innovations have been the result of empirical studies conducted in order to deal with anchoring systems, channels, debris protection, and maintenance [8]. Flow dynamics in the horizontal axis hydrokinetic turbines (HAHT) is complex and has attracted the interest of the scientific community during the last years, specifically aimed to understand their performance and to improve efficiencies. To reach such objectives, a deep understanding of the involved hydrodynamics is required. In that sense, since a few years ago, Computational Fluid Dynamics (CFD) has become an essential approach for describing the fluid flow behavior around hydro turbines. CFD numerically solves the governing equations of Fluid Mechanics (i.e., mass, momentum, and energy conservation) in complex geometries in a general framework. Due to its advantages over other simplified methods [9], it has been the approach adopted in the present study and, in the following analysis, several recent studies that employ CFD to investigate different aspects of the design, development, and operation of HAHT’s are described. Kang et al. [10] conducted a numerical study with two kinds of geometry composed of a rectangular box and a rotating domain; in the first case they only analyzed the rotor, while in the second case the complete structure (rotor and mounting) was analyzed to determine the effect of the support in the turbine hydrodynamic efficiency. The results of these authors illustrated the flow complexity and showed that the extracted power of the full turbine mainly depends on the rotor geometry and the TSR (Tip Speed Ratio), as they were not very affected by the mounting components of the turbine and the channel bed. The authors carried out an experimental analysis used to validate the CFD results; they found that the refined grid presented a discrepancy at the power coefficient less than 5%, which is considered quite satisfactory taking into account that measurements were carried out for the complete turbine geometry including an ambient turbulence in the site. In Reference [11], the authors wanted to identify the main design parameters affecting the performance of a Horizontal Axis Water Turbine by presenting numerical results in comparison with experimental measurements. In such work, it was demonstrated that, when the other parameters were kept constant, the numerical output power of the turbine was roughly proportional to the square of the blade span and to the cube of the incoming velocity. Regarding the blade number, the authors found that the optimum number was three and that an increase beyond that caused a decrease in power production. Again,

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the authors validated the simulation with experimental data obtaining a difference of power coefficient between experimental and numerical results lower than 15%; the discrepancy could be attributed to the generator losses and possible measuring errors. Guo et al. [12] used a three-dimensional CFD simulation to analyze the turbulent flow characteristics in the velocity field up and downstream of the turbine and the effects of a discrete number of blades. Motivated by its use in BEM (Blade Element Momentum theory), the authors derived the flow induction factors (axial and tangential) at several locations downstream of the rotor from their CFD results. It was concluded that the main induced velocity component by the vortices was the axial component. Additionally, the computations showed that vortices developed at the tip of each blade induced a down-wash velocity near the rotor and generated an azimuthal variation of velocity components; these are responsible for the appearance of flow non-uniformities upstream and downstream the rotor. The authors concluded that the calculation model used provided an acceptable accuracy because the differences between the numerical results and experimental values of power and thrust coefficients were lower than 5%. With the objective of reducing the computational effort of CFD, some authors have coupled BEM and CFD. In this context, BEM, using the hydrofoil characteristics in two dimensions, can be employed to predict the hydrodynamic performance of a hydrokinetic turbine, while the CFD coupled with BEM take into account three dimensions using an actuator disc which in addition to predicting the performance also allows us to predict wake features of the turbine; however, these estimations do not include the rotating blades and are not able to predict some details of the flow field. For instance, Reference [13] present a usable tool which was applied to predict the behavior of tidal stream turbines in typical offshore conditions. The obtained results were satisfactory because the comparison of the power coefficient estimation by BEM-CFD with experimental data showed a difference between 0.3% and 8.8%. As another example of the coupling BEM-CFD, Reference [14] concludes that the BEM-CFD results of the hydrokinetic turbine were able to accurately predict the thrust; however, the power was overestimated. This behavior was present at lower values of TSR. In particular, the BEM-CFD calculations provided a fairly good approximation to the near rotor circumferentially averaged fluid velocity with the exception of the tip vortices [14]. In Reference [15] the authors reviewed and compared results from various models of horizontal axis water turbines at different spatial resolutions; the aim of the study was to investigate the effect of small variations in lift and drag characteristics of the hydrofoils employed in the blade design on the turbine performance. They found that from a practical perspective, relatively small changes on the blade aerodynamic properties are improbable to cause a significant decrease in the performance. However, such modifications had the effect of altering the value of the optimum power coefficient as well as the tip speed ratio at which it is achieved. Understanding the behavior of turbine wakes is crucial if turbines are to be deployed in arrays; for such reason, a comparison between BEM-CFD and full CFD method was focused on determination of velocity deficit in the turbine wake. When comparing with experimental data, Reference [15] found that both models captured reasonably well the wake dynamics, although there was around a 5% difference between both predictions. Reference [16] presented comparisons between experiments and CFD numerical computations focused on the velocity profiles in the wake region of a HAHT. The agreement between them was very reasonable, showing the same predicted wake recovery trend. Moreover, the turbine closeness to the water surface promoted the flow modification around the turbine which affected the wake development downstream the rotor. Finally, supported by the presented results, Zhang et al. [16] claimed that CFD is an appropriate tool to simulate the performance of tidal turbines and that the turbine proximity to the water surface influences the wake recovery. In a HAHT, the lowest pressure near the blade tip is due to the high revolution speed around these sections. Therefore, the accurate description of the flow field near the blade tip becomes important for two reasons: to analyze the turbine power performance and because cavitation is prone to occur in these areas, which of course alters turbine efficiency [17]. Following Reference [4] in order to design a high-performance rotor, the cavitation and pressure coefficient should be as low as possible while

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the lift to drag ratio should be kept high. In particular, Lee et al. [17] introduced a new blade design 4 of 23 included a raked tip shape aimed to noise reduction and cavitation inception delay. The concept was evaluated by numerical CFD simulations showing positive results in cavitation inceptionwithout delay. The concept evaluated by numerical CFD simulations showing delaying cavitation degrading thewas turbine efficiency. positive in contribution delaying cavitation without degrading theestimation turbine efficiency. Theresults present deals with the performance of small HAHT’s of Garman The present contribution deals with the performance estimation of small HAHT’s Garman type using CFD. The arrangement of such turbines can be appreciated in Figure 1b: theofturbine is type using CFD. The arrangement turbines canoperating be appreciated Figure 1b: the turbinethe is assembled in a floating structure onofa such channel or river with itsinaxis inclined regarding assembled in a floating structure on a channel oruse river its axisisinclined regarding the flow direction. As it was mentioned, the main ofoperating this kind with of turbines to provide electricity flow direction. As it was mentioned, the main use of this kind of turbines is to provide electricity to to isolated communities so their design has been essentially empirical and only a few experimental isolated communities their design has been essentially and only a fewonexperimental studies have appearedso [18,19]. For instance, Al Mamun [18]empirical performed experiments a laboratory ◦ studies have appeared [18,19]. For instance, Al Mamun [18] performed experiments on a laboratory Garman turbine with three blades operating with an inclination of 45 with respect to the main channel Garman turbineExperiments with three were blades operating inclination of and 45° with respect angles to the aimed main flow direction. conducted forwith threean incoming speeds two pitching channel flow Experimentsversus were tip conducted for three incoming speeds and twoofpitching to analyze thedirection. turbine performance speed ratio. As a result, a power coefficient around angles aimed to analyze thenoturbine versus tipofspeed ratio. As a have result,been a power 30% was reached. However, reports performance about the CFD analysis inclined HAHT’s found coefficient of around 30% was However, theknowledge, CFD analysis in the literature. Therefore, the reached. authors believe that,notoreports the bestabout of their thisofisinclined the first HAHT’s have been found in the literature. Therefore, thebehavior authors of believe that,which to theoperates best of their time in which the CFD simulation of the hydrodynamic a HAHT with knowledge, this is the first time in which the CFD simulation of the hydrodynamic behavior of a an inclined axis respect to the main stream is attempted. HAHT which operates with an inclined axis respect to the main stream is attempted. Energies 2018, 11, x water FOR PEER REVIEW for horizontal rotors that

(a)

(b)

Figure 1. The Theschematics schematicsof of inclined hydrokinetic turbine showing its components (a) and Figure 1. thethe inclined hydrokinetic turbine showing its components (a) and isometric isometric view of the geometrical model (b). view of the geometrical model (b).

This This paper paperisisstructured structured in inthe thefollowing followingway. way. After Afterthe theintroduction, introduction,the theconsidered consideredgeometrical geometrical configurations andthethe meshing process are described in 1.Section 1. The simulation numericalmethodology simulation configurations and meshing process are described in Section The numerical methodology and the key parameters the operation HAHT’s are Section and the key parameters governing the governing operation of HAHT’s are of summarized insummarized Section 2. Theinobtained 2. The obtained results for the non-dimensional turbine coefficients presented in are Section 3 which results for the non-dimensional turbine coefficients are presented in are Section 3 which organized in are organized in several theirabehavior along a turbine revolution described and several subsections: theirsubsections: behavior along turbine revolution is described first is and later thefirst analysis later the analysis is extended to build the versus respective curvesratio; versus tip speed moreover, the is extended to build the respective curves tip speed moreover, theratio; effects of including effects of including the modeling of theoftransitional behavior the boundary layerareondiscussed turbine the modeling of the transitional behavior the boundary layer onofturbine performance performance discussed in 4.3. Comparison ofwith the computed CFD results with available in Section 4.3.are Comparison of Section the computed CFD results available experimental data and those experimental data and those obtained with more simplified models is performed in Section 4; also, obtained with more simplified models is performed in Section 4; also, in this section, a comparison of in this section, a comparison additionaldata CFDin results the experimental dataisin another additional CFD results with the of experimental anotherwith horizontal axis tidal turbine performed. horizontal tidal turbine Finally,and theperspectives. last section draws the main conclusions and Finally, theaxis last section draws is theperformed. main conclusions perspectives. 2. Geometrical Configuration and Mesh Generation 2. Geometrical Configuration Mesh Generation The numerically evaluatedand horizontal axis hydrokinetic turbine in this study has been an existing machine Aquavatio. Such ahorizontal HAHT wasaxis empirically built, adopting Garman turbine The called numerically evaluated hydrokinetic turbine ina previous this study has been an design. machine Such a machine was operating situ” on the Cauca River (Colombia) doing feasibility existing called Aquavatio. Such“in a HAHT was empirically built, adopting for a previous Garman studies during years 2010–2011, a careful“in experimental characterization was never performed. turbine design. the Such a machine wasbut operating situ” on the Cauca River (Colombia) for doing feasibility studies during the years 2010–2011, but a careful experimental characterization was never performed. Aquavatio consists of a three-bladed rotor, with a diameter D = 1.8 m and a truncated conical hub connects the blades to the shaft (see Figure 1a). The blade design was adopted from an existing wind turbine IT-PE-100 [20] which has nearly the same rotor size as Aquavatio; this design is based on the NACA 4412 airfoil with pitch angle and chord distributions lineal from root to tip.

