1. Identification of Fundamental Design Parameter for A Wind Turbine
P M V Subbarao
Professor
Mechanical Engineering Department
I I T Delhi
A Simple Measure of Complex Fluid Dynamic Actions…..

2. Euler Wind Turbine Equation
For an infinitesimal displacement of steady wind past a steady Wind turbine
Torque developed by a Wind turbine
Euler Theory:
Power :
A change in Whirl Velocity of fluid can only establish Power Exchange between fluid and rotor in a turbo-machine !
A successful Wind Turbine must generate a net change in angular velocity by any means…..

3. Mechanical Power Extraction :The fundamental Aerodynamic Phenomena
The type of aerodynamic forces used for generation of change in tangential velocity across a rotor greatly influences the actual power developed by a wind turbine.
All bodies exposed to an airflow experience an aerodynamic force.
The components of which are defined as aerodynamic drag (in the direction of flow), and as aerodynamic lift (at a right angle to the direction of flow}.
The real power coefficients obtained vary greatly in dependence on whether aerodynamic drag or aerodynamic lift is used for power generation.
A significant enhancement in power generation can be achieved in lift machines when compared to and drag machine.
This is due to the fact that much higher relative wind velocities can be achieved with lift machines.

4. Basic Principle of Changing Angular Momentum
Lift driven WT
Drag driven WT

5. The Power Donating Stream Tube of A Wind Turbine

6. Cooperation from Surroundings of A Successful Stream Tube

7. Support from Surroundings of A Donating Stream Tube
Arotor
The Mach number is small and the air density is thus constant and the axial velocity must decrease continuously from Vo to u1.

8. Layout of An Offshore Wind Farm

9. Structure of Offshore Wind Farms
Name of Wind Farm
Horns Rev. 1
Nysted
Scorby Sands
Egmond aan Zee
Available site at harbour (km) 15 64 30
Project Capacity
160 MW
165.6 MW
60 MW
108 MW
Turbine Capacity
2 MW
2.3 MW
3 MW
Number of Turbines 80 72 36
Total Turbine Height
110 m
110m
100 m
115 m
Hub Height
70 m
69 m m
Rotor Diameter
80 m
82 m
90 m
CO2 reduced per year (tons)
187135
180806
67802
122044

10. Thermodynamic Description of Flow Past A Working Wind Turbine
Front view of Stream Tube for HAWT
The rotor disc acts as an energy extractor slowing the wind speed from V0 far upstream of the rotor to u at the rotor plane and to u1 in the wake.
Top view of Stream Tube for VAWT

11. Basic Assumptions to Identify the Important Design Parameter
This analysis uses the following assumptions:
Homogenous, incompressible, steady state fluid flow;
No frictional drag;
An infinite number of blades;
Uniform thrust over the disc or rotor area;
A non–rotating wake;
The static pressure far upstream and far downstream of the rotor is equal to the undisturbed ambient static pressure

12. Momentum Theory for an Ideal Wind Turbine
For a frictionless wind turbine:
DpWT : Utilized Pressure Deficit
Thrust Generated at the rotor Plane:

13. Identification of Cooperating Surroundings to Wind Turbine
The axial momentum equation using the simplified assumptions of an ideal rotor in a control volume

14. Momentum Theory for an Ideal Wind Turbine
The conservation of mass for the inner CV gives a relationship between A and A1 as:
It is seen that the velocity in the rotor plane is the mean of the wind speed Vo and the unused wind speed in the wake u1.

15. Characteristic Design Parameter of A Wind Turbine Rotor
Define this design parameter as axial induction factor: