Environmental Engineering Reference
In-Depth Information
Table 6.2 Values of A for
several aerofoil sections
Aerofoil
A
SD7062
0.08818
SG6040
0.10411
SG6041
0.06955
SG6042
0.06916
SG6043
0.06850
NACA0012
0.08213
NACA4412
0.08211
¼
t
0
c
3
cos
2
h
p
þ
t
0
3
c sin
2
h
p
12
ð
6
:
24b
Þ
When all lengths are normalised by the blade tip radius, R,
J
¼
Nq
b
AR
5
Z
Z
c
4
cos
2
h
p
dr
þ
A
2
Z
c
4
sin
2
h
p
dr
c
ð
2
dr
þ
A
12
ð
6
:
25
Þ
where the first integral in the square brackets corresponds to J
1
and the second to
J
2
. The relative magnitude of the integrals is at most (c/r)
2
. The rotor shown in
Fig.
6.1
had composite blades but subsequently these were replaced by timber ones
for which q
b
= 550 kg/m
3
and J = 0.190 kg m
2
from Eq.
6.25
when the rectan-
gular attachment section was included. This value agrees with that obtained from
finite element analysis. The ratio of the second to first term in (
6.25
) was
3.23 9 10
-3
, which justifies the approximate treatment of J
2
. To look at the
magnitude of the terms another way: for a three bladed turbine with k
p
= 7.5, and
C
l,max
= 1, cr * 0.03. If further, A * 0.1, and r
h
* 0.1, the three integrands are
9 9 10
-4
, 6.75 9 10
-5
, and 6.75 9 10
-7
at the hub. Thus the contribution to J
2
is
an order of magnitude less than that to J
1
even when the chord at the hub is 30% of
the tip radius.
6.5 Matlab Program for Starting
This section describes a Matlab program
start_calc.m
which reads in the blade
characteristics in exactly the same manner as
power_calc.m
(described in
Chap. 5
),
calculates blade inertia, and then determines the time to start for user-specified wind
speed in two ways. First, Matlab's adaptive Runge-Kutta 4th/5th order solver
ode45
is used to solve Eq.
6.20
with no resistive torque. This solution is expected to
be very accurate. The second calculation uses the standard Adams-Moulton method,
designated ABM4 in Sect. 12.2.2 of Fausett [
5
], which has only two function
evaluations per step and is, therefore, more attractive for the large number of starting
calculations
needed
for
numerical
design
optimisation
in
the
next
chapter.
The program listing is:
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