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The effect of the vortex is to produce a suction peak in the mid-chord region, resulting
Rotor aerodynamics in forward flight 231
remarkably similar. Figure 6.48 shows the variation of CN and CM with blade azimuth
angle for the point r/R = 0.75 on the rotor blade, and the corresponding values from
the two-dimensional tests for similar values of the incidence α and of α˙ .
From the similarity of the curves, it can be inferred that the performance of the
blade section at high incidence has little to do with the three-dimensional rotating
environment and that the section characteristics can be obtained with sufficient accuracy
from unsteady two-dimensional aerofoil tests.
The particular flow states mentioned above can be identified on Fig. 6.48; thus, for
the model rotor results (full line), for ψ increasing from 90°, the normal force coefficient
increases to beyond the maximum steady state value (about 1.5) until ψ = 210°.
in a large nose down pitching moment. The lift continues to grow even after the
leading edge suction has started to collapse. After this, the aerofoil moves into a
condition of deep stall and the tests show that torsion flutter may occur. When the
blade reaches approximately the rear of the disc, where the blade incidence is greatly
reduced, the flow returns to the steady pattern of low incidence. The aerofoil’s chordwise
pressure distributions in the sequence described are sketched in Fig. 6.47, with typical
values of CN and incidence at four azimuth angles on the retreating blade.
McCroskey and Fisher35 have observed that the relationship between the normal
force and pitching moment coefficients in their model helicopter measurements and
those of the two-dimensional aerofoil measurements of Ham and Garelick34 are
Forward flight
Hover or non-rotating data
ψ = 180°
α = 9°
CN = 1.2
6
4
2
0
–2
0.2 0.4 0.6 0.8 1
x/c
–Cp
8
6
4
2
0
–2 0.2 0.4 0.6 0.8 1
x/c
–Cp
6
4
2
0
–2
–Cp
6
4
2
0
0.2 0.4 0.6 0.8 1 –2
x/c
–Cp
0.2 0.4 0.6 0.8 1
x/c
ψ = 270°
α = 34°
CN = 2.5
ψ = 240°
α = 24°
CN = 1.2
ψ = 210°
α = 17°
CN = 2.1
Fig. 6.47 Chordwise pressure distributions at high incidence
232 Bramwell’s Helicopter Dynamics
Beyond this azimuth angle, CN continues to increase but accompanied by a significant
nose down pitching moment; this is associated with the shedding and movement
rearwards of the concentrated vorticity from the leading edge region. After ψ = 240°,
CN decreases corresponding to the aerofoil being fully stalled, and the vortex having
passed clear of the trailing edge. At about 360°, the flow re-attaches.
This sequence of events has been modelled by Leishman and Beddoes36 and
validated through comparison with experiment following initial work by Beddoes37
to produce a practical and versatile design tool. For the attached flow in the initial
phase, the changing normal force and moment are modelled indicially using lift and
moment deficiency functions, rather as for fixed wing theory in relation to gusts and
other time-dependent conditions. Leading edge separation occurs when CN achieves
a critical value which is dependent on local Mach number; however, there is a lag or
time delay in unsteady flow which allows CN to reach higher than normal static
values. This delay is determined empirically and has been found to be largely
independent of aerofoil shape.
Subsequently, the vortex which separates from the leading edge is transported
downstream causing the centre of pressure also to move rearwards. Meanwhile, the
vortex itself generates lift which dissipates (exponentially) as fast as it accumulates,
until the vortex passes clear of the trailing edge, whereupon the lift (or CN) decays
rapidly to a value appropriate to fully separated flow, assuming the angle of incidence
is still sufficiently high. The speed of convection of the vortex downstream is derived
from a large body of experimental data involving dynamic stall over a wide range of
Mach numbers.
The indicial approach has been further implemented by Leishman38 to account for
arbitrary motion of a rotor blade section, as well as encounters with gusts or interactions
with vortices shed by other blades.
0
–0.2
–0.4
–0.6
CM
0 1 2 3
McCroskey and
Fisher (model rotor)
Ham and Garelick
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Bramwell’s Helicopter Dynamics(116)
