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Proceedings of International Symposium on EcoTopia Science 2007, ISETS07 (2007) Effects of Swept and Coning Angle of HAWT Rotor Blades on Aerodynamic Performance Examined by Numerical Analysis Masashi YOKOYAMA1, Yutaka HASEGAWA2, Hiroshi IMAMURA2 Junsuke MURATA1, Koji KIKUYAMA3 and Kensuke HIRATE1 1. Department of Mechanical Science & Engineering, Nagoya University, Nagoya, Japan 2. Ecotopia Science Institute, Nagoya University, Nagoya, Japan 3. Department of Environmental Information, Nagoya Sangyo University, Nagoya, Japan Abstract: Small and micro scale wind turbine generator systems have low efficiency relative to the large WTGS and need more improvement in their aerodynamic performance, although they are of great value as the power plants for an emergency case and/or remote, isolated locations. The present study aims at increasing the power coefficient of a micro scale horizontal axis wind turbine rotor by adopting blades with swept and/or coning angles. Those blades are expected to move the shedding position of the tip vor- tices away from the main part of the blade, and decrease the axial induced velocity in the rotor plane, leading to the increase of the rotor output. This paper presents the effects of the swept and coning angles of the blade on the flow field around the rotor and on the blade load, which have been examined by nu- merical analysis based on the panel method with free wake model. The calculated results show that mod- erate amount of the backward sweeping of the blade tip slightly increases the circulation around the blade section near the tip. The coning of the rotor blade shifts the vortex wake structure downstream, resulting in the increased circulation near the blade root. The expected increase in the power coefficient of the rotor is also discussed in relations to the swept and coning angles. Keywords: Wind Turbine, Panel Method, Free Wake Model, Swept Angle, Coning Angle 1. INTRODUCTION Laplace’s equation for a velocity potential F expressed In order to prevent global warming caused by emission as follows [2], of carbon dioxide, the wind turbine generator system Ñ 2F * = Ñ 2 (F + F 0 ) = 0 (1) (WTGS) is drawing attention as a generating power sys- where F0 is a velocity potential for an uniform flow and tem with low environmental load. Most of the Large F is perturbation velocity potential. Applying the scale WTGSs have attained generating cost comparable Green’s identity, the general solution for Eq. (1) satisfies to that of the thermal power plant, so that their utilization the following boundary integral equation, has become widely spread especially in European coun- tries. Small and micro scale WTGSs, in contrast, seem to 1 ¶ 1 have low efficiency relative to the large WTGS partly F * (r ) = 4p ò BLADE +WAKE m ¶n r ' dS because of the scale effects and need more improvement 1 1 in their aerodynamic performance, although they are of great value as the power plants for an emergency case - òs dS + F 0 ( 2) 4p BLADE r ' and/or remote, isolated locations. where s is a sink of singular element distributed on the The present study aims at increasing the power coeffi- object surface and m is a doublet. To solve Eq. (2), Neu- cient of a micro scale horizontal axis wind turbine mann type boundary condition is applied, which specifies (HAWT) rotor by adopting blades with swept and/or zero normal velocity component ¶F ¶n = 0 on the coning angles. Those blades are expected to shift the blade surface. This condition is expressed on the blade shedding position of the tip vortices away from the main coordinate system (xb, yb, z) (see Fig. 1) as below, part of the blade, and decrease the axial induced velocity ( W0 - Ω ´ rb + ÑΦ) × n = 0 (3) in the rotor plane. It can increase the kinetic energy flux where W and rb are angular velocity vector and position through the rotor plane, leading to the increase of the ro- vector on blade coordinate system, respectively. tor output. Vortex lattice method based on panel method was The present paper examines the effects of the swept adopted as a solution method for Eqs. (1) and (2). Divid- and coning angles of the blade on the flow field around ing blades into panel elements, aerodynamic effects of the rotor and on the blade load, by showing calculated panel elements are given by lattice panels which have results obtained from numerical analysis based on the vortex filaments with circulation G on four sides. Un- panel method with free wake model[1]. known quantity G is determined by collocation method. The circulation around blade is conserved by the Kel- 2. CALCULATION METHOD vin’s theorem and is released into the wake as vortex 2.1 Panel method with free wake model panels by time-marching method. For the advection of The governing equation for inviscid and incompressi- vortex panel, free wake model (by using Euler method) ble flow around a three-dimensional body is given as was adopted, in which vortex panels move with local Corresponding author: M. Yokoyama, h074128m@mbox.nagoya-u.ac.jp 420 Proceedings of International Symposium on EcoTopia Science 2007, ISETS07 (2007) velocities at each nodal position every time step. The swept angle is positive if the blade is folded to the Aerodynamic forces on the blade are calculated from opposite direction to the rotating direction. The coning the local angle of attack calculated from velocity field, angle bC is defined as an inclining angle of the blade by referring to two-dimensional airfoil characteristics from the rotor plane, as shown in Fig.4. obtained by wind tunnel tests. Attack angle is deduced For the evaluation of aerodynamic properties of the from the relation, Cl=a0a, using inviscid lift force calcu- wind turbine, those properties are normalized by the ro- lated