Environmental Engineering Reference
In-Depth Information
Fig. 4.4 Computed pressure
distribution around a NACA
0012 aerofoil
5
4
α
α
α
= 0 °
= 4 °
= 8 °
3
2
1
0
-1
0
0.2
0.4
0.6
0.8
1
Distance along chord line, x/c
C p ¼ P P 0
1
ð 4 : 5 Þ
2 qU 0
and aerodynamic convention has been followed by plotting negative (lift-pro-
ducing) C p upwards. Unfortunately the pressure coefficient has the same symbol as
the turbine's power coefficient, but the former is used only in this section. Note
that there are two values of C P for each x/c; the (usually) negative value for
the upper surface and the other for the lower surface. The upper surface of negative
gauge pressure is often called the ''suction'' surface and the lower one the
''pressure'' surface. It is easy to show that the area between the upper and lower
surface values gives C l ; note the coincidence of the values for this symmetric
section at a = 0. These simple calculations do not include the effects of viscosity,
and so apply, in principle, only at infinite Re, but are sufficiently representative to
indicate
the
acceleration
of
the
flow
over
the
upper
surface
that
becomes
increasingly rapid as a increases.
The boundary layers on the upper and lower surfaces begin at the stagnation
point where C p = 1. As Re decreases, these boundary layers remain laminar for
a longer distance along the aerofoil surface. After the minimum pressure point
on the upper surface, the boundary layer faces a region of adverse pressure
gradient—where C p is decreasing—which it is more easily withstood when
turbulent at higher Re than when laminar at low Re. The usual result is sepa-
ration for the low Re flow followed by a laminar separation bubble. Soon after
the flow separates, it goes through transition to turbulence, and reattaches, often
quickly. The separation region is usually identifiable on the C p plot by its nearly
constant pressure, e.g. [ 2 ].
There is very little data on aerofoil performance at Re \ 10 5 partly because it is
difficult to measure accurately the small forces involved. Laitone [ 6 ] and others
suggested that the best aerofoils at Re \ 10 5 are very thin—less than about 2.5%
of the chord—and have around 5% camber. The thinness can be a major problem,
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