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Aquavatio consists of a three-bladed rotor, with a diameter D = 1.8 m and a truncated conical hub connects the blades to the shaft (see Figure 1a). The blade design was adopted from an existing wind turbine IT-PE-100 [20] which has nearly the same rotor size as Aquavatio; this design is based on the Energies 11, x with FOR PEER REVIEW 5 of 23 the NACA 44122018, airfoil pitch angle and chord distributions lineal from root to tip. Figure 1a shows geometry of the HAHT schematically and illustrates its real operation configuration while Figure 1b Figure 1a shows the geometry of the HAHT schematically and illustrates its real operation presents the generated modelthe ofgenerated the turbine in isometric view; here, the stream direction configuration while geometrical Figure 1b presents geometrical model of the turbine in isometric follows the ‘z’ direction, ‘y’ represents the vertical and ‘x’ the lateral coordinate. view; here, the stream direction follows the ‘z’ direction, ‘y’ represents the vertical and ‘x’ the lateral In the present study, three configurations have been analyzed: a first assembly where the rotor coordinate. the present study, threeincoming configurations have so been analyzed: a first assembly where the is placedInperpendicular to the velocity that the turbine axis is parallel to rotor the flow is placed perpendicular toand thetwo incoming velocity so that thewhere turbine parallelantoangle the flow direction (SP configuration), inclined arrangements theaxis axisismakes γ of 15◦ (SP configuration), and two inclined arrangements the axis respectively makes an angle γ of 15° 2b). (SI15 direction configuration) and 30◦ (SI30 configuration) regarding thewhere free surface, (see Figure (SI15 configuration) and 30° (SI30 configuration) regarding the free surface, respectively (see Figure Obviously, the two last cases mimic the conditions in which the real HAHT operates. The three 2b). Obviously, the two last cases mimic the conditions in which the real HAHT operates. The three configurations considered allowing for a quantitative estimation of the influence of the inclination configurations considered allowing for a quantitative estimation of the influence of the inclination angle on machine performance as well as on the forces acting on the turbine. angle on machine performance as well as on the forces acting on the turbine.

(a)

(b) Figure 2. The front view and sideview view(b) (b) of of the the geometry the inclined HAHT. The The employed Figure 2. The front view (a)(a) and side geometryfor for the inclined HAHT. employed boundary conditions are also shown. boundary conditions are also shown.

considered computational domain has the following dimensions, which are expressed in The The considered computational domain has the following dimensions, which are expressed in terms of the rotor diameter D: length, 20D height, 4D and width, 6D. With such dimensions, the terms of the rotor diameter D: length, 20D height, 4D and width, 6D. With such dimensions, the turbine turbine operates in almost isolated conditions, as the resulting blockage ratio is lower than 5%. operates in almost isolated conditions, as the resulting blockage ratio is lower than 5%. Moreover, Moreover, the computational domain is divided into two sub-domains: an inner rotating domain of the computational domain dividedthe into two sub-domains: anhub), innerand rotating domain cylindrical cylindrical shape, whichisincludes turbine rotor (blades and an outer steadyofdomain shape, which includes the turbine rotor (blades and hub), and an outer steady domain encompassing encompassing the water environment. In the cases of inclined configurations, the shaft was included the water In the cases of inclined therepresent shaft was included this domain, in thisenvironment. domain, but not in the parallel to flowconfigurations, configuration. To the physicalin rotational motion of parallel the blades, the cylindrical domainTorotates with the a prescribed velocity withofrespect but not in the to flow configuration. represent physicalangular rotational motion the blades, to the steady domain,rotates which with numerically is realized by a sliding mesh technique in domain, the the cylindrical domain a prescribed angular velocity with respectimplemented to the steady commercial software employed, (Fluent v. 14.0, ANSYS, Inc., Canonsburg, PA, USA). which numerically is realized by a sliding mesh technique implemented in the commercial software employed boundary conditions can be appreciated in Figure 2a,b. As indicated in Figure 2b, employedThe (Fluent v. 14.0, ANSYS, Inc., Canonsburg, PA, USA). the left side is specified as a velocity inlet with a constant velocity (equal to 1.0 m/s in this study), the The employed boundary conditions can be appreciated in Figure 2a,b. As indicated in Figure 2b, right face is set as a pressure outlet (0 Pa), the bottom boundary (channel bed) consists on a steady the left side is specified as a velocity inlet with a constant velocity (equal to 1.0 m/s in this study), non-slip wall) whereas the top border, representing the free surface, was established as a zero stress the right facewall is settranslating as a pressure (0 Pa), the bottom consists on aas steady moving with outlet the same velocity as that boundary imposed at(channel the inlet.bed) The lateral walls, shown in Figure 2a, are defined to be non-slip walls. Inside the rotating subdomain is the rotor, this

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non-slip wall) whereas the top border, representing the free surface, was established as a zero stress moving wall translating with the same velocity as that imposed at the inlet. The lateral walls, as shown in Figure 2a, are defined to be non-slip walls. Inside the rotating subdomain is the rotor, this cylinder is Energies 2018, 11, x FOR PEER REVIEW 6 of 23 connected with the outer domain though interfaces specified as the sliding mesh boundary condition. cylinder is connected with the outer domain though interfaces specified as the sliding mesh boundary Moreover, because the turbulence levels at the inlet were not known, it was decided to work with condition. Moreover, because the turbulence levels at the inlet were not known, it was decided to a moderate turbulence intensity equal to 5%. work with a moderate turbulence intensity equal to 5%. The computational domain has been discretized by means of a non-structured mesh created with The computational domain has been discretized by means of a non-structured mesh created with the ANSYS ICEM-CFD software (v. 14.0, ANSYS, Inc., Canonsburg, PA, USA). Figure 3a presents the ANSYS ICEM-CFD software (v. 14.0, ANSYS, Inc., Canonsburg, PA, USA). Figure 3a presents a a perspective of the employed mesh where the darkest area corresponds to the rotating sub-domain. perspective of the employed mesh where the darkest area corresponds to the rotating sub-domain. To adequately describe thethe boundary thegrid grid closest to the blades be fine To adequately describe boundarylayer layerdevelopment, development, the closest to the blades mustmust be fine enough; as an Figure surfacemesh meshemployed employed in the blades the hub, enough; as illustration, an illustration, Figure3b 3bshows shows the the surface in the blades and and the hub, which is pretty uniform. Consequently, the mesh around the blade has an O-grid topology which is pretty uniform. Consequently, the mesh around the blade has an O-grid topology with with twelve prism layers. Outside the tetrasbased basednon-structured non-structured constructed, twelve prism layers. Outside theprisms prismsregion, region, a tetras gridgrid waswas constructed, taking their aspect ratioisissimilar similar to prisms with the the purpose of guaranteeing a taking carecare thatthat their aspect ratio to that thatofofthe the prisms with purpose of guaranteeing smooth transitionbetween betweenboth both mesh mesh regions. density is higher downstream than than a smooth transition regions.Finally, Finally,the thegrid grid density is higher downstream upstream the rotor to the complexityof ofthe the flow flow in TheThe quality parameters of of upstream the rotor duedue to the complexity in the theturbine turbinewake. wake. quality parameters the meshes have been checked with the tools available in ANSYS ICEM-CFD and are listed in Table the meshes have been checked with the tools available in ANSYS ICEM-CFD and are listed in Table 1. 1.

(a)

(b)

Figure 3. The overview meshused usedat atthe the steady steady domain and thethe surface mesh on the Figure 3. The overview of of thethe mesh domain(a)(a) and surface mesh onturbine the turbine blades and hub (b). blades and hub (b). 1. The parameters describingthe thequality quality of the different turbine configurations. TableTable 1. The parameters describing the mesh meshfor forthe the different turbine configurations. Parameter SP Configuration SP Configuration Aspect ratio (average) 0.95 Aspect ratio (average) 0.95 Equiangle skewness (average) 0.52 Equiangle skewness (average) 0.52 Determinant (average) 0.93 Determinant (average) 0.93 Expansion factor 1.20

Parameter

Expansion factor

1.20

SI15 Configuration SI30 Configuration SI15 Configuration SI30 Configuration 0.96 0.95 0.96 0.46 0.45 0.95 0.46 0.91 0.91 0.45 0.91 1.20 1.20 0.91

1.20

1.20

3. Numerical Simulation Methodology

3. Numerical Simulation The transient flow Methodology around the HAHT was computed with the help of the transient rotor-stator framework, realized by the sliding mesh approach. In that model, the turbine hub and blades rotate

The transient flow around the HAHT was computed with the help of the transient rotor-stator counterclockwise (see Figure 4) with a prescribed angular velocity; in this way, the development of framework, realized by the sliding mesh approach. In that model, the turbine hub and blades rotate the flow field at each time step is described. The interface position between the rotating inner and counterclockwise (see Figure 4) with a prescribed angular velocity; way, theflux development steady outer sub-domains is actualized every time step allowing forina this conservative interchangeof the flow between field at each step is described. The interface between the rotating innerfeatures and steady them.time The Shear Stress Transport (SST) model position was adopted to describe the turbulent outerofsub-domains is actualized every time stepofallowing for[21,22] a conservative interchange between the flow. In this study the standard version such model was mainlyflux employed, however, them.the The Shear Stress Transport (SST) model was adopted to describe the turbulent features of the flow. transition version [23] was also tested. It is well known that the SST model improves the predictions other two-equation turbulence flow configurations where strongthe adverse In this study theof standard version of such modelmodels [21,22]in was mainly employed, however, transition pressure gradients occur, such those happening around HAHT,improves and it has the beenpredictions widely usedofinother version [23] was also tested. It is as well known that the SSTamodel the simulation of hydraulic turbines [24–33], where it has become a sort of standard. two-equation turbulence models in flow configurations where strong adverse pressure gradients occur, Regarding the employed discretization schemes, all the results converged at each time step using second order schemes in space, upwind for the convective and centered for the diffusive terms,

