Abstract
In this paper, numerical simulations and experimental validation were carried out to study the Reynolds number effect on a NACA2415 airfoil type wind turbine. The software “SolidWorks Flow Simulation” has been used to present the local characteristics in different transverse and longitudinal planes. The considered numerical model is based on the resolution of the Navier-Stokes equations in conjunction with the k-ε turbulence model. Experiments have been also conducted on an open wind tunnel equipped by a small NACA2415 airfoil type wind turbine to validate the numerical results. The obtained results will help improving the aerodynamic efficiency in the design of packaged installations of the NACA2415 airfoil type wind turbine.
Keywords: NACA2415 airfoil wind turbine, Reynolds number, wind tunnel, turbulent flow, aerodynamic structure, CFD.
1. Introduction
Wind power is one the most widely used renewable energy resources. It is very important to use this wind resource to reduce fossil fuel dependency and promote sustainable development. Wind turbines are used to convert the kinetic energy present in the wind to mechanical energy and into electricity. There are many different types of wind turbines. Nevertheless, theses turbines can be classified in two main categories depending on the orientation of their axis of rotation: the horizontal axis wind turbines and the vertical axis wind turbines. The horizontal axis wind turbine is the most common type of turbine. Design parameter choice is critical for optimising wind turbine performance and wind turbines can be optimized from different aspects. In this context, scientists have performed numerical and experimental studies to improve the aerodynamic performance of wind turbines. For example, Chaudhary and Roy [1] present the design and optimization of the rotor blade performance for a 400 W small wind turbine at the lower values of operating wind speed based on blade element momentum theory (BEM). They focus on the rela[tionship between solidity, pitch angle, tip speed ratio, and maximum power coefficient. In their study, they selected an airfoil SG 6043 and they conducted studies for variable chord and twisted blade, with solidities in the range of 2% to 30% and blade numbers 3, 5. Singh et al. [2] have designed a new airfoil, permitting a small wind turbine to start up at lower wind speeds. The new airfoil also increased the startup torque and improved the overall performance of the turbine. A 400 W 2-blade wind turbine which its rotor was designed using the new airfoil was tested at wind speed range of 3e6 m/s. The results showed that the new 2-blade rotor produces more electrical power in comparison with the baseline 3-blade rotor at the same free stream velocity. Strinath and Mittal [3] utilized a continuous adjoint method for the design of airfoils in unsteady viscous flows for α=4° and Re=104. A stabilized finite element method based on the SUPG/PSPG stabilizations has been used to solve, both, flow and adjoint equations. The airfoil surface is parametrized by a 4th order NURBS curve with 13 control points. The y-coordinates of the control points are used as the design parameters. Henriques et al. [4] showed that a pressure-load inverse design method was successfully applied to the design of a high-loaded airfoil for application in a small wind turbine for urban environment. Predescu et al. [5] described the experimental work in a wind tunnel on wind turbine rotors having different number of blades and different twist angle. The aim of the work is to study the effects of the number of blades, the blade tip angles and twist angle of the blades on the power coefficient of the rotor. Also, the experiments evaluate the dependence of the power coefficient of the turbine rotor on the operating wind speed. Sicot et al. [6] investigated the aerodynamic properties of a wind turbine airfoil. Particularly, they studied the influence of the inflow turbulence level (from 4.5% to 12%) and of the rotation on the stall mechanisms in the blade. A local approach was used to study the influence of these parameters on the separation point position on the suction surface of the airfoil, through simultaneous surface pressure measurements around the airfoil. Duquette et al. [7] conducted a numerical study in order to examine the impact of rotor solidity and blade number on the aerodynamic performance of small wind turbines. Blade element momentum theory and lifting line based wake theory were utilized to assess the effects of blade number and solidity on rotor performance. An increase in power coefficients at lower tip speed ratios was observed with increase in the