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

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.

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

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.

Wind Flow Past A Locked HAWT

Wind Flow Past A Locked VAWT

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.

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

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

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.

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.

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

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

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

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.

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

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

Power generated by an Ideal Wind Turbine

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:

Signatures of Wind Turbine on Wind & Recovery

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:

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.

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