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 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,
4,
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, 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 the lift to drag ratio should be kept high. In particular, Lee et al. [
17] introduced a new blade design for horizontal water rotors that 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 delaying cavitation without degrading the turbine efficiency.
The present contribution deals with the performance estimation of small HAHT’s of Garman type using CFD. The arrangement of such turbines can be appreciated in
Figure 1b: the turbine is assembled in a floating structure on a channel or river operating with its axis inclined regarding the flow direction. As it was mentioned, the main use of this kind of turbines is to provide electricity to isolated communities so their design has been essentially empirical and only a few experimental 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 flow direction. Experiments were conducted for three incoming speeds and two pitching angles aimed to analyze the turbine performance versus tip speed ratio. As a result, a power coefficient of around 30% was reached. However, no reports about the CFD analysis of inclined HAHT’s have been found in the literature. Therefore, the authors believe that, to the best of their knowledge, this is the first time in which the CFD simulation of the hydrodynamic behavior of a HAHT which operates with an inclined axis respect to the main stream is attempted.
This paper is structured in the following way. After the introduction, the considered geometrical configurations and the meshing process are described in
Section 1. The numerical simulation methodology and the key parameters governing the operation of HAHT’s are summarized in
Section 2. The obtained results for the non-dimensional turbine coefficients are presented in
Section 3 which are organized in several subsections: their behavior along a turbine revolution is described first and later the analysis is extended to build the respective curves versus tip speed ratio; moreover, the effects of including the modeling of the transitional behavior of the boundary layer on turbine performance are discussed in
Section 4.3. Comparison of the computed CFD results with available experimental data and those obtained with more simplified models is performed in
Section 4; also, in this section, a comparison of additional CFD results with the experimental data in another horizontal axis tidal turbine is performed. Finally, the last section draws the main conclusions and perspectives.
2. Geometrical Configuration and Mesh Generation
The numerically evaluated horizontal axis hydrokinetic turbine in this study has been an existing machine called Aquavatio. Such a HAHT was empirically built, adopting a previous Garman turbine design. Such a machine was operating “in 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.
Figure 1a shows the geometry of the HAHT schematically and illustrates its real operation configuration while
Figure 1b presents the generated geometrical model of the turbine in isometric view; here, the stream direction follows the ‘z’ direction, ‘y’ represents the vertical and ‘x’ the lateral coordinate.
In the present study, three configurations have been analyzed: a first assembly where the rotor is placed perpendicular to the incoming velocity so that the turbine axis is parallel to the flow direction (SP configuration), and two inclined arrangements where the axis makes an angle
γ of 15° (SI15 configuration) and 30° (SI30 configuration) regarding the free surface, respectively (see
Figure 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 angle on machine performance as well as on the forces acting on the turbine.
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 turbine operates in almost isolated conditions, as the resulting blockage ratio is lower than 5%. Moreover, the computational domain is divided into two sub-domains: an inner rotating domain of cylindrical shape, which includes the turbine rotor (blades and hub), and an outer steady domain encompassing the water environment. In the cases of inclined configurations, the shaft was included in this domain, but not in the parallel to flow configuration. To represent the physical rotational motion of the blades, the cylindrical domain rotates with a prescribed angular velocity with respect to the steady domain, which numerically is realized by a sliding mesh technique implemented in the commercial software employed (Fluent v. 14.0, ANSYS, Inc., Canonsburg, PA, USA).
The employed boundary conditions can be appreciated in
Figure 2a,b. As indicated in
Figure 2b, the left side is specified as a velocity inlet with a constant velocity (equal to 1.0 m/s in this study), the right face is set as a pressure outlet (0 Pa), the bottom boundary (channel bed) consists on a steady 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 connected with the outer domain though interfaces specified as the sliding mesh boundary condition. Moreover, because the turbulence levels at the inlet were not known, it was decided to 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 ANSYS ICEM-CFD software (v. 14.0, ANSYS, Inc., Canonsburg, PA, USA).
Figure 3a presents a perspective of the employed mesh where the darkest area corresponds to the rotating sub-domain. To adequately describe the boundary layer development, the grid closest to the blades must be fine enough; as an illustration,
Figure 3b shows the surface mesh employed in the blades and the hub, which is pretty uniform. Consequently, the mesh around the blade has an O-grid topology with twelve prism layers. Outside the prisms region, a tetras based non-structured grid was constructed, taking care that their aspect ratio is similar to that of the prisms with the purpose of guaranteeing a smooth transition between both mesh regions. Finally, the grid density is higher downstream than upstream the rotor due to the complexity of the flow in the turbine wake. The quality parameters of the meshes have been checked with the tools available in ANSYS ICEM-CFD and are listed in
Table 1.