solidity. Also, the power coefficients increased with the increase in the blade number at a given solidity. Tahar Bouzaher [8] studied the flow around a NACA2415 airfoil, with an 18° angle of attack, and flow separation control using a rod. It involves putting a cylindrical rod-upstream of the leading edge- in vertical translation movement in order to accelerate the transition of the boundary layer by interaction between the rod wake and the boundary layer. The rod movement is reproduced using the dynamic mesh technique and an in-house developed UDF (User Define Function). Results showed a substantial modification in the flow behavior and a maximum drag reduction of 61%. Lanzafame and Messina [9] give a methodology which allows a horizontal axis wind turbine to work continuously at its maximum power coefficient according to a law of the rotor velocity rotation as a function of the wind speed. To determine this law, a calculation code based on Blade Element Momentum theory was produced to create a power curve and power coefficient as the rotational velocity of a wind rotor varied. Thumthae and Chitsomboon [10] proposed four pitch angles for an untwisted blade corresponding to the maximum power coefficient at four wind speeds. The study by Jureczko et al. [11] has developed a computer program to optimize wind turbine blades taking into account different criteria such as blade vibration, output power, blade material cost, local and global stabilities, and appropriate blade structure strength. They used a modified genetic algorithm for optimization with and without copying of the best individual cases. Maalawi and Badr [12] present a practical methodology for generating optimized wind rotor configurations, which produce the largest possible power output. The aerodynamic optimization of the rotor blades is associated with optimization of the chord and twist distribution, number of blades, choice of airfoil shape, and the tip speed ratio. Vardar and Alibas [13] compared the rotation rates and the power coefficients of the small wind turbines using the different NACA profiles for the various geometrical parameters like the twist angle, blade angle and the number of blades. Out of four blade profiles (namely NACA 0012, NACA 4412, NACA 4415, and NACA 23012) tested, it was found that NACA 4412 profiles with 0 grade twisting angle, 5 grade blade angle and double blades had the highest rotation rate, while NACA 4415 profiles with 0 grade twisting angle, 18 grade blade angle, 4 blades had the highest power coefficient.
In this paper, we are interested to study the Reynolds number effect of a NACA2415 airfoil type wind turbine. The experimental results are presented in order to validate the numerical results computed by a computational fluid dynamics code “SolidWorks Flow Simulation”. A good agreement between the numerical and experimental results is obtained which confirms the validity of the adopted method.
2. Experimental device
The considered wind turbine is a horizontal axis with a NACA2415 airfoil type placed in the test section of the wind tunnel. The wind tunnel is an open type and provides a stable and uniform air flow in the test section through a downstream vacuum. The compounds of the wind tunnel are presented in figure 1. The wind turbine consists of three adjustable blades of a length L=110 mm and a width C=45 mm. The rotor radius of the turbine is equal to R=157 mm. The wedging angle is measured between the rotation plane of the wind turbine and the chord (Figure 2).
Ref. designation
7 Wind turbine
6 Support
5 Ventilation chamber
4 Diffuser
3 Test section
2 Collector
1 Plenum
Figure 1. Wind tunnel
Figure 2. Geometric parameters of wind turbine
To determine the velocity profiles in different directions preselected in the test section of the wind tunnel, the anemometer type AM 4204 has been used (Figure 3). This anemometer measures the wind speed in different positions with a range variation between 0.2 and 20 m.s-1 and a resolution reaching 0.1 m.s-1. The different characteristics of this anemometer are summarized in table 1.
Figure 3. Anemometer emplacement
Description Anemometer type AM 4204
Maker Lutron
Probe type telescopic
Measurement parameters Air velocity, temperature, gas flow
Resolution Air velocity 0.1 m.s-1
Temperature 0.1°C
Precision Air velocity 5%
Temperature ± 0.8°C
Measuring range Velocity 0.1 m.s-1
Temperature from -20°C to +70°C
Table 1. Characteristics of the anemometer.
A tachometer type CA1725 is used for measuring the rotation speed of the rotor as presented in figure 4. The optical sensor can provide results without disrupting the movement of the rotor. Tachometer features are summarized in table 2.
