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Vr /Ωx
Vθ /Ωy
Ωx or Ωy
1/2z√(Ωy/νx)
Fig. 6.50 Velocity distributions in laminar boundary layer
Rotor aerodynamics in forward flight 235
Then, if Ω is 25 rad/s, Ωx = 7.5 m/s and the largest spanwise velocity is about
7.5 × 0.3 = 2.25 m/s, compared with the free stream chordwise velocity of 150 m/s.
The spanwise flow becomes considerable only near the hub, where x/y is no longer
a small quantity. Thus, for the conventional rotor blade the spanwise, or secondary,
flow appears to be insignificant, although it might be important for wide blades such
as marine propellers.
McCroskey et al. 41 have calculated the details for a turbulent boundary layer, the
results of which are shown in Fig. 6.51. We see that the spanwise flow is even
smaller, due mainly to the larger stresses in the turbulent layer.
McCroskey and Yaggy42 have extended the theorem of Sears to the forward flight
case and have made calculations on the basis of Fogarty’s laminar flow theory in
hovering flight. The calculations show that the spanwise flow is dominated by the
spanwise component of forward speed, as the example in Fig. 6.52 shows.
The chordwise flow is affected by several terms which are additional to those
arising in the hovering case. Generally, the effects represented by these terms are
favourable with regard to the delay of laminar separation, particularly in the retreating
quadrant 180° to 270°. This may be another reason for the improved performance of
the rotor blade compared with steady two-dimensional aerofoil characteristics although,
as we saw in the previous section, it seems that it is the unsteady motion which is
largely responsible for the peculiar behaviour of the aerodynamic characteristics at
high incidence.
7
6
5
4
3
2
1
–0.5 –0.4 –0.3 –0.2 –0.1 0 0.1 0.2 0.3 0.4 0.5
y√(ν/Ωyx)
180°
135°
225°
90°
270°
45°
ψ = 0°
315°
V∞/Ωy = 0.3
x/y = 0.1
V /Ωy
Fig. 6.52 Laminar boundary profiles in forward flight
1
0.5
Turbulent
Laminar
0 0.1 0.2
y/δ
Vr /Ωx
Fig. 6.51 Velocity distribution in turbulent boundary layer
236 Bramwell’s Helicopter Dynamics
References
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(see p. 244 for ‘Vortex Theory of V. E. Baskin’).
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1964.
3. Willmer, M. A. P. ‘The loading of helicopter blades in forward flight’, Aeronautical Research
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NACA Tech. Rep. 496, 1935.
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and Vibration, 4(3), 1966.
12. Landgrebe, A. J., ‘An analytical method for predicting rotor wake geometry’ J. Amer. Helicopter
Soc., 14(4), October 1969.
13. Cook, C. V., ‘The structure of the rotor blade tip vortex’, AGARD Conf. Proc. CP–111, 1972.
14. Bagai, A. and Leishman, J. G., ‘Rotor free-wake modeling using a pseudo-implicit technique
– including comparisons with experimental data’, J. Amer. Helicopter Soc., 40(3), 1995.
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using a high order panel method’, Paper No. AE11, 24th European Rotorcraft Forum, Marseilles,
France, Sept. 1998.
16. Tangler, J. L., ‘Schlieren and noise studies of rotors in forward flight’, Paper No. 33-05, 33rd
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