Environmental Engineering Reference
In-Depth Information
3.
If the pressure in the far-wake was not ambient (or zero gauge pressure), how
would Eq.
2.4
be altered?
4.
At the end of
Sect. 2.2
it was stated that any circumferential velocity behind
the blades does not appear in the conservation mass equations. Explain why
this is so.
5.
If there is swirl in the far-wake, i.e. non-zero W
?
, then the pressure in the far-
wake, P
?
, is modified according to
dP
1
dr
ΒΌ
qW
2
1
r
where r is the radius. The derivation of this ''centrifugal force'' equation can
be found in any standard fluid mechanics text, e.g. [
1
]. Under what conditions
is Eq.
2.12
unaffected by swirl?
6. What effect does swirl have on the thrust equation, (
2.5a
,
b
)?
7. Why did this chapter contain no discussion of Reynolds number, torque
coefficient and tip speed ratio?
8. An inventor claims to have developed a water turbine of 1 m diameter that
produces 5 kW in a tidal flow of five knots (1 knot = 0.515 m/s). The density
of water is 1000 kg/m
3
. Do you believe the inventor's claim?
9. Starting from Eq.
2.14
, derive the relation between C
T
and C
P
for ideal flow.
10. It is generally held that the results such as shown in Fig.
2.2
, imply that the
thrust coefficient C
T
never exceeds a value of 2. Using this constraint, estimate
the maximum horizontal force exerted on the tower by the 5 m diameter
turbine described in
Chap. 1
for wind speeds of 10 and 25 m/s.
11. Is there an optimum value of C
Q
as there is for C
P
?
References
1. White F (2011) Fluid mechanics, 7th edn. McGraw Hill, New York
2. Lock CNH, Bateman H, Townend HCH (1925) An extension of the vortex theory of airscrews
with applications to airscrews of small pitch, including experimental results. ARC reports &
memoranda no 1014
3. Buhl ML Jr (2005) A new empirical relationship between thrust coefficient and induction
factor for the turbulent wind state, NREL/TP-500-36834, National Renewable Energy
Laboratory, Golden,
http://www.nrel.gov/docs/fy05osti/36834.pdf
. (accessed 1 Oct 2010)
4. Leishman JG (2006) Principles of helicopter aerodynamics, 2nd edn. Cambridge University
Press, Cambridge
5. Clifton-Smith M (2009) Wind turbine blade optimisation with tip loss correction. Wind Eng
33:477-496
6. Lanzafame M, Messina M (2007) Fluid dynamics wind turbine design: critical analysis,
optimization and application of BEM theory. Renew Energy 32:2291-2305
7. Ebert PR, Wood DH (2002) The near wake of a model horizontal-axis wind turbine at
runaway. Renew Energy 25:41-54
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