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such as those happening around a HAHT, and it has been widely used in the simulation of hydraulic turbines [24–33], where it has become a sort of standard. Regarding the employed discretization schemes, all the results converged at each time step using second order schemes in space, upwind for the convective and centered for the diffusive terms, respectively, and the second order in time for all the variables. Pressure-velocity coupling is dealt with Energies 2018, 11, x FOR PEER REVIEW 7 of 23 the SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) approach. Computations were performed for anand incident velocity V0in=time 1 m/s angular velocities, coupling depending on the tip respectively, the second order for with all thedifferent variables. Pressure-velocity is dealt speed ratio (see Equation (1) below). Theforemployed time step corresponds to a Computations turbine rotation of with theλSIMPLE (Semi-Implicit Method Pressure-Linked Equations) approach. around , was chosen after a sensitivity which a trade-off between computational were1◦performed for an incident velocityanalysis 𝑉 = 1 m/s with represents different angular velocities, depending on speed ratio 𝜆 (see Equation (1) below). The of employed time step corresponds to each a turbine cost the andtipaccuracy. Moreover, a maximum number 200 iterations was specified at time step −5 . rotation of around 1°, was chosen after analysis which represents a trade-off between using a residual convergence criterion of a10sensitivity computational cost and accuracy. Moreover, a maximum number of 200 iterations specified Simulations are started by computing the flow around the HAHT using thewas steady MFRatmodel each time step using a residual convergence criterion of 10−5. of ANSYS-Fluent software (v. 14.0, ANSYS, Inc., Canonsburg, PA, USA), which is used as an initial Simulations are started by computing the flow around the HAHT using the steady MFR model condition for the transient computation. The unsteady computation is launched, initially using schemes of ANSYS-Fluent software (v. 14.0, ANSYS, Inc., Canonsburg, PA, USA), which is used as an initial of the first order during approximately ten turbine revolutions to get the flow developed. When the condition for the transient computation. The unsteady computation is launched, initially using torque has settled down, i.e., the torque curve shows a quasi-periodic the discretization schemes of the first order during approximately ten turbine revolutions to behavior, get the flow developed. schemes of the advective terms are changed to second order, firstly for the continuity and momentum When the torque has settled down, i.e., the torque curve shows a quasi-periodic behavior, the equations and later also for the turbulent variables equations. Finally, the simulation was run until the discretization schemes of advective terms are changed to second order, firstly for the continuity and momentum equationsbetween and later also the turbulent variables equations. simulation averaged torque difference twofor successive turns was below 0.2%Finally, [24]. Inthe the present study, was run until thecase, averaged torque difference between two have successive was below 0.2% [24]. In for each computed at least twenty rotor revolutions been turns simulated. the presentverification study, for each computed case, at least rotor revolutions beentosimulated. A spatial study was performed for twenty the rotor with the shaft have parallel the flow direction A spatial verification study was performed for the rotor with the shaft parallel to the flow (SP configuration). The evaluated operating point was the nominal condition of the wind rotor IT-PE-100 direction (SP configuration). The evaluated operating point was the nominal condition of the wind because the same blade design was used for both machines and it corresponds to a tip speed ratio λ = 5.7 rotor IT-PE-100 because the same blade design was used for both machines and it corresponds to a (see tip Equation (1) below) using a rotor angular velocity of 60 rpm. For this grid independence study, speed ratio λ = 5.7 (see Equation (1) below) using a rotor angular velocity of 60 rpm. For this grid the sampled variable was to be the power coefficient Equation (3) C below). According to P (see independence study, thechosen sampled variable was chosen to be C the power coefficient P (see Equation the usual procedure, three meshes with an increasing number of cells were considered: a coarse (3) below). According to the usual procedure, three meshes with an increasing number of cells were 6 6 gridconsidered: with 5.2 ×a10 elements, an5.2 intermediate mesh with 8.2 × 10 , elements refined grid coarse grid with 10 elements, an intermediate mesh with 8.2 and 10 a, elements and with grid with 10.5 10 elements. obtained averaged power have 0.2383 been the 10.5 a×refined 106 elements. The obtained averagedThe power coefficients have beencoefficients the following: (coarse), following: 0.2383 (coarse), 0.2430 (intermediate) and 0.2410 (refined). As the difference in 𝐶 is 0.8% 0.2430 (intermediate) and 0.2410 (refined). As the difference in C p is 0.8% between the medium and fine between the medium and the in intermediate grid was employed the computations meshes, the intermediate gridfine wasmeshes, employed the computations allowing us in to maintain an affordable allowing us to maintain an affordable computational time. Based on this result, representing a computational time. Based on this result, representing a compromise between the computational cost compromise between the computational cost and accuracy, it was decided to mesh the inclined and accuracy, it was decided to mesh the inclined configurations with a similar distribution and number configurations with a similar distribution and number of elements than the SP case. In those cases, of elements than the SP case. In those cases, the employed number of elements in the meshes has been the employed number of elements in the meshes has been 8.2 10 elements (SI15 configuration) 8.2 ×and 1067.9 elements (SI15 configuration) and 7.9 × 106 elements (SI30 configuration). 10 elements (SI30 configuration).

Figure Therotor rotor view the blades’ position and the and employed coordinate system. Blades Figure 4. 4.The viewillustrating illustrating the blades’ position the employed coordinate system. rotate counterclockwise. Blades rotate counterclockwise.

The following non-dimensional parameters govern the behavior of the HAHT: the tip speed ratio or TSR (𝜆) is the non-dimensional angular velocity regarding the incoming velocity, 𝑉 :

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The following non-dimensional parameters govern the behavior of the HAHT: the tip speed ratio or TSR (λ) is the non-dimensional angular velocity regarding the incoming velocity, V0 : ωD 2V0

λ=

(1)

where ω is the rotor angular velocity and D its diameter. The torque coefficient Cm relates to the total torque M, the density of the fluid ρ, and the area swept by the rotor, Sre f = πD2 /4; it is written as: Cm =

M

(2)

1 2D 2 ρV0 2 Sre f

The turbine efficiency, or performance, is expressed by the power coefficient Cp , which is the non-dimensional variable associated with the power produced by the turbine, P: Cp =

P 1 3 2 ρV0 Sre f

= Cm λ

(3)

Cp is obtained as the product of the torque coefficient Cm and the tip speed ratio λ. Therefore, the operating point of the turbine is defined by the pair (λ, CP ). The total hydrodynamic force F acting on each blade is projected on the directions perpendicular to the rotation plane, or normal force Fn , and parallel to it, or tangential force Ft . The tangential force is connected with the torque transmitted by the fluid to the blade while the normal force is responsible for the cyclic loading and fatigue on the blades. In the last case, each blade contribution can be added to compute the normal force acting on the whole rotor—the thrust—which is characterized by the thrust coefficient Cn . Fn Cn = 1 (4) 2 2 ρV0 Sre f Moreover, on the whole rotor, as an object immersed in a moving fluid, the total hydrodynamic force can be decomposed in a component parallel to the incoming flow velocity, which constitutes the drag, D, and in a component in the vertical plane perpendicular to such velocity which constitutes the lift force, L. Coefficients associated with such forces are written as: CD =

D 1 2 2 ρV0 Sre f

; CL =

L 1 2 2 ρV0 Sre f

(5)

4. Results 4.1. The Behavior of Non-Dimensional Coefficients Along A Turbine Revolution In this subsection, the behavior of the power and force coefficients along a cycle is discussed depending on the rotor inclination, and for a TSR λ = 5.7. For this operating point, the inflow velocity was 1 m/s and the angular velocity 60 rpm. As indicated previously, the employed turbulence model was k-ω SST [22]. Figure 5 presents the values obtained for the power coefficient C p in the three considered configurations, SP, SI15 and SI30. This figure illustrates the behavior during a turbine revolution of C p with the azimuthal angle, defined by Figure 4. Figure 5b shows the contribution of one blade to the power coefficient for the three configurations. In the SP case, the delivered power for one blade depends only very slightly on the azimuthal position, but in the case of the inclined turbines, it shows a clear dependence on such an angle. Therefore, the power coefficient curve consists on a fairly constant curve for SP configuration and on a periodic function with a maximum and a minimum in configurations SI15 and SI30. This fact is associated with differences in the relative velocity experienced

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Energies 2018, 11, xblades FOR PEER 9 ofclearly 23 by the turbine at REVIEW different angular positions in the inclined turbine cases. As it can be seen in Figure 5b, the oscillation amplitude in CP increases with the inclination angle (γ), keeping its can be clearly seen in Figure 5b, the oscillation amplitude in 𝐶 increases with the inclination angle maximum to very similar values slightly above 0.08 for all cases; however, the minimum value reduces (γ), keeping its maximum to very similar values slightly above 0.08 for all cases; however, the if angle γ increases. Interestingly, the maximum CP for the SI15 case is slightly higher than the value minimum value reduces if angle γ increases. Interestingly, the maximum 𝐶 for the SI15 case is computed for the SPthe configuration as it for canthe be SP appreciated in Figure 5b.beSuch a maximum value is slightly higher than value computed configuration as it can appreciated in Figure ◦ ◦ attained the blade azimuthal angle of −45 315 (see Figure 5b)or whilst 5b. Such when a maximum valueisisaround attainedthe when the blade is around the or azimuthal angle of −45° 315° the ◦ . This fact means that the angular distance between the maximum and minimum is reached around 150 (see Figure 5b) whilst the minimum is reached around 150°. This fact means that the angular distance ◦ ), implying that minimum is longer (aboutand 195◦minimum ) than between the minimum and than maximum (about between the maximum is longer (about 195°) between the165 minimum and the oscillation behavior is not fully Thebehavior turbine is CPnot can be harmonic. observed in 5a: maximum (about 165°), implying thatharmonic. the oscillation fully TheFigure turbine 𝐶 as it iscan clearly seen, the contributions to the power coefficient of each blade combine to produce a fairly be observed in Figure 5a: as it is clearly seen, the contributions to the power coefficient of each constant value for all the azimuthal positions. Only the azimuthal SI30 case can a gentle ripple curve blade combine to produce a fairly constant value for for all the positions. Only for in thethe SI30 case can a gentle Regarding ripple in thethe curve be appreciated. Regarding effect of inclination it was be appreciated. effect of inclination angle, itthe was found that in theangle, inclined cases, found thatcoefficient in the inclined cases, by the13% power coefficient decreases by30% 13%(SI30 (SI15configuration) configuration) compared and 30% to the power decreases (SI15 configuration) and (SI30 configuration) compared to the parallel configuration. necessary to mention that the SP the parallel configuration. It is necessary to mention that the ItSPisconfiguration presented a small value configuration presented smallattributed value in the efficiency, around 25%, the shape. hub geometry, in the efficiency, around a25%, to the hub geometry, of a attributed truncated to cone Such a hub of a truncatedproduces cone shape. Such wake a hub which configuration produces a wide wake which increases the drag configuration a wide increases the drag on the turbine. on the turbine.