Figure 4: Tachometer type CA1725
Description Tachometer type CA1725
Speed range 6 to 100000 tr/min
Resolution 0.0006 to 6 according size
Precision 10-4 reading ± 6 points
Supply 9 V
Autonomy 250 steps of 5 min with optical sensor
Dimension 21 × 72 × 47 mm
Weight 250 g
Table 2: Characteristics of the tachometer.
The dynamic torque exerted on the rotor shaft was measured with a DC generator which transforms the torque on its axis at an electrical current. For that, the generator, coupled with the dynamometer RZR-2102 model, display simultaneously the shape speed and the dynamic torque (Figure 5). This dynamometer has been used to provide mechanical power to the generator which delivers an electric current in a resistive load. Torque measurement integrated into the dynamometer, allows tracing the calibration curve that connects the electric current supplied by the generator to the dynamic torque. This calibration curve serves for determination of the dynamic torque after referring to the value of the electric current supplied by the generator (Figure 6).
Figure 5: electric dynamometer.
Figure 6: Calibration curve.
3. Numerical model
3.1 Mathematical formulation
In this study, the continuity equations, the momentum equations, the turbulent kinetic energy (k) and the dissipation rate of turbulent kinetic energy (ε) equations have been solved with the CFD code “Solid Works Flow simulation”. This code is based on solving Navier-Stokes equations with a finite volume discretization method. This technique consists in dividing the computational domain into elementary volumes around each node in the grid and it ensures continuity of flow between nodes. The spatial discretization is obtained by following a procedure for the tetrahedral interpolation scheme. As for the temporal discretization, the implicit formulation is adopted. The transport equation is integrated over the control volume.
The mathematical formulation is based on the Navier-Stokes equations. The equations for the conservation of the mass and momentum for the compressible and incompressible flow positions in the numerical analysis can be written in the Cartesian system:
The continuity equation is written as follows:
(1)
The Momentum equation is:
(2)
They appear a number of additional unknown defined by:
(3)
The Kronecker delta is defined by if elsewhere, .
In the present work, we have used the standard k-ε turbulence model. The transport equations for the turbulent kinetic energy k and the dissipation rate of the turbulent kinetic energy ε are written as follows:
(4)
(5)
The turbulent viscosity is defined by:
(6)
3.2. Computational domain and Boundary conditions
The computational domain is defined by the interior volume of the wind tunnel blocked by two planes: the first one is in the tranquillization chamber entry and the second one is in the exit of the diffuser (Figure 7). The velocity inlet, measured in the tranquilization chamber, is equal to V=3 m.s-1. The static pressure of the air flow through the drive section is made at the atmospheric conditions. For this reason, the pressure outlet is set equal to p=101325 Pa. Around the wind turbine, a rotating area with an angular velocity was considered. This model has been used in different anterior works and satisfactory results were obtained [16, 17].
Figure 7: Boundary conditions
4. Numerical results
In this study, the wedge angle is set equal to the value β = 24°. Different flow regimes defined by the Reynolds numbers equal to Re=217338, Re=242415, Re=257044 and Re=265403 are investigated. We present the aerodynamic characteristics such as the velocity fields, the average velocity, the static pressure, the dynamic pressure, the turbulent kinetic energy, the dissipation rate of the turbulent kinetic energy, the turbulent viscosity and the vorticity in different longitudinal and transverse planes defined by x = 0 mm and y = 0 mm (Figure 8).
Figure 8. Compliance planes
4.1. Velocity fields
Figures 9 and 10 present the distribution of the velocity field in different longitudinal planes in the rotating area defined by x=0 mm and y=0 mm for different values of the Reynolds numbers equal to Re=217338, Re=242415, Re=257044 and Re=265403. According to these results, it has been noted that the maximum value of the magnitude velocity reaches V=15 m.s-1 at the level of the test vein. In the test vein inlet, the flow has a horizontal direction, in the upstream rotor a deceleration movement appears. This fact is clearer in the rotor downstream, when a recirculation zone appears. The acceleration of the flow appears at the level of the blade and the downstream. Otherwise, it has been noted that the Reynolds number has a direct effect on the distribution of the velocity fields. In fact, the velocity values increase with the increase of the Reynolds numbers.
