Environmental Engineering Reference
In-Depth Information
Gap Drag Correction
Because no power is extracted from the streamtube containing the gap, the relative ve-
locity causing drag is equal to the local tangential velocity,
r
W. Neglecting the rotational
induction factor, the gap drag effect on power coefficient is
D
C
P
,
GD
=
B C
D
,
g
l
3
p
s
g
R
t
g
R
r
R
3
cos
3
q
(5-39c)
where
C
D
,
g
= drag coefficient of the structure in the gap
t
g
= average thickness of the structure in the gap (m)
An aerodynamic
fairing
usually covers some or all of the components in the gap, in order to
reduce
C
D
,
g
to a minimum. Otherwise, the lost power could be significant.
Comparison of Strip Theory with Free-Wake Analysis
Two methods of predicting HAWT performance will now be compared. The
strip theory
(modified blade-element theory) approach developed previously is compared with
lifting
line
,
free-wake vortex
calculations performed with the
VORTEX
code, a steady-state analy-
sis developed at the Massachusetts Institute of Technology under sponsorship of the U.S.
Department of Energy [Gohard 1978]. The sample cases also offer an opportunity for a
controlled comparison of the flow fields predicted by both methods. The rotor configuration
for this comparative analysis has two, untwisted, constant-chord blades with a 20percent
root
cutout
(
i.e.
, no airfoil inboard of
r
/
R
= 0.2) and no hub interference. The aerodynamic lift
and drag properties of the blade airfoil are simple linear and quadratic functions of the angle
of attack, respectively, with approximations for the effects of stall.
Table 5-4 gives rotor thrust and power coefficients calculated using the two analysis
methods for four cases that include two tip-speed ratios and three blade pitch angles. Only
eight
nodes
(
i.e.
, blade stations) were used in the free-wake analysis, and this does not re-
ally warrant reporting the results with three significant figures. Nevertheless, the free-wake
calculations do represent the best theoretical predictions currently available of a HAWT flow
field. Examination of these results shows that the strip theory predictions of thrust are about
one percent lower and predictions of power coefficients are about four percent lower than
coefficients calculated using the VORTEX free-wake analysis code.
Table 5-4.
Comparison of HAWT Rotor Coefficients Calculated by Two Analytical Methods
Case
Tip-Speed
Ratio,
l
Pitch Angle
b
(deg)
Thrust Coefficient,
C
T
Power Coefficient,
C
P
Strip
Theory
1
Free-Wake
Analysis
2
Strip
Theory
Free-Wake
Analysis
1
6.49
0
1.051
1.077
0.421
0.443
2
"
2
0.910
0.920
0.430
0.443
3
"
4
0.758
0.769
0.406
0.422
4
9.52
2
1.036
1.042
0.322
0.338
1
[Wilson and Walker 1984]
2
[Gohard 1978]
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