(a)

(b)

◦ ) and Figure 5. 5. The The power the three studied configurations, SP, SP, SI15SI15 (15°)(15 and SI30 SI30 Figure powercoefficient coefficientatatλλ= =5.7 5.7forfor the three studied configurations, ◦ ) inclined (30°) inclined with one blade; (b)(b) complete turbine. (30 with respect respectto tothe theflow flowdirection: direction:(a)(a) one blade; complete turbine.

In Figure Figure 6, 6, the the behavior behavior of Equation (4))(4)) versus azimuthal angle In of the thethrust thrustcoefficient coefficient𝐶 C(see Equation versus azimuthal angle n (see along a rotor revolution for one blade (Figure 6b) and the complete turbine (Figure 6a) is illustrated. along a rotor revolution for one blade (Figure 6b) and the complete turbine (Figure 6a) is illustrated. On the the SP SP configuration, configuration, the constant along the the turn, which also also On thethrust thruston oneach eachblade bladeis isroughly roughly constant along turn, which implies that the thrust of the turbine does not vary with the angular position (Figure 6a). However, implies that the thrust of the turbine does not vary with the angular position (Figure 6a). However, for the inclined configurations, the normal force on the rotor does vary with the azimuthal angle, for the inclined configurations, the normal force on the rotor does vary with the azimuthal angle, which generates alternating loads that could induce material fatigue in the long term. The maximum which generates alternating loads that could induce material fatigue in the long term. The maximum value of the thrust is experienced by a single blade between the −45° and 0° angles, whereas the value of the thrust is experienced by a single blade between the −45◦ and 0◦ angles, whereas the minimum appears around 150°. The difference between both thrust values also increases with the minimum appears around 150◦ . The difference between both thrust values also increases with the inclination angle γ. For instance, in Figure 6b, it can be appreciated that for the SI15, the maximum inclination angle γ. For instance, in Figure 6b, it can be appreciated that for the SI15, the maximum thrust on the blade overcomes the respective value for the SP turbine. When the total thrust on the thrust blade overcomes value for the SP turbine. smaller When the total thrust on the turbineonisthe computed (Figure 6a),the therespective inclined configurations experience loads than the SP turbine is computed (Figure 6a), the inclined configurations experience smaller loads than the SP case, around 4.1% and 10.9% for the SI15 and SI30 cases, respectively. Moreover, the thrust on thecase, around andconstant 10.9% for the SI15 SI30 cases, theathrust the for turbine turbine4.1% is pretty along withand a revolution forrespectively. all the cases, Moreover, showing only small on ripple an is pretty constant with a revolution for all the cases, showing only a small ripple for an azimuthal azimuthal anglealong of 30°. angle of 30◦ .

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(a) (b) (a) (b) Figure Figure 6. 6. The The thrust thrust coefficient coefficient at at λλ == 5.7 5.7 for for the the three three studied studied configurations, configurations, SP, SP, SI15 SI15 (15°) (15◦ ) and and SI30 SI30 Figure 6. The thrust coefficient at λ = 5.7 for the three studied configurations, SP, SI15 (15°) and SI30 ◦ (30°) (30 ) inclined inclined with with respect respect to to the the flow flow direction: direction: (a) (a) one one blade; blade; (b) (b) complete complete turbine. turbine. (30°) inclined with respect to the flow direction: (a) one blade; (b) complete turbine.

According to to Figure 7, as the γ given by by According γ inclination angle angle increases, increases, the the drag drag coefficient coefficient C 𝐶D given According to Figure 7, as the γ inclination angle increases, the drag coefficient 𝐶 given by Equation (5) decreases. thethe one blade andand thethe fullfull turbine coefficient. Consistent with Equation decreases.This Thisisistrue truefor forboth both one blade turbine coefficient. Consistent Equation (5) decreases. This is true for both the one blade and the full turbine coefficient. Consistent the previous results,results, it can be that the that inclined (SI15 and (SI15 SI30) present drag coefficients with the previous it noticed can be noticed the cases inclined cases and SI30) present drag with the previous results, it can be noticed that the inclined cases (SI15 and SI30) present drag smaller thansmaller that ofthan the parallel around 14% around and 20%, respectively. The main reason coefficients that of configuration, the parallel configuration, 14% and 20%, respectively. The coefficients smaller than that of the parallel configuration, around 14% and 20%, respectively. The for that behavior is behavior that, as the inclination angle grows, thegrows, rotor transversal area facing the flow main reason for that is that, as the inclination angle the rotor transversal area facing main reason for that behavior is that, as the inclination angle grows, the rotor transversal area facing decreases, reducingreducing the widththe of the wake results in aresults lower in value of thevalue pressure component the flow decreases, width of which the wake which a lower of the pressure the flow decreases, reducing the width of the wake which results in a lower value of the pressure of the drag force. SP configuration, the CD of one a roughly value along component of the For dragthe force. For the SP configuration, theblade 𝐶 ofkeeps one blade keepsconstant a roughly constant component of the drag force. For the SP configuration, the 𝐶 of one blade keeps a roughly constant the whole revolution, the inclined a maximum andaa maximum minimum. and In the value along the wholebutrevolution, butconfigurations the inclined present configurations present a value along the whole revolution, but the inclined configurations present a maximum and a◦ SI15 case, two minima similar at an azimuthal angle 90◦ and 150of, minimum. In the SI15 of case, two values minimaare ofobserved similar values are observed at of anaround azimuthal angle minimum. In the SI15 case, two minima of similar values are observed at an azimuthal angle of◦ whereas90° theand maximum is located around 300 ; for theatSI30 case,300°; the minimum is case, placed around 150 around 150°, whereas theat maximum is ◦located around for the SI30 the minimum around 90° and 150°, whereas the maximum is located at around 300°; for the SI30 case, the minimum ◦ and the maximum beyond curves beyond do not show particular For any the full turbine, is placed around 150° and310 the. Both maximum 310°.any Both curves symmetry. do not show particular is placed around 150° and the maximum beyond 310°. Both curves do not show any particular the drag coefficient curves exhibit approximately constant valueanwith a fairly small ripple for the symmetry. For the full turbine, thean drag coefficient curves exhibit approximately constant value symmetry. For the full turbine, the drag coefficient curves exhibit an approximately constant value SI30 configuration. with a fairly small ripple for the SI30 configuration. with a fairly small ripple for the SI30 configuration.

(a) (b) (a) (b) Figure 7. The drag coefficient at λ = 5.7 for the three studied configurations, SP, SI15 (15°), and SI30 Figure 7. drag coefficient at for studied configurations, SP, Figure 7. The Thewith dragrespect coefficient at λ λ ==5.7 5.7 for the the three three studied SP, SI15 SI15 (15°), (15◦ ), and and SI30 SI30 (30°) inclined to the flow direction: (a) one blade; configurations, (b) complete turbine. (30°) (30◦ )inclined inclinedwith withrespect respect to tothe the flow flow direction: direction: (a) (a) one one blade; blade; (b) (b) complete complete turbine. turbine.

From Figure 8a, it can be noticed that the inclined rotors experience a net upward lift force which From can be be noticed thatthat the inclined rotors experience a net upward lift force FromFigure Figure8a, 8a,it it can noticed the inclined rotors experience a net upward liftwhich force is absent in the parallel configuration. The lift coefficient 𝐶 is computed by Equation (5) and in the is absent in the parallel configuration. The liftThe coefficient 𝐶 is computed by Equation (5) and(5) in and the which is absent in the parallel configuration. lift coefficient C is computed by Equation SP case, each blade experiences a small lift force component whichLis positive or negative depending SP each blade experiences a small lift force component which is positive negative or depending in case, the SP case, each blade experiences a small lift force component which or is positive negative on its azimuthal position. In that case, the contributions of the three blades compensate among them on its azimuthalitsposition. In that case, the contributions of the three blades them depending azimuthal position. In that the contributions thecompensate three bladesamong to produce aon zero net lift coefficient (Figure 8a)case, for the turbine at eachofposition. This fact compensate is expected, to produce a zero net lift acoefficient (Figure 8a) for the turbine each position. This fact is expected, among to produce net lift coefficient (Figure 8a) foratthe turbine at each owing tothem the symmetry of zero the geometrical configuration. As the inclination angle γposition. increases,This the fact lift owing to the symmetry of the geometrical configuration. As the inclination angle γ increases, the lift coefficient turns positive and augments with it (Figure 8b). It can be observed that in a cycle, the coefficient turns positive and augments with it (Figure 8b). It can be observed that in a cycle, the

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is expected, owing to the symmetry of the geometrical configuration. As the inclination angle γ 11 of 23 increases, the lift coefficient turns positive and augments with it (Figure 8b). It can be observed that inEnergies a cycle, lift experienced by one blade is located at the azimuthal angle of 11 0◦ofand 2018,the 11, xmaximum FOR PEER REVIEW 23 maximum lift experienced◦ by one blade is located at the azimuthal angle of 0° and the minimum the minimum around 210 for the inclined configurations. Again, the contributions to the lift of the around 210° for the inclined configurations. Again, the contributions to the lift of the three blades maximum experienced by one blade is located the azimuthal 0° and the minimum three bladeslift compensate providing a fairly constantatvalue of the lift angle along of with a revolution for all compensate providing a fairly constant value of the the contributions lift along with a revolution for blades all the around 210° for the inclined configurations. Again, to the lift of the three the configurations. configurations. compensate providing a fairly constant value of the lift along with a revolution for all the configurations. Energies 2018, 11, x FOR PEER REVIEW

(a)

(b)

(a) (b) Figure Figure8. 8.The Thelift liftcoefficient coefficientat atλλ==5.7 5.7for forthe thethree threestudied studiedconfigurations, configurations,SP, SP, SI15 SI15 (15°) (15◦ )and andSI30 SI30(30°) (30◦ ) inclined with to (a) one blade; complete Figure 8. Therespect lift coefficient at λ =direction: 5.7 for the three configurations, SP, SI15 (15°) and SI30 (30°) inclined with respect to the the flow flow direction: (a) onestudied blade; (b) (b) complete turbine. turbine. inclined with respect to the flow direction: (a) one blade; (b) complete turbine.

