1. Thermo-aero Dynamic Analysis of Wind Turbines
P M V Subbarao
Professor
Mechanical Engineering Department
Development of Fundamental Design Rules….

2. Translating Aerodynamic Devices
As an English army officer, Thomas Savery was once ejected from the Lord of the Admiralty's office as a lunatic because he proposed a ship that could be propelled by side-mounted wheels rather than by wind or oars.

3. Introductory Remarks
Wind turbine power production depends on the interaction between the rotor and the wind.
The major aspects of wind turbine performance are determined by the aerodynamic forces generated by the mean wind.
Focus is primarily on steady state aerodynamics.
The classical analysis of the wind turbine was originally developed by Betz and Glauert.
Betz model, can be used to determine;
the power from an ideal turbine rotor,
the thrust of the wind on the ideal rotor,
the effect of the rotor operation on the local wind field

4. Creation of Finite Control Volume Around Rotor
The analysis assumes a control volume, in which the control volume boundaries are the surface of a stream tube and two cross-sections of the stream tube.
Note that this analysis is not limited to any particular type of wind turbine.
The only flow is across the ends of the stream tube.

5. Wind Flow Past A Locked HAWT

6. Wind Flow Past A Locked VAWT

7. Model for Working Turbines
The running turbine is represented by a uniform ‘Permeable Actuator Disc’.
Creates a discontinuity of pressure in the stream tube of air flowing through it.
Creation of simple one-dimensional (1-D) model for an ideal permeable rotor is first step in analysis.
This model considers the fact of a wind turbine extracts mechanical energy from the kinetic energy of the wind.

8. Basic Assumptions 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

9. 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
Thought experiment is in any case a necessary precondition for physical experiment.
Every experimenter and inventor must have the planned arrangement in his head before translating it into fact.
— Ernst Mach

10. Description of Flow Past A Working Wind Turbine
Bernoulli's principle is applicable form far upstream to just in front of the rotor
Bernoulli's principle is applicable form plane of rotor to far upstream
Close upstream of the rotor there is a small pressure rise from the atmospheric level po to p.
The energy extraction behaviour of disc leads to a discontinuous pressure drop ∆p over the rotor.
Downstream of the rotor the pressure recovers continuously to the atmospheric level.

11. Signatures of Wind Turbine on Wind & Recovery
The Mach number is small and the air density is thus constant and the axial velocity must decrease continuously from Vo to u1.

12. Layout of An Offshore Wind Farm

13. 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

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

15. Identification of Surroundings to Wind Turbine
Consider a Larger Control Volume covering the entire wind turbine fluid domain:
The axial momentum equation using the simplified assumptions of an ideal rotor in a control volume

16. 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.

17. First Law Analysis of SSSF past a Wind turbine
There is no heat transfer across the boundary of CV.

18. Frictionless Low Mach Number Flow Past a WT
SSSF: Conservation of mass
The flow is assumed to be frictionless and incompressible.

19. Power generated by an Ideal Wind Turbine

20. Characteristic Parameter of A Wind Turbine Rotor
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:

21. Signatures of Wind Turbine on Wind & Recovery

22. The absorbed power is often non-dimensionalized with respect to Pavail as a power coefficient CP:
Similarly a thrust coefficient CT is defined as:
the power and thrust coefficients for the ideal 1-D wind turbine may be written as:

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

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