Wind Turbine Project Recap Wind Power & Blade Aerodynamics

Wind Turbine Project  Turbines tested indoors under controlled conditions  A single metric for success - amount of electricity generated  Design will be executed using theoretical calculations- build and test ONCE at end! (with one trial fitting)

Harnessing available power in wind Max available power How can we predict blade performance? Blade aerodynamics Rotor performance

Power coefficient C p = Rotor power Power in the wind requires blade and rotor physics How well is our turbine performing? At best only 45% can be captured by real turbines (theoretical limit).

Project estimates – class exercise (5 min) Available power Estimating maximum P generated

Project estimates – class exercise (5 min) Available power Estimating maximum P generated P = 60 W

Atlantic City estimates – class exercise (5 min) Now assuming the offshore wind velocity is12 m/s The diameter of a turbine is 73 m, there are 5 turbines Estimate of maximum P generated

Blade aerodynamics Turbine blades are airfoils We need to understand blade aerodynamics to determine effectiveness and performance

Airfoil terminology W α R U∞U∞ Free stream velocity C Relative wind velocity

Airfoil types NACA airfoils National Advisory Committee for Aeronautics NACA 2412 maximum camber of 2% located 40% from the leading edge with a maximum thickness of 12% of the chord NACA 0012 symmetrical airfoil, 00 indicating no camber.12 indicates that the airfoil has a 12% thickness to chord

Airfoil function – generation of lift weight thrust drag lift ‘suction’ side ‘pressure’ side

Airfoil forces Lift force perpendicular to airflow Drag force parallel to the airflow

Calculating lift and drag Power = Force x Velocity geometric factor Force generated by airfoil Force in the wind

Coefficients of lift and drag C D = how much of the pressure (kinetic energy) is converted to drag LiftLift coefficient Drag force Drag coefficient C L = how effectively the wing turns available dynamic pressure (kinetic energy) into lift

Coefficients of lift and drag

Geometric factors C D and C L Depend on: airfoil shape angle of attack Empirically determined Angle of Attack (degrees) Lift/Drag Coefficient lift coefficient drag coefficient

Airfoil behavior

Performance parameters Wind turbine performance based on lift and drag coefficients Pitch angle,  - angle btwn chord line and plane of rotation Angle of attack,  - angle btwn blade and relative wind, which changes depending on speed of blade and wind speed K.L. Johnson (2006)  Lift Drag Thrust Torque Direction of translation Rotational Speed Relative wind velocity Free stream Wind velocity

Lift and drag on translating air foil What force actually provides useful work to rotate the turbine? A)Lift B)Drag C)F 1 D)F 2 K.L. Johnson (2006)

Lift and drag on translating air foil F 1 is force to rotate the turbine Tower must be strong enough to withstand thrust force F 2 K.L. Johnson (2006)

Connection to wind turbines lift and drag cause the rotor to spin angle of attack changes over the span of the blade lift and drag forces also change over the span of the blade Next How to calculate torque generated from lift and drag on each blade?

Complications  Free stream characteristics change approaching and across blades  Rotation of blades causes counter rotation in wind  Things vary with r  Must use  conservation of mass  Conservation of momentum  Conservation of energy

Things vary with r : Blade Element Theory (BET) Blade divided into sections, on which momentum is applied Result is nonlinear equations that can be solved iteratively *Does not consider shed tip vortex. Some flow assumptions made breakdown for extreme conditions when flow becomes stalled or a significant proportion of the propeller blade is in windmilling configuration while other parts are still thrust producing.

Free stream characteristics change… Circular tube of air flowing through ideal wind turbine (K.L. Johnson 2006) Variables  – density (constant) A – cross-section area U – wind speed p – pressure T – thrust of wind on turbine If a tube of air is moving with diameter d 1, speed u 1, and pressure p 1 as it approaches turbine, the air speed decreases, causing the tube of air to increase to d 2. Air pressure rises in front of turbine and drops behind the turbine. Part of the kinetic energy (KE) of air is converted to potential energy (PE) to create the pressure increase and more KE is converted to PE after the turbine to return the pressure to atmospheric. Wind speed decreases until pressure is in equilibrium and u 4 = u 1.

