energies

Article Optimization of a Small Wind Turbine for a Rural Area: A Case Study of Deniliquin, New South Wales, Australia

Nour Khlaifat, Ali Altaee * , John Zhou, Yuhan Huang and Ali Braytee

Centre of Green Technology, University of Technology Sydney, Ultimo 2007, Australia; [email protected] (N.K.); [email protected] (J.Z.); [email protected] (Y.H.); [email protected] (A.B.) * Correspondence: [email protected]; Tel.: +61-295-142-025



Received: 22 March 2020; Accepted: 25 April 2020; Published: 6 May 2020


Abstract: The performance of a wind turbine is affected by wind conditions and blade shape. This study aimed to optimize the performance of a 20 kW horizontal-axis wind turbine (HAWT) under local wind conditions at Deniliquin, New South Wales, Australia. Ansys Fluent (version 18.2, Canonsburg, PA, USA) was used to investigate the aerodynamic performance of the HAWT. The effects of four Reynolds-averaged Navier–Stokes turbulence models on predicting the flows under separation condition were examined. The transition SST model had the best agreement with the NREL CER data. Then, the aerodynamic shape of the rotor was optimized to maximize the annual energy production (AEP) in the Deniliquin region. Statistical wind analysis was applied to define the Weibull function and scale parameters which were 2.096 and 5.042 m/s, respectively. The HARP_Opt (National Renewable Energy Laboratory, Golden, CO, USA) was enhanced with design variables concerning the shape of the blade, rated rotational speed, and pitch angle. The pitch angle remained at 0◦ while the rising wind speed improved rotor speed to 148.4482 rpm at rated speed. This optimization improved the AEP rate by 9.068% when compared to the original NREL design.

Keywords: horizontal-axis wind turbine (HAWT); optimization; computational fluid dynamics (CFD); aerodynamic; genetic algorithm

1. Introduction Energy demands are increasing worldwide and exponentially, given the rising population and needs for economic growth [1]. Consumption of energy is expected to increase by 56% from 553 quadrillion kJ to 855 quadrillion kJ for the period 2010 to 2040 [2]. The extensive consumption of fossil fuels is the primary source of CO2 emissions into the atmosphere, which is estimated to increase from 31 to 36 billion metric tons during 2010–2020 and may reach 45 billion metric tons by 2040 [3]. The demand for what is termed “clean energy” has increased enormously in recent years due to the fact of people’s environmental awareness, desire for energy security, and governments enacting increasingly strict environmental policies [4]. Of all the renewable energy sources, wind energy seems to be favored due to the fact of its low price and rapid global development [5]. The global power installation from wind energy rose from 296,581 MW in 2013 to 539,291 MW in 2017, and it is predicted to reach 817 GW by 2021 [3]. Location has a significant effect on the power output of wind turbines. Accounting for environmental conditions when designing the HWAT for a specific area or region could improve the power output. Many researchers have optimized the rotor shape of wind turbines to maximize the annual energy output. Optimization of the wind turbine blade shape was undertaken at Gökçeada [6]

Energies 2020, 13, 2292; doi:10.3390/en13092292 www.mdpi.com/journal/energies Energies 2020, 13, 2292 2 of 26 in Turkey using different blade design parameters, i.e., twist angle and chord length. The results showed that the highest AEP of 92,972 kW-hr was comparable to the combined experiment rotor (CER) test of the National Renewable Energy Laboratory (NREL) with the original design. Darwish et al. [7] improved the AEP for low wind speed regions by selecting, laying out, and matching the most suitable wind turbine system for a case study conducted in Iraq. Liu et al. [8] demonstrated a novel optimal blade design method for the twist angle and chord length radial profiles of a fixed-pitch, fixed-speed wind turbine which performed excellently with lower manufacturing costs. Blade element momentum (BEM) theory helped to design the rotor diameter, nominal speed ratio, and the tip speed ratio of a 300 kW HAWT based on wind speed data in Semnan, Iran [9]. Blade element momentum theory and computational fluid dynamics (CFD) are the most popular methods for estimating the performance and aerodynamic characteristics of wind turbines. Plaza et al. [10] analyzed the aerodynamic performance of a New Mexico wind turbine rotor using the k-ω SST model and compared the results with that of BEM. At low wind speeds, the BEM model achieved better results than the k-ω SST CFD model. However, at high wind speeds, BEM failed in separating the flow conditions when a detachment occurred in the blade. The inaccuracy was due to the three-dimensional effects and blade tip losses. Conversely, CFD agreed well with the experimental data over a wide range of wind speeds. The literature is abundant with various CFD computation models. For example, Li et al. [11] investigated NREL Phase VI using unsteady Reynolds-averaged Navier–Stokes (RANS) and detached eddy simulation (DES) models. The study found that the RANS results of thrust forces and moments differed from the experimental work. The DES generated considerable improvements in the unsteady flow of wind turbines. Lanzafame et al. [12] and Rajvanshi et al. [13] simulated NREL Phase VI using k-ω SST and transitional k-ω. The results demonstrated that transitional k-ω agreed better with experimental data than k-ω SST. Moshfeghi et al. [14] investigated the effects of near-wall grid treatment on the aerodynamic performance of a wind turbine. The thrust forces results of k-ω SST for eight different cases did not agree well with the test results. In general, the k-ω SST model over-predicted the performance of the wind turbine. Transitional k-ω, on the other hand, confirmed better prediction accuracy and particularly in the inboard regions. Until now, there was no unique model that could predict all the physical characteristics of turbulent flows. The k-ε turbulence models were used to study the flow around the wind turbine and wake dynamic behavior. Kasmi and Masson [15] and AbdelSalam and Ramalingam [16] executed a full-scale study of three wind turbines based on different k-ε turbulence models and compared results with experimental work. Their findings confirmed that the modified k-ε agreed better with previous experimental measurements than standard k-ε. Abdelsalam et al. [17] simulated the upstream and downstream velocities for a 2 MW HAWT using a modified k-ε turbulence model which showed good agreement between measured and predicted results. Siddiqui et al. [18] studied the dynamic wake behavior of an NREL 5 MW wind turbine with two different approaches, i.e., multiple reference frame (MRF) and sliding mesh interface (SMI). They found that SMI had a better prediction ability near the hub than MRF. However, SMI required a tremendous amount of computational resources to deliver fully converged results. Rütten et al. [19] computed the NREL Phase VI using k-ω and k-ω SST using Open-FOAM code. Their findings revealed that the k-ω model overestimated the turbulent kinetic energy when compared to the k-ω SST turbulence model. The CFD modelling has been widely used to investigate aerodynamic characteristics concerning the wind turbine. In the present work, the aerodynamic characteristics of a 20 kW wind turbine were investigated using four RANS models including k-ω SST, transition SST, Spalart–Allmaras, and realizable k-ε. In addition, the NREL test results of mechanical torque and blade pressure distribution were used for model validation. Depending on this numerical validation, the best performing CFD model will be used to examine the mechanical output with different rotational speeds and variable pitch angle, so that the optimized blade design can be compared. Location has a significant effect on the wind turbines’ power output. Accounting for the environmental conditions when designing the Energies 2020, 13, 2292 3 of 26

HWAT for a specific area or region could improve the power output. Research has focused on the aerodynamic optimization of the shape of the wind turbine; this is critical in the manufacturing and design of the wind turbine. Australia has widespread and plentifully distributed wind resources. There is a lack of research about the design of wind turbines that takes into account the prevailing environmental conditions in Australia. This study aims to optimize a 20 kW wind turbine for the rural region at Deniliquin, New South Wales, using the horizontal axis rotor performance optimization (HARP_Opt) code. This paper optimized the wind turbine shape to maximize AEP, depending on the Weibull distribution function. The present study is structured as follows. Sections2 and3 present the numerical modelling and optimization methods, respectively. Section4 discusses the simulation results, and Section5 summarizes and concludes the critical findings of this study.

2. Numerical Modeling of HAWT Under Separation Conditions

2.1. Governing Equations of Selected Turbulence Models The principle of the mathematical concept of the RANS equations is based on the calculation method of the Navier–Stokes equation which is divided into the instantaneous fluctuating part and the average flow part. In the present work, the aerodynamics of the wind turbine is predicted with a commercial CFD code known as Ansys Fluent 18.2 [20]. The flow around a wind turbine blade is considered to be incompressible and is modelled utilizing the RANS method. The software uses the finite volume method for solving the mass and momentum equations in addition to equations of turbulence for each control volume cell. The mass and momentum conservation equations are:

du i = 0 (1) dx

2 ∂ui ∂   1 ∂p ∂ ui ∂   + ui uj = + v u´i u´ j (2) ∂t ∂xj −ρ ∂xi ∂xj∂xj − ∂xj where u´i is the fluctuating velocity, ui the mean velocity, and v the fluid kinematic viscosity. The realizable k-ε [21], k-ω SST [22], Spalart–Allmaras [23], and transition SST [24] models are the four RANS models which were investigated. The governing equations of the four RANS models are described in AppendixA. This section of the paper aims to investigate the effect of those four turbulence models on predicting the aerodynamic characteristics of the twisted wind turbine where the mechanical torque and blade pressure distribution are used for model validation when compared with the NREL test results. Secondly, the differences among the turbulence models under different wind speeds that include stall conditions are documented through simulation of the wind turbine.

2.2. CFD of Wind Turbine

2.2.1. Computational Domain The NREL (CER) extends the NREL (VI) experiment rotor [25] which was performed in the National Renewable Energy Laboratory. The geometry of the 20 kW wind turbine blade was optimized to maximize the annual energy [26]. The results explained the prediction complexity of the aerodynamic performance of the tapered-twisted HAWT turbine when compared with an untwisted blade. As such, the NREL CER performs excellently compared to the commercial blades. The NREL CER was used as a reference for validating the aerodynamic performance of a three-blade wind turbine with variable speed operations. Table1 summarizes the main characteristics of the wind turbine blade with S809 airfoil applied from a 25% span at the root to the tip. Energies 2020, 13, 2292 4 of 26

Table 1. Specification and operating parameters of the NREL CER.

Parameters Value Rated power 20 kW Energies 2020, 13, x FOR PEER REVIEW 4 of 26 Blade diameter 10.58 m Number ofRated blades power 20 kW 3 blades Hub heightBlade diameter 10.58 12.192m m PitchNumber angle of blades 3 blades 5◦ Rotational directionHub height 12.192 Counterclockwise m RotationalPitch speed angle 5° 72 rpm Power regulationRotational direction Counterclockwise Stall regulation Rotational speed 72 rpm Power regulation Stall regulation The blade geometry was created using SolidWorks [27] and disregarded the effect of the tower and nacelle to reduceThe blade computational geometry was timecreated and using enhance SolidWorks numerical [27] and stability disregarded [28]. Thethe effect wind of blade the tower consisted of 18 sectionsand nacelle as to shown reduce in computational Figure1a. These time sectionsand enhance had numerical di fferent stability twist angles [28]. The and wind chord blade lengths along theconsisted blade of as 18 shown sections in as Figure shown1b. in TheFigure geometry 1a. These of sections the cylindrical had different part twist ended angles at 0.66 and m chord from the axis oflengths rotation along and the then blade started as shown to change in Figure until 1b. The the geometry transition of area the cylindrical ended at part 1.25 ended m. From at 0.66 Figure m 1b, from the axis of rotation and then started to change until the transition area ended at 1.25 m. From the maximum twist angle reached 20.040◦ at 0.25 span and later became zero at a 0.75 span and a Figure 1b, the maximum twist angle reached 20.040° at 0.25 span and later became zero at a 0.75 span negative value at a 1.00 span. and a negative value at a 1.00 span.

