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Wind Energy Conversion Systems April 21-22, 2003

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.

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Wind Energy Conversion Systems April 21-22, 2003

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  1. Wind Energy Conversion SystemsApril 21-22, 2003 K Sudhakar Centre for Aerospace Systems Design & Engineering Department of Aerospace Engineering http://www.casde.iitb.ac.in/~sudhakar

  2. Horizontal Axis WECS Energy extraction at a plane normal to wind stream. Rotor plane - a disc

  3. Aerodynamics of Wind Turbines Aerodynamics 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.

  4. Atmosphere • International Standard Atmosphere • Sea level pressure = 101325 Pa • Sea level temperature = 288.16 K (IRA 303.16) • Sea level density = 1.226 kg/m^3 (IRA 1.164) • dt/dh = -0.0065 K/m • p/pSL = (t/tSL)5.2579 • Planetary boundary layer extends to 2000m V(50 m) / V(20 m) = 1.3 city = 1.2 grassy = 1.1 smooth

  5. A1, V1 A2, V2 Bernoulli Equation p + 0.5  V2 = constant Incompressible flows; along a streamline, . . Internal flows: Conservation of mass;  A V = constant If  is constant, A1 V1 =A2 V2

  6. A  V p  pd+ pd- A d Vd A 1 V1 p Actuator Disc Theory A  V= A d Vd =A1 V1 ; mass flow rate, m =  Ad Vd P = 0.5 m (V2 - V12) = 0.5  Ad Vd (V2 - V12) T = m (V- V1) =  Ad Vd (V- V1) = Ad ( pd- - pd+) pd- - pd+ =  Vd (V- V1)

  7. A  V p  pd+ pd- A d Vd A 1 V1 p Actuator Disc Theory p  + 0.5  V2 = pd- + 0.5  Vd2 p  + 0.5  V12 = pd+ + 0.5  Vd2 pd- - pd+ = 0.5  (V2- V12 ) =  Vd (V- V1) Vd = 0.5 (V+ V1) ; Vd = V( 1 - a); V1 = V( 1 - 2 a) P = 0.5  Ad Vd (V2 - V12) = 0.5  Ad Vd 2Vd (V- V1) =  Ad Vd2(V- V1) =  Ad V2(1 - a)2 2aV = 2  Ad V3 a (1 - a)2

  8. Actuator Disc Theory P = 2  Ad V3 a (1 - a)2 Non-dimensional quantities, CP= P / (0.5  Ad V3 ) ; CQ = Q/ (0.5  AdR V2 ) CT = T/ (0.5  Ad V2 ) ;  = 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

  9. Rotor & Blades Energy extraction through cranking of a rotor Cranking torque supplied by air steam Forces / moments applied by air stream? Blade element theory of rotors?

  10. M F *P1 V Po Aerodynamics Aerodynamics - Forces and Moments on a body in relative motion with respect to air

  11. y n u rMRP ds V Forces & Moments Basic Mechanisms • Force due to normal pressure, p = - p ds n • Force due to tangential stress,  =  ds (  n = 0)

  12. drag V Drag & Lift • D - Drag is along V • L - Lift is the force in the harnessed direction How to maximise L/D

  13. Skin friction drag, Df Pressure drag, DP Drag For steam lined shapes Df >> DP For bluff bodies DP >> Df

  14. Streamlining! Equal Drag Bodies Airfoil of chord 150 mm 1 mm dia wire

  15. r  ,Q Tower loads V Wind Turbine Typical Vertical Axis WECS - Rotor with n-blades Cranked by airflow. Cranking torque?

  16. Lift drag V Wind Turbine Rotor How to compute Q = Torque, T = Tower load

  17. Why non-dimensional Coefficients • With dimensional values • At each (, , , V , a, c) measure L, D, M • Many tests required • With non-dimensional coefficients • At desired Re, M,  and V • for each  measure L, D, M • Convert to CL, CD, CM • At any other  and V compute L, D M

  18. Camber line t h V C Airfoil Characteristics h(x)  0 camber  symmetric airfoil (h/c)max and (x/c) @ (h/C)max (t/c)max and (x/c) @ (t/c)max Leading edge radius

  19. stall Moment Ref Pt = 0.25 c CL CM CD i    13o Airfoil Characteristics i = f(h/c)max CM = constant = f(h/c)max CL = dCL/d = 2  rad-1 = 0.11 deg -1 CLo = f (h/c)max Special airfoils for wind turbines with high t/c @ low Re  SERI / NREL

  20. , Q Cranking Torque? • Air cranks rotor  equal, opposite reaction on air • Rotor angular velocity,  • Torque on rotor Q • Angular velocity of air downstream of rotor, = 2a’ • Angular velocity at rotor mid-plane, 0.5  = a’ • a’- circumferential inflow

  21. dr r  , Q Cranking Torque?  = 2a’

  22. CL CD  Flow velocities r a’ r   V W a V  =  -  CL, CD = f () Cx = CLSin  - CD Cos  = CLSin  ( 1 -  Cot ) CT = CLCos  +CD Sin  = CLCos  ( 1+  Tan )

  23. Betz 16/27 CP Cpi - Energy extraction is through cranking 

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