In In order order to to determine determine the the loads loads on on the the configurations configurations studied, studied, the the total total force force acting acting on on the the rotor rotor In order toSuch determine loads on force acting aaon therelated rotor was aa force is for the inclined than parallel turbine, fact was computed. computed. Such forcethe is smaller smaller forthe theconfigurations inclined cases casesstudied, than for forthe thetotal parallel turbine, fact related wasthe computed. Suchin a force iscase smaller for the inclined cases than for thethe parallel turbine, a fact related with wider the (which has the of pressure component of with the wider wake wake in the SP SP case (which has the effect effect of increasing increasing the pressure component of the the withforce). the wider wake the SP case has effect of pressure increasing the skin pressure component of the drag This fact in(which Figure 9, where thethe pressure andand skin friction coefficients on the drag force). This factisin isillustrated illustrated in Figure 9,the where friction coefficients on drag force). This fact is illustrated in Figure 9, where the pressure and skin friction coefficients on the blades pressure sideside are shown. The The top row of Figure 9 presents the the pressure coefficient for the SP the blades pressure are shown. top row of Figure 9 presents pressure coefficient for the blades pressure side shown. The top rowthe of Figure 9row presents thefigure pressure coefficient for friction the SP (a), SI1 SI1 (b) andand SI2 (c)are configurations while bottom exhibits the SP (a), (b) SI2 (c) configurations while the bottom rowofofthat that figure exhibits theskin skin friction ◦ (e) ◦ (f) (a), SI1 (b)for and (c) configurations: configurations axis while the bottom row of 15° that figure exhibits the skinthe friction coefficient the same parallel (d), inclined and main coefficient theSI2 same configurations: 15 (e) and 30° 30 (f)regarding regarding the main coefficient for the same configurations: axis parallel (d), inclined 15° (e) and 30° (f) regarding the main flow. flow. From From Figure Figure 9a–c 9a–c itit is is obvious obvious that that pressure pressure acting acting on on the the blades blades decreases decreases with with increasing increasing axis axis flow. Fromthis Figure it is obvious that pressurein acting onof the blades with increasing axis inclination; fact is well observed the the three blades. 9d–f inclination; this fact9a–c is particularly particularly well observed in the tip tip of the threedecreases blades. Figure Figure 9d–f illustrates illustrates inclination; this fact is particularly well observed in the tipangle; of the in three 9d–f illustrates the behavior skin friction with case, slight of the behavior of of the the skin friction coefficient coefficient with inclination inclination angle; in this thisblades. case, aaFigure slightincrease increase of such such the behavior of the skin friction coefficient with inclination angle; in this case, a slight increase of such coefficient coefficient is is found found by by increasing increasing the the operation operation slant slant angle, angle, mainly mainly visible visible at at the the blade’s blade’s mid-span mid-span coefficient is found by increasing the operation slant angle, mainly visible at the blade’s mid-span where aa transition between the and light color is However, is where transition between the dark dark and light blue blue color is appreciated. appreciated. However, is the the considered considered where a transition between theof and blue over colorthe is appreciated. However, is the the considered cases, the pressure the prevails friction and cases, the pressure component component ofdark the force forcelight prevails over the friction component component and the net net result result is is cases, the pressure component of the force prevails over the friction component and the net result that that the the slanted slanted configurations configurations experience experience smaller hydrodynamic forces than the SP configuration.is that the slanted configurations experience smaller hydrodynamic forces than the SP configuration. (b) (b)

(a) (a)

Figure 9. Cont.

(c) (c)

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(d) (d)

SP configuration SP configuration

(e) (e)

SI1 configuration SI1 configuration

(f) (f)

SI2 configuration SI2 configuration

Figure9.9. The Thepressure pressurecoefficient coefficient(a–c) (a–c)and andskin skinfriction frictioncoefficient coefficient(d–f) (d–f)atatthe theblade’s blade’spressure pressureside sidein Figure Figure 9. The pressure coefficient (a–c) and skin friction coefficient (d–f) at the blade’s pressure side in the three considered inclinations. the three considered inclinations. in the three considered inclinations.

Figure10 10presents presents aa vorticity vorticity iso-surface of value 1.5 Hz Figure Hz at at the thetip tipspeed speedratio ratio𝜆λ==5.7 5.7illustrating illustrating Figure 10 presents a vorticity iso-surface of value 1.5 Hz at the tip speed ratio 𝜆 = 5.7 illustrating thedifferences differences in in the the trailing trailing vortices between the between the the cases cases of of the the parallel paralleland andinclined inclinedturbines. turbines.Here, Here, the differences in the trailing vorticesdetached between from the cases of the parallel and inclinedby turbines. Here, besides the trailing thethe blades, the the wakes generated besides the trailing and andshed shedvortices vortices detached from blades, wakes generatedthe byhub theand hub besides thecan trailing and shed vortices detached from the the wakes generated bythat the induces hub and the shaft also observed. The hub wake onblades, a quasi-steady toroidal vortex and the shaft can be also be observed. The hubconsists wake consists on a quasi-steady toroidal vortex that the shaft canand alsolow be observed. wake consists on a quasi-steady toroidal vortex that induces a backflow pressure inThe thathub zone. As zone. a consequence, the drag force, as well as as the thrust, is induces a backflow and low pressure in that As a consequence, the drag force, well as the aincreased backflow on andthe lowrotor, pressure in that zone. As a consequence, the drag force, as well as the thrust, the efficiency of the of turbine. From From FigureFigure 10, it10, is it possible tois thrust, is increased on thereducing rotor, reducing the efficiency the turbine. is possible increased on the rotor, reducing the efficiency of the turbine. From Figure 10, it is possible to appreciate that the to appreciate that thehub hubwake wakeininthe theSP SPconfiguration configurationisissignificantly significantlywider widerthan thanininthe theinclined inclined appreciate that moreover, the hub wake in theofSP significantly wider than in the inclined configurations; thelength length theconfiguration tip vortices vortices is is is also larger configurations; moreover, the of the tip also larger in in the the SP SP case. case. configurations; moreover, the length of the tip vortices is also larger in the SP case. (a) (a)

(b) (b)

(c) (c)

Figure 10. The vorticity isosurface of 1.5 Hz showing the detached boundary layer for the SP (a), SI15 (b), and SI30 (c) configurations from the turbine axis and the blades.boundary The bladelayer tip layer vortices clearly Figure 10. The vorticity isosurface of of 1.51.5 Hz showing the the detached for the SP Figure 10. The vorticity isosurface Hz showing detached boundary forare the(a), SPSI15 (a), visible. (b), and SI30 (c) configurations from the turbine axis and the blades. The blade tip vortices are clearly SI15 (b), and SI30 (c) configurations from the turbine axis and the blades. The blade tip vortices are

visible. clearly visible.

4.2. Variation of Non-Dimensional Coefficients with the Tip Speed Ratio 4.2. Variation of of Non-Dimensional Non-Dimensional Coefficients Coefficients with with the the Tip Tip Speed Ratio 4.2. Variation Speed Ratio versus 𝜆 is discussed depending In this section, the behavior of the non-dimensional coefficients In this this section, the behavior behavior ofcase, the non-dimensional non-dimensional coefficients versus 𝜆λequal is discussed discussed depending on the turbine inclination. In this the inflow velocity is kept constant, to 1 m/s, and the In section, the of the coefficients versus is depending turbine angular velocity is varied in the range 40–70 rpm to build the curves. on the turbine inclination. In this case, the inflow velocity is kept constant, equal to 1 m/s, and the the on the turbine inclination. In this case, the inflow velocity is kept constant, equal to m/s, and Previously to discuss performance curve CP-λ, it isto comment that computing the turbine angular velocity velocity is the varied in the the range range 40–70 rpm tonecessary build the turbine angular is varied in 40–70 rpm build thetocurves. curves. power coefficient using Equation (5) is somehow unfair with the inclined configurations as Previously to discuss the performance curve C -λ, it is necessary to turbine comment that computing P Previously to discuss the performance curve CP-λ, it is necessary to comment that computing the in such cases the rotor area faced to the incoming flow is reduced by a factor cos 𝛾 regarding the SP the power coefficient using Equation (5) is somehow unfair with the inclined turbine configurations power coefficient using Equation (5) is somehow unfair with the inclined turbine configurations as configuration. Because the extracted power is proportional the by area transversal flow,the it the is as in such cases the rotor area faced to the incoming flow isto reduced by a factor γthe regarding in such cases the rotor area faced to the incoming flow is reduced a factor coscos 𝛾 to regarding SP customary to redefine the power coefficient taking into account this effect. Therefore, a corrected SP configuration. Because the extracted power is proportional to the area transversal to the flow, it is configuration. Because the extracted power is proportional to the area transversal to the flow, it is power coefficient, 𝐶 , is defined by Equation (6), where 𝐶 is the power coefficient given by Equation , the power coefficient taking into account this effect. Therefore, a corrected customary to redefine (3): coefficient, 𝐶 , is defined by Equation (6), where 𝐶 is the power coefficient given by Equation power ,

(3):

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customary to redefine the power coefficient taking into account this effect. Therefore, a corrected power Energies 2018, 11, x FOR PEER REVIEW 13 of 23 coefficient, CP,c , is defined by Equation (6), where CP is the power coefficient given by Equation (3): CP,c C P , c==

CPP cos cos γ γ

(6) (6)