(a) 25 0.8 (b) Twist Angle 20 Chord length 0.6 15

10 0.4

5 Chord length (m)

Twist angle (degree) 0.2 0

‐5 0.0 0.0 0.2 0.4 0.6 0.8 1.0 Span station (‐) (b)

FigureFigure 1. (a) 1. A ( 3Da) A geometry 3D geometry model model of of a a 20 20 kW kW wind wind turbine turbine blade. blade. (b) ( bThe) The chord chord and andtwist twist distribution distribution along thealong span the span of the of blade.the blade.

The fluidThe fluid domain domain was was divided divided into into two two zones zones as as shownshown in Figure Figure 2a.2 a.The The first first zone zone with witha a 120° radial stream tube was generated with periodic faces to decrease computational time due 120◦ radial stream tube was generated with periodic faces to decrease computational time due to the to the symmetrical flow around the wind turbine model. The upstream velocity was specified symmetrical flow around the wind turbine model. The upstream velocity was specified with an 18 m Energies 2020, 13, x; doi: FOR PEER REVIEW www.mdpi.com/journal/energies

Energies 2020, 13, 2292 5 of 26

Energies 2020, 13, x FOR PEER REVIEW 5 of 26 radius, offset 12 m in front of the blade. Meanwhile, the downstream outlet was defined with a 36 m radius,with o anffset 18 24 m mradius, behind offset the 12 blade, m in and front specified of the blade. as an Meanwhile, atmospheric the pressure downstream outlet. outlet The was second zonedefined was near with the a 36 blade m radius, with a offset 10 m radius24 m behind and 5 mthe from blade, the and center specified of the as root. an atmospheric This zone was createdpressure to separate outlet. theThe rotating second zone and stationary was near the zones blade and with to increase a 10 m radius the number and 5 ofm meshfrom the cells center near the blade.of the The root. upstream This zone velocity was created and upper to separate surface the of rotating the domain and werestationary specified zones as and free to stream increase wind the number of mesh cells near the blade. The upstream velocity and upper surface of the domain speed. This conical shape of the domain was used to permit wake conical expansion on the back of the were specified as free stream wind speed. This conical shape of the domain was used to permit blade. An important step is choosing the most suitable computational domain. First of all, a proper wake conical expansion on the back of the blade. An important step is choosing the most suitable computational domain that permits rotation of the wind turbine blade with a no-slip wall effect is computational domain. First of all, a proper computational domain that permits rotation of the essentialwind whenturbine considering blade with thea no optimization‐slip wall effect of is mesh essential quality. when Consequently, considering the a large optimization computational of domainmesh will quality. not permit Consequently, enough grid a large generation computational around the domain wind turbine.will not On permit the other enough hand, grid a vast domaingeneration would around increase the the wind computational turbine. On time the other corresponding hand, a vast with domain an increase would in increase the calculated the numbercomputational of cells. time corresponding with an increase in the calculated number of cells.

(a)

Stationary domain Rotating domain

Rotating domain

(b)

Energies 2020, 13, x; doi: FOR PEER REVIEW Figure 2. Cont. www.mdpi.com/journal/energies

Energies 2020, 13, 2292 6 of 26 Energies 2020, 13, x FOR PEER REVIEW 6 of 26

(c)

FigureFigure 2. 2.( a()a Computational) Computational domain; domain; (b )( computationalb) computational mesh mesh generation, generation and (c, )and cell meshing(c) cell meshing around thearound rotor. the rotor. 2.2.2. Computational Mesh Generation 2.2.2. Computational Mesh Generation The S809 airfoil has a very sharp trailing edge along the blade which produces non-orthogonal face The S809 airfoil has a very sharp trailing edge along the blade which produces non‐ cells [29]. These cells lead to low-quality mesh and inaccurate or unstable CFD solutions. Generating a orthogonal face cells [29]. These cells lead to low‐quality mesh and inaccurate or unstable CFD sharp trailing edge is not possible in the experimental work, so rounding this sharp edge through a solutions. Generating a sharp trailing edge is not possible in the experimental work, so rounding radius of 1 mm will improve the quality of the mesh with an insignificant effect on the CFD results. this sharp edge through a radius of 1 mm will improve the quality of the mesh with an The present study used different turbulence models to predict the output power and pressure insignificant effect on the CFD results. distribution under a variety of wind speed conditions which was crucial to refining the mesh around The present study used different turbulence models to predict the output power and the blade rotor. As shown in Figure2b, the cells were refined gradually away from the blade to reduce pressure distribution under a variety of wind speed conditions which was crucial to refining the the computational time. The ANSYS meshing was used to generate unstructured mesh, and a local mesh around the blade rotor. As shown in Figure 2b, the cells were refined gradually away from and global sizing was used to produce a high-quality grid. The minimum mesh size was 0.008 m3 the blade to reduce the computational time. The ANSYS meshing was used to generate around the blade. After that, inflation was used to refine the prismatic cells at the blade surface, and it unstructured mesh, and a local and global sizing was used to produce a high‐quality grid. The generated fifteen prismatic layers with a growth rate of 1.2 as shown in Figure2c. minimum mesh size was 0.008 m3 around the blade. After that, inflation was used to refine the Also, he proximity and curvature with the fine relevance center were defined as the specification prismatic cells at the blade surface, and it generated fifteen prismatic layers with a growth rate of the local mesh size function which helped to refine the mesh grid. Mesh quality plays a crucial role in of 1.2 as shown in Figure 2c. the accuracy of CFD results. However, a smaller mesh size requires a longer computation time and more Also, he proximity and curvature with the fine relevance center were defined as the specification computer memory. For this reason, it is essential to compromise between accuracy and computational of the local mesh size function which helped to refine the mesh grid. Mesh quality plays a crucial role time. On the other hand, it is crucial to achieve mesh independence. Nine meshes were tested at a in the accuracy of CFD results. However, a smaller mesh size requires a longer computation time and 7.2 m/s wind speed to achieve grid independence by monitoring the mechanical torque. As shown more computer memory. For this reason, it is essential to compromise between accuracy and in Figure3, the CFD results converged when the number of mesh cells was 3,559,082, which had an computational time. On the other hand, it is crucial to achieve mesh independence. Nine meshes were error rate of 3.82% when compared with the measurement value. Any further increase in the number tested at a 7.2 m/s wind speed to achieve grid independence by monitoring the mechanical torque. of mesh cells will significantly raise the computational time but will lead to no improvement in the As shown in Figure 3, the CFD results converged when the number of mesh cells was 3,559,082, which accuracy. For this reason, 3,559,082 mesh cells is deemed to be the most suitable mesh configuration in had an error rate of 3.82% when compared with the measurement value. Any further increase in the terms of computational time and efficiency. number of mesh cells will significantly raise the computational time but will lead to no improvement Three models are used in ANSYS Fluent for handling the rotational effect, namely, dynamic mesh, in the accuracy. For this reason, 3,559,082 mesh cells is deemed to be the most suitable mesh sliding mesh, and moving reference frame (MRF) models. The sliding mesh model is appropriate configuration in terms of computational time and efficiency. for the transient flow problem but requires a full-scale model. Both dynamic mesh and sliding mesh models require high computational resources. The MRF model is the simplest way for modelling the flow of steady-state rotating objects without using rotating mesh to reduce the computational time [30]. Thus, MRF is applied in the small zone near the blade to apply the rotational speed of the wind turbine with periodic boundary conditions. The transformation from a stationary to a moving frame in terms of relative fluid particle velocities, Coriolis, and centripetal accelerations have been used to calculate the MRF model. The MRF was set-up for computation domain by applying a rotational speed of 72 rpm with the absolute reference frame. The blade was assumed to be a non-slip stationary wall that had a zero-relative velocity with other adjacent cells.

Energies 2020, 13, x; doi: FOR PEER REVIEW www.mdpi.com/journal/energies

Energies 2020, 13, 2292 7 of 26 Energies 2020, 13, x FOR PEER REVIEW 7 of 26

950 Measured Calculated (N.m) 900 3,559,082 Torque

850 Mechanical

800 3,300,000 3,800,000 4,300,000 4,800,000 5,300,000 Number of Cells Figure 3. Grid sensitivity. Figure 3. Grid sensitivity. 2.2.3. Numerical Method and Boundary Conditions Three models are used in ANSYS Fluent for handling the rotational effect, namely, dynamic Four turbulence models were used to predict wind turbine aerodynamics. All regions in the mesh, sliding mesh, and moving reference frame (MRF) models. The sliding mesh model is domain were applied to the boundary conditions. Domain outlet was applied to the pressure appropriate for the transient flow problem but requires a full‐scale model. Both dynamic mesh and boundary conditions of zero gauges pressure with 101,325 Pa of atmospheric conditions. The current sliding mesh models require high computational resources. The MRF model is the simplest way for investigation focused on 15 inlet velocities ranging from 4.9m/s to 15.2 m/s which was enough to modelling the flow of steady‐state rotating objects without using rotating mesh to reduce the investigate the prediction of different turbulence models for stall delay phenomena. The air density computational time [30]. Thus, MRF is applied in the small zone near the blade to apply the rotational waas approximately constant due to the assumption of incompressible fluid [11]. In this study, speed of the wind turbine with periodic boundary conditions. The transformation from a stationary the standard air properties were used, where air density and dynamic viscosity were 1.225 kg/s and to a moving frame in terms of relative fluid particle velocities, Coriolis, and centripetal accelerations 1.7894 10 5 kg/ms 1, respectively. have ×been− used to− calculate the MRF model. The MRF was set‐up for computation domain by The steady-state, pressure-based method was used to solve the incompressible RANS models. applying a rotational speed of 72 rpm with the absolute reference frame. The blade was assumed to A semi-implicit method was used to model the velocity and pressure in momentum and continuity be a non‐slip stationary wall that had a zero‐relative velocity with other adjacent cells. equations. The convergence rate is improved when using a combined algorithm rather than a simple2.2.3. Numerical algorithm. Method and Boundary Conditions The first-order upwind was used for solving turbulent kinetic energy and the turbulent dissipation rate, whileFour a turbulence second-order models upwind were scheme used to was predict used for wind solving turbine the aerodynamics. momentum equations. All regions The leastin the squaresdomain cell-based were applied method to the was boundary used in conditions. a gradient spatialDomain discretization outlet was applied scheme. to Athe standard pressure discretizationboundary conditions scheme was of usedzero ingauges the pressure pressure values with interpolation. 101,325 Pa of atmospheric conditions. The currentIn the investigation simulation process focused (Figure on 154 ),inlet it is velocities essential to ranging monitor from the convergence 4.9m/s to 15.2 of them/s simulation which was analysis.enough In to this investigate study, two the methods prediction were of used different to assess turbulence the convergence models of for the stall fluent delay analysis. phenomena. Firstly, theThe residual air density values waas method approximately is a popular constant method fordue evaluating to the assumption the convergence of incompressible of the CFD fluid solution. [11]. InIn this this study, study, during the standard the calculation air properties process, were different used, variables where air of density the residual and dynamic values were viscosity monitored were such1.225 as kg/s continuity, and 1.7894 x-velocity, × 10−5 y-velocity,kg/ms−1, respectively. z-velocity, specific dissipation rate, and turbulent kinetic The steady‐state, pressure‐based method was used to solve the incompressible RANS5 energy. The solution was considered to be converged when these residual values were below 10− . Secondly,models. aA net semi mass‐implicit imbalance method was was used used to check to model the convergence the velocity of and the solution.pressure Thisin momentum method is theand dicontinuityfference between equations. the inlet The and convergence outlet mass rate flows. is Itimproved was considered when tousing be converged a combined when algorithm the net massrather imbalance than a simple was less algorithm. than 0.001 kg/s [31]. DueThe to first the‐ non-linearorder upwind nature was of the used fluid for flow, solving the solution turbulent should kinetic be calculated energy and iteratively. the turbulent In this study,dissipation the solution rate, was while achieved a second after‐ theorder 1500 upwind iterations. scheme Also, thewas study used used for the solving standard the initialization momentum method,equations. where The the least inlet squares boundary cell layer‐based was method used for was calculating used in the a initial gradient values. spatial After discretization the solution wasscheme. converged, A standard the aerodynamic discretization power scheme output was results used were in the validated pressure against values experimental interpolation. data. In the simulation process (Figure 4), it is essential to monitor the convergence of the simulation analysis. In this study, two methods were used to assess the convergence of the fluent analysis. Firstly, the residual values method is a popular method for evaluating the convergence

