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

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

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

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

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 Pgenerated

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

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

Airfoil types NACA airfoils NACA 2412 NACA 0012 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 Force in the wind geometric factor Force generated by airfoil

Coefficients of lift and drag Lift coefficient CL = how effectively the wing turns available dynamic pressure (kinetic energy) into lift Drag force Drag coefficient CD = how much of the pressure (kinetic energy) is converted to drag

Coefficients of lift and drag

Coefficients of lift and drag 5 10 15 20 25 30 0.25 0.50 0.75 1.00 1.25 1.50 1.75 Angle of Attack (degrees) Lift/Drag Coefficient lift coefficient drag Geometric factors CD and CL Depend on: airfoil shape angle of attack Empirically determined

Airfoil behavior

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

Lift and drag on translating air foil What force actually provides useful work to rotate the turbine? Lift Drag F1 F2 K.L. Johnson (2006)

Lift and drag on translating air foil K.L. Johnson (2006) F1 is force to rotate the turbine Tower must be strong enough to withstand thrust force F2

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. http://www-mdp.eng.cam.ac.uk/web/library/enginfo/aerothermal_dvd_only/aero/propeller/prop1.html

Free stream characteristics change… Variables r – 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 d1, speed u1, and pressure p1 as it approaches turbine, the air speed decreases, causing the tube of air to increase to d2. 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 u4 = u1. Circular tube of air flowing through ideal wind turbine (K.L. Johnson 2006)

BET Limitation – 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 = 0.5927 (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 Angular Induction factor accounts for reduction due to rotational wake Consider the limits: No induced rotation Induced rotation, w equal and opposite to rotor rotation Rotor induces rotation in opposite direction of blade rotation W – Rotor rotational velocity w – Induced wind rotational velocity

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

Power Generated by Turbine Power = Torque * rotational velocity

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

Blade Element Theory (cont’d) Difference in angle between thrust and lift directions V0 - axial flow at propeller disk, V2 - Angular flow velocity vector V1 - section local flow velocity vector, sum of vectors V0 and V2 Blade will be set at a given geometric pitch angle (q), lift and drag components calculated so that the contribution to thrust and torque of the complete propeller from this single element can be found http://www-mdp.eng.cam.ac.uk/web/library/enginfo/aerothermal_dvd_only/aero/propeller/prop1.html

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 w, Rotational Speed

Definitions W – relative wind speed Uinf - free stream wind speed a – angle of attack b – blade pitch a – axial induction factor a’ – angular induction factor f – relative angle of wind B – number of blades CL – coeficient of lift CD – coefficient of drag Q, dQ- total blade torque, torque on differential element Cp - 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 a 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 Calculate power by the product of total torque Q and rotational speed ψ Calculate coefficient of performance Cp for the rotational speed ψ 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