Design of Vertical Axis Wind Turbines P M V Subbarao Professor Mechanical Engineering Department A Stable and Rugged Configuration .....

General Configuration of a Vertical-Axis Wind Turbine

The Turbine Rotor Subsystem : VAWT Blades are shaped to approximate a troposkien

Local Details of The VAWT Z (m) r (m) V (m/s) 

Problem Statement

Annual Energy Fraction vs velocity Bromma Malamo Visby

Power Law Wind Profile The power law is used by many wind energy researchers. From the roughness length Lawn, water: z0 = 0.01 m Bushland: z0 = 0.1 m Towns, forests: z0 = 1m

Single Stream Tube (SST) Model V V Vw  VAWT blades project a cylinder that is parallel to the stream tube. The blades cross the normal actuator disc twice along their upwind and downwind path. The induction factor:  azimuth angle

Local Instantaneous Airfoil velocity and Force diagrams  The relative velocity component (VR)  Normalized relative velocity

Local Details of The VAWT Z (m) r (m)

Rotor and blade element coordinate system Rotor coordinate system Top view Blade element coordinate system

Kinetics Vs Kinematics of VWAT Normalized relative velocity angle of attack Normal Force Coefficient Tangential Force Coefficient

Local Instantaneous Torque per Blade The local instantaneous Tangential force (dFti) on one single airfoil at certain θ is The local instantaneous Torque (di) on one single airfoil at certain θ is A single blade passes each stream tube twice per revolution in the upstream and downsteam.

Local Details of The VAWT Z (m) r (m)

  VR(m/s) CL CD

Submitted By: Lt Col Vivek Bandal 2016MET2570 Ajay Singh 2016MET2563 Wind Power Farm Assgn:6 Submitted By: Lt Col Vivek Bandal 2016MET2570 Ajay Singh 2016MET2563

1st Quadrant θ in degrees α in degrees Vr Cl Cd 34.27054 0.00575 10 34.27054 0.00575 10 1.319134 34.16601 0.1427 0.00596 20 2.590579 33.94651 0.2793 0.00667 30 3.79075 33.61962 0.4202 0.00782 40 4.897208 33.19458 0.5793 0.00932 50 5.888261 32.68203 0.7225 0.01076 60 6.742567 32.09372 0.8143 0.0119 70 7.438771 31.44252 0.8723 0.01289 80 7.955274 30.74233 0.9142 0.01378 90 8.270232 30.00832 0.9418 0.01419

2nd Quadrant θ in degrees α in degrees Vr Cl Cd 90 8.270232 30.00832 0.9418 0.01419 100 8.361955 29.25706 0.9497 0.01433 110 8.209882 28.50677 0.9366 0.0141 120 7.796329 27.77751 0.9024 0.0134 130 7.109159 27.09119 0.8453 0.01237 140 6.14534 26.47122 0.7599 0.01114 150 4.915107 25.94184 0.5819 0.00935 160 3.445947 25.52685 0.3772 0.00743 170 1.785219 25.2478 0.1929 0.00616 180 1.28E-15 25.12196 0.00575

3rd Quadrant θ in degrees α in degrees Vr Cl Cd 180 1.28E-15 25.12196 0.00575 190 -1.82687 25.16015 -0.1972 0.00618 200 -3.60446 25.36514 -0.3955 0.0076 210 -5.24371 25.73084 -0.6287 0.00984 220 -6.66719 26.24266 -0.8082 0.01179 230 -7.81624 26.87872 -0.904 0.01344 240 -8.65431 27.61185 -0.9717 0.01506 250 -9.16649 28.41172 -1.0161 0.01592 260 -9.35645 29.24695 -1.0318 0.01634 270 -9.24207 30.08682 -1.0225 0.01607

