Aerodynamics and Design for Ultra-Low Reynolds Number Flight

Chapter 2
The control volume method has been applied to INS2d analyses of a NACA 4402 aifoil
operating at two degrees and six degrees angle of attack. The control volume has been
applied at various distances from the airfoil surface for several Reynolds numbers. The
resulting drag coefficients, are compared to the results from surface force integration in
Figure 2.1. The maximum variation at any single Reynolds number is less than one
percent for control volumes out to a radius of approximately six chordlengths. Beyond
this point the variations increase due to the rapid growth in cell size, reaching 25% at 12
chordlengths. Dissipative effects may be visible in the systematic increase in the drag
variation seen with decreasing Reynolds number at two degrees, but the maximum
variation across the Reynolds number range of interest is only two percent and the
variation is absent from the six degree cases. Variations in the predicted lift are smaller,
averaging 0.5% out to six chordlengths.
% Variation in C d from the On-Body Result
2.5
2.0
1.5
1.0
0.5
0.0
-0.5
-1.0
All cases at α=2.0 deg. unless noted otherwise
Re=1000
Re=2000
Re=6000
Re=12000
Re=1000, 6 deg.
Re=2000, 6 deg.
Re=6000, 6 deg.
0 1 2 3 4 5 6 7
CV Wakecut Location (Chordlengths from Trailing Edge)
FIGURE 2.1 Comparison of INS2d on-body and control volume drag values for the NACA 4402.
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