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…..

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…..

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.

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

The Power Donating Stream Tube of A Wind Turbine

Cooperation from Surroundings of A Successful Stream Tube

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.

Layout of An Offshore Wind Farm

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

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

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

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

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

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.

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