Aerodynamic Structural Noise - Hybrid Anisotropic Materials for Wind Power Turbine Blades - page 200

Wind Speed Increase During Time

600

400

200

0

1 2 3

Wind Speed M/S

4 5 6

Series 1 Series 2

FIGURE 7.1
Wind. speed. increase. during. hurricanes. is. shown.. (From. University. of. Massachusetts.. 2011..
Wind. turbine. aerodynamics. measuring. wind. turbine. noise.. Online. at. www.en.wikipedia/
wiki/Wind_turbine_aerodynamics..With.permission.)

thermal.energy..Gravitational.and.thermal.energy.have.a.negligible.effect.on.
the.energy.extraction.process..From.a.macroscopic.point.of.view,.the.air.low.
about. the. wind. turbine. is. at. atmospheric. pressure.. If. pressure. is. constant,.
then.only.kinetic.energy.is.extracted..However,.up.close.near.the.rotor.itself.
the.air.velocity.is.constant.as.it.passes.through.the.rotor.plane..This.is.because.
of. conservation. of. mass.. The. air. that. passes. through. the. rotor. cannot. slow.
down.because.it.needs.to.stay.out.of.the.way.of.the.air.behind.it..So,.at.the.
rotor,.the.energy.is.extracted.by.a.pressure.drop..The.air.directly.behind.the.
wind.turbine.is.at.subatmospheric.pressure;.the.air.in.front.is.under.greater.
than.atmospheric.pressure..It.is.this.high.pressure.in.front.of.the.wind.tur-
bine.that.delects.some.of.the.upstream.air.around.the.turbine.(Figure 7.2).
Albert.Betz.and.Frederick.W..Lanchester.were.the.irst.to.study.this.phenom-
enon. 2 .Betz.notably.determined.the.maximum.limit.of.wind.turbine.perfor-
mance..The.limit.is.now.referred.to.as.the. Betz limit ..This.is.derived.by.looking.
at.the.axial.momentum.of.the.air.passing.through.the.wind.turbine..As.stated.
above,.some.of.the.air.is.delected.away.from.the.turbine..This.causes.the.air.
passing.through.the.rotor.plane.to.have.a.smaller.velocity.than.the.free.stream.
velocity..The.ratio.of.this.reduction.to.that.of.the.air.velocity.far.away.from.the.
wind.turbine.is.called.the. axial induction factor ..It.is.deined.as:

U U
U

-

≡ 1

2

. a . (7.1)

1

where:
a .is.the.axial.induction.factor;
U 1 .is.the.wind.speed.far.away.upstream.from.the.rotor;
U 2 .is.the.wind.speed.at.the.rotor.