3. Numerical Simulation Methodology
The transient flow 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 counterclockwise (see
Figure 4) with a prescribed angular velocity; in this way, the development of the flow field at each time step is described. The interface position between the rotating inner and steady outer sub-domains is actualized every time step allowing for a conservative flux interchange between them. The Shear Stress Transport (SST) model was adopted to describe the turbulent features of the flow. In this study the standard version of such model [
21,
22] was mainly employed, however, the transition version [
23] was also tested. It is well known that the SST model improves the predictions of other two-equation turbulence models in flow configurations where strong adverse pressure gradients occur, such as those happening around a HAHT, and it has been widely used in the simulation of hydraulic turbines [
24,
25,
26,
27,
28,
29,
30,
31,
32,
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 the SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) approach. Computations were performed for an incident velocity m/s with different angular velocities, depending on the tip speed ratio (see Equation (1) below). The employed time step corresponds to a turbine rotation of around 1°, was chosen after a sensitivity analysis which represents a trade-off between computational cost and accuracy. Moreover, a maximum number of 200 iterations was specified at each time step using a residual convergence criterion of 10−5.
Simulations are started by computing the flow around the HAHT using the steady MFR model of ANSYS-Fluent software (v. 14.0, ANSYS, Inc., Canonsburg, PA, USA), which is used as an initial condition for the transient computation. The unsteady computation is launched, initially using schemes of the first order during approximately ten turbine revolutions to get the flow developed. When the torque has settled down, i.e., the torque curve shows a quasi-periodic behavior, the discretization schemes of the advective terms are changed to second order, firstly for the continuity and momentum equations and later also for the turbulent variables equations. Finally, the simulation was run until the averaged torque difference between two successive turns was below 0.2% [
24]. In the present study, for each computed case, at least twenty rotor revolutions have been simulated.
A spatial verification study was performed for the rotor with the shaft parallel to the flow direction (SP configuration). The evaluated operating point was the nominal condition of the wind rotor IT-PE-100 because the same blade design was used for both machines and it corresponds to a tip speed ratio λ = 5.7 (see Equation (1) below) using a rotor angular velocity of 60 rpm. For this grid independence study, the sampled variable was chosen to be the power coefficient CP (see Equation (3) below). According to the usual procedure, three meshes with an increasing number of cells were considered: a coarse grid with elements, an intermediate mesh with , elements and a refined grid with elements. The obtained averaged power coefficients have been the following: 0.2383 (coarse), 0.2430 (intermediate) and 0.2410 (refined). As the difference in is 0.8% between the medium and fine meshes, the intermediate grid was employed in the computations allowing us to maintain an affordable computational time. Based on this result, representing a compromise between the computational cost and accuracy, it was decided to mesh the inclined configurations with a similar distribution and number of elements than the SP case. In those cases, the employed number of elements in the meshes has been elements (SI15 configuration) and elements (SI30 configuration).
The following non-dimensional parameters govern the behavior of the HAHT: the tip speed ratio or TSR (
) is the non-dimensional angular velocity regarding the incoming velocity,
:
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,
; it is written as:
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 is obtained as the product of the torque coefficient
and the tip speed ratio
. Therefore, the operating point of the turbine is defined by the pair
.
The total hydrodynamic force
acting on each blade is projected on the directions perpendicular to the rotation plane, or normal force
, and parallel to it, or tangential force
. 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
.
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,
, and in a component in the vertical plane perpendicular to such velocity which constitutes the lift force,
. Coefficients associated with such forces are written as:
5. Comparison of CFD Simulations with Other Sources
As previously commented; the evaluated turbine was empirically designed and tested in situ only for feasibility purposes, on the Cauca river in the southwest of Colombia. However, the prototype was never adequately experimentally characterized. Therefore, data on the extracted power in terms of incident flow velocity or turbine angular velocity are not available. Consequently, some alternative for comparing the obtained CFD results have to be devised.
As a first step, the CFD computations have to be validated versus the experimental results in the HAHT configuration. For that purpose, the experimental measurements reported in Reference [
34] have been considered. Such experiments have been employed by several authors to validate different types of numerical computations, from BEM to CFD [
11,
34]; therefore, they constitute an appropriate source for validating the CFD computations. In the experiments of Reference [
34], the model turbine rotor is placed perpendicularly to the main flow direction, so its inclination angle
γ is zero; the rotor diameter was 800 mm with blades based on the profile NACA 63-8XX. The considered experiments for comparison are those corresponding to a pitch set angle of 0° and with an inflow velocity of 1.4 m/s.
The additional CFD simulations consider a grid arrangement similar to that of the case of the inclined rotor: the computational domain has the same dimensions as those shown in
Figure 2. The boundary conditions are also the same and the grid size is similar to that employed for the Aquavatio model comprising around eight million elements, also using 12 prisms layers 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 data, the BEM results slightly over-predict them, while the CFD predictions of Reference [
11] (based on the standard
k-
ε turbulence model) are below the experiments, except for
λ = 6. The present CFD computations based on the SST model of turbulence, provide values that are fairly close to the measurements, at least in the three computed TSR, a fact that is attributed to the better performance of the SST model regarding the
k-
ε model in these kinds of rotating machines [
27]. The results presented in
Figure 15 show that the employed CFD simulations are appropriate enough to be used in the computations of HAHTs. References [
35,
36,
37] present additional examples in other Engineering applications where CFD techniques have been found to perform adequately.
