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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




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