Environmental Engineering Reference
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taken, new gearboxes were sourced which had a resistive torque of 0.9 Nm. The
calculations show that the turbine would then start with two blades and that using
three blades would again improve starting but not by as large an amount. However,
using three blades would allow them to be pitched out by 2 and still produce the
same power as two blades. With this pitch, three blades provide even better
starting.
6.5.1 Exercises
1. Derive Eqs.
6.9a
and
6.9b
.
2. Show that for any form of C
l
and C
d
, Eq.
3.11
can be written as
2
NqU
2
q
dQ
dr
¼
1
1
þ
k
r
cr
ð
C
l
k
r
C
d
Þ
when there is no axial or circumferential inflow. Hence derive Eq.
6.16
for the
special case of C
l
= 2 sin a cos a and C
d
= 2 sin
2
a.
3. Use the above result for dQ/dr to derive Eq.
6.19
by assuming only that C
l
/
C
d
= 1/tan a.
4. You are required to design a 20 kW blade on the basis of the 5 kW design
described in this chapter. The turbine is to use a PM generator whose designer
can guarantee a cogging torque of 8 Nm or less. In designing the blade would
you make any special provision for the starting performance?
5. The twist and chord data for the blade used to obtain the data in Figs.
6.2
to
6.4
is stored in the file
baby_blade.dat
in the online materials
http://extras.
springer.com
. Use that data to estimate the blade's aspect ratio.
6. Looking carefully at Fig.
6.1
you will notice that the aerodynamic section of
the blades starts at a larger radius than the PMG cover, mainly because the
blade was designed before the importance of the hub region for starting was
appreciated and was designed to be mounted in the existing blade holder. How
would you redesign the blade holder (and possibly the blade attachment) to
improve starting?
7. Assume it is possible to obtain a PMG for the 500 W turbine whose power
curve is shown in Fig.
6.2
, with a cogging torque of 0.2 Nm and that the new
generator would cause the cost of the turbine to increase by 15%. Estimate the
new cut-in wind speed and the amount of extra power that would be extracted
given the Rayleigh distribution of wind speed with a mean wind speed of
5.7 m/sec., as statistics described in
Sect. 1.6
. Could you justify using the new
generator?
8. You are told to design blades for a small wind turbine using Eqs.
5.12a
and
5.13a
for a given generator with no resistive torque, U
p
, k
p
, R, and aerofoil
section. The only choice you have is whether N = 2, 3, or 4. Which value
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