7390150.pdf

American Journal of Mechanical Engineering and Automation 2015; 2(1): 16-25 Published online January 30, 2015 (http://www.openscienceonline.com/journal/ajmea)

Effect of Number of Blades and Blade Chord Length on the Performance of Darrieus Wind Turbine Taher G. Abu-El-Yazied1, Ahmad M. Ali1, Mahdi S. Al-Ajmi2, Islam M. Hassan1, * 1 2

Design and Production Engineering Department, Faculty of Engineering, Ain Shams University, Cairo, Egypt Department of Production Engineering Technologies, College of Technological Studies, PAAET, Kuwait

Email address [email protected] (T. G. Abu-El-Yazied), [email protected] (A. M. Ali), [email protected] (I. M. Hassan)

To cite this article Taher G. Abu-El-Yazied, Ahmad M. Ali, Mahdi S. Al-Ajmi, Islam M. Hassan. Effect of Number of Blades and Blade Chord Length on the Performance of Darrieus Wind Turbine. American Journal of Mechanical Engineering and Automation. Vol. 2, No. 1, 2015, pp. 16-25.

Abstract In this article we will go through some parameters like number of blades and blade chord length that influencing the efficiency of straight Darrieus wind turbines. For this purpose, twelve models created with different number of blades and blade chord lengths to study there effect on the performance of Darrieus wind turbine. Two dimensional Computational fluid dynamics (CFD) analyses have been performed on a straight-bladed Darrieus-type rotor. After describing the computational model, a complete campaign of simulations using K-ε turbulence model is chosen to perform the transient simulations and multiple reference frame (MRF) model capability of a (CFD) solver is used to express the dimensionless form of power output of the wind turbine as a function of the wind free stream velocity and the rotor’s rotational speed for a two, three, four and six-bladed architecture characterized by a NACA 0021 airfoil. It was found that, max power coefficient and its corresponding tip speed ratio were obtained at number of blades equal two and increase in power coefficient related to castelli wind turbine by 3.35%. Increasing in blade chord length increase the power coefficient till a certain limit after which power coefficient was dramatically decreased due to increase in solidity and decreasing corresponding tip speed ratio. Both torque ripple factor and normal force on turbine blade were decreased with increasing of the number of blades and decreasing the blade chord length.

Keywords Darrieus, Number of Blades, Blade Chord Length and Solidity

1. Introduction and Background It is a well-known that wind energy is very important as one of clean energy resources, and wind rotors are the most important of the wind energy. There are two different physical principles to extract power from wind. The first of them is the airfoil drag method, and the second is the airfoil lift principle. The Darrieus turbine is the most common VAWT invented in 1931 [1-5]. On the basis of the second principle, a lot of investigations aim to improve the performance of vertical axis wind turbine like Darrieus and Savonius by increasing wind velocity. The differences between a horizontal and a vertical axis wind turbine are many, including their utilization: horizontal axis wind turbine is popular for large scale power generation, while the vertical axis wind turbine is utilized for

small scale power generation [6, 7]. The Number of blade is a very important term in any kind of turbine. Number of blades are affected the speed and efficiency of turbine. The most commonly used wind turbines use three blades [8]. Considerable improvements in the understanding of VAWT can be achieved through the use of CFD. This paper aims at studying the effect of changing the design parameters, number of blades, blade chord length, and turbine solidity, on the performance of the H-Darrieus vertical axis wind turbine with fixed pitch angle through CFD simulations [9, 10].

2. Problem Formulation The speed ratio (λ) is defined as:

American Journal of Mechanical Engineering and Automation 2015; 201 2(1): 16-25 16

λ

(1)

A relation between the azimuth angle (θ), the angle of attack (α) and the speed ratio (λ) has been obtained from the velocity triangle in Figure 1,, this relation is as follow: α

tan

(2)

If the airfoil is set at an angle of incidence (α) in a fluid flow and according to the standard airfoil theory, it will generate a lift force (FL) normal to the free stream and a drag force (FD) in the direction of the free stream. These lift and drag forces can then be resolved to get the tangential force ce (FT) and the axial force (FN) as shown in Figure 1.. The tangential force (FT) has the instantaneous responsibility of the torque and the power outputs from the Darrieus turbine. For a Darrieus rotor of height (H), a wind of incoming velocity (V), the mechanical power (P) and the mechanical torque on the axis of a Darrieus turbine can respectively be write as follows:

C

17

! " # $ "

C C C C

(3)

% ! " # $ " ! #$ "

(4) "

&'() ! #$ * "

C

(5) (6)

λ

(7)

Where CT and Cp are respectively the torque coefficient and the power coefficient, (P) is the mechanical power extracted, (ρ) is the air density, (A) is the turbine swept area, (R) is radius of turbine and (V) is wind free stream velocity. Power Coefficient depends ds on wind speed due to aerodynamic complexities of blade designs. And CL and CD are respectively Lift and drag coefficients.

