Comparative study of the performances of twisted two-bladed and three-bladed airfoil shaped H-Darrieus turbines by computational and experimental methods PDF

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Int. J. Renewable Energy Technology, Vol. 2, No. 4, 2011 425 Comparative study of the performances of twisted two-bladed and three-bladed airfoil shaped H-Darrieus turbines by computational and experimental methods Rajat Gupta* and Agnimitra Biswas National Institute of Technology Silchar, Silchar, ...

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Comparative study of the performances of twisted two-bladed and three-bladed airfoil shaped HDarrieus turbines ... Agnimitra Biswas International Journal of Renewable Energy Technology

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Int. J. Renewable Energy Technology, Vol. 2, No. 4, 2011

Comparative study of the performances of twisted two-bladed and three-bladed airfoil shaped H-Darrieus turbines by computational and experimental methods Rajat Gupta* and Agnimitra Biswas National Institute of Technology Silchar, Silchar, Assam, 788010, India Fax: +091-3842-224797 E-mail: [email protected] E-mail: [email protected] *Corresponding author Abstract: The vertical axis H-Darrieus turbines are simple in construction, self-starting, omni-directional, and self-regulating at all wind speeds. A comparative study of the performances of twisted two-bladed and three-bladed airfoil shaped H-Darrieus turbines was made. The models of the turbines were designed, fabricated, and tested in a subsonic wind tunnel. The power coefficients (Cp) and torque coefficients (Ct) were evaluated for ten numbers of height-to-diameter (H/D) ratios. Both Cp and Ct of the two-bladed turbine were higher than the three-bladed turbine. The maximum Cp for the two-bladed turbine was 0.237 and that for the three-bladed turbine was 0.151. The performances of the turbines were also compared computationally through 2D steady-state CFD simulations using Fluent 6.2 software. The agreement between the computational and experimental Cp was within ± 5.86%. The contour plots of static and dynamic pressures and velocity magnitudes were generated for chord Reynolds number of 8.5 × 104. At any position on the blade, dynamic pressure, velocity and also the velocity gradient between the ends were higher for the two-bladed turbine than the three-bladed turbine. Keywords: H-Darrieus turbine; power coefficient; torque coefficient; tip speed ratio; H/D ratio; CFD analysis; comparative study. Reference to this paper should be made as follows: Gupta, R. and Biswas, A. (2011) ‘Comparative study of the performances of twisted two-bladed and three-bladed airfoil shaped H-Darrieus turbines by computational and experimental methods’, Int. J. Renewable Energy Technology, Vol. 2, No. 4, pp.425–445. Biographical notes: Rajat Gupta received his PhD from the Indian Institute of Technology Delhi. He has been a Professor in Mechanical Engineering Department at NIT Silchar since 1996. He has published about 100 papers in various national/international journals/conferences. He is currently holding the post of Dean (Research and Consultancy) at NIT Silchar. Agnimitra Biswas received his PhD in Thermal Engineering from NIT Silchar under the guidance of Prof. Rajat Gupta. Currently, he is working as a Lecturer in Mechanical Engineering Department at NIT Silchar.

Copyright © 2011 Inderscience Enterprises Ltd.

