Thermo-aero Dynamic Analysis of Wind Turbines

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Thermo-aero Dynamic Analysis of Wind Turbines
P M V Subbarao Professor Mechanical Engineering
Department
Development of Characteristic Design Variables .
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Wind Flow Past A Locked Wind Turbine
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Thermodynamic Description of Flow Past A Working
Wind Turbine
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Description of Flow Past A Working Wind Turbine

• The rotor disc acts as a resistance device
  slowing the wind speed Vo from far upstream of
  the rotor to u at the rotor plane and to u1 in
  the wake.
• The drag is obtained by a pressure drop over the
  rotor.
• Close upstream of the rotor there is a small
  pressure rise from the atmospheric level po to p.
• A discontinuous pressure drop ?p over the rotor.
• Downstream of the rotor the pressure recovers
  continuously to the atmospheric level.

The Mach number is small and the air density is
thus constant and the axial velocity must
decrease continuously from Vo to u1.
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Signatures of Wind Turbine on Wind Recovery
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Layout of An Offshore Wind Farm
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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 30
Project Capacity 160 MW 165.6 MW 60 MW 108 MW
Turbine Capacity 2 MW 2.3 MW 2 MW 3 MW
Number of Turbines 80 72 30 36
Total Turbine Height 110 m 110m 100 m 115 m
Hub Height 70 m 69 m m 70 m
Rotor Diameter 80 m 82 m 80 m 90 m
CO2 reduced per year (tons) 187135 180806 67802 122044
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Momentum Theory for an Ideal Wind Turbine
For a frictionless wind turbine
DpWT Utilized Pressure Deficit
Thrust Generated at the rotor Plane
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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 applied on control
volume
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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.
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Ideal Power Absorbed by an Wind turbine
The flow is assumed to be frictionless and
incompressible. There is no heat transfer across
the boundary of CV.
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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
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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