Figure 1. Forces and velocities distribution on Darrieus rotor airfoil a [3, 11, 12]

Between the many factors that influence the aerodynamic behavior of the rotor, an important role is played by its solidity, its means how much of the area that the turbine blades sweep through (swept swept area), is occupied by the turbines blades, and defined as: σ

to verified turbulence model [11, 13]. Rotor azimuthal position was identified by the angular coordinate of the pressure center of blade No. 1 (set at 0.25c for NACA 0021 airfoil), starting between the 2nd and 3rd Cartesian plane octants, as can be seen from Figure 2. 2

(8)

Where, (n) denotes the number of blades and (c) the chord length.

3. Geometrical Models The aim of the present work is to numerically analyze the aerodynamic behavior of a two, three, four and six bladed Darrieus VAWT operating at different angular velocities, for a constant wind speed of 9 m/s. The main features and models solidity of the tested sted turbines models are summarized in Table 1.. Model 3 has the same dimensions of published experimental Darrieus wind turbine results and it will be used

Figure 2. Azimuthal coordinate of blade midsection’s center of pressure [11].

18 Taher G. Abu-El-Yazied et al.: Effect of Number of Blades and Blade Chord Length on the Performance of Darrieus Wind Turbine

Table 1. Main geometrical features of the tested models Models 1 2 1030 1 (2D simulation) NACA 0021 85.8 128.7 0.17 0.25 2 2

Features Drotor [mm] Hrotor [m] Blade profile c [mm] Solidity σ Number of blades(n)

3

4

5

6

7

8

9

10

11

12

85.8 0.25 3

170 0.5 3

85.8 0.33 4

170 0.66 4

64.35 0.25 4

85.8 0.5 6

170 0.99 6

42.9 0.25 6

250 0.48 2

300 0.87 3

Table 2. Mesh size for the tested models Features Number of elements(n) Blade Size Element [mm] Growth rate

Models 1

2

3

4

5

6

7

8

9

10

11

12

148888

155487

149125

177107

165969

191154

158166

185383

223009

161255

155955

179636

0.71 1.1

4. Description of the Numerical Flow Field

square far-field being stationary and shaft field being stationary as shown in Figure 3. The far-field mesh which is of hexahedral type is less dense as compared to hexahedral mesh in the rotary zone.

Three separate zones are created, rotor zone being rotary,

Figure 3. Schema of rotor sub-grid area and open domain for the three bladed VAWT

Inlet was set as a velocity inlet, with a constant velocity profile of 9 m/s, while outlet was set as a pressure outlet. Two symmetry boundary conditions were used for the two side walls. The appropriate size of the computational domain has been investigated. A computational domain of increasing dimensions (square domain of size, suitably normalized by the rotor radius R, in this work, the ratio between the square domain length and the rotor radius is 28, after different domain sizes ranging from 20R to 60Rperformed for one geometrical configuration “at TSR 2.62” as a domain size independent test lead to a relative variation of the output quantity below 0.5 %., by using Gambit 2.4 for modeling and meshing and Ansys Fluent 14.5 for CFD simulation [13].

5. Discretization of the Numerical Flow Field All created meshes with the same grid size and growth factor. Turbulence model used in this work is Realizable K-ɛ Turbulence model with standard wall function. After implementing simulation software we found that the y+ values found in present work near all walls are around 40 which fall within the recommended range [Best-practice CFD (30 < y+ < 300)]. Samples of 2-D mesh discretization of the tested models shown in Figure 4and Figure 5 and setting mesh size to neutralized its effect on the power coefficient is shown in Table 2.

