Wind Energy Conversion Systems April 21-22, 2003. K Sudhakar Centre for Aerospace Systems Design & Engineering Department of Aerospace Engineering http://www.casde.iitb.ac.in/~sudhakar. Horizontal Axis WECS. Energy extraction at a plane normal to wind stream. Rotor plane - a disc.
Centre for Aerospace Systems Design & Engineering
Department of Aerospace Engineering
Energy extraction at a plane normal to wind stream.
Rotor plane - a disc
Forces and Moments on a body in relative motion with respect to air
Topics of intense study
aerospace vehicles, road vehicles, civil structures, wind turbines, etc.
V(50 m) / V(20 m) = 1.3 city
= 1.2 grassy
= 1.1 smooth
pActuator Disc Theory
p + 0.5 V2 = pd- + 0.5 Vd2
p + 0.5 V12 = pd+ + 0.5 Vd2
pd- - pd+ = 0.5 (V2- V12 ) = Vd (V- V1)
Vd = 0.5 (V+ V1) ; Vd = V( 1 - a); V1 = V( 1 - 2 a)
P = 0.5 Ad Vd (V2 - V12) = 0.5 Ad Vd 2Vd (V- V1)
= Ad Vd2(V- V1)
= Ad V2(1 - a)2 2aV
= 2 Ad V3 a (1 - a)2
P = 2 Ad V3 a (1 - a)2
CP= P / (0.5 Ad V3 ) ; CQ = Q/ (0.5 AdR V2 )
CT = T/ (0.5 Ad V2 ) ; = r / V
CP = 4 a (1 - a)2 ;CT = 4 a (1 - a)
dCP/da = 0 a = 1/3
CP-max = 16/27 ; CT @CP-max = 8/9 a = 1/3
CT-max = 1 ; CP @CT-max = 1/2 a = 1/2
Energy extraction through cranking of a rotor
Cranking torque supplied by air steam
Forces / moments applied by air stream?
Blade element theory of rotors?
Equal Drag Bodies
Airfoil of chord 150 mm
1 mm dia wire
Cpi - Energy extraction is through cranking