Energies 2020, 13, x; doi: FOR PEER REVIEW www.mdpi.com/journal/energies

Energies 2020, 13, x FOR PEER REVIEW 8 of 26 of the CFD solution. In this study, during the calculation process, different variables of the residual values were monitored such as continuity, x‐velocity, y‐velocity, z‐velocity, specific dissipation rate, and turbulent kinetic energy. The solution was considered to be converged when these residual values were below 10−5. Secondly, a net mass imbalance was used to check the convergence of the solution. This method is the difference between the inlet and outlet mass flows. It was considered to be converged when the net mass imbalance was less than 0.001 kg/s [31]. Due to the non‐linear nature of the fluid flow, the solution should be calculated iteratively. In this study, the solution was achieved after the 1500 iterations. Also, the study used the standard initialization method, where the inlet boundary layer was used for calculating the initial values. After the solution was converged, the aerodynamic power output results were Energies 2020, 13, 2292 8 of 26 validated against experimental data.

Figure 4. Numerical modelling of HAWT. Figure 4. Numerical modelling of HAWT. The computing system details are discussed in Table2a. The corresponding computation time is illustratedThe computing in Table system2b. As candetails be seen are discussed in the table, in theTable computation 2a. The corresponding times for the computation four models exhibittime is illustratedno noticeable in Table differences. 2b. As can Consequently, be seen in the the table, selected the computation model will depend times for on the the four accuracy models rather exhibit than nocomputational noticeable differences. time. Consequently, the selected model will depend on the accuracy rather than computational time. Table 2. (a) Computing system. (b) Model-related computation time. Table 2. (a) Computing system. (b) Model‐related computation time. (a) (a) 2.9 GHz Intel Xeon E5-2690 (8 cores) 20 megabytes L3 QuickPath CPU Energies 2020, 13, x; doi: FOR PEER REVIEW Interconnect (QPI) (max turbo frequencywww.mdpi.com/journal/energies 3.8 GHz, min 3.3 GHz) Random access memory (RAM) 32 gigabytes 1600 MHz ECC DDR3-RAM (quad channel) Memory 2 1 terabyte 7200 rpm sata III hard drives (raid) × (b) Realizable k-ε 4.15 h Transition SST 5.46 h k-ω SST 4.66 h Spalart–Allmaras 3.74 h

3. Optimization of Wind Turbine Optimizing the wind turbine design’s operating parameters has significant impacts on the amount of energy output. It is therefore critical when specifying the shape design of wind turbines, taking into Energies 2020, 13, 2292 9 of 26 consideration the wind data available in the specific location. The following section deals with the modification of the blade geometric parameters to meet wind velocity at the Deniliquin site.

3.1. Wind Data Modelling Australia has significant wind resources, and many of the best places are located in New South Wales. Wind speed plays a vital role in the performance of the wind turbine, since it is the primary source of energy. Wind speeds at a specific site vary according to annual, seasonal, and daily changes. It is crucial to conduct a statistical analysis with a probability distribution to study the potential of wind resources. Deniliquin is located in the Riverina region of New South Wales close to the border with Victoria, Australia. This area functions economically as a service center for the surrounding agricultural area. Thus, in this area, small wind turbines could be used for a remote, small electrical generation and agricultural application project. The wind data of the Deniliquin Airport AWS station (station number 074258) were chosen to analyze the wind energy potentials in this study. This station has a coordinate of 35.56, 144.95, and an elevation of 94.0 m. It is necessary to use some statistical analysis − for the wind data. The probability distribution describes the occurrence frequency of wind speed [32]. Observations for the period from June 2018 to July 2019 were studied using Weibull probability density function. The Weibull probability density function, as shown in Equation 2, depends on two factors: scale and shape factor [33,34]. " # k vk 1 vk f (v) = − exp (3) c c − c where, k is the shape factor (dimensionless), c is the scale factor (m/s), and v is the wind speed (m/s) [35]. The shape parameter decides the curvature of the probability distribution; any variation in the shape parameter is affected by the estimated wind potential. Determination of the Weibull probability density function requires defining the shape and scale parameters, using different estimation methods. Employing the maximum likelihood method is typically done for defining shape and scale parameters as seen in the following equations [36,37]:

Pn k Pn  1  = vi ln(vi) = ln(vi) − k =  i 1 i 1  (4)  Pn k  i=1 vi − n

1 Pn k  k  = vi  c =  i 1  (5)  n  where vi is the wind speed at (i) time, and n is the number of readings of wind speed data [38,39]. To define the AEP of the wind turbine, the probability distribution f (v) is combined with the power curve of wind turbine P (v) as shown in the following equation:

Z vcut,out AEP = P(v) f (v)dv (6) vcut,in where vcut,in is the cut-in wind speed (m/s), and vcut,out is the cut-out wind speed (m/s). Assessment of the available resource at Deniliquin was defined by the shape and scale of the Weibull probability density function. The shape and scale factors are used as inputs for the optimization process, of which the objective is to maximize the AEP of a 20 kW wind turbine depending on the wind speed data in Deniliquin. The following section describes the optimization methodology.

3.2. Optimization Blade Shape Methodology National Renewable Energy Labs (NREL) developed HARP_Opt in the USA [40]. The HARP_Opt open-source code is used to conduct the horizontal axis rotor performance optimization process. The HARP_Opt gathers a BEM theory code with a genetic algorithm (GA) code to optimize and design Energies 2020, 13, 2292 10 of 26 the wind turbine’s rotor shape. Genetic algorithms [41] are evolutionary algorithms, and they are robust and reliable search techniques depending on the mechanism of natural selection [42]. The optimization process of the GA is done by iterating a set of individual solutions, where a set of solutions is called a population. An iteration is carried out from one population to the next to obtain subsequent populations of superior individuals. The WT_Perf software (National Renewable Energy Laboratory, Golden, CO, USA) [43] is used as the essential BEM code in HARP_Opt. The WT_Perf is developed to analyze the aerodynamic performance of the wind turbine using the BEM code. The HARP_Opt uses the WT_Perf code to predict the performance of the rotor wind turbine and the MATLAB GA code to carry out the optimization. The HARP_Opt could be used for a single or multiple objective optimization code for the objective function in the HARP_Opt software, either maximization of the AEP of the wind turbine or wind turbine efficiency.

3.2.1. Design Variables and Objective Function The blade shape of the wind turbine is defined by the airfoil, chord length, and twist angle of each section along the blade. The validated wind turbine model of 20 kW, which has been discussed before, is used as a baseline for the optimization process and the same family of S809 airfoil was used. The airfoil lift and drag polar was done using spreadsheet AirfoilPrep v2.02 (v2.02.03, Windward Engineering, LLC, USA) This type of Excel formatting was used to generate airfoil data to be imported into WT_Perf. After preparing the airfoil data file, the file was imported into HARP_Opt. The objective of the optimization process was to maximize the AEP of 20 kW wind turbine depending on the wind speed data in Deniliquin using the output of optimal chord length and twist distributions along the wind turbine blade. In this study, a single objective method was considered where the optimization was focused on the optimization of the aerodynamic shape without including structural optimization studies [44–48]. The Bezier curves were used to define the chord length and twist angle distributions to smooth the span-wise distribution along the blade. There were five control points for each chord length and twist angle parameters; thus, the total overall decision variables amounted to 25 control points. The same rated power, the rotor diameter, and the hub height were used as input in HARP_Opt, with the baseline validated wind turbine model as shown in Figure5. In this study, the variable rotor speed and variable pitch control were used for the control system to produce more energy output [32]. The allowable rotor speeds range from 25 rpm to 150 rpm. Table3 below summarizes different parameters of turbine configurations.

Table 3. Turbine configurations.

Wind Turbine Parameters Value Rotor diameter 11 m Rated power capacity 20 kW Number of blade segment 30 m Number of blades 3 Hub diameter 0.6 Hub distance from the bottom surface 13 m Air density 1.225 kg/s

3.2.2. Constraints Specific design parameters should be in place to generate acceptable blade geometry [28,49,50] which are described in AppendixA. As shown in Table4, the lower and upper bounds represent the five control sections’ control twist and chord values, respectively. Energies 2020, 13, 2292 11 of 26 Energies 2020, 13, x FOR PEER REVIEW 12 of 26

Figure 5. Figure 5.Optimization Optimization flowchart. flowchart. Table 4. Genetic algorithm (GA) configuration. 4. Results and Discussion Radial Position 1.25 1.535 2.345 3.565 5.5 4.1. ModelTwist Validation angle (degree) This sectionMinimum firstly investigates10 the effect10 of those four10 turbulence 10models on predicting10 the − − − − − Maximum 25 17 5 3 1 aerodynamic characteristics of the twisted wind turbine, where the mechanical torque− and blade pressure distribution were used for modelChord validation Length (m)when compared with the NREL test results. Secondly, theMinimum differences among 0.5 the turbulence 0.1 models under 0.1 different 0.1 wind speeds 0.1 that included stall conditionsMaximum were captured 0.8by simulating 0.72 the wind 0.65turbine. Thirdly, 0.55 the main 0.37 aerodynamic parameters, such as lift coefficient, were extracted at a different span‐wise sections along the blade. Fourthly,Trial and and errorfinally, were the used aerodynamic to tune the flow GA’s of the parameters. S809 airfoil The was values visualized input intounder this different optimization angles runof attack, were the and final they ones revealed after using the variation trial and of error. the flow Table from5 summarizes the attached the GAseparated configuration flow conditions. employed.