BET Limitation – Axial Induction factor Axial Induction factor accounts for wind speed reduction as wind approaches turbine Consider the limits: No reduction in wind speed Wind stops downstream, model invalid

Power and Power coefficient Theoretical Power Coefficient of Power Theoretical max Cp, set Sub 1/3 into Cp to get max of 16/27 = (Betz Limit) only 59% of max theoretically possible. Value of 1 invalidates model (not btwn 0 and ½)

Counter rotation of wind: Blade Momentum Theory Rotor induces rotation in opposite direction of blade rotation  – Rotor rotational velocity  – Induced wind rotational velocity Angular Induction factor accounts for reduction due to rotational wake Consider the limits: No induced rotation Induced rotation,  equal and opposite to rotor rotation

Angular velocity of rotor affects local wind at blade Lift Drag T Q

Power Generated by Turbine Power = Torque * rotational velocity

Solidity ratio Closed versus open area B*c = net chord length of ALL blades 2  r = total circumference at radius, r

Blade Element Theory (cont’d) V 0 - axial flow at propeller disk, V 2 - Angular flow velocity vector V 1 - section local flow velocity vector, sum of vectors V 0 and V 2 Blade will be set at a given geometric pitch angle (  ), lift and drag components calculated so that the contribution to thrust and torque of the complete propeller from this single element can be found Difference in angle between thrust and lift directions

Constraints and Materials  Max diameter of wind turbine = 1 meter  Max number of blades is 12  Hub is given and has a radius of 0.05 meter made of plastic  Must be a horizontal axis wind turbine  With blades that are thin flat plates (remember that our model is also developed for aerodynamics of blades/airfoils that are thin flat plates), so we’ll use foam board  Attach blades to hub with wooden dowel rods

Parameters and/or Variables Primary  Pitch of blades, which in turn affects angle of attack  Cord/shape of blades  Constant cord – to make simple rectangular blades  Variable cord – to make another shape (triangle, parallelogram, etc.) Secondary  Number of blades <=12  Radius <= 0.5 meter

Performance metrics and evalutation  Plot theoretical results of Coefficient of Power (Cp) versus angular velocity of the hub and determine the conditions for which a max occurs (note, power is related to performance, how well does your turbine perform)  On test day, we will measure electrical output (voltage and current, recall P(elect) = V*I) and angular velocity.  You’ll see how well results match predictions. Just as in the bottle rocket project, that’s what matters to find a max for your conditions, predict it and achieve it. Cp, Coefficient of Power , Rotational Speed

Definitions  W – relative wind speed  U inf -free stream wind speed   – angle of attack   – blade pitch  a – axial induction factor  a’ – angular induction factor   – relative angle of wind  B – number of blades  C L – coeficient of lift  C D – coefficient of drag  Q, dQ- total blade torque, torque on differential element  C p -coefficient of power

Matlab Pseudo Code: Find these steps!  Inputs: number of blades N, chord length c, blade span R, blade angle δ  For a range of rotational speeds ψ  For a range of blade elements dr up to the blade span R  While a and a’ converge  Calculate relative wind velocity W using  Calculate  using Eq.  Calculate angle of attack χ using  Use the empirical data to evaluate CL and CD for the χ  Calculate new a and a’ using  End  Calculate the differential blade torque dQ for the blade element  Sum the elemental contributions dQ to the total torque Q  End  Calculate power by the product of total torque Q and rotational speed ψ  Calculate coefficient of performance Cp for the rotational speed ψ  End  Plot coefficient of performance as a function of rotational speeds ψ

Generator Performance Curves  Recall that losses occur converting mechanical power from the turbine to electric power by the generator  Test or find specifications for generator performance