from Kutta-Joukowski theorem[2], where a0 and a tor radius and swept area of the standard turbine rotor are lift curve slope and lift coefficient, respectively. whose blades are not inclined at all, i.e. bS= bC= 0deg. 3 2.2 Calculation conditions A series of numerical calculations have been per- formed in the present study for newly designed micro 2 scale HAWTs. Specifications of the turbine are listed in Drag coefficient Cd Lift coefficient Cl Table 1. For the airfoil section of the rotor blade, geome- try of M-F072[3] is used throughout the blade span. For 1 spatial discretization, the blade is divided into the vortex panel array of 8 times 10 in chordwise and spanwise di- rection based on cosine function. The azimuth step size 0 for the aerodynamic calculation is taken to be 10deg/step, that is, 36 steps per one revolution of the rotor. Two di- Cl mensional airfoil characteristic of M-F072 obtained at Re -1 Cd = 3.0×105 (see Fig. 2) was used for the viscous correc- a0(a+a Cl =0) tion of the aerodynamic force on the blade. The compu- tation was truncated when the vortex wake panels shed -2 -100 -50 0 50 100 from the rotor blade moved downwind from the rotor Angle of attack a plane with the distance more than 3 times the rotor di- Fig. 2 Aerofoil characteristic of M-F072(Re=3×105) ameter. Rotating y Wake panel direction Blade R Collocation bS Fig. 1 Coordinate systems and discretization of blade rcut Table 1 Specifications of wind turbine x O Number of Blades Nb 2 Radius R 0.8[m] Fig. 3 Definition of sweep angle Root Cut Off rcut 0.20R yb Blade Length b 0.64[m] Preset Angle θtip 0[deg] Blade Profile M-F072 blade 2.3 Definitions of swept and coning angles The definitions of swept and coning angle are illus- trated in Fig. 3. The swept angle bS at blade tip is taken bC W0 as an angle between a line connecting the center of the rotor to the 1/4 chord point of the blade tip, as shown in zb O W Fig. 3(a). And swept angle b at other position is deter- mined by linearly interpolating bs and angle at root as Fig. 4 Definition of coning angle follows; b = b S + b S * ( yb - rcut / b) (4) 421 Proceedings of International Symposium on EcoTopia Science 2007, ISETS07 (2007) 3. RESULTS AND DISCUSSIONS blade. 3.1 Effect of swept angle The distribution of the local circulation changes with Figure 5 shows the results of calculation for the stan- the coning angle as shown in Fig. 9. The circulation near dard rotor whose swept and coning angles of the blades the blade root increases with the coning angle. This are both zero, where Cp is power coefficient. The power comes from the reduction of the axial induced velocity, coefficient of the standard rotor has the maximum value which is similar to the case of swept angle. of CpMax= 0.380 at the design tip speed ratio of l=5. Variation of axial induced velocity with swept angle of the blades is shown for l=5 in Fig. 6. This shows that -0.2 Axial induced velocity wind/W0 axial induced velocity decreases at the blade root and in- -0.3 creases at blade tip as the swept angle increases. -0.4 Figure 7 shows the variation of circulation around lo- cal blade section with the swept angle, corresponding to -0.5 bC=0deg the results in Fig. 6. According to the increase of the -0.6 bC=5deg bC=10deg swept angle, the circulation at the blade tip rises and de- -0.7 bC=15deg scends at root. This is because variation of axial induced -0.8 velocity affects the velocity of inflow to the rotor. -0.9 -1.0 0.5 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1 Spanwise position yb/Rb 0.4 Power coefficient Cp Fig. 8 Axial induced velocity, l=5 0.3 0.2 0.3 0.30 0.25 Circulation G /W0Rb 0.1 0 0.2 0.20 2 4 6 8 10 12 0.15 0deg bC=0deg Tip speed ratiol 5deg bC=5deg 0.10 0.1 10deg bC=10deg Fig. 5 Power coefficient of standard rotor 0.05 15deg bC=15deg -0.2 0 Axial induced velocity wind/W0 -0.3 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.0 Spanwise position yb/Rb -0.4 -0.5 Fig. 9 Circulation, l=5 -0.6 bS=0deg -0.7 bS=5deg 4. CONCLUSION -0.8 bS=10deg The present paper analyzes numerically HAWT rotors -0.9 with swept and coning angles by panel method, and has -1.0 -1 investigated the effects of those angles on aerodynamic 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 properties of the rotors and variation of the flow field. 1 Spanwise position yb/Rb 1. When the swept angle is applied to the rotor blades, the axial induced velocity increases near the blade Fig. 6 Axial induced velocity, l=5 root and therefore circulation decreases there. 0.30 0.3 2. When the coning angle is applied to the rotor blade, 0.25 the shedding point of tip vortex shifts downstream Circulation G /W0Rb and axial induced velocity decreases, resulting in 0.2 0.20 the increase in the local circulation. 0.15 REFERENCES bS=0deg 0.1 0.10 1. H. Imamura, et al., Study on Unsteady Flow around bS=5deg 0.05 bS=10deg a HAWT Rotor by Panel Method: Calculation of Yawed Inflow Effects and Evaluation of Angle of 0 Attack in the Three-Dimensional Flow Field, Trans. 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1 of JASME. B, Vol.71, No.701, 2005, pp.154-161 Spanwise position yb/Rb 2. Katz,J. and Plotkin, A Low-speed aerodynamics, Fig. 7 Circulation, l=5 McGraw - Hill, 1991 3.2 Effect of coning angle 3. H. Matsumiya and Tetsuya Ogaki, Performance and Figure 8 shows variation of axial induced velocity Geometry of Airfoils Supply System (PEGASUS), with coning angle for l=5. With the increase of the con- National Institute of advanced industrial science and ing angle, the axial induced velocity decreases at blade technology root. This can be attributed to the fact that the wake vor- http://riodb.ibase.aist.go.jp/db060/index.html tices get distance from the blade root by inclining the 422

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