4.1.1. Mechanical Torque Table 5. Genetic algorithm configuration.

Figure 6 compares the Optimizationmodelled shaft Parameters torque values using different Value RANS models and the measured results for the NREL rotor, which operated at a fixed speed of 72 rpm and a pitch angle of Population size 200 5°. The CFD results demonstrated goodGeneration agreement with the measurements 150 at low and medium wind speeds between 4.9 and 9.0 m/s.The Transition cross-over played fraction an insignificant role 0.25 in the prediction of the flow behavior of the wind turbineError tolerance at this speed for the range. GA fitness All values RANS models made1 10 an6 excellent prediction of × − the flow around the wind turbine at the area where the flow was still attached. It is important to note here that at a flow velocity between 9.0 and 10.5 m/s, the boundary layer was driven from the laminar to the turbulent transition area where the onset of a stall occurs. The transition SST model made the best prediction for that region due to the fact of its ability to resolve

Energies 2020, 13, x; doi: FOR PEER REVIEW www.mdpi.com/journal/energies

Energies 2020, 13, 2292 12 of 26

4. Results and Discussion

4.1. Model Validation This section firstly investigates the effect of those four turbulence models on predicting the aerodynamic characteristics of the twisted wind turbine, where the mechanical torque and blade pressure distribution were used for model validation when compared with the NREL test results. Secondly, the differences among the turbulence models under different wind speeds that included stall conditions were captured by simulating the wind turbine. Thirdly, the main aerodynamic parameters, such as lift coefficient, were extracted at a different span-wise sections along the blade. Fourthly, and finally, the aerodynamic flow of the S809 airfoil was visualized under different angles of attack, and they revealed the variation of the flow from the attached separated flow conditions.

4.1.1. Mechanical Torque Energies 2020, 13, x FOR PEER REVIEW 13 of 26 Figure6 compares the modelled shaft torque values using di fferent RANS models and the measured results for the NREL rotor, which operated at a fixed speed of 72 rpm and a pitch angle of the laminar transition that considers the turbulent boundary layer which starts at the stall 5 . The CFD results demonstrated good agreement with the measurements at low and medium wind ◦phenomenon. After 10 m/s, the results showed a marked difference for mechanical torque between speeds between 4.9 and 9.0 m/s. Transition played an insignificant role in the prediction of the flow the measured and RANS models. The significant separation of the flow and stall phenomena played behavior of the wind turbine at this speed range. All RANS models made an excellent prediction of a role in the difficulty of mechanical torque prediction using the RANS models. the flow around the wind turbine at the area where the flow was still attached.

3200

2800

2400 (N.m)

2000

1600 Torque

Measured 1200 k‐ω SST

800 Transition SST Mechanical Realizable k‐ε 400 Spalart‐Allmaras 0 246810121416 Wind speed (m/s)

FigureFigure 6. 6.Mechanical Mechanical torque. torque.

4.1.2.It isPressure important Distribution to note here that at a flow velocity between 9.0 and 10.5 m/s, the boundary layer was driven from the laminar to the turbulent transition area where the onset of a stall occurs. The transition SST modelFigure made 7 and the Figure best prediction8 show comparisons for that region of the due measured to the fact and of computed its ability topressure resolve coefficients the laminar at transitionthe four most that considersimportant theradial turbulent span sections boundary (0.47 layer R, 0.63 which R, 0.8 starts R, and at the0.95 stall R) for phenomenon. two different After wind 10speeds m/s, the of results7.2 and showed 10.2 m/s. a marked The pressure difference coefficient for mechanical is calculated torque as between in Equation the measured (7): and RANS models. The significant separation of the flow and stall phenomena played a role in the difficulty of 𝑃𝑃 𝐶𝑝 mechanical torque prediction using the RANS models. (7) 0.5𝜌 𝑉 𝑟𝛺

where 𝑃 is the local static pressure, 𝑃 is the free stream pressure, 𝑉 is relative wind speed, Ω is the rotational wind speed (rad/s), 𝑟 is the radius of the section (m), and 𝜌 is the air density (kg/m3). For a 7.2 m/s inlet wind speed, as shown in Figure 7, the modelled pressure distributions matched well with the experimental values, where the flow was almost attached to this wind speed with no stall boundary layer separation having yet started. Thus, all RANS models agreed well with the experimental data except realizable k‐ε. In effect, this model had some limitations when the domain included two fluid zones, i.e., stationary and rotating zones [51]. In this case, non‐physical turbulent viscosities were produced, and these affected the value of the turbulent viscosity. Since the present simulation had two domains, the realizable k‐ε was not appropriate for predicting the current wind turbine simulation.

Energies 2020, 13, x; doi: FOR PEER REVIEW www.mdpi.com/journal/energies

Energies 2020, 13, 2292 13 of 26

4.1.2. Pressure Distribution Figures7 and8 show comparisons of the measured and computed pressure coe fficients at the four most important radial span sections (0.47 R, 0.63 R, 0.8 R, and 0.95 R) for two different wind speeds of 7.2 and 10.2 m/s. The pressure coefficient is calculated as in Equation (7):

P Prel Cp =  −  (7) 2 2 0.5ρ Vrel + (rΩ) where P is the local static pressure, Prel is the free stream pressure, Vrel is relative wind speed, Ω is the rotationalEnergies 2020 wind, 13, x speedFOR PEER (rad REVIEW/s), r is the radius of the section (m), and ρ is the air density (kg/m3).14 of 26

‐4 ‐4 Measured (a) (b) Measured Transition SST k‐ω SST ‐3 ‐3 Spalart‐Allmaras Transition SST k‐ω SST Spalart‐Allmaras ‐2 Realizable k‐ε ‐2 Realizable k‐ε

‐1 ‐1 Cp Cp 0 0

1 1

2 2 0 0.2 0.4 0.6 0.8 1 1.2 0 0.2 0.4 0.6 0.8 1 1.2 Non‐dimensional Chord Length x/c Non‐dimensional Chord Length x/c ‐4 ‐4 Measured Measured (d) (c) Transition SST Transition SST ‐3 ‐3 Spalart‐Allmaras Spalart‐Allmaras k‐ω SST k‐ω SST ‐2 ‐2 Realizable k‐ε Realizable k‐ε

‐1 ‐1 Cp

Cp 0 0

1 1

2 2 0 0.2 0.4 0.6 0.8 1 1.2 0 0.2 0.4 0.6 0.8 1 1.2 Non‐dimensional Chord Length x/c Non‐dimensional Chord Length x/c

FigureFigure 7. 7.Comparison Comparison of of span-wise span‐wise pressure pressure distribution distribution among among the the di differentfferent turbulence turbulence models models and and NRELNREL measurements measurements at at 7.2 7.2 m/ sm/s for: for: (a) 47%(a) 47% section, section, (b) 63% (b) section, 63% section, (c) 80% (c section,) 80% section, and (d) 95%and section.(d) 95% section.

For an inlet wind speed of 10.2 m/s, which was classified as the onset of stall and shown in Figure 8, the best way to predict the airfoil’s pressure coefficient was to use the transition SST model. Any changes in the adverse pressure gradients would be reflected directly on the laminar boundary layer, and hence the early separation for the laminar boundary layer will happen when compared to the turbulent boundary layer. The transition SST model could predict the boundary layer for the flow region that changed from the laminar flow region to the turbulent transition region. Changing between boundary layers enabled the transition SST model to better predict the aerodynamic flow of the wind turbine for a stall wind condition when compared with other RANS models as shown in Figure 8a. At the 47% span location, the stall phenomena begin, and the separation was evident among the RANS models for predicting the wind turbine’s aerodynamics.

Energies 2020, 13, x; doi: FOR PEER REVIEW www.mdpi.com/journal/energies

Energies 2020, 13, 2292 14 of 26 Energies 2020, 13, x FOR PEER REVIEW 15 of 26

‐7 ‐7 Measured Measured (a) (b) ‐6 k‐ω SST ‐6 Transition SST ‐5 Transition SST ‐5 Spalart‐Allmaras Realizable k‐ε Realizable k‐ε ‐4 ‐4 k‐ω SST Spalart‐Allmaras ‐3 ‐3 ‐2 ‐2 Cp ‐1 ‐1 Cp 0 0 1 1 2 2 0 0.2 0.4 0.6 0.8 1 1.2 0 0.2 0.4 0.6 0.8 1 1.2 Non‐dimensional Chord Length x/c Non‐dimensional Chord Length x/c ‐7 ‐7 Measured (c) (d) Measured ‐6 Transition SST ‐6 Transition SST ‐5 k‐ω SST ‐5 k‐ω SST Spalart‐Allmaras Spalart‐Allmaras ‐4 ‐4 Realizable k‐ε Realizable k‐ε ‐3 ‐3

‐2 Cp ‐2

Cp ‐1 ‐1 0 0 1 1 2 2 0 0.2 0.4 0.6 0.8 1 1.2 0 0.2 0.4 0.6 0.8 1 1.2 Non‐dimensional Chord Length x/c Non‐dimensional Chord Length x/c

FigureFigure 8. 8.Comparison Comparison of of span-wise span‐wise pressure pressure distribution distribution among among the the di differentfferent turbulence turbulence models models and and NRELNREL measurements measurements at at 10.2 10.2 m/ sm/s for: for: (a) 47%(a) 47% section, section, (b) 63% (b) section, 63% section, (c) 80% (c section,) 80% section, and (d) 95%and section.(d) 95% section. For a 7.2 m/s inlet wind speed, as shown in Figure7, the modelled pressure distributions matched well4.1.3. with Investigation the experimental of the Airfoil values, Characteristics where the flow was almost attached to this wind speed with no stall boundary layer separation having yet started. Thus, all RANS models agreed well with the experimentalIt is essential data exceptto improverealizable our k-understandingε. In effect, this of model the main had aerodynamic some limitations characteristics when the domain of each includedsection along two fluid the blade. zones, Determination i.e., stationary and of the rotating lift and zones drag [51 coefficient]. In this case, of each non-physical airfoil section turbulent along viscositiesthe blade were is a produced,critical parameter and these for affected calculating the value the of angle the turbulent of attack. viscosity. The Reynolds Since the presentnumber simulationincreases hadas the two wind domains, speed the rises, realizable whichk- εaffectswas not the appropriate angle of forattack predicting and corresponding the current wind lift turbinecoefficient simulation. [52]. The results of the lift coefficient were obtained from simulation over NREL at a pitchFor angle an inlet equal wind to 5° speed and wind of 10.2 speeds m/s, varied which wasfrom classified 4.9 to 15.2 as m/s the at onset a fixed of stallangular and speed, shown i.e., in Figure72 rpm.8, the As bestshown way in to Figure predict 9a the, the airfoil’s lift coefficient pressure varied coe fficient with was both to radial use the sections transition and SST velocities. model. Any changesAs shown in the in Figure adverse 9b pressure, the calculated gradients angle would of beattack reflected had a directly high twist on the angle laminar of 12.13 boundary° at 7.2 layer,m/s wind and hence speed the on early a plane separation through for the the blade laminar at boundarya distance layer of 1.51 will m. happen At the when same compared length, the to theangle turbulent of attack boundary at 10.2 layer.m/s was The 22.04 transition°. Thus, SST the model angle could of attack predict increased the boundary with layer increasing for the wind flow regionspeed that and changed decreased from with the laminarthe radial flow position. region to At the 7.2 turbulent m/s near transition the hub region. region, Changing minor transition between boundaryand separation layers enabledmay occur the transitiondue to the SST slightly model high to better angle predict of attack, the aerodynamic but the flow flow was of still the below wind turbinethe stall for region a stall and wind almost condition always when attached. compared When with increasing other RANS the models wind asvelocity, shown inthe Figure angle8 a.of Atattack the 47% increased span location, at 10.2 them/s stall to the phenomena onset of stall. begin, At and this the wind separation speed, was the evident full separation among the occurred RANS modelsbetween for the predicting hub and the 80% wind of the turbine’s tip sections. aerodynamics. Thus, the separation on the flow from the leading edge to the trailing edge occurred at 47% section of the blade and remained until 80% section.