(a) Re=217338 (b) Re=242415
(c) Re=257044 (d) Re=265403
Figure 9: Velocity fields distribution in the longitudinal plane defined by x=0 mm.
(a) Re=217338 (b) Re=242415
(c) Re=257044 (d) Re=265403
Figure 10: Velocity fields distribution in the longitudinal plane defined by y=0 mm.
4.2. Average velocity
Figures 11 and 12 present the distribution of the average velocity in different longitudinal planes in the rotating area defined by x=0 mm and y=0 mm for different values of the Reynolds numbers equal to Re=217338, Re=242415, Re=257044 and Re=265403. According to these results, it has been noted that a wake characteristics of the maximum value of the magnitude velocity appears and the average velocity reaches the value V=15 m.s-1. This wake is more developed for Re=265403. In downstream of the wind rotor, the wake of characteristic of the minimum value is more developed for Re=217338. Otherwise, it has been noted that the Reynolds number has a direct effect on the distribution of the average velocity.
(a) Re=217338 (b) Re=242415
(c) Re=257044 (d) Re=265403
Figure 11: Average velocity distribution in the longitudinal plane defined by x=0 mm.
(a) Re=217338 (b) Re=242415
(c) Re=257044 (d) Re=265403
Figure 12: Average velocity distribution in the longitudinal plane defined by y=0 mm. 4.3. Static pressure
Figures 13 and 14 present the distribution of the static pressure in different longitudinal planes in the rotating area defined by x=0 mm and y=0 mm for different values of the Reynolds numbers equal to Re=217338, Re=242415, Re=257044 and Re=265403. According to these results, a compression zone has been observed in the wind turbine upstream. Also, a depression zone appears in the wind turbine downstream. Otherwise, it has been noted that the Reynolds number has a direct effect on the distribution of the static pressure. In fact, it has been noted that the depression zone is wider with the Re=265403.
(a) Re=217338 (b) Re=242415
(c) Re=257044 (d) Re=265403
Figure 13: Static pressure distribution in the longitudinal plane defined by x=0 mm.
(a) Re=217338 (b) Re=242415
(c) Re=257044 (d) Re=265403
Figure 14: Static pressure distribution in the longitudinal plane defined by y=0 mm.
4.4. Dynamic pressure
Figures 15 and 16 present the distribution of the dynamic pressure in different longitudinal planes in the rotating area defined by x=0 mm and y=0 mm for different values of the Reynolds numbers equal to Re=217338, Re=242415, Re=257044 and Re=265403. According to these results, it is clear that the dynamic pressure is uniform in the inlet of the test section. It increases with the air flow advancement. While approaching of the wind turbine, the dynamic pressure decreases again. The same fact is observed in the wind turbine downstream where a depression zone is developed more clearly. At level of the blades, a compression zone appears and extended around the turbine. Otherwise, it has been noted that the Reynolds number has a direct effect on the distribution of the dynamic pressure. In fact, it has been noted that the compression zone is more developed for a Reynolds number equal to Re=265403. However, the depression zone is wider for the Reynolds number equal to Re=217338.
(a) Re=217338 (b) Re=242415
(c) Re=257044 (d) Re=265403
Figure 15: Dynamic pressure distribution in the longitudinal plane defined by x=0 mm.
(a) Re=217338 (b) Re=242415
(c) Re=257044 (d) Re=265403
Figure 16: Dynamic pressure distribution in the longitudinal plane defined by y=0 mm.
4.5. Turbulent kinetic energy
Figures 17 and 18 present the distribution of the turbulent kinetic energy in different longitudinal planes in the rotating area defined by x=0 mm and y=0 mm for different values of the Reynolds numbers equal to Re=217338, Re=242415, Re=257044 and Re=265403. According to these results, a wake characteristic of the maximum values of the turbulent kinetic energy is developed in the wind turbine upstream and around the turbine blades. Also, it has been noted that the Reynolds number has a direct effect on the distributor of the turbulent kinetic energy. In fact, the wake extension is more developed with the Reynolds number equal to Re=265403.
