Aerodynamics and Design for Ultra-Low Reynolds Number Flight

Chapter 4
60
FIGURE 4.3 Effect of Reynolds Number on wake velocity profiles one chordlength aft of trailing
edge. INS2d calculation of a 2% thick NACA 4402 camberline, α=4.0 degrees.
This average wake deficit model for v v is based on a power law fitting across the blade
separation arclength and quadratic fitting of the coefficients across Reynolds number:
where:
u / U ∞
1.0
0.8
0.6
0.4
0.2
Re 1000
Re 2000
Re 6000
0.0
-0.5 -0.3 -0.1 0.1 0.3 0.5
y/c
E 1
E 2
v v
=
3.0e 10 – 2
ReΩr E1( arclength)
E2 – Re Ωr
– ( ( ) ) 3.0e 6
=
– ( ( ) ) + 0.241
3.0e 9 – 2
ReΩr – Re Ωr
( ( ) ) 7.0e 5
=
– ( ( ) ) – 0.372
(4.29)
(4.30)
(4.31)
The most conspicuous simplification in this model is that the CFD computations are for
a single airfoil in a constant free-stream flow. Modeling the viscous swirl effect as a
two-element system, the forward blade and the trailing blade, neglects the fact the
forward blade itself is operating in a non-uniform flow field. This is a large