Energies 2020, 13, x; doi: FOR PEER REVIEW www.mdpi.com/journal/energies

Energies 2020, 13, 2292 15 of 26

4.1.3. Investigation of the Airfoil Characteristics It is essential to improve our understanding of the main aerodynamic characteristics of each section along the blade. Determination of the lift and drag coefficient of each airfoil section along the blade is a critical parameter for calculating the angle of attack. The Reynolds number increases as the wind speed rises, which affects the angle of attack and corresponding lift coefficient [52]. The results of the lift coefficient were obtained from simulation over NREL at a pitch angle equal to 5◦ and wind speeds varied from 4.9 to 15.2 m/s at a fixed angular speed, i.e., 72 rpm. As shown in Figure9a, the lift Energies 2020, 13, x FOR PEER REVIEW 16 of 26 coefficient varied with both radial sections and velocities.

1.4 (a) 7.2 m/s 1.2 10.2 m/s

1

coefficient 0.8 Lift

0.6

0.4 20% 40% 60% 80% 100%

Non‐dimensional Chord Length x/c

25

(b) 7.2 m/s 20 10.2 m/s

15 (degree)

attack 10

of

Angle 5

0 10% 30% 50% 70% 90% Non‐dimensional Chord Length x/c Figure 9. (a) Variation of lift coefficient with different non-dimensional chord length sections along the Figure 9. (a) Variation of lift coefficient with different non‐dimensional chord length sections along blade. (b) Variation of the angle of attack with different non-dimensional chord length sections along the blade. (b) Variation of the angle of attack with different non‐dimensional chord length sections the blade. along the blade.

As shown in Figure9b, the calculated angle of attack had a high twist angle of 12.13 ◦ at 7.2 m/s windThe speed flow on abehavior plane through at different the blade airfoil at asections distance along of 1.51 the m. blade At the was same visualized length, thearound angle the of attackairfoil with velocity and pressure contours. Transition SST indicated good results amongst the four at 10.2 m/s was 22.04◦. Thus, the angle of attack increased with increasing wind speed and decreased withturbulence the radial models position. with the At 7.2 measurements m/s near the shown hub region, above. minor As such, transition the velocity and separation vectors and may pressure occur contours results were predicted by the transition SST model. The blade cross‐section at a 1.51 m radius investigated the flow on the inner region of the blade. In contrast, the blade cross‐section at a 4.78 m radius studied the flow on the outer area of the blade. The figures below explain that the pressure fell to a small value as the flow over the airfoil accelerated. As the results in Figure 10a,c,e,g,i illustrate, the pressure coefficient dropped quickly to zero and reached a negative value. As the flow slowed down, the pressure increased, and the magnitude of the pressure coefficient decreased. As a result, the pressure of the lower surface became far more significant than the pressure of the upper surface, causing the blade to rotate. These results confirmed that the values of the pressure coefficient were negative at high air velocity. The separation will start when the flow on the upper surface at the trailing edge of the airfoil decelerates and mixes with the airflow from the lower surface. The point

Energies 2020, 13, x; doi: FOR PEER REVIEW www.mdpi.com/journal/energies Energies 2020, 13, 2292 16 of 26 due to the slightly high angle of attack, but the flow was still below the stall region and almost always attached. When increasing the wind velocity, the angle of attack increased at 10.2 m/s to the onset of stall. At this wind speed, the full separation occurred between the hub and 80% of the tip sections. Thus, the separation on the flow from the leading edge to the trailing edge occurred at 47% section of the blade and remained until 80% section. The flow behavior at different airfoil sections along the blade was visualized around the airfoil with velocity and pressure contours. Transition SST indicated good results amongst the four turbulence models with the measurements shown above. As such, the velocity vectors and pressure contours results were predicted by the transition SST model. The blade cross-section at a 1.51 m radius investigated the flow on the inner region of the blade. In contrast, the blade cross-section at a 4.78 m radius studied the flow on the outer area of the blade. The figures below explain that the pressure fell to a small value as the flow over the airfoil accelerated. As the results in Figure 10a,c,e,g,i illustrate, Energies 2020, 13, x FOR PEER REVIEW 17 of 26 the pressure coefficient dropped quickly to zero and reached a negative value. As the flow slowed down,of flow the separation pressure increased,happens earlier and the at magnitude larger angles of theof attack, pressure and coe asffi thecient intensity decreased. of the As adverse a result, thepressure pressure rises, of the the lower separation surface point became shifts far forward more significanton the airfoil. than the pressure of the upper surface, causingAs the seen blade in Figure to rotate. 10b,d,f,h,j These, results the velocity confirmed vectors that on the the values airfoil of sections the pressure varied coe followingfficient were the negativedifferences at high of velocity air velocity. along The the separation blade. The will velocity start when vectors the increased flow on the from upper the root surface to the at the tip trailingwhere edgethe highest of the airfoil velocity decelerates vector was and achieved mixes withby the the outer airflow section from of the the lowerblade surface.which was The affected point ofby flow the separationboundary happens layer separation earlier at [53]. larger The angles axial of velocity attack, andincreased as the at intensity a uniform of the pattern adverse along pressure the blade, rises, theexplaining separation the point effect shifts of the forward centrifugal on the force airfoil. on the rotating blade.

(a) (b)

(c) (d)

Figure 10. Cont. (e) (f)

Energies 2020, 13, x; doi: FOR PEER REVIEW www.mdpi.com/journal/energies

Energies 2020, 13, x FOR PEER REVIEW 17 of 26

of flow separation happens earlier at larger angles of attack, and as the intensity of the adverse pressure rises, the separation point shifts forward on the airfoil. As seen in Figure 10b,d,f,h,j, the velocity vectors on the airfoil sections varied following the differences of velocity along the blade. The velocity vectors increased from the root to the tip where the highest velocity vector was achieved by the outer section of the blade which was affected by the boundary layer separation [53]. The axial velocity increased at a uniform pattern along the blade, explaining the effect of the centrifugal force on the rotating blade.

(a) (b)

(c) (d)

Energies 2020, 13, 2292 17 of 26

(e) (f)

Energies 2020, 13, x FOR PEER REVIEW 18 of 26

(g) (h)

Energies 2020, 13, x; doi: FOR PEER REVIEW www.mdpi.com/journal/energies

(i) (j)

FigureFigure 10. 10.Pressure Pressure and and velocity velocity vector vector distributions distributions atat 7.27.2 mm/s/s ofof didifferentfferent spanspan stations: ( (aa)) pressure pressure andand (b ()b velocity) velocity vector vector of of 30% 30% span; span; ( (cc)) pressure pressure and and ((dd)) velocityvelocity vectorvector of 47% span; (e) (e) pressure and and (f)(f velocity) velocity vector vector of of 63% 63% span; span; ( g(g)) pressure pressure and and ( (hh)) velocity velocity vectorvector ofof 80%80% span; and (i) (i) pressure and and (j)(j velocity) velocity vector vector of of 95% 95% span. span.

AsThe seen NREL in Figure CER wind10b,d,f,h,j, turbine the will velocity use the vectors original on theblade airfoil geometry sections design. varied The following numerical the dimodellingfferences of of velocity this wind along turbine the will blade. serve The to velocity investigate vectors the mechanical increased from output the at root different to the rotational tip where thespeeds highest and velocity variable vector pitch wasangles. achieved Transition by the SST outer is the section RANS of model the blade that was which selected was a ffforected use bywhen the boundarythe output layer power separation of the original [53]. The blade axial geometry velocity was increased compared at a with uniform the optimized pattern along blade the design. blade, explainingTransition the SST eff canect ofpredict the centrifugal well the forcemechanical on the torque rotating and blade. the pressure distribution of different sections along the blade.

4.2. Optimization of Wind Turbine The objective of this optimization process is to maximize the AEP at the Deniliquin site. It is essential to obtain the Weibull probability density function (see Figure 11a) to maximize the energy output. The Weibull function shape and scale parameters were defined as 2.096 and 5.042 m/s, respectively. The root mean square error (RMSE) and the coefficient of determination (R2) were used to evaluate the accuracy of the Weibull probability density function. The values of R2 and RMSE were evaluated as 0.998587 and 0.013567, respectively. Those values reflected the fact that the Weibull probability distribution was very accurate in representing the recorded wind data. Depending on Weibull function parameters for the selected site and the 20kW rated capacity, the rotor diameter chosen seemed good with AEP as shown in Figure 11b.

Energies 2020, 13, x; doi: FOR PEER REVIEW www.mdpi.com/journal/energies

Energies 2020, 13, 2292 18 of 26

The NREL CER wind turbine will use the original blade geometry design. The numerical modelling of this wind turbine will serve to investigate the mechanical output at different rotational speeds and variable pitch angles. Transition SST is the RANS model that was selected for use when the output power of the original blade geometry was compared with the optimized blade design. Transition SST can predict well the mechanical torque and the pressure distribution of different sections along the blade.