American Journal of Mechanical Engineering and Automation 2015; 2(1): 16-25

19

Figure 4. Sample 2-D mesh discretization of the VAWT

Figure 5. Mesh for NACA 0021 blade section

6. Main Features of the Numerical Simulations A complete campaign of simulations, based on full RANS unsteady calculations, was performed for a two, three, four and six-bladed rotor architecture characterized by a NACA 0021 airfoil. The tip speed ratio (λ) was varied from a value of λ=1.44 (which corresponds to an angular velocity of ω=25.1 rad/s) to λ=3.3 (which corresponds to an angular velocity of ω=57.6 rad/s). These conditions correspond to a range of blade Reynolds numbers from 2.69*104 to 1.05*105 for all Twelve models in Table 1. The blade Reynolds number for this work was defined as: Re

#

μ

(9)

The dynamic viscosity (µ) was assumed to be 1.78·10-5 Pa·s, the density (ρ) was set to 1.225 kg/m3 and the free stream velocity (V) was set to 9 m/s.

7. Numerical Solution The effect of the turbulence model is verified and shown in

Figure 6. These results give a good agreement obtained between experiments and present CFD for the target function, Cp, when using the realizable k-ε turbulence model. Same tendency has been observed for other studies, proving the interest of this model for fast CFD simulations. This model is usually recommended for rotating bodies. The realizable k-ε model usually provides improved results for swirling flows and flow involving separation when compared to the standard k-ε model. The near-wall treatment relies on standard wall functions. The present study involves the application of SIMPLE scheme. Among several special discretization schemes available in FLUENT, Least squares cell based gradient with Standard pressure and second order upwind scheme are found to be appropriate for the present study. Simulation begins with continues with the second order, and among several Transient formulation available second order implicit are found to be appropriate for the present work. Convergence criterion for the solution is set as 10-5. Currently, our area of consideration is to determine the forces acting on each of the three rotating airfoils and to obtain an optimum value of tip speed ratio which gives the maximum power output when wind passes the turbine at a speed of 9 m/s. The two transport equations that need to be solved for this model are for the kinetic energy of turbulence, k, and the rate of dissipation of turbulence, ε [14]: .(01)

+

.(0D)

+

.3

.3

.

.56 .

.56

.

(783 9)

(783 C)

.56 .

.56

;< + =

;< + 6 @

=6

@

.1

>? .56 .D

>E .56

+F

+ A1 − 7C D

1

A1 − F 7

(10)

D" 1

(11)

The quantities C1, C2, σk, and se are empirical constants. The quantity Gk appearing in both equations is a generation term for turbulence. It contains products of velocity gradients, and also depends on the turbulent viscosity:

20 Taher G. Abu-El-Yazied et al.: Effect of Number of Blades and Blade Chord Length on the Performance of Darrieus Wind Turbine

A1

.G6

<3 (

.5H

+

.GH .GH ) .56 .56

(12)

Figure 7, Figure 8 and Figure 9, and with blade chord length 170 mm as shown in Figure 10, Figure 11 and Figure 12.

Other source terms can be added to Equations (11) and (12) to include other physical effects such as swirl, buoyancy or compressibility, for example. The turbulent viscosity is derived from both k and ɛ, and involves a constant taken from experimental data, Cm, which has a value of 0.09: <3

7F=

1" D

(13)

All values of setting parameters for fluent software, used in the present work were shown in Table 3.

8. Results and Discussion The following results represent the values of the power coefficient of the analyzed models mentioned in Table 1 as a function of the tip speed ratio, for an incident wind speed of 9 m/s. The peak power coefficients for the analyzed rotor configurations are presented in Table 4, using the power coefficient of the verified three-bladed turbine as a reference, a percentage of maximum performance calculated for other configurations. And a percentage of the value of tip speed ratio to obtain the peak power is calculated for other configurations as shown in Table 4.