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R. Gupta and A. Biswas

Introduction

The straight-bladed VAWT, i.e., H-Darrieus turbine was an invention included in the Darrieus (1931) patent. The H-Darrieus turbine, also known as H-rotor after its inventor, is a lift type device having two to three blades designed as airfoils. The blades are attached vertically to the central shaft through support arms. The support to the vertical axis helps the turbine maintain its shape. The H-Darrieus turbine is normally placed on the top of a tower in order to reach higher grade winds. Moreover, H-Darrieus turbine is the most suitable in extreme wind conditions, like wind gusts, cyclone, and its efficiency could be as high as HAWT when placed on rooftops (Mertens, 2003). Guy wires are generally used to support the shaft of eggbeater Darrieus turbine since it gives a stiffer, more robust construction. However, guy wires are optional for H-Darrieus turbine, which is an advantage. It is self-regulating in all wind speeds reaching its optimal rotational speed shortly after its cut-in wind speed (Islam et al., 2005). The blades of H-Darrieus turbine are much easier to manufacture than the blades of a HAWT or of an eggbeater Darrieus turbine. Light weight, highly flexible turbines are usually two-bladed turbines. Visual aesthetics, lower noise are the reasons for using three-bladed designs. Tangtonsakulwong and Chitsomboon (2006) did CFD simulation of wind flow over an untwisted three-bladed H-Darrieus turbine of NACA 0015 blade profile by using 3D unstructured-mesh finite volume method together with the sliding mesh technique to solve mass and momentum conservation equations. The maximum power coefficient of 0.20 was obtained at a tip speed ratio of 2.9. Jiang et al. (2007) developed 2D CFD models to study the effects of number of blades and tip speed ratio on the performance of multi-bladed H-Darrieus turbines. However, the highest power coefficient of their turbine was about 19%. Debnath et al. (2009) evaluated the performance of a combined Savonius-Darrieus rotor for various overlap conditions using Fluent 6.2 package and obtained a maximum power coefficient of 0.35 at 16.2% overlap. Jiang and Doi (2005) studied the performance of a straight-bladed Darrieus rotor with regards mounting position of blade, radius of rotor, tip speed ratio, blade numbers etc. Blade section is an important design parameter for any vertical axis wind turbine. Any twist given at the blade end can locally modify the angle of attack and the inflow dynamic pressure and hence minimise separation. Moreover, performance of the turbine could also improve since twist would increase the positive wetted part in the side-projected area of the blades and hence increase the average projected area. But experimental works on such turbines having blade twists are very few. Keeping this in view, in this paper, an attempt was made to compare the performances of twisted two-bladed and three-bladed airfoil shaped H-Darrieus turbines both experimentally and computationally. For this, the models of such turbines were designed, fabricated and tested in a subsonic wind tunnel available in the department. Blade twist of 30° was adopted for 10% of chord length from the trailing end such that twist on each blade was symmetrical. Power coefficients and torque coefficients of the turbines were evaluated for ten numbers of H/D ratios, namely 0.85, 1.0, 1.10, 1.33, 1.54, 1.72, 1.80, 1.92, 2.1 and 2.2. Further, the performances of both the turbines were compared computationally through 2D CFD simulations using Fluent 6.2 software.

Comparative study of the performances of twisted two-bladed

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The wind tunnel

The tests were conducted in an open-circuit subsonic wind tunnel available in the department (Figure 1). The cross-sectional area of the wind tunnel test section was 30 cm × 30 cm. The length of the test section was three meters. The operating range of the wind tunnel was 0–35 m/s. The blower section consisted of a three phase 15 kW motor having rated rpm of 2,890 that drove the fan. The motor had a starter for switching on and off the fan. The turbulence intensity of the wind tunnel was less than ± 1%. Moreover, the wind tunnel had a settling chamber of length 100 cm ahead of the test section with damping screens whose function was to break the large-scale disturbances and eddies up front, and then the contracting cone just upstream of the test section produced uniform velocity distribution in the test section. The brief description of the tunnel can be found in the available literature (Gupta et al., 2006). Figure 1

Schematic layout of open circuit subsonic wind tunnel

2.1 Wind tunnel blockage corrections When a wind turbine is placed in a wind tunnel, the object creates blockage to the flow, and it increases the local free stream wind velocity in the test section. In wind tunnel testing, wind tunnel blockage effect was taken into consideration to determine the actual power produced by the turbines. The total blockage correction factor is the sum of the correction factors for three major blockage effects namely, solid blockage, wake blockage and wind tunnel sidewall blockage. The turbine creates blockage to the flow by its physical presence in the tunnel, called solid blockage. As the turbine starts to rotate, there is a deficit of velocity downstream the turbine followed by a wake zone. The loss of performance due to this effect is taken into consideration in the form of wake blockage. In addition, sidewall blockage effect is also to be considered for the small-sized test section (30 cm × 30 cm). The solid blockage correction factor as given in the literature (Blackwell et al., 1978) can be expressed as:

φ=

AF AF = 4 ATS 4 H 'W

(1)

The wake blockage correction factor is given by

β=

qc − qu qu

(2)

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Further, qc Cd ,u = qu Cd ,c

(3)

where

Cd ,u Cd , c

⎡ 1 ⎛ A ⎞⎤ = ⎢1 + ⎜ F ⎟ ⎥ ⎣⎢ 4 ⎝ AS ⎠ ⎥⎦

2

(4)

And the correction factor for sidewall blockage ( ), as derived using the concept of Glauert correction methodology (Langer et al., 1996) for fixed pitch blades, can be expressed as:

γ =

2nδ w AS δ w n 2 c / H = 4 ATS 2 H 'W

(5)

