Aerodynamics and Design for Ultra-Low Reynolds Number Flight

Chapter 4
simplification, particularly at low advance ratios, but attempting to include the coupled
effects of all the blades would be difficult with this simple model. An iterative approach
to solving the system would steadily drive the total velocity to zero as the viscous terms
accumulated. For this reason, the local rotational velocity is taken as the normalization
velocity for v v and as the velocity for the chord Reynolds number. This model should
capture the first order viscous wake effects for the specified range of Reynolds numbers,
discouraging designs with extremely high local solidity, particularly in the hub region.
Unfortunately, as will be discussed in Chapter 6, this model appears to generally over-
estimate the viscous swirl effect.
v viscous / U∞
0.6
0.4
0.2
0.0
0 2 4 6 8 10
x/c aft of Trailing edge
FIGURE 4.4 Average wake deficit model and INS2d data points at three Reynolds numbers.
4.3.2 Gaussian Wake Viscous Swirl Model
Re 1000
Re 2000
Re 6000
The average wake deficit model neglects the effects of rotor downwash and the detail of
the wake velocity distribution. That model has been modified in an attempt to account
for these two factors. Based on the same INS2d data, the wake deficit velocity profile is
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