Figure 7. Power coefficient as a function of tip speed ratio for models with chord equal 85.8 mm

Figure 8. Effect of solidity and number of blades on power coefficient at c=85.6 mm

Figure 6. Verification of computational model, compared to experimental and CFD results for a Darrieus turbine [13]

8.1. The Effect of Turbine Parameters on Power Coefficient

Figure 9. Effect of solidity and number of blades on TSR that obtained maximum power coefficient at c=85.6 mm

8.1.1. Effect of Number of Blades Numerical analysis was performed in order to understand the effect of blade number and solidity on the behavior of a straight-bladed vertical-axis wind turbine. It was found that, maximum power coefficient was increased with increasing in Solidity and number of blades for number of blade lower than 3.And Maximum power coefficient was decreased with increasing in Solidity and number of blades for blade number upper than 3. Also it was found that, corresponding tip speed ratio obtained this maximum power coefficient was decreased with increase solidity and number of blades. These analyses obtained with blade chord length equal 85.6 as shown in

Figure 10. Power coefficient as a function of tip speed ratio for models with blade chord equal to 170 mm

American Journal of Mechanical Engineering and Automation 2015; 2(1): 16-25

Figure 11. Effect of solidity and number of blades on max power coefficient with chord length equal 170 mm

21

Figure 12. Effect of solidity and number of blades on λ obtained max power coefficient with chord length equal 170 mm

Table 3. Values of setting parameters for fluent software Solution type Transient Steady state Turbulence Pressure Momentum

Sliding mesh 2nd order implicit pseudo-transient Realizable k-ε (standard wall function) 2nd order 2nd order 2nd order 2nd order Coupled Simple

ε k P-V Coupling (steady state) P-V Coupling (Transient)

Table 4. Values of peak power and corresponding tip speed ratios with respect to model 3 Model no. 1 2 3 4 5 6 7 8 9 10 11 12

n 2 2 3 3 4 4 4 6 6 6 2 3

λCp,max 3.5 2.62 2.62 2.03 2.62 1.67 2.8 2.32 1.67 2.8 2.03 1.43

Cp,max 0.289 0.3235 0.313 0.319 0.274 0.273 0.205 0.217 0.214 0.022 0.29 0.249

σ 0.17 0.25 0.25 0.5 0.33 0.66 0.25 0.5 0.99 0.25 0.48 0.87

%Cp,max -7.67 3.35 0 1.92 -12.46 -12.78 -34.5 -30.67 -31.63 -92.97 -7 -20.45

% λCp,max 33.59 0 0 -22.52 0 -36.26 6.87 -11.45 -36.26 6.87 -22.52 -45.41

8.1.2. Combined Effect of Number of Blades and Chord Length at Same Solidity

Figure 14. Tip speed ration for maximum Cp as a function of number of blades at same solidity 0.25

Figure 13. Power coefficient as a function of tip speed ratio for models with solidity equal to 0.25

It was found “as in Figure 13” that; maximum power coefficient was increased with increasing solidity and increasing blade chord length at same number of blades as shown in Figure 14. Also it was found that, corresponding tip

22 Taher G. Abu-El-Yazied et al.: Effect of Number of Blades and Blade Chord Length on the Performance of Darrieus Wind Turbine

speed ratio obtained this maximum power coefficient was decreased with increasing solidity and increasing chord length at same blade numbers as shown in Figure 15.

Figure 18. Maximum Cp as a function of solidity at same number of blades

Figure 15. Maximum Cp as a function of number of blades at same solidity 0.25

8.1.3. Effect of Blade Chord Length It was found “as in Figure 16” that; corresponding tip speed ratio obtained maximum power coefficient was decreased with increasing solidity and increasing chord length at same blade numbers as shown in Figure 19. Also it was found that, maximum power coefficient was increased with increasing solidity and increasing blade chord length at same number of blades as shown in Figure 18.But after certain value of solidity “as in number of blades equal 4” power coefficient was decreased was increasing blade chord length and increasing solidity.

The velocity distributions obtained through numerical analysis for some rotor configurations are given in figures from Figure 19 to Figure 22. Figures from Figure 23 to Figure 26 display the distribution of the instantaneous power coefficient as a function of time for the rotor blades and for optimum TSR for some models, showing the contribution of each blade to overall rotor performance. Three peaks or two peaks according to number of blades of the instantaneous power coefficient can be seen.