The standard value of w for rectangular bladed turbine in an open circuit rectangular wind tunnel is approximately 0.1383 (Theodorsen, 1934). Therefore, the total blockage correction factor can be expressed as

ε = φ + β +γ

3

(6)

Model tests

The models of the twisted two-bladed and three -bladed airfoil shaped H-Darrieus turbines were designed and fabricated in the workshop. The height of the turbines was 20 cm, and the chord length of the blades was 5 cm. The actual shape of the airfoil blade of unit size is shown in Figure 2(a). An angular twist of 30° was provided at the trailing ends of the blades for 10% of chord length from the end, as shown in Figure 2(a), such that twist on each blade was symmetrical. The two-bladed and the three-bladed turbines are shown in Figure 2(b) and 2(c) respectively. The blades were mounted in such a fashion that the concave side of the twisted portion of the blades faced the upstream flow so that maximum power is extracted in the upwind pass. Though such cambered sections at negative incidence (which happens in the downwind pass) develops little lift, but such blades are better off than symmetrical NACA airfoil blades where upwind and downwind phenomenon are more or less even especially at low Reynolds number flows. The blades were supported on bolts of 5 mm in diameter and 12 cm in length. The central shaft of the turbines was 1.5 cm in diameter and about 25 cm in length. By changing the overall diameter but keeping the height constant, ten numbers of H/D ratios were obtained. The central shaft, base and the supports were made from mild steel, and the blades were made from lightweight aluminium. Ball bearings were used to support the shaft of the turbines at the base. The base was 7 cm wide and 2.4 cm thick.

Comparative study of the performances of twisted two-bladed Figure 2

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(a) The airfoil section with twist at the trailing end and twisted (b) two-bladed and (c) three-bladed airfoil shaped H-Darrieus turbine with Al blades (see online version for colours)

(a)

(b)

(c)

The models were tested in an open circuit subsonic wind tunnel. The turbine rpm was measured by a digital tachometer having a least count of 1 rpm, and wind velocity was measured with the help of pitot static tube connected to a U-tube

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manometer. There was a traversing mechanism by which pitot static tube was traversed vertically and horizontally. Two pitot static tubes were employed: one upstream and the other downstream of the turbine, which recorded the upstream and downstream wind velocities respectively. The tubes were fixed in the mid plane of the turbine. Wind velocity was adjusted by controlling the gate opening at the exit of the wind tunnel. The turbines were allowed to rotate from no load speed. The tip speed ratio is the ratio of blade tip speed to the wind velocity. Power output from the turbines was measured as the product of force transmitted by the turbines and the blade tip speed [equation (8)]. The force is nothing but the rate of change of angular momentum of wind stream across upstream to downstream of the turbine. The aerodynamic torque was calculated from the standard relationship of power and torque [equation (12)].

4

Analysis of the experimental performances of twisted two-bladed and three-bladed airfoil shaped H-Darrieus turbines

The performances of vertical axis wind turbines were determined in terms of the variations of power coefficients (Cp) and torque coefficients (Ct) with respect to tip speed ratios for ten numbers of height-to-diameter (H/D) ratios of the turbines, namely 0.85, 1.0, 1.10, 1.33, 1.54, 1.72, 1.80, 1.92, 2.1 and 2.2. For analysis, the following relations were used: Cp =

Pturbine Pmax

Pturbine = Pmax =

(7)

(

)

1 ρ A V12 − V22 Rω 2

1 3 ρ AV free _ block 2

V free _ block = V free * (1 + ε )

λ= T=

Rω V free

60 Pturbine 2π N

Ct =

Cp

λ

(8)

(9) (10) (11)

(12)

(13)

Figure 3(a) shows the comparison of power coefficients (Cp) versus H/D ratio for the two-bladed and three-bladed turbines, and Figure 3(b) shows the comparison of torque

