Aerodynamics and Design for Ultra-Low Reynolds Number Flight

Chapter 4
4.3 Viscous Swirl Modeling
The extreme operating conditions being considered precipitates a more detailed
consideration of viscous swirl effects, where it might otherwise be neglected at higher
Reynolds numbers. Typical section lift to drag ratios range from 50 to 100 at chord
Reynolds numbers above 100,000, but, as shown in Chapter 3, section lift to drag ratios
drop below ten in the ultra-low Reynolds number regime. In addition, the rotors
developed for ultra-low Reynolds number applications typically exhibit high solidity,
decreasing the separation between adjacent blades and increasing the likelihood of
strong leading/trailing blade viscous wake interactions. The fact that commonly used
swirl models have been implemented only on large scale, high Reynolds number rotor
blades, if at all, led to the development of several alternative models that directly utilize
the 2-D CFD analyses of Chapter 3. The goal is to determine both the need and
effectiveness of enhanced viscous swirl models.
4.3.1 Average Wake Deficit Viscous Swirl Model
The first viscous swirl model is based on computed airfoil wake profiles at ultra-low
Reynolds numbers. Based on this data, the value of v v is taken as a predicted average
wake deficit velocity. The current data is from INS2d calculations at Re 1000, 2000, and
6000. The section is a 2% constant thickness airfoil with a NACA 4402 camberline, a
blunt leading edge, and a radiused trailing edge. The airfoil is operating at 4.0 degrees
geometric angle of attack placing it close to conditions for maximum lift to drag ratio.
The 2% constant thickness is representative of manufacturing minimum gage constraints
and moderate variations to the camberline would have a small effect on the wake profiles
compared to the much larger variations caused by Reynolds number and distance from
the trailing edge. Therefore, analysis of this single airfoil provides a sufficient basis for
this model.
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