Another option to compare the results obtained in this work is provided by the wind turbine IT-PE-100 developed by the company ITDG [
20,
28] because the blade design was adopted by the computed hydrokinetic turbine Aquavatio. However, the hub design is very different in both machines; in the river turbine, the hub has a shape of a truncated cone (see
Figure 1a) motivated for structural reasons. This hub geometry, as already shown in
Figure 10, generates a wide wake that affects the performance of the turbine.
The experimental power-velocity curve of the wind rotor IT-PE-100 is available [
28]. Nominal values of incident velocity and angular velocity are 6.5 m/s and 420 rpm, respectively, giving a nominal tip speed ratio of
λ = 5.75, for the nominal diameter of 1.7 m; this TSR is very close to the value considered initially in this work for the hydrokinetic turbine,
λ = 5.7. With the previous data, the performance curve for turbine IT-PE-100 can be constructed.
vs.
λ curves for both turbines are shown in
Figure 17. It can be seen that the performance of both is roughly the same for
λ = 5.75, which is around 25% (SP configuration). The wind turbine presents a fairly flat
curve for the considered range of tip speed ratios, while the hydrokinetic turbine presents a clear maximum at
λ = 4.8 and decreasing for larger and lower values, as discussed in
Section 4.2. In
Figure 17, the performance curves for the inclined turbines are also included just for comparison. From that figure, it can be seen that, for the SP configuration, the efficiency curve is displaced towards lower values of
λ than that of the IT-PE-100 rotor, which is obviously a consequence of the different operating conditions. However, the maximum
of both turbines is totally comparable, about 25–30%. Therefore, although the working conditions of both machines differ, their performance curves are similar because they share the blade design and have very similar dimensions.
The third comparison was carried out versus the results provided by the Qblade software [
29] which is available online at
www.q-blade.org. Qblade is a general purpose software for wind turbine 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 Vortex Wake) and includes extra features such as structural and aeroelastic modules. In spite of Qblade being developed for wind turbines, it allows us to modify the physical properties of the working fluid so it is applicable to evaluate hydrokinetic turbines. Here, the results obtained by the BEM and LLFVW methods are compared with the CFD results for the SP configuration in
Figure 18.
From
Figure 18 it is obvious that the simplified models provide substantially higher power coefficients than those obtained with CFD. This assertion is true for both methods, BEM and LLFVW, even including the Prandtl tip and root losses. It is interesting to remark that the LLFVW method, which is one of the most sophisticated techniques among the simplified approaches, provides results very close to those of the BEM. The differences between such predictions and those obtained with CFD can be explained as follows: on the one hand, it is known that BEM tends to overestimate the power coefficient, specifically for high solidity turbines and, on the other hand, in the simplified methods the hub is not taken into account in the computation. It has been already remarked that the truncated cone shape of the hub produces a broad wake responsible for augmenting the thrust and drag forces on the rotor, consequently reducing the turbine performance.
Additionally, as a reference,
Figure 18 includes the results computed with the SST Transition turbulence model, which are also well below the simplified method’s predictions.
As a final comparison, the experimental results of Reference [
18] have been considered. Al Mamun [
18] conducted an experimental study of the performance of a small three-bladed hydrokinetic turbine in a water channel working with an inclination angle
γ = 45. The rotor diameter was small, 0.223 m, and the blade was based on the NACA 4412 profile. The rotation angular velocity was about 120 rpm. The experimental results are summarized in Appendix G of Reference [
18] and those corresponding to an incident velocity of 0.65 m/s are presented in
Figure 19 compared with the CFD computations of the present study.
Although the tip speed ratio ranges between both turbines are different, the maximum values of the power coefficient are comparable for the pitch angle of 0 (see
Figure 19). For
λ < 4, the experimental power coefficient of Reference [
18] dropped drastically, so the range of TSRs for which the turbine was able to produce power is much reduced than for the turbine simulated in this work. Al Mamun [
18] found that when the blade was installed with a pitch angle of 5°,
increased for the particular value of the employed incident velocity. Moreover, if the incoming flow speed was also reduced, the maximum value of
decreased and it was displaced toward lower values of the tip speed ratio.
In summary, although a proper validation of the performed CFD simulations has not been possible due to the absence of experimental measurements in the HAHT studied, comparisons with experimental measurements in similar systems and with the results provided by more simplified methods indicate that the obtained numerical results are consistent and plausible. They provide the expected trends for the influence of turbine inclination on its performance, allowing us to quantitatively estimate the reduction of efficiency and thrust coefficient on the rotor when its operation slant angle increases.