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431

coefficients (Ct) versus H/D ratio for the turbines. These figures show that both Cp and Ct increase with the increase of H/D ratio up to the maximum and then decrease. Therefore, there are optimum H/D ratios at which both Cp and Ct are the highest. Further, Figure 3(a) shows that the optimum H/D ratios at the highest Cp of the turbines are same, i.e., 1.10. However, Figure 3(b) shows that the optimum H/D ratio at the highest Ct for the three-bladed turbine, i.e., 1.0 is less than that of the two-bladed turbine for which it is 1.10. Moreover, Figure 3(a) and 3(b) show that, for the three-bladed turbine, the optimum H/D ratio at the highest Ct is less than the optimum H/D ratio at the highest Cp. On the other hand, for the two-bladed turbine, the optimum H/D ratios at the highest Cp and Ct are same, i.e., 1.10. And the two-bladed turbine has overall higher Cp and Ct compared to the three-bladed turbine. The highest Cp for the two-bladed turbine at H/D = 1.10 is 0.237 whereas the highest Cp for the three-bladed turbine at the same optimum H/D = 0.151. The highest Ct for the two-bladed turbine at the optimum H/D = 1.10 is 0.103 whereas the highest Ct for the three-bladed turbine at the optimum H/D = 1.0 is 0.084. Figure 4(a) shows the comparison of power coefficient versus tip speed ratio for the two-bladed and the three-bladed turbines. Figure 4(b) shows the comparison of torque coefficient versus tip speed ratio for the turbines. Figure 4(a) shows that the maximum Cp of 0.237 is obtained for tip speed ratio of 2.524 for the two-bladed turbine, and the maximum Cp of 0.151 is obtained for tip speed ratio of 3.175 for the three-bladed turbine. Figure 4(b) shows that the maximum Ct of 0.103 is obtained for tip speed ratio of 1.636 for the two-bladed turbine, and the maximum Ct of 0.085 is obtained for tip speed ratio of 1.385 for the three-bladed turbine. To study the dependence of tip speed ratio on H/D ratio for the H-Darrieus turbines, the comparison of tip speed ratio versus H/D ratio for the turbines is shown in Figure 5. The tip speed ratio (2.524) at the maximum Cp is lower for the two-bladed turbine as compared to the three-bladed turbine for which it is 3.175. However, overall tip speed ratios for the three-bladed turbine are less than those for two-bladed turbine at any H/D ratio. Hence, the former would minimise the structural problems of vertical axis wind turbines. Figure 3

(a) Comparison of power coefficient vs. H/D ratio for two- and three-bladed airfoil shaped H-Darrieus turbines and (b) comparison of torque coefficient vs. H/D ratio for two- and three-bladed airfoil shaped H-Darrieus turbines

(a)

(b)

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R. Gupta and A. Biswas

Figure 4

(a) Comparison of power coefficient vs. tip speed ratio for two and three-bladed airfoil shaped H-Darrieus turbines and (b) comparison of torque coefficient vs. tip speed ratio for two and three-bladed airfoil shaped H-Darrieus turbines

(a) Figure 5

5

(b)

Comparison of tip speed ratio vs. H/D ratio for two and three-bladed airfoil chord H-Darrieus turbines

The computational methodology

The CFD simulations were carried out using Fluent 6.2 software in which the meshing was done in gambit of the package. The computational models of the twisted two-bladed and three-bladed airfoil shaped H-Darrieus turbines along with the boundary conditions are shown in Figure 6(a) and 6(b). Velocity inlet and outflow conditions were taken on the left and right boundaries respectively. The top and bottom boundaries of the computational domain, which signify the sidewalls of the wind tunnel, had symmetry conditions on them. The blades, central shaft and the support arms were set to standard wall conditions. For an H-Darrieus turbine, the general geometric properties of the blade cross-section are usually constant with varying span section. Both uniform and non-uniform meshing was done. On the four surrounding edges of the computational domain, uniform grid spaces were taken. The density of the mesh was kept higher at the blade ends since sudden change in blade section at the ends requires more dense nodes on them. On the blade surfaces of both the turbines, near wall boundary layers were built such that the distance of the first row of grid points (i.e., nodes) in direction normal to the

Comparative study of the performances of twisted two-bladed

433

solid boundary was 0.0001 cm. There were 28 rows of boundary points on each blade surface for both the turbines such that the total number of cells within the boundary layer was 5,300 for a total depth of boundary layer of 0.01 cm. The simulations of flows over the turbines were carried out for a same chord Reynolds number of 8.5 × 104. Unstructured (triangular) meshing was done on the face external to the turbines. The computations were initially carried out with various levels of refinement for the mesh until the grid independent limit (GIL) mesh (Masson et al., 1997) was attained. The resolution of the mesh at the important areas was varied in an attempt to reach grid independent limit mesh. Each refinement level was solved in Fluent with the same set of input parameters. The computed y+ value of the mesh considered for final simulation was less than 15 for both the turbines. The unstructured triangular mesh around an airfoil blade of such turbines is shown in Figure 7. Figure 6

(a) Computational domain of the two-bladed airfoil chord H-Darrieus turbine (b) computational domain of the three-bladed ai...