4.2. Optimization of Wind Turbine The objective of this optimization process is to maximize the AEP at the Deniliquin site. It is essential to obtain the Weibull probability density function (see Figure 11a) to maximize the energy output. The Weibull function shape and scale parameters were defined as 2.096 and 5.042 m/s, respectively. The root mean square error (RMSE) and the coefficient of determination (R2) were used to evaluate the accuracy of the Weibull probability density function. The values of R2 and RMSE were evaluated as 0.998587 and 0.013567, respectively. Those values reflected the fact that the Weibull probability distribution was very accurate in representing the recorded wind data. Depending on Weibull function parameters for the selected site and the 20kW rated capacity, the rotor diameter chosen seemed good with AEP as shown in Figure 11b. In this study, the optimization process modified the shape of the blade design using chord and twist distribution along the blade. The chord and twist distributions of the optimized wind turbine blade are shown in Figure 12. The power coefficient of the optimized rotor with wind speed is depicted in Figure 13a.The power coefficient had the highest value of 0.433108 until the rated wind speed (9.5 m/s). Due to the Weibull probability density function being high in the low wind speed range, it is essential to have a high-power coefficient to increase the AEP. The blade pitch control is the variable pitch to stall angle; the control system will be able to brake the turbine at high winds safely. As shown in Figure 13b, the variation of rotor speed and pitch angle with different wind speeds shows the change of rotor speed and pitch angle with varying speeds of wind. The rotor speed at the cut-in speed (2 m/s) was approximately 32.98848 rpm. The pitch remained at 0◦, while the rising wind speed improved the rotor speed to 148.4482 rpm at the rated speed of 9.5 m/s. The active pitch control began at this point and regulated the rotor speed to 150 rpm until 25 m/s was reached. As seen below in Figure 14, the optimized rotor had a higher power output when compared to the reference rotor. According to Weibull probability density function for the Deniliquin site, 2 m/s speed was a well-suited value for cut-in speed. For the optimized rotor, a cut in the was is producing only 0.201682 kW which was approximately 1% of rated power capacity. As the wind speed rose to 8 m/s, the turbine output was 18.37828 kW with a power coefficient of 0.433108. This output was approximately 76% of the turbine’s rated capacity. At 9.5 m/s, the 20 kW rated power was reached. These differences between the power output of the tested and optimized rotor will be reflected in the AEP for the tested and optimized wind turbine. In this study, the AEP increased from 30,819.3 kW-hr/year in the original turbine to 33,614 kW-hr/year in the optimized wind turbine. Optimization improved the AEP by 9.068% when compared to the initial tested wind turbine design. Energies 2020, 13, x FOR PEER REVIEW 19 of 26

Energies 2020, 13, x FOR PEER REVIEW 19 of 26 Energies 2020, 13, 2292 19 of 26 0.20

0.200.18 (a) 0.16 0.18 (a) 0.160.14 0.140.12 0.120.10 Probability

0.100.08 Probability

Flow 0.080.06

Flow 0.060.04 0.040.02 0.020.00 0.00 0.0 5.0 10.0 15.0 20.0 25.0 30.0 Flow Speed (m/s) 0.0 5.0 10.0 15.0 20.0 25.0 30.0 Flow Speed (m/s)

(b) (b)

Figure 11. (a) Weibull probability density function at the Deniliquin site. (b) The AEP for different turbineFigure diameters11. (a) Weibull for Weibull probability function density parameters: function k = 2.096 at the and Deniliquin c = 5.042 m site./s. (b) The AEP for different Figureturbine 11. diameters (a) Weibull for probability Weibull function density parameters: function kat = the 2.096 Deniliquin and c = site.5.042 (b m/s.) The AEP for different turbine diameters for Weibull function parameters: k = 2.096 and c = 5.042 m/s. In this study, the optimization process modified the shape of the blade design using chord andIn twist this distributionstudy, the optimization along the blade. process The modified chord and the twist shape distributions of the blade ofdesign the optimized using chord wind andturbine twist blade distribution are shown along in theFigure blade. 12. The powerchord andcoefficient twist distributions of the optimized of the rotor optimized with wind wind speed turbineis depicted blade in are Figure shown 13a .inThe Figure power 12. coefficient The power had coefficient the highest of the value optimized of 0.433108 rotor untilwith thewind rated speed wind isspeed depicted (9.5 in m/s). Figure Due 13a to.The the powerWeibull coefficient probability had density the highest function value being of 0.433108 high inuntil the the low rated wind wind speed speedrange, (9.5 it ism/s). essential Due toto thehave Weibull a high ‐probabilitypower coefficient density to function increase being the AEP. high Thein the blade low pitchwind controlspeed is range,the variable it is essential pitch toto stallhave angle; a high the‐power control coefficient system to will increase be able the to AEP. brake The the blade turbine pitch at controlhigh winds is thesafely. variable As shownpitch to in stall Figure angle; 13b, the the control variation system of willrotor be speed able toand brake pitch the angle turbine with at differenthigh winds wind safely.speeds As shows shown the in change Figure of 13b, rotor the speed variation and pitch of rotor angle speed with varyingand pitch speeds angle of with wind. different The rotor wind speed speedsat the cutshows‐in speed the change (2 m/s) of wasrotor approximately speed and pitch 32.98848 angle with rpm. varying The pitch speeds remained of wind. at 0The°, while rotor the speed rising at the cut‐in speed (2 m/s) was approximately 32.98848 rpm. The pitch remained at 0°, while the rising

Energies 2020, 13, x; doi: FOR PEER REVIEW www.mdpi.com/journal/energies Energies 2020, 13, x; doi: FOR PEER REVIEW www.mdpi.com/journal/energies

EnergiesEnergies 2020, 13 2020, x FOR, 13, PEERx FOR REVIEWPEER REVIEW 20 of20 26of 26

wind speedwind speed improved improved the rotor the rotorspeed speed to 148.4482 to 148.4482 rpm rpmat the at ratedthe rated speed speed of 9.5 of m/s.9.5 m/s. The The active active pitch pitch Energies 2020, 13, 2292 20 of 26 controlcontrol began began at this at point this point and regulated and regulated the rotor the rotor speed speed to 150 to rpm150 rpm until until 25 m/s 25 m/s was was reached. reached.

0.80 0.80 25.025.0 ChordChord 0.70 0.70 Pre‐PreTwist‐Twist 20.020.0 0.60 0.60 15.015.0 0.50 0.50 (deg) (m) (deg)

(m)

0.40 0.40 10.010.0 Twist Twist ‐ Chord ‐ Chord 0.30 0.30

5.0 Pre 5.0 Pre 0.20 0.20 0.0 0.0 0.10 0.10 0.00 ‐5.0 0.00 ‐5.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 Blade Radius (m) Blade Radius (m) Figure 12. Twist angle and Chord length distribution along the blade. FigureFigure 12. Twist 12. Twist angle angle and andChord Chord length length distribution distribution along along the blade. the blade.

0.5 0.5 0.5 0.5 (a) 0.4 (a) 0.4 0.4 0.4 0.3 0.3 0.3

0.3 Coefficient 0.2 Coefficient 0.2 0.2

0.2 Power 0.1 Power 0.1 0.1 0.1 0.0 Energies 20200.0, 13, x FOR0.0 PEER REVIEW 5.0 10.0 15.0 20.0 25.021 of 30.026 0.0 5.0 10.0 15.0 20.0 25.0 30.0 Flow Speed (m/s) 160.0 Flow Speed (m/s) 0.00

140.0 ‐0.50 120.0

(b) ) ‐1.00 (rpm) deg

100.0 Rotor Speed

80.0 Blade Pitch ‐1.50 Speed

60.0 Blade Pitch (

Rotor ‐2.00 40.0 ‐2.50 20.0

0.0 ‐3.00 Energies 20200.0, 13, x; doi: FOR 5.0 PEER REVIEW 10.0 15.0 20.0 25.0www.mdpi.com/journal/energies 30.0 Flow Speed (m/s) Energies 2020, 13, x; doi: FOR PEER REVIEW www.mdpi.com/journal/energies

FigureFigure 13. (a 13.) Variation(a) Variation of power of power coefficient coeffi withcient wind with speeds. wind speeds.(b) Change (b) Changeof rotor speed of rotor and speed pitch and pitch angleangle with withwind windspeeds. speeds.

As seen below in Figure 14, the optimized rotor had a higher power output when compared to the reference rotor. According to Weibull probability density function for the Deniliquin site, 2 m/s speed was a well‐suited value for cut‐in speed. For the optimized rotor, a cut in the was is producing only 0.201682 kW which was approximately 1% of rated power capacity. As the wind speed rose to 8 m/s, the turbine output was 18.37828 kW with a power coefficient of 0.433108. This output was approximately 76% of the turbine’s rated capacity. At 9.5 m/s, the 20 kW rated power was reached. These differences between the power output of the tested and optimized rotor will be reflected in the AEP for the tested and optimized wind turbine. In this study, the AEP increased from 30,819.3 kW‐ hr/year in the original turbine to 33,614 kW‐hr/year in the optimized wind turbine. Optimization improved the AEP by 9.068% when compared to the initial tested wind turbine design.

25 Optimized geometry

20 Test geometry

15 (kW)

power

10 Rotor 5

0 0 5 10 15 20 25 30 Flow speed (m/s)

Energies 2020, 13, x; doi: FOR PEER REVIEW www.mdpi.com/journal/energies

Energies 2020, 13, x FOR PEER REVIEW 21 of 26

160.0 0.00

140.0 ‐0.50 120.0

(b) ) ‐1.00 (rpm) deg

100.0 Rotor Speed

80.0 Blade Pitch ‐1.50 Speed

60.0 Blade Pitch (

Rotor ‐2.00 40.0 ‐2.50 20.0

0.0 ‐3.00 0.0 5.0 10.0 15.0 20.0 25.0 30.0 Flow Speed (m/s)

Figure 13. (a) Variation of power coefficient with wind speeds. (b) Change of rotor speed and pitch angle with wind speeds.

As seen below in Figure 14, the optimized rotor had a higher power output when compared to the reference rotor. According to Weibull probability density function for the Deniliquin site, 2 m/s speed was a well‐suited value for cut‐in speed. For the optimized rotor, a cut in the was is producing only 0.201682 kW which was approximately 1% of rated power capacity. As the wind speed rose to 8 m/s, the turbine output was 18.37828 kW with a power coefficient of 0.433108. This output was approximately 76% of the turbine’s rated capacity. At 9.5 m/s, the 20 kW rated power was reached. These differences between the power output of the tested and optimized rotor will be reflected in the AEP for the tested and optimized wind turbine. In this study, the AEP increased from 30,819.3 kW‐ hr/year in the original turbine to 33,614 kW‐hr/year in the optimized wind turbine. Optimization improvedEnergies 2020 the, 13, AEP 2292 by 9.068% when compared to the initial tested wind turbine design. 21 of 26

25 Optimized geometry

20 Test geometry

15 (kW)

power

10 Rotor 5

0 0 5 10 15 20 25 30 Flow speed (m/s)

Figure 14. Power output of the reference tested rotor and optimized rotor.

Energies5. Conclusions 2020, 13, x; doi: FOR PEER REVIEW www.mdpi.com/journal/energies

This study aimed to optimize the NREL (CER) wind turbine by CFD modelling. It investigated the aerodynamic characteristics of a 20 kW wind turbine at three-bladed twisted angles and tapered blades. Grid independence was achieved in terms of mechanical torque. As well, the study investigated the effect of four turbulence models in predicting the mechanical torque and pressure distributions. Simulated wind conditions varied from attached to separated flow conditions. Finally, a HARP_Opt code was used to optimize the wind turbine design using a genetic algorithm, aiming to maximize the AEP at the Deniliquin site. The major findings of this study are summarized as follows:

(1) All four RANS models agreed well with experimental data at low wind speed ranges. Differences appeared among the four turbulence models as the wind speed increased; (2) At the onset of a stall condition of 10.2 m/s, the ttransition SST reported the best accuracy for predicting the pressure coefficient of the airfoil. The angle of attack increased with increasing wind speed and decreased with the radial position. The full separation occurred between the hub and 80% of the tip sections; (3) The shape of the rotor was modified by changing the chord and twist distribution along the blade, leading to 9.1% improvement in AEP.

