Aerodynamics and Design for Ultra-Low Reynolds Number Flight

FIGURE 4.6 Converged wake streamlines for a candidate rotor after 6 iterations.
Chapter 4
The inviscid induced rotor inflow velocities are calculated using second order central-
differencing of the stream-function along the blade. These velocities are utilized to
derive a modified κ distribution. Eliminating κ and directly using the results to modify
the inflow velocities is inconsistent with the initial separation of viscous and inviscid
components of the thrust and torque equations as derived earlier. Utilizing a corrected κ
allows the classically derived equations to be used in an unmodified form. The inviscid
momentum and blade element thrust equations may be solved for BΓ and equivalently
Γ ∞ blades :
x/R
2
1.5
1
0.5
0
0.5
1
1.5
4πru( u + U∞) = =
----------------------------------
( Ωr – v)
BΓ Γ ∞ blades
0.5 1 1.5 2
y/R
(4.44)
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