Fluid Mechanics and Thermodynamics of Turbomachinery, 5e

134 Fluid Mechanics, Thermodynamics of Turbomachinery
Rotation
The turbine characteristics under steady flow conditions were determined in the form
of the output torque coefficient Ct and the input power coefficient CP against the flow
coefficient, f =cx/Uav, defined as
2 2
C = p r c + U ZlHc
p D 0 x av x
(4.42)
(4.43)
where t0 is the output torque and Dp 0 is the total pressure difference across the turbine.
Figure 4.30a shows the Ct vs. f characteristics for the turbine for various bladesetting
angles. The solid line (g =0deg) represents the result obtained for the original,
fixed-blade Wells turbine. For values of g >0deg, Ct decreases with increasing g in the
stall-free zone but, beyond the original stall point for g =0, much higher values of Ct
were obtained.
Figure 4.30b shows the CP vs f characteristics for the turbine for various bladesetting
angles. This figure indicates that for g >0deg the input power coefficient CP
is lower than the case where g =0deg for all values of f. Clearly, this is due to the
variation in the rotor blade setting angle.
The instantaneous efficiency of the turbine is given by
Wt0
C
h = =
QDp f
{ ( ) 2}
2 2
Ct = t0r c + U ZlHr
0
x av av
{ ( ) 2}
t
C p
and the mean efficiency over the period of the wave, T = 1/f(s), is
T
T
hav t f p
T C = C t
T
È 1 ˘ È 1 ˘
ÎÍ Ú ˚˙ ÎÍ Ú d
0 0 ˚˙
g
g
Air flow
Air flow
M
M
Pivot
Air foil
FIG 4.29. Air turbine using self-pitch-controlled blades for wave energy conversion.
(From Kim et al. 2002, with permission of Elsevier.)
(4.44a)
(4.44b)
Using the measured characteristics for Ct and CP and assuming a sinusoidal variation
of the axial velocity with a different maximum amplitude* for each half cycle, as
*Kim et al. reported a lower maximum axial velocity cxi during inhalation than exhalation cxo.