Author Contributions: The following statements should be used Conceptualization, N.K. and A.A.; methodology, N.K., A.A. and J.Z.; software, N.K., A.B. and Y.H.; validation, N.K., A.A. and Y.H.; formal analysis, N.K., A.B. and Y.H.; investigation, N.K.; resources, A.A. and J.Z., A.A.; writing—original draft preparation, N.K.; writing—review and editing, A.A., J.Z., A.B. and Y.H.; supervision, A.A. and J.Z. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Acknowledgments: The authors would like to sincerely thank Isra University for their financial support given through doctoral scholarship to the student Nour Khlaifat. Conflicts of Interest: The authors declare no conflict of interest.

Appendix A Standard k-ε was specified by Launder and Sharma [54]. Another improvement and modification on the standard k-ε has been done to obtain the renormalization group (RNG) k-ε and Realizable k-ε turbulence models [55,56]. The RNG k-ε and realizable k-ε use the same transport equation as standard Energies 2020, 13, 2292 22 of 26 k-ε for dissipation rate (ε) and turbulent kinetic energy (k). However, the turbulent viscosity generation and calculation method are different in these models. The other RANS model used for wind turbine simulation is k-ω turbulence model, which was initially proposed by [57]. The Imperial College group has made a new improvement to this model, but the most outstanding development was done by Wilcox [58]. In some applications, the k-ω model is more accurate than standard k-ε; for example, in boundary layers with adverse pressure gradient and sublayer able to be integrated without any extra damping functions required [58]. However, k-ω is still sensitive to some flows with free stream boundary applications. k-ω SST Shear Stress Transport (SST) is an advanced turbulent model proposed by [59]. This model combines the advantages of k-ω and k-ε turbulence models. In the inner part of the boundary layer, it uses the k-ω models, and then it is converted gradually to k-ε in the free shear layer and wake regions’ outer layer. The other advantages of this model are the modification of eddy viscosity, which considers the effect of turbulent shear stress transportation. The Spalart–Allmaras version is the simplest RANS turbulence model which uses one transport equation and has the advantage of less computational time. The computation of turbulence quantity is formulated by one transport equation, in which the kinematic eddy turbulent viscosity is the equation’s variable [23]. This model was designed and optimized for compressible flow over airfoils and wings in aerospace applications and demonstrated good results. It could simply give stable and converge results in different practical situations that include adverse pressure gradients. However, this model could generate enormous diffusion, especially in regions of 3D vortices flow [60]. Various improvements were added to the model, including the effects of rotation, near wall, and reduction of diffusion [61,62]. Thus, the main advantage of the fast convergence of this model is reflected in the low computation time when compared to other turbulence models. Another RANS model is the transition SST (γ-Reθ) model which was extended based on the k-ω SST [63]. This model has four transport equations that combine k-ω (SST) equations with the momentum thickness Reynolds number transition outset method (Reθ) and the intermittency (γ) transport equations. The transition SST model is more precise than classical fully turbulent models due to the fact of its ability to deal with the laminar-turbulent transition flow model where the separation of flow and stall phenomena occurred. The governing equations of the four RANS models are described in Table A1.

Table A1. Governing equations of RANS models.

RANS Models Governing Equations k2 Turbulence eddy viscosity (vt): vt = Cµ ε    ∂k ∂ k ∂ v+Vt ∂k ∂ui Turbulence kinetic energy (k): + uj = ε + τij ∂t ∂xj ∂xj σk ∂xj − ∂xj    2 Realizable k-ε ∂ε ∂ε ∂ v+Vt ∂ε ε ∂ui ε Turbulence dissipation rate (ε): + uj = + Cε1 τij Cε2 ∂t ∂xj ∂xj σε ∂xj k ∂xj − k where σε = 1.2 and σk = 1.0 are the Prandtl numbers for ε and k, respectively. The residual model constants are: Cε1 = 1.44, Cε2 = 1.9, and Cµ = 0.09 [21].   ∂k + ∂k = e + ∂ [ + ] ∂k ρ ∂t ρuj ∂x Pk β∗ρkω ∂x µ σk1µt ∂x j − j  j  ∂ω ∂ω 2 2 ∂ ∂ω 1 ∂k ∂ω ρ + ρuj = αρS βρω + (µ + σωµt) + 2(1 F1)ρσω2 ∂t ∂xj − ∂xj ∂xj − ω ∂xj ∂xj ρa1k Turbulence eddy viscosity (µt): µt = max(a1ω,SF2) k-ω SST "    4# √k 500v 4ρσω2k F1 = tanh min max , 2 , 2 β∗ωy y ω CDkω y "  2# 2 √k 500v F2 = tanh [max , 2 ) β∗ωy y ω

F1, F2 are the first and second blending function, respectively [64]. Energies 2020, 13, 2292 23 of 26

Table A1. Cont.

RANS Models Governing Equations X3 Turbulence eddy viscosity (vt): vt = ev fv1, fv1 = 3 3 , X ev/v Cv1 +X ≡ Spalart-Allmaras where fv1 is a damping function ranging from zero value at the wall to 1 at far away from the boundary.    ∂(ργ) ∂(ρUj γ) µ ∂γ + = P E + ∂ µ + t ∂t ∂x γ γ ∂x σγ ∂x Transition SST j − j j eRe U eRe   ∂(ρ θt) ∂(ρ j θt) ∂ ∂eReθt + = P + σ (µ + µt) ∂t ∂xj θt ∂xj θt ∂xj

Specific design parameters should be in place to generate acceptable blade geometry [28,49,50]. In References [49], the maximum and minimum values for twist angle and chord length at the control points were decreased along the radial direction as the following equation:

X X X i = 1, 2, 3, 4, 5 (A1) i min ≤ i ≤ i max where Xi min is the lower limit and Xi max is the upper limit for the chord and the twist angle [65]. This limitation was applied in the current study. For the twist angle, it was given a lower bound of 10 degree, which was used in References [50,66]. − The upper limit was calculated to the original twist angle, adding 0.3 increments to twist angle. In References [50,66], the lower bound of chord length was 0.05 m, except for the first section which should be the maximum chord length, then decreased with the chord length. In this study, the chord length was given a lower bound of 0.1 m, except for 25% radial station of the blade, where the maximum chord value should be higher than 0.5 m. The chord value decreased after this section. The maximum bond was calculated to the original chord, adding 4% increments according to the chord length.

References

1. Conti, J.; Holtberg, P.; Diefenderfer, J.; LaRose, A.; Turnure, J.T.; Westfall, L. International Energy Outlook 2016 with Projections to 2040; USDOE Energy Information Administration (EIA): Washington, DC, USA, 2016. 2. Sims, R.E.; Rogner, H.-H.; Gregory, K. Carbon emission and mitigation cost comparisons between fossil fuel, nuclear and renewable energy resources for electricity generation. Energy policy 2003, 31, 1315–1326. [CrossRef] 3. Wind Power Capacity Reaches 546 GW, 60 GW added in 2017; World Wind Energy Association: Bonn, Germany, 2018. 4. Kaviani, H.; Nejat, A. Aerodynamic noise prediction of a MW-class HAWT using shear wind profile. J. Wind Eng. Ind. Aerodyn. 2017, 168, 164–176. [CrossRef] 5. Ashrafi, Z.N.; Ghaderi, M.; Sedaghat, A. Parametric study on off-design aerodynamic performance of a horizontal axis wind turbine blade and proposed pitch control. Energy Convers. Manag. 2015, 93, 349–356. [CrossRef] 6. Alpman, E. Effect of selection of design parameters on the optimization of a horizontal axis wind turbine via genetic algorithm. In Proceedings of the Journal of Physics: Conference Series, Denpasar, Indonesia, 23–24 August 2016; p. 012044. 7. Darwish, A.S.; Shaaban, S.; Marsillac, E.; Mahmood, N.M. A methodology for improving wind energy production in low wind speed regions, with a case study application in Iraq. Comput. Ind. Eng. 2019, 127, 89–102. [CrossRef] 8. Liu, X.; Wang, L.; Tang, X. Optimized linearization of chord and twist angle profiles for fixed-pitch fixed-speed wind turbine blades. Renew. Energy 2013, 57, 111–119. [CrossRef] 9. Sedaghat, A.; Mirhosseini, M. Aerodynamic design of a 300 kW horizontal axis wind turbine for province of Semnan. Energy Convers. Manag. 2012, 63, 87–94. [CrossRef] 10. Plaza, B.; Bardera, R.; Visiedo, S. Comparison of BEM and CFD results for MEXICO rotor aerodynamics. J. Wind Eng. Ind.l Aerodyn. 2015, 145, 115–122. [CrossRef] Energies 2020, 13, 2292 24 of 26

