Design of Wind Turbines P M V Subbarao Professor Mechanical Engineering Department Selection of Optimal Geometrical & Kinematic Variables ….

Signatures of Wind Turbine on Wind & Recovery

The axial induction factor (of rotor) a is defined as: The available power in a cross-section equal to the swept area A by the rotor is: Characteristic Parameter of A Wind Turbine Rotor

The absorbed power is often non-dimensionalized with respect to P avail as a power coefficient C P : Similarly a thrust coefficient C T is defined as: the power and thrust coefficients for the ideal 1-D wind turbine may be written as:

Differentiating C P with respect to a yields: It is easily seen that C P, max = 16/27 for a = 1/3. This theoretical maximum for an ideal wind turbine is known as the Betz limit.

The axial induction factor (of rotor) a is defined as: The Compact Ideal Wind Turbine

Increasing Capacity & Real Flow Past A Wind Turbine

Turbulent-wake state induced by the unstable shear flow at the edge of the wake

Wind & Rotor Interaction

Kinematics of Blade V ai =u U b =r  V fe =u At any radius r VwVw

Schematic drawing of the vortex system behind a wind turbine

Selection of Blade Speed

Selection of Diameter Vs Capacity

Size, Speed & Efficiency

Optimum Available Power due to Turbulent Wake Fraction of Betz Limit

Intersection of Wind & Blade

Capacity Vs Number of Blades For a given efficiency, a wind turbine with large capacity will run at lower speed. What is the lowest RPM (Revolution Per Minute) a single bladed turbine can make without loosing its efficiency drastically? It is 60 RPM or one revolution per second. Why? Because it should sweep whole rotor area in one second. If turbine rotates slower than this, it will miss some air particles and it's output power will be low. However if it rotates faster than one revolution per second it will produce more power which is better. But faster rotating blades create more stresses on overall structure. Therefore one bladed turbine should run at highest possible safe rpm.

Low Speed for Higher Number of Blades A two bladed turbine can run at lower speed with high efficiency. This is because while one blade sweeping one half of the circle area, the other blade is sweeping the other half. By using same analogy a three bladed turbine can run much lower speeds with high efficiency. Low speed turbine increase the cost of electrical equipment. Higher number of large blades will increase wind turbine and civil structure costs. A techno-economically viable option is essential.

Common Industrial Practice

Aerofoil Geometry of Blades Wind = u Rotation = r *  Relative Wind = u r 

Causes of Extraneous Loads

Wind Turbine Field Performance Issues effecting wind turbine performance –Blade Design Efficiency of large turbine blades are close to the aerodynamic optimum for steady uniform winds. Unsteady and non-uniform wind conditions cause: – Blade section stall. – Degradation of Wind Turbine performance. –Noise issues with the local community Wind turbine noise increases due to: –Unsteady in-flow conditions. –Flow interaction from support structure or wakes from other wind turbines.

Off-design Characteristics of Wind Turbines

Torque Produced in a Linear Wind shear Decreasing Turbine Torque with increasing wind gradient

Desired Airfoil Qualities For a fixed-pitch, constant speed machine, recommended airfoil qualities at 0.75R are: –High L/D –Low c lmax near tip reduces tendency to overpower generator in high wind speeds –Insensitive to surface roughness (bugs, birds, bullets)

Wind Turbine Blade Specifications 3.45 m 1.43 m 13.7 m 45.7 m Diameter = 91.4 m No. of Blades = 2 Average Wind Speed = 12.5 m/s Rotation Rate = 17.5 rpm Airfoil: NACA Power Output = 2.5 MW Wind = V 0 Rotation = r *  Relative Wind = V r 

Blade Designs

Aerofoil Design Leading Edge Root Section Blade Tip Airfoil NACA