Figure 11 shows ofof thethe studied configurations. Additionally, for Figure shows the theperformance performancecurves curvesfor foreach each studied configurations. Additionally, the the inclined configurations, thethe corrected that for inclined configurations, correctedpower powercoefficient coefficientisisshown shown in in comparison comparison with that computed using using Equation Equation (3). (3). As Ascos cosγ𝛾 ≤ ≤ 1, 1, C 𝐶 P,c the SP SP computed ≥ 𝐶CPand andthe thecorrected corrected values values are are closer to the , ≥ values. In In all all the the cases, cases, the the maximum maximum of of the the curve curve isisobtained obtainedfor forλ𝜆 = = 4.8 4.8 with with an an approximate approximate value value values. of 0.3 0.3 for forthe theSP SPconfiguration configurationand andsome someconsistent consistentlower lowervalues values the inclined turbines. For higher of forfor the inclined turbines. For higher λ 𝜆 values, angle of attack experienced theisblade is reduced, with the subsequent effect of values, thethe angle of attack experienced by theby blade reduced, with the subsequent effect of decreasing decreasing thelift generated and coefficient. the power coefficient. Onhand, the other hand,TSR for lower TSR the generated and the lift power On the other for lower values, thevalues, anglesthe of anglesofofthe attack of the flow approaching the blades increase, eventuallythe overcoming the attack relative flowrelative approaching the blades increase, eventually overcoming dynamic stall dynamic stall anglesaugmenting of the profiles, augmenting and decreasing which reduces the angles of the profiles, drag and decreasingdrag lift, which reduces the lift, transmitted torque from transmitted torque fromFigure the fluid to the blades. Figure 11highest demonstrates that theishighest performance the fluid to the blades. 11 demonstrates that the performance obtained for the SP is obtained forwhich, the SPregarding configuration which, regarding the corrected power coefficient, on average configuration to the corrected powertocoefficient, is on average 6.5% andis25% higher 6.5%that andfor 25% higher thanSI30 thatconfigurations, for the SI15 andrespectively. SI30 configurations, respectively. than the SI15 and

Figure 11. 11. The power coefficient coefficient versus versus tip tip speed speed ratio ratio for for the the different differentconfigurations. configurations. Figure

Figure Figure 12 12 illustrates illustrates the the behavior behavior of of the the force force coefficients coefficients versus versus tip tip speed speed ratio ratio for for the the three three turbine turbine configurations. configurations. Figure Figure 12a 12a shows shows the the variation variation of of the the thrust thrustcoefficient coefficientwith withλ. 𝜆. It It is is seen seen that that in all the cases it grows monotonically with the tip speed ratio and, according to the results found in all the cases it grows monotonically with the tip speed ratio and, according to the results found previously, previously,ititisishigher higherfor forthe theSP SPconfiguration configurationthan thanfor for the theinclined inclined turbines. turbines. As As mentioned mentioned before, this smaller width width of of the thehub hubwake wakefor forthe theinclined inclinedcases, cases,resulting resultinginina this phenomenon phenomenon is related to the smaller alower lowerpressure pressuredrag. drag.However, However,ininspite spiteof ofthe the lower lower thrust, thrust, the the blades of the inclined inclined turbines turbines are are exposed exposed to to alternating alternating loads loads that that can caninduce inducematerial materialfatigue fatiguein inthe thelong longterm. term.

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(a)

(b)

(c) Figure 12. The force coefficient versus tip speed ratio for the different configurations: (a) thrust Figure 12. The force coefficient versus tip speed ratio for the different configurations: (a) thrust coefficient; (b) drag coefficient; (c) lift coefficient. coefficient; (b) drag coefficient; (c) lift coefficient.

By thinking thinking of of the the turbine turbine as as aa whole whole object object immersed immersed in in aa moving moving fluid, fluid, itit is is interesting interesting to to look look By to the behavior of the drag and lift forces through its coefficients because such forces have some to the behavior of the drag and lift forces through its coefficients because such forces have some effects effects on the turbine operation that should be considered the design process. Figure 12b presents on the turbine operation that should be considered in thein design process. Figure 12b presents the the variation of the drag coefficient in terms of the tip speed ratio for the studied configurations. In variation of the drag coefficient in terms of the tip speed ratio for the studied configurations. In the the same way, as happened for the thrust coefficient, the drag coefficient increases monotonically same way, as happened for the thrust coefficient, the drag coefficient increases monotonically with and decreases withturbine the turbine inclination, approximately and 23.2% forSI15 the and SI15SI30 and λwith and𝜆decreases with the inclination, approximately 7.5% 7.5% and 23.2% for the SI30 cases, respectively, regarding the SP configuration. Figure 12c shows the change of the lift coefficient with 𝜆 for the three turbine cases. Of course, 𝐶 for the SP configuration, owing to the

geometrical symmetry, is very close to zero for all tip speed ratios. For the inclined configurations, on the other hand, it grows monotonically with 𝜆 and also increases with the inclination angle γ. Such a positive lift tends to effectively push up the turbine and eventually could produce vertical oscillations during Energies 2018, 11, 3151 the turbine’s operation. 15 of 23 Summarizing the results for the performance and force coefficients curves, the inclined configurations have a lower power coefficient than the SP configuration but also experience lower cases, respectively, regarding the SP configuration. Figure 12c shows the change of the lift coefficient loads. In particular, the rotor drag and thrust decrease with the increasing inclination angle γ and the with λ for the three turbine cases. Of course, CL for the SP configuration, owing to the geometrical counterpart of the amplitude of the experienced alternating stresses grows with it. This fact may symmetry, is very close to zero for all tip speed ratios. For the inclined configurations, on the other cause material fatigue in the blades after long periods of operation. Additionally, the fluid forces hand, it grows monotonically with λ and also increases with the inclination angle γ. Such a positive acting on the blades increase with tip speed ratio for all the studied turbine configurations. lift tends to effectively push up the turbine and eventually could produce vertical oscillations during As a final comment, the actuator disc theory can be extended to consider situations where the the turbine’s operation. incident flow makes an angle γ with the direction perpendicular to the rotor [25]. In that case, the Summarizing the results for the performance and force coefficients curves, the inclined maximum power coefficient is given by Equation (7): configurations have a lower power coefficient than the SP configuration but also experience lower 16 with loads. In particular, the rotor drag and thrust the cos 3 γ the increasing inclination angle γ and (7) C Pdecrease max = 27 counterpart of the amplitude of the experienced alternating stresses grows with it. This fact may cause material fatigue aincommon the blades after long periods operation.the Additionally, theoffluid acting on Therefore, practical approach forofestimating performance windforces turbines when the blades increase with tip speed ratio for all the studied turbine configurations. the flow is not perpendicular to the rotor is to multiply the power coefficient by the cube of the cosine Asangle a final comment, the actuator disc theory be revolution extended to consider situationsiswhere of the between the incoming velocity and thecan rotor axis. This procedure knownthe as incident flow makes an angle γ with the direction perpendicular to the rotor [25]. In that case, the cos 𝛾 correlation. In this study, the comparison was made using Equation (8), which is an the maximum power coefficient (7): extension of Equation (7) whereis𝐶givenisby theEquation power coefficient obtained for the SP configuration at ,

each considered TSR and 𝛾 is the inclination angle16of the rotor. This value was compared with that CPmax = cos3 γ (7) obtained in the simulation, which is given by Equation 27 (3). See the lines (solid for SI1 and dashed for SI2) in Figure 13. Therefore, a common practical approach for estimating3 the performance of wind turbines when ) = CP , SP (the λ) cos γ coefficient by the cube of the cosine(8) P (λ the flow is not perpendicular to the rotor isCto multiply power of the angle between the incoming velocity and the rotor revolution axis. Thiswith procedure is known Figure 13 presents the comparison of applying such a correlation the CFD results as in the the 3 γ correlation. In this study, the comparison was made using Equation (8), which is an extension of cos inclined configurations. As it can be clearly noticed, for the SI15 case, the correlation works pretty Equation (7) where CP,SP is the power coefficient for thethe SPtwo configuration at each well for the four tip speed ratios computed. In obtained the SI30 case, central values forconsidered λ are well TSR and γ is the inclination angle of the rotor. This value was compared with that obtained in the approximated but for the extreme values, noticeable differences appear: for λ = 3.8 the CFD result is simulation, which is given by Equation (3). See the lines (solid for SI1 and dashed for SI2) in Figure 13. underpredicted by the correlation (about 12%) and for λ = 6.7 it is overpredicted (about 21%). Nevertheless, owing to the simplicity of the correlation, the3results are approximate enough from an CP (λ) = CP,SP (λ) cos γ (8) engineering point of view.

Figure 13. 13.The The evaluation the correlation cos 𝛾 , Equation for turbine the inclined turbine Figure evaluation of theofcorrelation cos3 γ, Equation (8), for the (8), inclined configurations. ◦ configurations. Lines indicate 15 the inclination: correlation: solid 15° inclination: solid line; dashed 30° inclination: dashed line. Lines indicate the correlation: line; 30◦ inclination: line.

Figure 13 presents the comparison of applying such a correlation with the CFD results in the inclined configurations. As it can be clearly noticed, for the SI15 case, the correlation works pretty well for the four tip speed ratios computed. In the SI30 case, the two central values for λ are well approximated but for the extreme values, noticeable differences appear: for λ = 3.8 the CFD result

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is underpredicted by the correlation (about 12%) and for λ = 6.7 it is overpredicted (about 21%). Nevertheless, owing to the simplicity of the correlation, the results are approximate enough from Energies 2018, 11, xpoint FOR PEER REVIEW 16 of 23 an engineering of view.