(a) Re=217338 (b) Re=242415
(c) Re=257044 (d) Re=265403
Figure 17: Turbulent kinetic energy distribution in the longitudinal plane defined by x=0 mm.
(a) Re=217338 (b) Re=242415
(c) Re=257044 (c) Re=265403
Figure 18: Turbulent kinetic energy distribution in the longitudinal plane defined by y=0 mm.
4.6. Dissipation rate of the turbulent kinetic energy
Figures 19 and 20 present the distribution of the dissipation rate of the turbulent kinetic energy in different longitudinal planes in the rotating area defined by x=0 mm and y=0 mm for different values of the Reynolds numbers equal to Re=217338, Re=242415, Re=257044 and Re=265403. According to these results, a wake characteristic of the high dissipation rate of the turbulent kinetic energy is developed around the wind turbine upstream. The dissipation rate of the turbulent kinetic energy reached its minimum value in the turbine upstream. The maximum value of the dissipation rate of the turbulent kinetic energy has been observed around the axis and the wind turbine. Also, it has been noted that Reynolds number has an effect on the distribution of the dissipation rate of the turbulent kinetic energy. The largest wake is observed with Re=265403.
(a) Re=217338 (b) Re=242415
(c) Re=257044 (d) Re=265403
Figure 19: Dissipation rate of the turbulent kinetic energy distribution in the longitudinal plane defined by x=0 mm.
(a) Re=217338 (b) Re=242415
(c) Re=257044 (d) Re=265403
Figure 20: Dissipation rate of the turbulent kinetic energy distribution in the longitudinal plane defined by y=0 mm.
4.7. Turbulent viscosity
Figures 21 and 22 present the distribution of the turbulent viscosity in different longitudinal planes in the rotating area defined by x=0 mm and y=0 mm for different values of the Reynolds numbers equal to Re=217338, Re=242415, Re=257044 and Re=265403. According to these results, it has been noted that the turbulence viscosity reached its maximum value in the upstream of the wind rotor. While approaching to the turbine the turbulent viscosity drops rapidly. In the test vein, a wake characteristic of the maximum value of the turbulent viscosity is developed. Otherwise it has been noted that the Reynolds number has a direct effect on the distribution of the turbulent viscosity. In fact, the extension of the wake characteristic of the maximum value of the turbulent viscosity is more developed for Re=265403.
(a) Re=217338 (b) Re=242415
(c) Re=257044 (d) Re=265403
Figure 21: Turbulent viscosity distribution in the longitudinal plane defined by x=0 mm.
(a) Re=217338 (b) Re=242415
(c) Re=257044 (d) Re=265403
Figure 21: Turbulent viscosity distribution in the longitudinal plane defined by y=0 mm.
4.8. Vorticity
Figures 23 and 24 present the distribution of the vorticity in different longitudinal planes in the rotating area defined by x=0 mm and y=0 mm for different values of the Reynolds numbers equal to Re=217338, Re=242415, Re=257044 and Re=265403. According to these results, it has been noted that the turbulence viscosity increases near the wall. Indeed, a wake characteristic of the maximum value appears around the wind turbine and in the wind turbine downstream. Also it has been noted that the Reynolds number has an effect on the distribution of the vorticity. In fact, the extension of the wake increases with the increase of the Reynolds number. The vorticity gets its maximum values with Re=265403.
(a) Re=217338 (b) Re=242415
(c) Re=257044 (d) Re=265403
Figure 23: Vorticity distribution in the longitudinal plane defined by x=0 mm.
(a) Re=217338 (b) Re=242415
(c) Re=257044 (d) Re=265403
Figure 24: Vorticity distribution in the longitudinal plane defined by y=0 mm.
