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where it can be seen that the magnitudes and shapes of the CL values and contours are
quite different from those of Meyer and Falabella.
Now, it has been known for some considerable time31 that, when a wing is changing
its incidence, the stalling angle and associated lift may be different from that in
steady flow. In particular, when the aerofoil is oscillating about a mean incidence
above that of the steady-state stall, the lift coefficient may exceed the steady-state
Rotor aerodynamics in forward flight 229
Fig. 6.44 Effect of applying oscillating aerofoil data to rotor calculations (RAE)
Unsteady
‘synthesised’
aerofoil data
0.13
0.12
0.11
0.10
0.09
0.08
0.07
0.06
0.05
‘Nonlinear’
steady
2-D aerodynamics
–20° –18°–16°–14°–12° –10° –8° –6° –4°
tc
αnf
Fig. 6.43 Hysteresis loop for aerofoil oscillating above stall
2.0
1.5
1.0
0.5
0 5° 10° 15° 20°
NACA 0012
f = 4Hz
Steady
6°
αmean = 12°
CL
α
6°
value when the incidence is increasing and fall below it when the incidence is decreasing.
Further results have been given by Halfman et al.32 for flutter investigations, but
valuable data for helicopter applications were first given by Carta33, who reported
oscillation tests on a NACA 0012 aerofoil. A typical result of Carta’s tests is shown
in Fig. 6.43. The aerofoil in this case was oscillated at 4 Hz (typical rotor frequency)
with an amplitude of 6° about a mean incidence of 12°.
It can be seen that under these conditions the lift coefficient varies by as much as
0.5 from the steady values, and the difference may often be far greater. In the papers
by Bramwell et al.27 and Harris et al.28, attempts were made to express the oscillating
aerofoil data of the kind shown in Fig. 6.42 in numerical or mathematical form and
apply it to rotor force calculations. In Bramwell’s paper the difference between the
steady and unsteady lift coefficients was superimposed on the experimentally derived
hovering aerofoil characteristics (‘synthesised’ data); in Harris’s paper the values
were superimposed on two-dimensional steady aerofoil data in which the CL was
corrected for the local sweep angle. The improvement in the calculated performance
is shown in Figs 6.44 and 6.45. The former also paid attention to the CL contours over
the disc. Figure 6.46 shows the contours obtained by superimposing oscillating aerofoil
230 Bramwell’s Helicopter Dynamics
0.16
0.12
0.08
0.04
–16° –8° 0° 8° 16°
Effect of including
unsteady aerodynamics
Effect of including
spanwise flow
μ = 0.35
αnf
tc
Fig. 6.45 Effect of applying oscillating aerofoil data to rotor calculations (Boeing-Vertol)
30°
180°
150°
120°
90°
60°
330°
300°
270°
240°
210°
0.3
0.3
0.7
1.1
0.9
Reversed
flow
1.7
ψ = 0°
μ = 0.3
θ0 = 12°
αnf = –10°
Fig. 6.46 Effect of applying oscillating aerofoil data on CL contours
1.5
1.3
0.7
0.5
0.9
0.5
0
data on the synthesised aerofoil characteristics; these should be compared with those
of Figs 6.41 and 6.42. Although the test conditions were not exactly the same as those
of the calculations, the figures show that the use of oscillating aerofoil data results in
contours whose appearance resembles those of the rotor tests far more closely than
the steady two-dimensional calculations.
Since the work of Carta, many others have investigated the unusual aerofoil behaviour
which occurs at high incidence under unsteady conditions, notably Ham and Garelick34,
and McCroskey and Fisher35. From the analysis of chordwise pressure distributions
on the blade, it is seen that, as the blade moves into the retreating region, the rapid
rate of increase of incidence allows the aerofoil section to exceed the normal steady
stall incidence without signs of a flow breakdown; i.e. there is still a large suction
peak near the leading edge. As pointed out by Carta, this may be due, in part at least,
to the apparent increase of camber due to the rotation of the aerofoil. As the incidence
increases further, a vortex is formed and shed from the leading edge and moves
backwards across the aerofoil at a speed somewhat less than the local flow speed.
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Bramwell’s Helicopter Dynamics(115)
