Keywords

1 Introduction

More than 5000 years ago, in the Mediterranean region, has been documented that it was probably the first device that used the wind force: the sailing ships (Singer et al. 1954, 1956). Another mechanism that deserves mention is the windmill, which had its first mention around 400 B.C. and uses the kinetic energy of the wind to rotate a shaft in order to pump water or grind grains (Freese 1957).

However, these devices already captured the energy present in the winds, and the term wind turbine was not yet used. This nomenclature was only applied after the Scotsman James Blyth in 1887 built a device that extracted energy from the winds with the objective of generating electrical energy, storing it in accumulators, and using it to light lamps (Sørensen 2016). Blyth’s wind turbine was improved with metallic materials in the structure and blades (Price 2005), whose better and bigger version was installed on the Montrose Lunatic Asylum (UoE 2018).

The 1930s in the United States, wind turbines produced by Jacobs Wind Electric Company were used to supply electricity to farms and to charge batteries. Later they fell into disuse because the energy generated by fuel has become economically more advantageous (Sørensen 2016).

Some decades ago, there was a new change in this concept (Luguang and Li 1997; Erdinc and Uzunoglu 2012). Many works aim to supply the need to find new sources of energy and to improve the efficiency of the existing ones, since the energy generation using only fossil fuels will not supply the global demand and its burning produces undesirable gases (greenhouse effect) (Ferreira et al. 2018; Jacobson et al. 2018). These characteristics of fossil fuels motivate studies to focus on clean and renewable energy sources. It is important to note that renewable energy is that generated from resources that are naturally replenished in a shorter period than the human life (Frewin 2020). Examples of renewable energy sources include sunlight, wind, biomass, and water currents (rivers, lakes, and ocean (Ng et al. 2013). As an example, it is estimated that the global tidal energy capacity is around 570 TWh/yr (Behrens et al. 2012). These sources can be exploited in different ways to extract their energy. Examples are the different wind turbine models, such as the horizontal axis wind turbines (HAWT) and vertical-axis wind turbines (VAWT).

The basic principle of wind turbines is the friction generated between the blades and air molecules that pass around them. Currently, the blades have aerodynamic profiles. Thus, when there is a flow, an aerodynamic force is generated that can be decomposed, in relation to the flow direction, in the parallel (drag) and perpendicular (lift) directions, as shown in Fig. 1.

Fig. 1
A diagram begins with a right-slanted upward arrow labeled V wind that points to an aerodynamic profile with drag and lift labeled.

Forces generated in an aerodynamic profile. (Branlard 2017)—adapted

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Wind and current turbines are very similar because both convert the kinetic energy present in a fluid into electricity (Rahimian et al. 2017; Seng et al. 2009). Although they are quite similar and much of what has already been developed for a wind turbine can be applied to the current turbine, it is important and necessary to specifically study each type of turbine (Walker et al. 2014). It is essential to assess the performance of energy generation mechanisms for their development and improvement. In the case of these turbines, this assessment is usually modeled by means of computational fluid dynamics (CFD) or blade element momentum theory (BEM). CFD provides a greater level of detail of the interaction between the fluid (water, air) and the structure (turbine) which allows a more meticulous analysis, but involves a higher computational cost that has been mitigated with the computers progress (Rahimian et al. 2017; Noruzi et al. 2015; Hall 2012). On the other hand, BEM’s main characteristic is that it is simpler to implement and use when compared to CFD (Sørensen 2016). This methodology is also suitable for wind and current turbines (Bedon et al. 2013; Baltazar and Campos 2011).

In any simulation, it is essential to reproduce what happens in practice. All details present in the CFD will only be valid if appropriate numerical techniques are applied. The same is valid for BEM, since one of the data required for the application of the technique is the curves of litf (\({C}_{L}\)) and drag (\({C}_{D}\)) coefficients as a function of the angle of attack (\(\alpha\)). Such curves can be obtained experimentally or by CFD, and the simulation is generally the cheapest option. The choice of an appropriate turbulence model for the conditions to be simulated is essential to obtain good results.

In this study, some turbulence models have been selected to simulate of airfoil with NACA 63-618 cross section in order to determine the curves: \({C}_{L}\times \alpha\) and \({C}_{D}\times \alpha\). The results were compared with experimental data in the literature.