4th Quadrant θ in degrees α in degrees Vr Cl Cd 270 -9.24207 30.08682 -1.0225 0.01607 280 -8.851 30.90266 -0.989 0.01535 290 -8.21686 31.66872 -0.9372 0.01411 300 -7.37613 32.36285 -0.8669 0.01282 310 -6.36614 32.96679 -0.7823 0.01146 320 -5.22353 33.4663 -0.626 0.0098 330 -3.98349 33.85113 -0.4476 0.00805 340 -2.6792 34.11484 -0.2891 0.00673 350 -1.34174 34.25453 -0.1451 0.00597 360 -1.9E-15 34.27054 0.00575

z=23.80m;r=16.63m;Vo=3.89;Lambda=4.4; me1130645 Theta (degree) Relative velocity alfa (degree) Cl Cd df/dh dT/dh 21.01 0.00 0.01 10 20.91 1.83 0.19 3.05 50.74 20 20.73 3.60 0.38 12.99 216.04 30 20.46 5.28 0.57 28.38 472.04 40 20.11 6.84 0.80 50.62 841.79 50 19.70 8.27 0.97 71.28 1185.33 60 19.22 9.53 1.05 0.02 84.46 1404.60 70 18.68 10.59 1.11 94.12 1565.17 80 18.11 11.43 1.16 99.22 1650.10 90 17.50 12.00 1.18 99.27 1650.83 100 16.87 12.28 1.20 95.45 1587.29 110 16.23 12.21 87.70 1458.50 120 15.61 11.76 1.17 76.49 1272.01 130 15.01 10.88 1.13 63.14 1049.96 140 14.46 9.54 47.93 797.12 150 13.98 7.74 0.94 32.36 538.10 160 13.60 5.49 0.61 14.03 233.24 170 13.35 2.87 0.30 3.33 55.40 180 13.23

z=23.80m;r=16.63m;Vo=3.89;Lambda=4.4; me1130645 Theta (degree) Relative velocity alfa (degree) Cl Cd df/dh dT/dh 180 13.23 0.00 0.01 190 13.26 -2.95 -0.31 4.76 79.10 200 13.45 -5.81 -0.65 19.25 320.11 210 13.78 -8.38 -0.98 43.25 719.29 220 14.25 -10.54 -1.11 0.02 65.57 1090.36 230 14.82 -12.19 -1.20 88.68 1474.67 240 15.48 -13.30 -1.24 0.03 110.41 1836.16 250 16.18 -13.88 -1.26 128.44 2135.88 260 16.90 -13.97 141.19 2348.02 270 17.61 -13.61 148.16 2463.85 280 18.29 -12.88 -1.22 146.66 2438.93 290 18.93 -11.83 -1.18 138.84 2308.95 300 19.50 -10.52 122.40 2035.48 310 19.99 -9.01 -1.02 101.42 1686.56 320 20.39 -7.34 -0.87 74.08 1231.87 330 20.69 -5.57 -0.62 41.54 690.85 340 20.90 -3.73 -0.39 18.44 306.70 350 21.00 -1.86 -0.20 5.06 84.21

Tutorial 6 z 19.5 m   Uinf 3.67 m/s a/sin(Theta) 0.07 r 12.2 m lambda 3.4 Re 5.49E+05 Theta Rad alfa rad alfa deg Vr Cl Cd dFti/dH dTi 16.148 0.00713 -2.7559 -33.622 10 0.174533 0.039208 2.246444 16.06066 0.2357 0.00758 0.636515 7.765485 20 0.349066 0.077172 4.421658 15.8914 0.4685 0.00913 10.11326 123.3817 30 0.523598 0.113423 6.498682 15.6456 0.7564 0.01178 26.81613 327.1568 40 0.698131 0.1475 8.451122 15.32934 0.9787 0.01466 45.0502 549.6125 50 0.872664 0.178931 10.252 14.94921 1.0854 0.01751 58.28453 711.0713 60 1.047197 0.207212 11.87241 14.5122 1.1708 0.0212 68.71843 838.3648 70 1.221729 0.231778 13.27992 14.02571 1.2359 0.02621 75.34545 919.2144 80 1.396262 0.251969 14.43675 13.49757 1.2707 0.03322 76.86438 937.7455 90 1.570795 0.266998 15.2979 12.93638 1.29 0.04017 74.81659 912.7624