Figure 19. Velocity distributions for the rotor at TSR 2.62 on rotor and around blade for model 2

Figure 16. Power coefficient as a function of tip speed ratio for models with number of blades equal to 2 Figure 20. Velocity distributions for the rotor at TSR 2.03 on rotor and around blade for model 4

Figure 17. Tip speed ration for maximum Cp as a function of solidity at same number of blades

Figure 21. Velocity distributions for the rotor at TSR 2.62 on rotor and around blade for model 5

American Journal of Mechanical Engineering and Automation 2015; 2(1): 16-25

Figure 22. Velocity distributions for the rotor at TSR 2.32 on rotor and around blade for model 8

23

Figure 26. Value of instantaneous Cp as a function of azimuth angle θ for model 8 and the Betz’s limit at TSR 2.32

8.2. The Effect of Turbine Parameters on Torque Ripple It was found that, torque ripple factor for wind turbine was decreased with increasing number of blades and increasing blade chord length as shown in Figure 27.

Figure 23. Value of instantaneous Cp as a function of azimuth angle θ for model 2 and the Betz’s limit at TSR 2.62

Figure 27. Comparison of torque ripple factor for different number of blades models, at various TSR

8.3. The Effect of Turbine Parameters on Normal Force on Blade

Figure 24. Value of instantaneous Cp as a function of azimuth angle θ for model 4 and the Betz’s limit at TSR 2.03

Figure 25. Value of instantaneous Cp as a function of azimuth angle θ for model 5 and the Betz’s limit at TSR 2.62

Numerical analysis was performed in order to understand the effect of blade number and blade chord length on normal force on turbine blade. Aerodynamic radial force on the blade for the tip speed ratio of peak power coefficient (the force is considered as negative if the airfoil is pushed towards the rotor axis).

Figure 28. Dynamic normal forces as a function of airfoil position for 3blade h-rotor wind turbines at λCp, max with same solidity

24 Taher G. Abu-El-Yazied et al.: Effect of Number of Blades and Blade Chord Length on the Performance of Darrieus Wind Turbine

Figure 29. Dynamic normal forces as a function of airfoil position for 3blade h-rotor wind turbines at λCp, max with number of blades equal 3

ratio for maximum coefficient decrease so after certain point increasing in blade chord length minimize power coefficient. It was found that, normal force “radial component” was decreased with increasing number of blades and decreasing chord length at same solidity. With regard to the radial component of the aerodynamic forces, an increase in blade number brings to a decrease of this force, which is mush desirable from a structural perspective, but was penalized as much as efficiency is important. It was found that, torque ripple factor for wind turbine was decreased with increasing number of blades and increasing blade chord length. The combined effect of aerodynamic radial force and centrifugal force on the structural behavior of the blade should be investigating in the future.

Nomenclature

Figure 30. Dynamic normal forces as a function of airfoil position for 3blade h-rotor wind turbines at λCp, max with blade chord length equal 170 mm

It was found that, normal force was decrease with increasing blade number and decreasing chord length at same solidity as shown in Figure 28. And normal force on blade was increased with increasing solidity and increasing chord length at same number of blades as shown in Figure 29. Also it was found that, normal force on blade was increased with decreasing solidity and decreasing number of blades at same blade chord length as shown in Figure 30.

9. Conclusion The following conclusions are drawn on the basis of results obtained from Numerical analysis was performed to understand the effect of number of blades and blade chord length on the behavior of a straight-bladed vertical-axis wind turbine as shown in previous results: The numerically expected peak of power coefficient dropped with the increase of rotor solidity, while it moved to lower tip speed ratio. Actually, larger number of blades allowed to reach the maximum power coefficient for lower angular velocities, but was penalized as much as efficiency is important. Increasing in chord length and decreasing in number of blades maximize power coefficient. But influence of increasing blade chord length with limit, as chord length increase solidity increase and corresponding tip speed

A Cp CT C D FL FD FT FN FR H N n P R θ ω µ V w k ε Rec TRF T u α σ λ

projected area of rotor (DH), m2 power coefficient torque coefficient blade chord, m turbine diameter (2R), m lift force, N drag force, N tangential force, N axial force, N resultant force, N blade height, m rotational speed of rotor, rpm number of blades output power (2πNT/60), W radius of turbine, m azimuth angle, (˚) angular speed, 1/s Viscosity (kg/m s) [m/s] unperturbed wind velocity at computational domain entrance [m/s] relative wind velocity at blade position kinetic energy of turbulence the rate of dissipation of turbulence [-] blade Reynolds numbers torque ripple factor output torque, Nm peripheral velocity of the blade, m/s angle of attack, (˚) solidity, (nc/2R) [-] TSR tip-speed ratio,

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