2) Assume that at rated conditions, the IEA 15MW reference wind turbine operates at a tip...

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2) Assume that at rated conditions, the IEA 15MW reference wind turbine operates at a tip speed ratio ( == 9). An initial guess is that at the spanwise section r/R=75% the axial induction U factor is 0.3 and the tangential (rotational) induction factor is approximately zero. By referring to the sectional aerofoil properties of the IEA 15MW (Ref [2]; Figure 2-3 and 2.4(a,c)) and ignoring prebend, a) use Blade Element Momentum theory to calculate the sectional lift and drag forces (N/m) at the blade section at this radius and hence obtain a second estimate of the axial and tangential induction factors. Show all working. [6 marks] Lift coefficient, c Lift coefficient, c/ 2.0 1.5 1.0 0.5 0.0- -0.5 -1.0 -20 -15 -10 -505 10 Angle of Attack [deg] 15 20 2.0- 1.5 1.0 0.5+ 0.0 -0.5 -1.0 125 100 75 50- 25 0 -25 -50- Lift over drag, Ci/cd 0.00 0.02 0.04 -20 -15 -10 (a) Airfoil lift coefficients 0.06 0.08 0.10 0.12 0.14 Drag coefficient, cd (b) Airfoil lift-drag polars -5 5 10 15 20 Angle of Attack [deg] (c) Airfoil lift-to-drag coefficients SNL-FFA-W3-500 Re=8.1e6 FFA-W3-211 Re-1e7 FFA-W3-241 Re=1e7 FFA-W3-270blend Re-1e7 FFA-W3-301 Re-1e7 FFA-W3-330blend Re=1e7 FFA-W3-360 Re-1e7 SNL-FFA-W3-500 Re-8.1e6 FFA-W3-211 Re=1e7 FFA-W3-241 Re-1e7 FFA-W3-270blend Re=1e7 FFA-W3-301 Re=1e7 FFA-W3-330blend Re-1e7 FFA-W3-360 Re=1e7 SNL-FFA-W3-500 Re=8.1e6 FFA-W3-211 Re-1e7 FFA-W3-241 Re-1e7 FFA-W3-270blend Re=1e7 FFA-W3-301 Re=1e7 FFA-W3-330blend Re-1e7 FFA-W3-360 Re=1e7 Figure 2-3. Aerodynamic polars for the airfoils used on the blade 16 5. N Chord [m] 1 0.0 0.2 15.0 12.5- 10.0- 7.5 5.0- 2.5- 0.0 Twist [deg] 0.4 0.6 0.8 1.0 Nondimensional Blade Span (r/R) (a) Chord length -2.5- 0.0 0.2 0.4 0.6 0.8 Prebend [m] Relative Thickness [%] 0 100 90- 80 70 60 50 40 30 20 0.0 0.2 0.4 0.6 0.8 1.0 Nondimensional Blade Span (r/R) (b) Relative thickness 1.0 0.0 0.2 Nondimensional Blade Span (r/R) (c) Twist 50 45 40- Pitch Axis Chord Location [%] 35 30 0.0 0.2 0.4 0.6 0.8 0.4 0.6 0.8 1.0 Nondimensional Blade Span (r/R) 1.0 Nondimensional Blade Span (r/R) (e) Chordwise offset Figure 2-4. Blade planform spanwise quantities (d) Prebend 2) Assume that at rated conditions, the IEA 15MW reference wind turbine operates at a tip speed ratio ( == 9). An initial guess is that at the spanwise section r/R=75% the axial induction U factor is 0.3 and the tangential (rotational) induction factor is approximately zero. By referring to the sectional aerofoil properties of the IEA 15MW (Ref [2]; Figure 2-3 and 2.4(a,c)) and ignoring prebend, a) use Blade Element Momentum theory to calculate the sectional lift and drag forces (N/m) at the blade section at this radius and hence obtain a second estimate of the axial and tangential induction factors. Show all working. [6 marks] Lift coefficient, c Lift coefficient, c/ 2.0 1.5 1.0 0.5 0.0- -0.5 -1.0 -20 -15 -10 -505 10 Angle of Attack [deg] 15 20 2.0- 1.5 1.0 0.5+ 0.0 -0.5 -1.0 125 100 75 50- 25 0 -25 -50- Lift over drag, Ci/cd 0.00 0.02 0.04 -20 -15 -10 (a) Airfoil lift coefficients 0.06 0.08 0.10 0.12 0.14 Drag coefficient, cd (b) Airfoil lift-drag polars -5 5 10 15 20 Angle of Attack [deg] (c) Airfoil lift-to-drag coefficients SNL-FFA-W3-500 Re=8.1e6 FFA-W3-211 Re-1e7 FFA-W3-241 Re=1e7 FFA-W3-270blend Re-1e7 FFA-W3-301 Re-1e7 FFA-W3-330blend Re=1e7 FFA-W3-360 Re-1e7 SNL-FFA-W3-500 Re-8.1e6 FFA-W3-211 Re=1e7 FFA-W3-241 Re-1e7 FFA-W3-270blend Re=1e7 FFA-W3-301 Re=1e7 FFA-W3-330blend Re-1e7 FFA-W3-360 Re=1e7 SNL-FFA-W3-500 Re=8.1e6 FFA-W3-211 Re-1e7 FFA-W3-241 Re-1e7 FFA-W3-270blend Re=1e7 FFA-W3-301 Re=1e7 FFA-W3-330blend Re-1e7 FFA-W3-360 Re=1e7 Figure 2-3. Aerodynamic polars for the airfoils used on the blade 16 5. N Chord [m] 1 0.0 0.2 15.0 12.5- 10.0- 7.5 5.0- 2.5- 0.0 Twist [deg] 0.4 0.6 0.8 1.0 Nondimensional Blade Span (r/R) (a) Chord length -2.5- 0.0 0.2 0.4 0.6 0.8 Prebend [m] Relative Thickness [%] 0 100 90- 80 70 60 50 40 30 20 0.0 0.2 0.4 0.6 0.8 1.0 Nondimensional Blade Span (r/R) (b) Relative thickness 1.0 0.0 0.2 Nondimensional Blade Span (r/R) (c) Twist 50 45 40- Pitch Axis Chord Location [%] 35 30 0.0 0.2 0.4 0.6 0.8 0.4 0.6 0.8 1.0 Nondimensional Blade Span (r/R) 1.0 Nondimensional Blade Span (r/R) (e) Chordwise offset Figure 2-4. Blade planform spanwise quantities (d) Prebend