z=43.2m theta alfa(degrees) Vr cl cd dFt dtau 8.494759206 0.00665 8.494759206 0.00665 -3.997483812 -19.95543919 10 3.808707036 8.419699667 0.4063 0.00776 11.36561198 56.73713499 20 7.535774745 8.286663886 0.8597 0.01203 57.67221759 287.8997102 30 11.16600116 8.09918349 1.1712 0.01739 114.6136505 572.1513434 40 14.68473281 7.860969466 1.3334 0.0298 159.162729 794.5403431 50 18.07659472 7.575742616 1.3197 0.07213 162.9905744 813.6489475 60 21.32369583 7.247104185 1.183 0.14006 131.1274811 654.5883857 70 24.40303041 6.878464253 80 27.2826479 6.473045749 90 29.91588692 6.033983634

z=43.2m theta alfa(degrees) Vr cl cd dFt dtau 270 34.03455601 6.298042774 280 30.7530634 6.784506105 290 27.21329936 7.218534764 300 23.49495442 7.594597458 1.1171 0.1875 131.3609317 655.753771 310 19.65828545 7.908599623 1.2441 0.10571 166.1971646 829.6562458 320 15.75035715 8.157814091 1.3591 0.03813 184.1798892 919.426007 330 11.80896173 8.340810975 1.2029 0.01874 132.0348767 659.1181046 340 7.865143315 8.457367805 0.9149 0.01259 67.16670693 335.296201 350 3.944871752 8.508351448 0.4168 0.00783 12.58143357 62.80651638

z 45.9 : U∞ 4.74 NACA0015 θ α Vr Cl Cd dFti/dh dτ/dh 0.00 36.45 0.01   NACA0015 θ α Vr Cl Cd dFti/dh dτ/dh 0.00 36.45 0.01 -12.96 -391.90 10 1.29 36.34 0.14 252.87 7646.68 20 2.52 36.12 0.27 311.64 9424.04 30 3.64 35.78 0.39 -335.73 -10152.39 40 4.64 35.34 0.49 -895.78 -27088.50 50 5.48 34.81 0.59 -759.13 -22956.02 60 6.15 34.19 0.68 -172.03 -5202.30 70 6.63 33.52 0.75 401.06 12128.04 80 6.92 32.79 0.79 721.15 21807.50 90 7.01 32.03 0.80 784.96 23737.10 100 6.91 31.25 0.78 637.59 19280.87 110 6.60 30.47 0.74 299.34 9051.94 120 6.11 29.71 0.67 -165.32 -4999.42 130 5.43 29.00 0.58 -544.36 -16461.40 140 4.59 28.36 -567.03 -17147.07 150 3.60 27.81 0.38 -183.43 -5547.00 160 2.48 27.38 184.39 5575.94 170 1.27 27.10 137.76 4165.90 180 26.97 -7.10 -214.56

z 45.9 : U∞ 4.74 NACA0015 θ α Vr Cl Cd dFti/dh dτ/dh 190 -1.30 27.01   NACA0015 θ α Vr Cl Cd dFti/dh dτ/dh 190 -1.30 27.01 -0.14 0.01 140.70 4254.65 200 -2.58 27.22 -0.28 166.52 5035.55 210 -3.80 27.60 -0.41 -267.83 -8099.32 220 -4.92 28.13 -0.52 -592.69 -17923.05 230 -5.90 28.79 -0.64 -305.03 -9224.26 240 -6.70 29.54 -0.76 376.35 11380.77 250 -7.30 30.37 -0.84 950.08 28730.46 260 -7.67 31.23 -0.89 1240.50 37512.78 270 -7.80 32.10 -0.91 1360.90 41153.68 280 -7.69 32.95 1389.05 42005.00 290 -7.33 33.74 1204.59 36426.71 300 -6.75 34.46 572.96 17326.25 310 -5.95 35.09 -0.65 -400.28 -12104.48 320 -4.97 35.61 -0.53 -950.23 -28734.81 330 -3.84 36.01 -489.58 -14804.99 340 -2.61 36.28 284.19 8593.79 350 -1.31 36.43 -0.15 269.61 8153.03 360 0.00 36.45 -12.96 -391.90

Time Averaged Local Torque The time averaged local torque generated by “B” blades and twice per revolution can be expressed as The time averaged total torque generated by “B” blades and twice per revolution can be expressed as

Local Details of The VAWT Z (m) r (m) V (m/s)  davg,loc