Aerodynamics and Design for Ultra-Low Reynolds Number Flight

Thrust per unit span (g)
3.5
3.0
2.5
2.0
1.5
1.0
0.5
Classical Angular Momentum
Average Wake Deficit
Gaussian Wake
0.0
0.2 0.3 0.4 0.5 0.6
r/R
0.7 0.8 0.9 1.0
Chapter 6
FIGURE 6.35 Predicted spanwise torque distributions for the 4-blade 2.5cm rotor using three
different viscous swirl models.
The trends are consistent across the span and globally for both metrics. The Gaussian
wake model predicts the highest thrust and required power, 0.0455N and 0.485W. For
this example, the localized nature of the Gaussian velocity deficit distribution results in
zero viscous swirl effect all along the blade except at the inner-most stations. The thrust
and power values drop 5.5% and 4.7% respectively for the angular momentum model.
The average wake deficit model results in the lowest values, 17.4% and 15.3% lower
than the global thrust and power required predicted with the average wake deficit model.
It was initially thought that the choice of viscous swirl model might have a
significant effect on both the inflow angle and the local flow velocity, but this has proven
not to be the case. Due to the coupling between the vertical and tangential induced
velocities in the rotor relations, the effect on inflow angle is minimal. The predominant
effect of the viscous swirl corrections is a reduction in the flow velocity, resulting in a
reduction in Reynolds number and dynamic pressure.
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