11. Li, Y.; Paik, K.-J.; Xing, T.; Carrica, P.M. Dynamic overset CFD simulations of wind turbine aerodynamics. Renew. Energy 2012, 37, 285–298. [CrossRef] 12. Lanzafame, R.; Mauro, S.; Messina, M. Wind turbine CFD modeling using a correlation-based transitional model. Renew. Energy 2013, 52, 31–39. [CrossRef] 13. Rajvanshi, D.; Baig, R.; Pandya, R.; Nikam, K. Wind turbine blade aerodynamics and performance analysis using numerical simulations. In Proceedings of the 11th Asian International Conference on Fluid Machinery, Chennai, India, 21–23 November 2011. 14. Moshfeghi, M.; Song, Y.J.; Xie, Y.H. Effects of near-wall grid spacing on SST-K-ω model using NREL Phase VI horizontal axis wind turbine. J. Wind Eng. Ind. Aerodyn. 2012, 107–108, 94–105. [CrossRef] 15. El Kasmi, A.; Masson, C. An extended k–ε model for turbulent flow through horizontal-axis wind turbines. J. Wind Eng. Ind. Aerodyn. 2008, 96, 103–122. [CrossRef] 16. AbdelSalam, A.M.; Ramalingam, V.Wake prediction of horizontal-axis wind turbine using full-rotor modeling. J. Wind Eng. Ind. Aerodyn. 2014, 124, 7–19. [CrossRef] 17. Abdelsalam, A.M.; Boopathi, K.; Gomathinayagam, S.; Kumar, S.H.K.; Ramalingam, V. Experimental and numerical studies on the wake behavior of a horizontal axis wind turbine. J. Wind Eng. Ind. Aerodyn. 2014, 128, 54–65. [CrossRef] 18. Siddiqui, M.S.; Rasheed, A.; Tabib, M.; Kvamsdal, T. Numerical analysis of NREL 5MW wind turbine: A study towards a better understanding of wake characteristic and torque generation mechanism. In Proceedings of the Journal of Physics: Conference Series, Denpasar, Indonesia, 23–24 August 2016; p. 032059. 19. Rütten, M.; Penneçot, J.; Wagner, C. Unsteady Numerical Simulation of the Turbulent Flow around a Wind Turbine. In Progress in Turbulence III; Springer: Berlin, Germany, 2009; pp. 103–106. 20. ANSYS. ANSYS Fluent Tutorial Guide, Release 18.0; ANSYS, Inc.: Pittsburgh, PA, USA, 2017. 21. Argyropoulos, C.; Markatos, N. Recent advances on the numerical modelling of turbulent flows. Appl. Math. Model. 2015, 39, 693–732. [CrossRef] 22. Rocha, P.A.C.; Rocha, H.H.B.; Carneiro, F.O.M.; Vieira da Silva, M.E.; Bueno, A.V. k–ω SST (shear stress transport) turbulence model calibration: A case study on a small scale horizontal axis wind turbine. Energy 2014, 65, 412–418. [CrossRef] 23. Spalart, P.; Allmaras, S. A one-equation turbulence model for aerodynamic flows. In Proceedings of the 30th Aerospace Sciences Meeting and Exhibit, Reno, NV, USA, 6–9 January 1992; p. 439. 24. Wang, S.; Ingham, D.B.; Ma, L.; Pourkashanian, M.; Tao, Z. Turbulence modeling of deep dynamic stall at relatively low Reynolds number. J. Fluids Struct. 2012, 33, 191–209. [CrossRef] 25. Hand, M.; Simms, D.; Fingersh, L.; Jager, D.; Cotrell, J.; Schreck, S.; Larwood, S. Unsteady Aerodynamics Experiment Phase VI: Wind Tunnel Test Configurations and Available Data Campaigns; National Renewable Energy Laboratory: Golden, CO, USA, 2001. 26. Giguere, P.; Selig, M. Design of a Tapered and Twisted Blade for the NREL Combined Experiment Rotor; National Renewable Energy Laboratory: Golden, CO, USA, 1999. 27. Akpinar, E.K.; Akpinar, S. A statistical analysis of wind speed data used in installation of wind energy conversion systems. Energy Convers. Manag. 2005, 46, 515–532. [CrossRef] 28. Lawson, M.J.; Li, Y.; Sale, D.C. Development and verification of a computational fluid dynamics model of a horizontal-axis tidal current turbine. In Proceedings of the 30th International Conference on Ocean, Offshore and Arctic Engineering (ASME 2011), Denver, CO, USA, 11–17 November 2011; pp. 711–720. 29. Somers, D.M. Design and Experimental Results for the S809 Airfoil; National Renewable Energy Laboratory: Golden, CO, USA, 1997. 30. Bouhelal, A.; Smaili, A.; Guerri, O.; Masson, C. Numerical investigation of turbulent flow around a recent horizontal axis wind Turbine using low and high Reynolds models. J. Appl. Fluid Mech. 2018, 11, 151–164. [CrossRef] 31. Bourdin, P.; Wilson, J.D. Windbreak aerodynamics: Is computational fluid dynamics reliable? Boundary-Layer Meteorol. 2008, 126, 181–208. [CrossRef] 32. Infield, D.; Freris, L. Renewable Energy in Power Systems; John Wiley & Sons: Hoboken, NJ, USA, 2020. 33. Manwell, J.F.; McGowan, J.G.; Rogers, A.L. Wind Energy Explained: Theory, Design and Application; John Wiley & Sons: Hoboken, NJ, USA, 2010. Energies 2020, 13, 2292 25 of 26

34. Katsigiannis, Y.A.; Stavrakakis, G.S. Estimation of wind energy production in various sites in Australia for different wind turbine classes: A comparative technical and economic assessment. Renew. Energy 2014, 67, 230–236. [CrossRef] 35. Bai, C.-J.; Chen, P.-W.; Wang, W.-C. Aerodynamic design and analysis of a 10 kW horizontal-axis wind turbine for Tainan, Taiwan. Clean Technol. Environ. Policy 2016, 18, 1151–1166. [CrossRef] 36. Rocha, P.A.C.; de Sousa, R.C.; de Andrade, C.F.; da Silva, M.E.V. Comparison of seven numerical methods for determining Weibull parameters for wind energy generation in the northeast region of Brazil. Appl. Energy 2012, 89, 395–400. [CrossRef] 37. Seguro, J.; Lambert, T. Modern estimation of the parameters of the Weibull wind speed distribution for wind energy analysis. J. Wind Eng. Ind. Aerodyn. 2000, 85, 75–84. [CrossRef] 38. Lydia, M.; Kumar, S.S.; Selvakumar, A.I.; Kumar, G.E.P. A comprehensive review on wind turbine power curve modeling techniques. Renew. Sustain. Energy Rev. 2014, 30, 452–460. [CrossRef] 39. Yingcheng, X.; Nengling, T. Review of contribution to frequency control through variable speed wind turbine. Renew. Energy 2011, 36, 1671–1677. [CrossRef] 40. Sale, D.C. HARP_Opt User’s Guide. NWTC Design Codes. 2010. Available online: http://wind.nrel.gov/ designcodes/simulators/HARP_Opt/Lastmodified (accessed on 11 March 2020). 41. Selig, M.S.; Coverstone-Carroll, V.L. Application of a genetic algorithm to wind turbine design. J. Energy Resour. Technol. 1996, 118, 22–28. [CrossRef] 42. Zhang, T.-T.; Wang, Z.-G.; Huang, W.; Yan, L. Parameterization and optimization of hypersonic-gliding vehicle configurations during conceptual design. Aerosp. Sci. Technol. 2016, 58, 225–234. [CrossRef] 43. Platt, A.; Buhl, M. Wt Perf User Guide for Version 3.05; National Renewable Energy Laboratory: Golden, CO, USA, 2012. 44. Kröger, G.; Siller, U.; Dabrowski, J. Aerodynamic Design and Optimization of a Small Scale Wind Turbine. In Proceedings of the ASME Turbo Expo 2014: Turbine Technical Conference and Exposition, Dusseldorf, Germany, 16–20 June 2014. 45. Ceyhan, O. Aerodynamic design and optimization of horizontal axis wind turbines by using BEM theory and genetic algorithm. Middle East Tech. Univ. 2008. Available online: http://etd.lib.metu.edu.tr/upload/ 12610024/index.pdf (accessed on 11 March 2020). 46. Wang, L.; Tang, X.; Liu, X. Optimized chord and twist angle distributions of wind turbine blade considering Reynolds number effects. Wind Energy 2012. Available online: https://www.researchgate.net/ profile/Lin_Wang120/publication/258994126_Optimized_chord_and_twist_angle_distributions_of_wind_ turbine_blade_considering_Reynolds_number_effects/links/54ccebc10cf24601c08c6f46.pdf (accessed on 11 March 2020). 47. Vuˇcina,D.; Marini´c-Kragi´c,I.; Milas, Z. Numerical models for robust shape optimization of wind turbine blades. Renew. Energy 2016, 87, 849–862. [CrossRef] 48. Shen, X.; Yang, H.; Chen, J.; Zhu, X.; Du, Z. Aerodynamic shape optimization of non-straight small wind turbine blades. Energy Convers. Manag. 2016, 119, 266–278. [CrossRef] 49. Hassanzadeh, A.; Hassanabad, A.H.; Dadvand, A. Aerodynamic shape optimization and analysis of small wind turbine blades employing the Viterna approach for post-stall region. Alex. Eng. J. 2016, 55, 2035–2043. [CrossRef] 50. Seo, J.; Yi, J.-H.; Park, J.-S.; Lee, K.-S. Review of tidal characteristics of Uldolmok Strait and optimal design of blade shape for horizontal axis tidal current turbines. Renew. Sustain. Energy Rev. 2019, 113, 109273. [CrossRef] 51. Hamada, K.; Smith, T.; Durrani, N.; Qin, N.; Howell, R. Unsteady flow simulation and dynamic stall around vertical axis wind turbine blades. In Proceedings of the 46th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, USA, 7–10 January 2008; p. 1319. 52. Ge, M.; Tian, D.; Deng, Y. Reynolds number effect on the optimization of a wind turbine blade for maximum aerodynamic efficiency. J. Energy Eng. 2014, 142, 04014056. [CrossRef] 53. Du, Z.; Selig, M.S. The effect of rotation on the boundary layer of a wind turbine blade. Renew. Energy 2000, 20, 167–181. [CrossRef] 54. Launder, B.E.; Sharma, B. Application of the energy-dissipation model of turbulence to the calculation of flow near a spinning disc. Lett. Heat Mass Transf. 1974, 1, 131–137. [CrossRef] Energies 2020, 13, 2292 26 of 26

55. Shih, T.-H.; Liou, W.W.; Shabbir, A.; Yang, Z.; Zhu, J. A new k- eddy viscosity model for high reynolds number turbulent flows. Comput. Fluids 1995, 24, 227–238. [CrossRef] 56. Yakhot, V.; Orszag, S.; Thangam, S.; Gatski, T.; Speziale, C. Development of turbulence models for shear flows by a double expansion technique. Phys. Fluids A Fluid Dyn. 1992, 4, 1510–1520. [CrossRef] 57. Tikhomirov, V. Equations of turbulent motion in an incompressible fluid. In Selected Works of AN Kolmogorov; Springer: Berlin, Germany, 1991; pp. 328–330. 58. Wilcox, D.C. Formulation of the kw turbulence model revisited. AIAA J. 2008, 46, 2823–2838. [CrossRef] 59. Menter, F.R. Review of the shear-stress transport turbulence model experience from an industrial perspective. Int. J. Comput. Fluid Dyn. 2009, 23, 305–316. [CrossRef] 60. Gatski, T.B.; Rumsey, C.L.; Manceau, R. Current trends in modelling research for turbulent aerodynamic flows. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci. 2007, 365, 2389–2418. [CrossRef][PubMed] 61. Spalart, P.; Shur, M. On the sensitization of turbulence models to rotation and curvature. Aerosp. Sci. Technol. 1997, 1, 297–302. [CrossRef] 62. Rahman, M.; Siikonen, T.; Agarwal, R. Improved low-Reynolds-number one-equation turbulence model. AIAA J. 2011, 49, 735–747. [CrossRef] 63. Langtry, R.B.; Menter, F.R. Correlation-based transition modeling for unstructured parallelized computational fluid dynamics codes. AIAA J. 2009, 47, 2894–2906. [CrossRef] 64. Calomino, F.; Alfonsi, G.; Gaudio, R.; D’Ippolito, A.; Lauria, A.; Tafarojnoruz, A.; Artese, S. Experimental and numerical study of free-surface flows in a corrugated pipe. Water 2018, 10, 638. [CrossRef] 65. Xudong, W.; Shen, W.Z.; Zhu, W.J.; Sørensen, J.N.; Jin, C. Shape optimization of wind turbine blades. Wind Energy 2009, 12, 781–803. [CrossRef] 66. Li, Y.; Yi, J.-H.; Sale, D. Recent improvement of optimization methods in a tidal current turbine optimal design tool. 2012 Oceans 2012, 1–8. [CrossRef]

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).