4.3. Comparison Comparisonofofthe theResults Resultswith withTransitional TransitionalTurbulence TurbulenceModeling Modeling 4.3. Tostudy studythe thesensitivity sensitivityof ofthe theresults resultsto tothe themodeling modelingof ofthe thetransitional transitionaleffects effectson onthe theboundary boundary To layer, in addition to the k-ω SST model (SST Standard), the SST Transitional version has beenbeen also layer, in to the k-ω SST model (SST Standard), the SST Transitional version has employed. The Transition SST model includes two additional equations that describe the laminar– also employed. The Transition SST model includes two additional equations that describe the turbulent boundary layer transition: the first one for the intermittency factor (the time fraction in laminar–turbulent boundary layer transition: the first one for the intermittency factor (the time which the flow in point boundary layer is turbulent) and aand second equation for for the fraction in which theaflow in inside a pointthe inside the boundary layer is turbulent) a second equation transition momentum thickness Reynolds transition the transition momentum thickness Reynoldsnumber number[9,26]. [9,26].The Thereason reasonbehind behind employing aa transition model is is that that in the hydrokinetic and in model hydrokinetic turbine turbine the the blade bladeReynolds Reynoldsnumber numberchanges changesalong alongitsitsspan span and time, soso phenomena such as as laminar separation, thethe transition to turbulence, flowflow reattachment, and in time, phenomena such laminar separation, transition to turbulence, reattachment, turbulent separation take take placeplace in theinboundary layer. layer. These phenomena cannot cannot be captured by fully and turbulent separation the boundary These phenomena be captured turbulent models,models, even though the turbulent kinetic energy production could be be limited by fully turbulent even though the turbulent kinetic energy production could limitedbybya adamping dampingfunction. function. The performance curvefor forthe theSP SPand and SI30 SI30 configurations configurationsobtained obtainedwith withboth bothturbulence turbulencemodels models The performance curve areshown shownin inFigure Figure14. 14.For For the the SP SP and and the the SI30 SI30 inclined inclined configurations, configurations,the theaverage averagepower powercoefficient coefficient are estimatedwith withthe theSST SSTTransition Transitionmodel modelwas wasincremented incrementedregarding regardingthe theSST SSTstandard. standard.The Thesame samefact fact estimated was found previously in the case of vertical axis water turbines [26,27]. However, for the SP turbine, was found previously in the case of vertical axis water turbines [26,27]. However, for the SP turbine, thedifference differencebetween betweenthe thepredictions predictionsof ofboth bothturbulence turbulencemodels modelsincrease increaseas asthe thetip tipspeed speedratio ratiogrows grows the and,for forthe thelargest largestvalue valueconsidered considered = 6.7), it about is about 40%. This behavior found previously and, (λ(λ = 6.7), it is 40%. This behavior waswas found previously by by Reference [27] in a vertical axis tidal turbine with even larger differences in the 𝐶 values obtained Reference [27] in a vertical axis tidal turbine with even larger differences in the CP values obtained with withturbulence both turbulence the SP2 configuration, on hand, the other hand, the in differences in both models.models. For the For SP2 configuration, on the other the differences predictions predictions between both turbulent models decrease as the tip speed ratio increases, with the highest between both turbulent models decrease as the tip speed ratio increases, with the highest difference difference about 15% being aboutbeing 15% obtained forobtained λ = 3.8. for λ = 3.8.

Figure The power power coefficient coefficientversus versustip tipspeed speedratio ratiofor forthe the two evaluated turbulence models. Figure 14. 14. The two evaluated turbulence models. SP SP and SI30 configurations. and SI30 configurations.

Although coefficients with thethe turbulence model is similar to Althoughnot notshown, shown,the thebehavior behaviorofofthe theforce force coefficients with turbulence model is similar that of the power coefficients: the transitional version provides higher values than the standard SST. to that of the power coefficients: the transitional version provides higher values than the standard Therefore, it can it becan concluded that thethat transitional formulation predictspredicts that thethat transfer of energy SST. Therefore, be concluded the transitional formulation the transfer of from thefrom fluidthe to the blades improved regardingregarding the standard formulation, at least inatthe range of energy fluid to theisblades is improved the standard formulation, least in the TSRs in the present rangeconsidered of TSRs considered in thestudy. present study.

As an example to highlight the transitional behavior of the boundary layer computed with the SST Transition turbulence model, Figure 15 shows the intermittency contours on a section of the first blade (at mid-span) in the SP, SI15 and SI30 configurations at the 0° azimuthal position. In Figure 15, values close to zero (black color) indicate the laminar regime whereas values close to 1 (white color) indicate the mean turbulent boundary layer. In the contour plots flow proceeds from bottom to top.

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As an example to highlight the transitional behavior of the boundary layer computed with the SST Transition turbulence model, Figure 15 shows the intermittency contours on a section of the first blade (at mid-span) in the SP, SI15 and SI30 configurations at the 0◦ azimuthal position. In Figure 15, values close to zero (black color) indicate the laminar regime whereas values close to 1 (white color) indicate turbulent boundary layer. In the contour plots flow proceeds from bottom to 17 top. Energies the 2018,mean 11, x FOR PEER REVIEW of 23 As it is readily observed, the contour plots present noticeable differences. In the SP configuration (Figure 15a), the the intrados boundary layer develops entirelyentirely in the laminar in the extrados (Figure 15a), intrados boundary layer develops in the regime, laminarwhile regime, while in the layer, laminar-turbulent transition phenomena (the contours evolve from black to white along to extrados layer, laminar-turbulent transition happen phenomena happen (the contours evolve from black thewhite extrados surface); besides,surface); around the profile,around a laminar envelope is clearly visible (variable grey along the extrados besides, theflow profile, a laminar flow envelope is clearly intensity). Such an envelope is also present around the profile for the SI15 configuration (Figure 15b), visible (variable grey intensity). Such an envelope is also present around the profile for the SI15 butconfiguration here the boundary layer experiences laminar to turbulent transition in both surfaces (intrados and (Figure 15b), but here the boundary layer experiences laminar to turbulent transition extrados). However,(intrados for the SI30 (Figure 15c), suchSI30 a laminar flow envelope in both surfaces andconfiguration extrados). However, for the configuration (Figuredisappears, 15c), such a being turbulent the major part of thebeing flow around thefor profile; also, the transition between laminar and laminar flow for envelope disappears, turbulent the major part of the flow around the profile; turbulent is very clear for intrados and extrados.regimes Finally,isalthough not for shown, such and transitional also, theregimes transition between laminar and turbulent very clear intrados extrados. behavior changes along the blade span, a fact that illustrates the water flow complexity in the vicinity Finally, although not shown, such transitional behavior changes along the blade span, a fact that of illustrates the turbinethe blades offlow the HAHT. water complexity in the vicinity of the turbine blades of the HAHT.

(a) SP Configuration

(b) SI15 Configuration

(c) SI30 configuration

Figure The intermittency contours around first blade mid-span plane: SI15 (b), Figure 15.15. The intermittency contours around thethe first blade at at thethe mid-span plane: SPSP (a),(a), SI15 (b), and SI30 (c) configurations. The black color indicates the laminar flow. Flow progresses from bottom and SI30 (c) configurations. The black color indicates the laminar flow. Flow progresses from bottom top. to to top.

5. 5. Comparison ofof CFD Simulations with Other Sources Comparison CFD Simulations with Other Sources AsAs previously commented; the the evaluated turbine was empirically designed and tested in situ only previously commented; evaluated turbine was empirically designed and tested in situ foronly feasibility purposes, on the Cauca river in the southwest of Colombia. However, the prototype wasthe for feasibility purposes, on the Cauca river in the southwest of Colombia. However, never adequately characterized. Therefore, data on the extracted power in terms of prototype was experimentally never adequately experimentally characterized. Therefore, data on the extracted incident flow velocity or turbine angular velocity are not available. Consequently, some alternative for power in terms of incident flow velocity or turbine angular velocity are not available. Consequently, comparing the obtained CFD results to be CFD devised. some alternative for comparing thehave obtained results have to be devised. AsAs a first step, thethe CFD computations have to to bebe validated versus thethe experimental results in in thethe a first step, CFD computations have validated versus experimental results HAHT configuration. For that purpose, the experimental measurements reported in Reference [34] HAHT configuration. For that purpose, the experimental measurements reported in Reference [34] have been considered. Such experiments have been employed byby several authors to to validate different have been considered. Such experiments have been employed several authors validate different types of numerical computations, from BEM to CFD [11,34]; therefore, they constitute an appropriate types of numerical computations, from BEM to CFD [11,34]; therefore, they constitute an appropriate source forfor validating thethe CFD computations. In In thethe experiments of of Reference [34], thethe model turbine source validating CFD computations. experiments Reference [34], model turbine rotor is placed perpendicularly to to thethe main flow direction, so so itsits inclination angle γ is zero; thethe rotor rotor is placed perpendicularly main flow direction, inclination angle γ is zero; rotor diameter was 800 mm with blades based on the profile NACA 63-8XX. The considered experiments for diameter was 800 mm with blades based on the profile NACA 63-8XX. The considered experiments comparison are those to a pitch angle 0◦ and with anwith inflow of 1.4 m/s. for comparison are corresponding those corresponding to aset pitch setof angle of 0° and an velocity inflow velocity of 1.4 The additional CFD simulations consider a grid arrangement similar to that of the case of the m/s. inclinedThe rotor: the computational domain has the same dimensionssimilar as those shown in Figure additional CFD simulations consider a grid arrangement to that of the case of 2. the The boundary conditions are also the same andhas the the gridsame size isdimensions similar to that for the Aquavatio inclined rotor: the computational domain as employed those shown in Figure 2. The model comprising around million elements, also using prisms to resolvefor thethe flow in the boundary conditions areeight also the same and the grid size is12 similar to layers that employed Aquavatio boundary layer. Threearound tip speed ratios close to the pointalso of the maximum efficiency been simulated. model comprising eight million elements, using 12 prisms layershave to resolve the flow in

the boundary layer. Three tip speed ratios close to the point of the maximum efficiency have been simulated. The obtained results for the power coefficient are presented in Figure 16. In that figure, the crosses correspond to the experimental points and some other numerical simulations are also included for the purpose of comparison: the results of the commercial software GH-tidal (based on BEM) presented by Bahaj et al. [34] and the CFD results of Wu et al. [11]. Regarding the experimental

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The obtained results for the power coefficient are presented in Figure 16. In that figure, the crosses correspond to the experimental points and some other numerical simulations are also included for the purpose of comparison: the results of the commercial software GH-tidal (based on BEM) presented by Bahaj et al. [34] and the CFD results of Wu et al. [11]. Regarding the experimental data, the BEM results slightly over-predict them, while the CFD predictions of Reference [11] (based on the standard k-ε turbulence areREVIEW below the experiments, except for λ = 6. The present CFD computations Energies 2018, 11, xmodel) FOR PEER 18 of 23 based on the SST model of turbulence, provide values that are fairly close to the measurements, at least in the threeatcomputed TSR, a fact that is attributed the is better performance of theperformance SST model measurements, least in the three computed TSR, a facttothat attributed to the better regarding k-ε model in these of rotating machines The results presented Figure 15 of the SSTthemodel regarding thekinds k-ε model in these kinds[27]. of rotating machines [27].inThe results show that the employed CFD simulations are appropriate enough to be used in the computations of presented in Figure 15 show that the employed CFD simulations are appropriate enough to be used HAHTs. References [35–37] present additional examples in other Engineering applications where CFD in the computations of HAHTs. References [35–37] present additional examples in other Engineering techniques have beenCFD found to perform adequately. applications where techniques have been found to perform adequately.

