Fluid Mechanics and Thermodynamics of Turbomachinery, 5e

344 Fluid Mechanics, Thermodynamics of Turbomachinery
Using eqn. (10.20) we find
and, with eqn. (10.19), eqn. (10.32) becomes
Introducing a useful new dimensionless parameter, the blade loading coefficient,
into eqns. (10.31) and (10.33), we get
Tip–speed ratio
(10.32)
(10.33)
(10.34)
(10.35)
(10.36)
(10.37)
A most important non-dimensional parameter for the rotors of HAWTs is the
tip–speed ratio, defined as
J
(10.38)
This parameter controls the operating conditions of a turbine and strongly influences
the values of the flow induction factors, a and a¢.
Using eqn. (10.38) in eqn. (10.21) we write the tangent of the relative flow angle j
as
Turbine solidity
(10.39)
A primary non-dimensional parameter that characterises the geometry of a wind
turbine is the blade solidity, s. The solidity is defined as the ratio of the blade area to
the disc area,
where
2
cx2cqw = Zl( CLsinf -CDcosf)
( 8pr)
cqw = Ua¢ cosf { U( 1+ a¢ ) }= a¢ cosf
( 1+
a¢
)
a¢ ( 1+ a¢ )= Zl( C sinf -Ccosf)
( 8prsinfcosf)
l = ZlCL ( 8pr)
2
a ( 1-
a)=
l( cosf+ esinf) sin f
a¢ ( 1+ a¢
)= l( sinf -ecosf)
( sinfcosf) r
= W
cx1
tanf =
e = CD CL.
R
rJ
s ZA pR
2
= ( )
B = Ú () d = 2 av
1
A l r r Rl
This is usually written as
s = Zl ( pR)
av 2
Ê 1-
a ˆ
Ë 1+
a¢
¯
B
L D
where lav is the mean blade chord.
(10.40)