5. Comparison with experimental results
5.1. Velocity profiles
Experimental values of velocity gathered from the experiments conducted in the LASEM laboratories are compared with the numerical values obtained with the software “Solid Works Flow Simulation”. The velocity profiles are chosen for points situated in the test section in the planes defined by z=50 mm, z=100 mm, z=150 mm and z=-150 mm. The results are shown in figure 25 for the considered directions, values are taken along the direction defined by x=100 mm. The comparison between the numerical and experimental data leads us to the conclusion that despite some unconformities, the values are comparable. The numerical model seems to be able to predict the aerodynamic characteristics of the air flow.
Experimental Numerical
(a) z=50 mm (b) z=100 mm
(c) z=150 mm (d) z=100 mm
Figure 25: Velocity profiles in the plane x=100 mm for Re=217388.
(a) z=50 mm (b) z=100 mm
(c) z=150 mm (d) z=100 mm
Figure 25: Velocity profiles in the plane x=100 mm for Re=242415
(a) z=50 mm (b) z=100 mm
(c) z=150 mm (d) z=100 mm
Figure 25: Velocity profiles in the plane x=100 mm for Re=257044
(a) z=50 mm (b) z=100 mm
(c) z=150 mm (d) z=100 mm
Figure 25: Velocity profiles in the plane x=100 mm for Re=265403
5.2. Dynamic torque coefficient
Figure 26 shows the variation of the dynamic torque coefficient exerted on the rotor axis as a function of the specific speed λ for different Reynolds numbers equal to Re=217338, Re=242415, Re=257044 and Re=265403. Figure 27 presents a superposition of the different results obtained for the considered Reynolds number. According to these results, it has been noted that the presented curves show a parabolic branch. In these conditions, the maximum value of the dynamic torque coefficient depends directly on the value of the Reynolds number. In fact the maximum value of the dynamic torque coefficient is equal to CMd = 0.082 for Re=217338, CMd = 0.074 for Re=242415, CMd = 0.09 for Re=2507044 and CMd = 0.089 for Re=265403. The comparison between the numerical and experimental results shows a good agreement. This confirms again the validity of the numerical method.
Experimental Numerical
(b) Re=217338 (b) Re=242415
(c) Re=257044 (d) Re=265403
Figure 30: Dynamic torque coefficients CMd for different Reynolds numbers
Figure 31: Superposition of the dynamic torque coefficients CMd.
5.3. Power coefficient
Figure 26 shows the variation of the power coefficient exerted on the rotor axis as a function of the specific speed λ for different Reynolds numbers equal to Re=217338, Re=242415, Re=257044 and Re=265403. Figure 27 presents a superposition of the different results obtained for the considered Reynolds number. According to these results, it has been noted that the presented curves show a parabolic branch. In these conditions, the maximum value of the dynamic torque coefficient increase when the Reynolds number increases. As an example, for the Reynolds number Re= 217338, the maximum value of the recovered power coefficient is equal to Cp= 0.028. However, for a Reynolds number equal to Re=265403, the recover power coefficient is equal to Cp= 0.039. The comparison between the numerical and experimental results shows a good agreement.
Experimental Numerical
(a) Re=217338. (b) Re=242415.
(c) Re=257044. (d) Re=265403.
Figure 32: Variation of power coefficient Cp.
Figure 33: Comparison of power coefficients Cp.
6. Conclusion
In this paper, we are interested in the study of the Reynolds number effect on the aerodynamic characteristics developed around a NACA2415 airfoil type wind turbine. Particularly, we have presented results of computer simulation provided by the software “SolidWorks flow simulation” such as velocity fields, static pressure, static pressure and the turbulence characteristics. The validation of the numerical method is based on the experimental investigation developed using a wind tunnel in terms of velocity profiles dynamic torque coefficient and power coefficient. According to these results, it is clear that the Reynolds number has a direct effect on the aerodynamic characteristic. Also, the comparison between the numerical and experimental results shows a good agreement. This knowledge has a great importance for the design of the new systems in terms of energy captured and delivered power.
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