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Euler Theory for Wind Turbines

Euler Theory for Wind Turbines. P M V Subbarao Professor Mechanical Engineering Department I I T Delhi. Essential Symptoms to be Created by a WT on Wind…. Euler Theory:. Torque exerted by flow on A blade row = shaft output torque = t = Rate of change of Angular momentum of fluid.

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Euler Theory for Wind Turbines

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  1. Euler Theory for Wind Turbines P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Essential Symptoms to be Created by a WT on Wind….

  2. Euler Theory: Torque exerted by flow on A blade row = shaft output torque = t = Rate of change of Angular momentum of fluid

  3. Flow Kinematics in the Meridional Plane The momentum balance is considered in a plane constructed through axis of rotation and radial axis. This Plane is called Meridional Plane. Euler Differential Turbine Equation.

  4. Euler (Wind) Turbine Equation Wind turbine is an axial flow machine. For a SSSF Wind turbine Torque developed by a Wind turbine Euler Theory: Power :

  5. Euler Wind Turbine Theory 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…..

  6. Mechanical Power Extraction :The fundamental Aerodynamic Phenomena • The type of aerodynamic force 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 • Aerodynamic lift (at a right angle to the direction of flow).

  7. Mechanical Power Extraction :The fundamental Aerodynamic Phenomena • The real power obtained vary greatly 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.

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

  9. The Plane of Torque Generation • The adjectives horizontal or vertical attached to the two major classes of wind machines. • This classification refers to the plane in which the torque is generated. • Geometrical aspect of the driving shaft of the rotor/wheel will also agree to it. • A WT typified by the term Dutch windmill is now called as a Horizontal Axis Wind Turbine (HAWT). • A machine with a central vertical axis and a number of straight or bent vanes arranged in a direction more or less parallel to the shaft is today called as a Vertical-Axis Wind Turbine (VAWT).

  10. Schematic of Modern (Lift based) Large Capacity Wind Turbines

  11. Kinematics of HAWT Blades

  12. Kinematics of VAWT Blades

  13. The Art of Time Scale Analysis • There exist at least two important time scales in any fluid flow problem. • Time taken by any given blade to move into the position occupied by its predecessor, tb. • Time taken by the wind being disturbed to avoid to retain its natural state, tw.

  14. The Skill of Group Co-ordination

  15. Blade type, Number of Blades and Speed of Rotor Runs at high Speed Used for driving Generators Runs at Low Speed Used for driving Reciprocating Pumps

  16. 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.

  17. The Biological Pulse : A Thermodynamic Property

  18. The Elephant Weight : 4000 – 7000kg Heart Pulse : 28 per minute

  19. The world’s biggest engine : Wärtsilä-Sulzer RTA96. 14-cylinder, 2-stroke turbocharged diesel engine. Weight : 2.3 million kgs Speed : 102 rpm

  20. Formula Car Weight : 400 kg Speed : 18000 rpm

  21. The Cheetah Speed :112–120 km/h Weight ~ 65kg Heart Pulse ~ 170 per minute

  22. Speed of A Wind Turbine • A rotor rotating at low speed will allow the wind to pass unperturbed through the gaps between the blades. • A rotor rotating rapidly will appear as a solid wall to the wind. • It is a challenge to design the blades of the rotor to make the rotor to run at an optimal blade speed to angular speed to extract highest power. • This ratio is determined by the tangential velocity of the rotor blades in relation to the undisturbed axial airflow, the wind velocity. • This is called as the Tip Speed Ratio λ, commonly referenced to the tangential velocity of the rotor blade tip.

  23. An Ultimate Art of Wind Turbine Design

  24. Common Industrial Practice

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