Aerodynamic Structural Noise - Hybrid Anisotropic Materials for Wind Power Turbine Blades - page 201

Coning angle

Teeter axis

17°

Teeter
motion

Wind Wind

Upwind Downwind

Upwind and downwind rotor emission

FIGURE 7.2
An.overview.of.sound.emissions.from.wind.turbines..(From.Rogers,.A..L..2006..University.of.
Massachusetts..Online.at:.www.renewableenergy.world.com..With.permission.)

The. irst. step. in. deriving. the. Betz. limit. is. to. apply. conservation. of. axial.
momentum..As.stated.above,.the.wind.loses.speed.around.the.wind.turbine.
compared. to. the. speed. far. away. from. the. turbine.. This. would. violate. the.
conservation. of. momentum. if. the. wind. turbine. was. not. applying. a. thrust.
force. on. the. low.. This. thrust. force. manifests. itself. through. the. pressure.
drop. across. the. rotor.. The. front. operates. at. high. pressure. while. the. back.
operates. at. low. pressure.. The. pressure. difference. from. the. front. to. back.
causes. the. thrust. force.. The. momentum. lost. in. the. turbine. is. balanced. by.
the. thrust. force.. Another. equation. is. needed. to. relate. the. pressure. differ-
ence.to.the.velocity.of.the.low.near.the.turbine..Here,.the.Bernoulli.equation.
is. used. between. the. ield. low. and. the. low. near. the. wind. turbine.. There.
is.one.limitation.to.the.Bernoulli.equation:.The.equation.cannot.be.applied.
to.luid.passing.through.the.wind.turbine;.instead,.conservation.of.mass.is.
used.to.relate.the.incoming.air.to.the.outlet.air..Betz.used.these.equations.
and.managed.to.solve.the.velocities.of.the.low.in.the.far.wake.and.near.the.
wind.turbine.in.terms.of.the.far.ield.low.and.the.axial.induction.factor..The.
velocities.are.given.as:

U 2 .=. U 1 (1.−. a ). (7.2)