2 Methodology

The airfoil profile used in the simulations was a NACA 63-618, shown in Fig. 2. With this profile, the authors Walker et al. (2014) built and performed experimental tests on a turbine that is a 1:25 scale representation of the SeaGen turbine, justifying the role of this profile. The aerofoil coordinates were obtained from AirfoilTools (2020) and are presented in Fig. 3a. Figure 3b shows that for the leading and trailing edge regions more points were generated, as they are regions with more complex geometry and that could affect the mesh design and consequently the simulation results. The first point on the leading edge is placed at \(x=0\) and \(y=0\).

Fig. 2
2 graphs display the air profile in N A C A 63 618. A is the cross-section. B is the points generated.

NACA 63-618

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Fig. 3
A. A schematic representation has an inlet and outlet. B. An overview of the mesh. C. The airfoil region.

Two-dimensional mesh for NACA 63-618

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The two-dimensional mesh was generated in ICEM CFD 16.0. Its shape and all dimensions, which are based on the chord length (C) of the airfoil, are shown in Fig. 3a. It is worth noting that only the vertical line downstream of the airfoil was defined as outlet (pressure outlet), and all others were defined as inlet (velocity inlet). The airfoil chord is \(C=0.23\,\text{m}\) and the simulations were performed considering air as fluid (\(\rho =1.225\, \mathrm{kg}/{\mathrm{m}}^{3}\)) with a Reynolds number of \(R{e}_{c}=5.3\times 1{0}^{5}\) in order to match the experiment of Walker et al. (2014). The mesh, shown in Fig. 3b, c, was developed with \({y}^{+}=1\) and has a total of \(\mathrm{76,725}\) elements. This number of elements provided mesh-independent results.

The main objective of the present study is to compute both lift and drag coefficients by varying the angles of attack from \(-{5}^{\circ}<\alpha <1{5}^{\circ}\). For all the angles of attack, the freestream velocity \({U}_{0}=34.56522\, \mathrm{m}/\mathrm{s}\) was decomposed according to \(\alpha\) instead of changing the position of the airfoil in the mesh (Stephens et al. 2017), as shown in Fig. 3a. The velocity components for each angle of attack are presented in Table 1.

Table 1 Velocity components as a function of angle of attack
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The simulations were performed using the Fluent 16.0 and the UNSCYFL3D code (Souza et al. 2012; Pereira et al. 2014). The forces \({F}_{x}\) and \({F}_{y}\) were oriented according to the coordinate axes shown in Fig. 3a. Therefore, to obtain drag and lift forces, we decomposed them to the parallel and perpendicular directions in relation to the flow direction, as shown in Fig. 1, applying the following expressions:

$${F}_{Drag}={F}_{y}\mathrm{sin}(\alpha )+{F}_{x}\mathrm{cos}(\alpha )$$
(1)
$${F}_{Lift}={F}_{y}\mathrm{cos}(\alpha )-{F}_{x}\mathrm{sin}(\alpha )$$
(2)

Once the drag and lift forces are obtained, the coefficients can then be calculated:

$${C}_{D}=\frac{{F}_{Drag}}{(0.5 \rho {V}_{0}^{2} C s)}$$
(3)
$${C}_{L}=\frac{{F}_{Lift}}{(0.5 \rho {V}_{0}^{2} C s)}$$
(4)

Since the model is two dimensional, the blade span (s) must be considered equal to the unit.

3 Results

In order to obtain the values of \({C}_{L}\) and \({C}_{D}\) for the NACA 63-618 profile with different angles of attack and \(R{e}_{c}=5.3\times 1{0}^{5}\), simulations were carried out in Fluent 16.0 software and USNCYFL3D code in steady-state and performing 5000 iterations. The angle of attack was varied by modifying the velocity components, as shown in Table 1. Note that for the same case, the results of the software and the code did not present a significant difference.

An important factor, which is the central point of discussion of this work, is the different turbulence models that can be applied in the simulations. In the present study, for \(\alpha ={5}^{\circ}\) the conventional turbulence RANS (Reynolds Averaged Navier–Stokes) models were applied: k-\(\epsilon\), optimized k-\(\epsilon\), SST-DES (detached eddy simulation based on shear stress transport), and RSM (Reynolds stress model). However, none of them presented results in accordance with the literature: experiment \(R{e}_{c}=5.3\times 1{0}^{5}\)(Walker et al. 2014) and XFoil - \(R{e}_{c}=6\times 1{0}^{6}\) (Drela and Youngren 2006), as presented in Fig. 4. In some cases 15,000 iterations were also performed and the result for the RSM was not presented because it distorts the graph. Although the value of the Reynolds number for XFoil is higher, its results are valid for comparison, since \({C}_{L}\) is independent of \(R{e}_{c}\) and \({C}_{D}\) becomes independent when \(R{e}_{c}\ge 5\times 1{0}^{5}\) (Walker et al. 2014).

