Aerodynamics and Design for Ultra-Low Reynolds Number Flight

Abstract
Growing interest in micro-air-vehicles has created the need for improved understanding
of the relevant aerodynamics. A reasonable starting point is the study of airfoil
aerodynamics at Reynolds numbers below 10,000, here termed ultra-low Reynolds
numbers. The effects of airfoil geometry on performance are explored using an
incompressible Navier-Stokes solver. Variations in thickness, camber, and the shape of
leading and trailing edges are studied. Results indicate an increase in maximum lift
coefficient with decreasing Reynolds number, but the lift to drag ratio continues to
decrease, making the power required for flight a more restrictive consideration than lift.
This performance penalty can be mitigated by careful airfoil design. Contrary to the
notion that viscous fairing reduces airfoil geometry effectiveness, the computational
results indicate that geometry still has a profound effect on performance at ultra-low
Reynolds numbers. To further explore this design space, the flow solver has been
coupled with an optimizer, resulting in the first airfoils quantitatively designed for this
flow regime and demonstrating that unconventional camberlines can offer significant
performance gains.
Building on these results, tools are developed for ultra-low Reynolds number rotors,
combining enhanced classical rotor theory with airfoil data from Navier-Stokes
calculations. This performance prediction method is coupled with optimization for both
design and analysis. Performance predictions from these tools are compared with threedimensional
Navier-Stokes analyses and experimental data for several micro-rotor
designs. Comparisons among the analyses and experimental data show reasonable
agreement both in the global thrust and power, but the spanwise distributions of these
quantities exhibit deviations, partially attributable to three-dimensional and rotational
effects that effectively modify airfoil section performance. While these issues may limit
the applicability of blade-element type methods for detailed rotor design at ultra-low
Reynolds numbers, such methods are still useful for evaluating concept feasibility and
rapidly generating initial designs for prototyping and for further analysis and
optimization using more advanced tools. Moving toward controlled powered flight at
centimeter scales, several prototype rotorcraft have been fabricated and tested, exploring
both the aerodynamics and system integration issues.
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