Figure16. 16.The Thecomparison comparisonof ofthe theexperimental experimentalmeasurements measurementsand andCFD CFDcomputations computationsperformed performedin in Figure thiswork workon onthe theturbine turbineofofBahaj Bahajetetal. al.(2007) (2007)[34]. [34]. this

Another the results resultsobtained obtainedininthis thiswork workisisprovided provided wind turbine Another option option to to compare compare the byby thethe wind turbine ITIT-PE-100 developed by the company ITDG [20,28] because the blade design was adopted by the PE-100 developed by the company ITDG [20,28] because the blade design was adopted by the computed turbine Aquavatio. However, the hub is very different both machines; computedhydrokinetic hydrokinetic turbine Aquavatio. However, thedesign hub design is very in different in both in the river in turbine, theturbine, hub hasthe a shape of aatruncated (see Figure 1a) motivated structural machines; the river hub has shape of acone truncated cone (see Figure 1a) for motivated for reasons. This hub geometry, as already shown in Figure 10, generates a wide wake that affects the structural reasons. This hub geometry, as already shown in Figure 10, generates a wide wake that performance of the turbine. affects the performance of the turbine. The experimental power-velocity curve of the rotorrotor IT-PE-100 is available [28]. Nominal values The experimental power-velocity curve of wind the wind IT-PE-100 is available [28]. Nominal of incident velocity and angular velocity are 6.5 m/s and 420 rpm, respectively, giving a nominal tip speeda values of incident velocity and angular velocity are 6.5 m/s and 420 rpm, respectively, giving ratio of λ =tip 5.75, for the nominal m; this TSR is veryofclose to the initially nominal speed ratio of λ = diameter 5.75, for of the1.7 nominal diameter 1.7 m; thisvalue TSR considered is very close to the in this work for the hydrokinetic turbine, λ = 5.7. With the previous data, the performance curve for value considered initially in this work for the hydrokinetic turbine, λ = 5.7. With the previous data, turbine IT-PE-100 can be constructed. C vs. λ curves for both turbines are shown in Figure 17. It can be P the performance curve for turbine IT-PE-100 can be constructed. 𝐶 vs. λ curves for both turbines are seen thatinthe performance ofbe both is roughly same for λof = 5.75, is around 25% (SP configuration). shown Figure 17. It can seen that the the performance bothwhich is roughly the same for λ = 5.75, which The wind turbine presents a fairly flat C curve for the considered range of tip speed ratios, while the P is around 25% (SP configuration). The wind turbine presents a fairly flat 𝐶 curve for the considered hydrokinetic presents a clear at λturbine = 4.8 and decreasing formaximum larger and at lower values, range of tip turbine speed ratios, while the maximum hydrokinetic presents a clear λ = 4.8 and as discussed in Section 4.2. In Figure 17, the performance curves for the inclined turbines are also included decreasing for larger and lower values, as discussed in Section 4.2. In Figure 17, the performance just for comparison. From that figure, it can be seen just that,for forcomparison. the SP configuration, efficiency is curves for the inclined turbines are also included From thatthe figure, it cancurve be seen displaced towards lower values the of λefficiency than that of the IT-PE-100 rotor, which lower is obviously consequence that, for the SP configuration, curve is displaced towards valuesaof λ than thatof of the different operating conditions. However, the maximum C of both turbines is totally comparable, P the IT-PE-100 rotor, which is obviously a consequence of the different operating conditions. However, about 25–30%. Therefore, although conditions ofabout both machines their performance the maximum 𝐶 of both turbinesthe isworking totally comparable, 25–30%. differ, Therefore, although the curves areconditions similar because they share thediffer, bladetheir design and have very similar working of both machines performance curves are dimensions. similar because they share

the blade design and have very similar dimensions.

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Figure Figure 17. The of the CFD results inthe the present study versus the efficiency 17.comparison The comparison of the CFD resultsobtained obtained in present study versus the efficiency curve curve of the IT-PE-100 turbine. of the IT-PE-100 windwind turbine. The comparison third comparison carriedout outversus versus the by the software [29] The third waswas carried theresults resultsprovided provided by Qblade the Qblade software [29] which Figure is available online at www.q-blade.org. Qblade in is the a general purpose software for wind turbine 17. The comparison of the CFD results obtained present study versus the efficiency curve which is available online at www.q-blade.org. Qblade is a general purpose software for wind turbine evaluation, andturbine. vertical. It employs well established simplified methods such as the BEM of the horizontal IT-PE-100 wind evaluation, horizontal and vertical. It employs well established simplified methods such as the BEM (Blade Element Momentum) model and other vortex based models such as LLFVW (Lifting Line Free (Blade Element Momentum) model and other vortex based such as Qblade LLFVW (Lifting thirdand comparison was carried out such versus resultsmodels provided by the software [29]Line VortexThe Wake) includes extra features asthe structural and aeroelastic modules. In spite of Free whichand is available online at a general purpose software for wind turbine Vortex Wake) includes extra features such asitQblade structural and aeroelastic modules. In spite of Qblade Qblade being developed forwww.q-blade.org. wind turbines, allowsisus to modify the physical properties of the evaluation, horizontal and vertical. It employs well established simplified methods such theworking BEM working fluid so it is applicable to evaluate hydrokinetic turbines. Here, properties the results obtained by the fluid being developed for wind turbines, it allows us to modify the physical of as the (Blade Momentum) and other based models as configuration LLFVW (Lifting Line Free BEM andElement LLFVW methods aremodel compared withvortex the Here, CFD results for such the obtained SP Figure 18.LLFVW so it is applicable to evaluate hydrokinetic turbines. the results by the in BEM and Vortex Wake) and includes extra features such as structural and aeroelastic modules. In spite of From Figure 18 it is obvious that the simplified models provide substantially higher power methodsQblade are compared with the results forit the SP us configuration Figureproperties 18. being forCFD wind allows modify thein physical of the coefficients thandeveloped those obtained with turbines, CFD. This assertion isto true for both methods, BEM and LLFVW, From Figure 18 it is obvious that the simplified models provide substantially higher working fluid so it is applicable to evaluate hydrokinetic turbines. Here, the results obtained by the power even including the Prandtl tip and root losses. It is interesting to remark that the LLFVW method, BEM and LLFVW methods are compared with the CFD results for the SP configuration in Figure 18. LLFVW, coefficients those with CFD. This assertion is true for both methods, BEM results and whichthan is one of theobtained most sophisticated techniques among the simplified approaches, provides From Figure 18 it is obvious that the simplified models provide substantially higher power even including Prandtl tipBEM. andThe root losses. Itbetween is interesting to remark LLFVW method, very close the to those of the differences such predictions andthat thosethe obtained with coefficients than those obtained with CFD. This assertion is true for both methods, BEM and LLFVW, CFD as follows: ontechniques the one hand, it is known that BEM tends to overestimate the results which is onecan of be theexplained most sophisticated among the simplified approaches, provides even including the Prandtl tip and root losses. It is interesting to remark that the LLFVW method, power coefficient, specifically high solidity turbines and,predictions on the otherand hand, in the simplified very close to those BEM.sophisticated Thefor differences between those obtained with CFD which is oneof ofthe the most techniques amongsuch the simplified approaches, provides results methods the hub is not taken into account in the computation. It has been already remarked that the can be explained follows: onBEM. the one hand, it isbetween knownsuch thatpredictions BEM tends overestimate the power very close as to those of the The differences andto those obtained with truncated cone shape of the hub produces a broad wake responsible for augmenting the thrust and CFD can be explained as follows: onturbines the one hand, is known thathand, BEM tends to simplified overestimatemethods the coefficient, specifically for high solidity and,iton the other in the the drag forces on the rotor, consequently reducing the turbine performance. power coefficient, specifically for high solidity turbines and, on the other hand, in the simplified hub is not taken into account in the computation. It has been already remarked that the truncated cone methods the hub is not taken into account in the computation. It has been already remarked that the shape of the hub produces a broad wake responsible for augmenting the thrust and drag forces on the truncated cone shape of the hub produces a broad wake responsible for augmenting the thrust and rotor, consequently the turbine reducing performance. drag forces onreducing the rotor, consequently the turbine performance.

Figure 18. The comparison of the CFD results obtained in the present work versus those provided by BEM and LLFVM implemented in the Qblade software. The results computed by the SST Transition turbulence model are also included for reference.

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Figure 18. The comparison of the CFD results obtained in the present work versus those provided by BEM and LLFVM implemented in the Qblade software. The results computed by the SST Transition Energies 2018, 11, 3151 20 of 23 turbulence model are also included for reference.

Additionally, as as aa reference, reference, Figure Figure 18 18 includes includes the the results results computed computed with with the the SST SST Transition Transition Additionally, turbulence model, model, which which are are also also well well below below the the simplified simplifiedmethod’s method’spredictions. predictions. turbulence As aa final final comparison, comparison, the the experimental experimental results results of of Reference Reference[18] [18]have havebeen beenconsidered. considered. Al Al As Mamun [18] [18]conducted conducted an experimental of the performance a small three-bladed Mamun an experimental study study of the performance of a small of three-bladed hydrokinetic hydrokinetic turbine in aworking water channel with an γ inclination anglediameter γ = 45. The turbine in a water channel with anworking inclination angle = 45. The rotor wasrotor small,diameter 0.223 m, was small, 0.223 m, and the blade was based on the NACA 4412 profile. The rotation angular velocity and the blade was based on the NACA 4412 profile. The rotation angular velocity was about 120 rpm. wasexperimental about 120 rpm. The are experimental results are summarized in Appendix of Reference [18] and The results summarized in Appendix G of Reference [18] andGthose corresponding to those corresponding to an incident velocity of 0.65 m/s are presented in Figure 19 compared with the an incident velocity of 0.65 m/s are presented in Figure 19 compared with the CFD computations of the CFD computations of the present study. present study.

Figure Figure 19. 19. The comparison of the CFD CFD computation computation of the the present present study study versus versus the the experimental experimental ◦ measurements measurements of of Reference Reference[19] [19]in inaa45 45° inclined inclined rotor rotor with with the the incident incident flow flowvelocity velocityof of0.65 0.65m/s. m/s.

Although Although the the tip tip speed speed ratio ratio ranges ranges between between both both turbines turbines are are different, different, the the maximum maximum values values of of the areare comparable for the 0 (seeof Figure 19).Figure For λ