Fig. 4
A. A dot plot of the lift coefficient versus the angle of attack. B. A dot plot of the drag coefficient versus the angle of attack.

Lift and drag coefficients applying different turbulence models (NACA 63-618, \(\alpha ={5}^{\circ}\) and \(R{e}_{c}=5.3\times 1{0}^{5}\))

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Studying a NACA 64-618 profile with \(R{e}_{c}=6\times 1{0}^{6}\), whose profile is very similar to that considered in this study, Han et al. (2018) compared the results of its simulations with different turbulence models and those experimentally obtained by Abbott et al. (1945), as shown in Fig. 5. The authors noted that the results for the drag coefficient with completely turbulent models show significantly high errors. The SST k-\(\omega\) transition model presents a good approximation with the wind tunnel data for most angles of attack and, consequently, was the turbulence model applied in the simulations, and the turbulent intensity was set as 0.01%.

Fig. 5
A connected dot plot of the lift drag versus angle of attack. The lines follow an upward trend, stable region, followed by a downward trend.

Lift–drag ratios in various turbulence models for NACA 64–618 and \(R{e}_{c}=6\times 1{0}^{6}\). (Han et al. 2018)—adapted

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Therefore, NACA 63-618 profile was performed in Fluent 16.0 for \(\alpha ={5}^{\circ}\) and \(R{e}_{c}=5.3\times 1{0}^{5}\) using the Transition SST turbulence model and turbulent intensity equal to 0.01%. The coefficients \({C}_{L}\) and \({C}_{D}\) obtained were closer to the references, as shown in Fig. 4a, b, respectively (filled blue circle). In addition, the lift-drag ratio for this angle was also very close to the value obtained by Han et al. (2018), as presented in Fig. 5 (blue star).

Based on the difference in heat transfer coefficients by convection of laminar and turbulent flows, Ehrmann and White (2015) applied infrared thermography to determine the position of laminar-turbulent transition in a NACA 63–418 profile, also very close to NACA 63-618, with \(R{e}_{c}\) ranging from \(0.8\times 1{0}^{6}\) to \(4.8\times 1{0}^{6}\). Figure 6 presents one of the results obtained by the authors, proving a laminar-turbulent transition on the airfoil. This laminar flow that occurs on NACA 6-series sections is one of the motivations for using them in turbines (Tangler and Somers 1995).

Fig. 6
A graph of spanwise versus x forward-slash c in percentage. There is a vertical zigzag line plotted.

Red: transition front. Green: Mean (solid) and bound (dashed) locations. (Ehrmann and White, 2015)—adapted

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Finally, Fig. 7 presents the results obtained for the other angles of attack: \(-{5}^{\circ},{0}^{\circ},1{0}^{\circ}\) and \(1{5}^{\circ}\), using Fluent 16.0 and applying the Transition SST turbulence model and turbulent intensity equal to 0.01%. The results are very close to references. For \(\alpha =1{5}^{\circ}\) the \({C}_{L}\) obtained was closer to the experimental than XFoil. The \({C}_{D}\) is larger than the XFoil and there is no experimental data for this angle. However, Walker et al. (2014) show for \(R{e}_{c}=4.2\times 1{0}^{5}\) and \(\alpha \approx 1{2}^{\circ}\) and \(1{3}^{\circ}\) larger values of \({C}_{D}\) than those obtained using XFoil, suggesting that the result obtained is coherent.

Fig. 7
A. A dot plot of lift coefficient versus angle of attack. An increasing curve becomes stable. B. A dot plot of drag coefficient versus angle of attack. A stable curve rises at the end.

Lift and drag coefficients as a function of the angle of attack for NACA 63-618, \(R{e}_{c}=5.3\times 1{0}^{5}\)

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4 Conclusion

The curves of lift and drag coefficients as a function of the angle of attack for an airfoil with NACA 63-618 cross section in the considered conditions were obtained and are in agreement with experimental values and other simulations. This result was obtained only when the Transition SST turbulence model was applied, being that the most remarkable point. Therefore, it is evident that in these conditions there is a laminar-transient transition on the airfoil.

Other studies carried out with 6-series sections also show this transition and that the use of completely turbulent models generates errors in the estimates related to the drag. As already discussed, results extracted from the CFD models will only be valid if numerical techniques are properly applied, being the turbulence model one of these techniques. Therefore, the importance of the analysis and choice of the turbulence model to be used in the simulations is highlighted, based on comparisons with experiments and simulations performed with the same or similar geometries.