Wind Turbine Project Lift Drag Blade Aerodynamics Power
Wind Turbine Project Lift, Drag, Blade Aerodynamics & Power Professor Christiani 11/10/14
Goals � Grasp the physics behind a windturbine � Blade Element Theory � Blade Momentum Theory � Utilize � Fill MATLAB to model the physics in the code � Understand the syntax � Obtain a plot for the coefficient of power
Blade Element Theory
Lift and Drag F L Chord F D Lift force perpendicular to airflow Drag force parallel to the airflow
Airplane Angle of Attack http: //science. howstuffworks. com/transport/flight/modern/airplanes
What’s the difference between the blades? Wind turbine Airplane The turbine’s blades rotate, but the airplane’s wing does not!
Calculating lift and drag Power = (Force)(Velocity) Substitute for power provided by the wind geometric factor Resulting force generated on the airfoil
Coefficients of lift and drag Lift coefficient CL = how effectively the wing turns pressure into lift Drag force Drag coefficient CD = how much of the pressure is converted to drag
Coefficients of lift and drag Geometric factors CD and CL Empirically determined Lift/Drag Coefficient Depend on: • Airfoil shape • Angle of attack • Wing area • Air speed • Air density 1. 75 1. 50 lift coefficient 1. 25 1. 00 0. 75 0. 50 drag coefficient 0. 25 We will provide this for 0 blades that are thin flat plates 5 10 15 20 Angle of Attack (degrees) 25 30
Example: Lift Data
Piece-wise Function Boundary Conditions! Equation for coefficient!
Questions?
Harnessing wind energy Can we capture all of this available wind?
How do we predict output power of wind turbine rotor? r F
Approach �Need force at each point on the blade �Need angle of attack and wind velocity at each point on the blade �Sum the equivalent forces �Calculate the torque generated �Calculate power generated
Blade Element Theory d. F 1
Questions?
Blade Momentum Theory
Limits of the Formulation As the number of blades (N) or chord width (c) increases, the blades will begin to overlap!
BET Limitation
Comparison � Low σ, Low Q, High ω � High σ, High Q, Low ω Which type do you think you will build?
What is solidity? � Defined as the percentage of the circumference of the rotor that contains material rather than air � High-solidity � Carry a lot of material � Coarse blade angles � Generate higher torques � Low efficiency � Low-solidity � Less material = lower cost � Generate lower torques � High efficiency
Blade Momentum Theory
Axial Induction Factor Fraction of wind source that is diverging True undisturbed wind
Radial Induction Factor Streamlines from wind are rotating as blades rotate
Calculating a & a’
Inclusion of the Factors What does W equal now? What does φ equal now?
Power Generated by Turbine and Coefficient Of Power Sum torques of blade elements Power generated = (Torque)(Rotational velocity) Performance measure is the Coefficient of Power:
Questions?
Code Review
Classwork � MATLAB � Download and review the provided MATLAB code and coefficients from excel file on PBworks � Fill in missing information � Basic constants � CL and CD from plots � Physics equations � Plot Cp vs. ω � Next steps � Plan out process for parametrization � Brainstorm ideas for blade shapes
- Slides: 41