Aerodynamics and Design for Ultra-Low Reynolds Number Flight

Chapter 3
extrapolation based on higher Reynolds number experience, the resulting geometries
represent the first quantitatively designed airfoils for use under these conditions.
3.2 General Reynolds Number Effects
The most obvious effect of operation at ultra-low Reynolds numbers is a large increase
in the section drag coefficients. Zero lift drag coefficients for airfoils range from 300 to
800 counts depending on the Reynolds number and geometry. The increase in drag is
not reciprocated in lift. Lift coefficients remain of order one, resulting in a large
reduction in the L/D. Flight at these Reynolds numbers is much less efficient than at
higher Reynolds numbers and available power is a limiting technological factor at small
scales. It is important to operate the airfoil at its maximum L/D operating point, but this
requires operating close to the maximum steady-state lift coefficient. Even small
increases in the maximum lift coefficient are significant and generally translate to higher
L/D.
Flow at ultra-low Reynolds numbers is dominated by viscosity, and as the Reynolds
number is reduced, the effects of increasing boundary layer thickness become more
pronounced. The concept of a ‘boundary layer’ at such low Reynolds numbers in a fully
viscous flow field is an inexact notion. Here it is generalized as the low velocity flow
adjacent to the body over which the pressure gradient perpendicular to the surface is
close to zero. Regions of constant pressure extend a significant distance away from the
surface of the airfoil and the effective geometry is significantly altered by the presence of
the boundary layer.
In this operating regime the boundary layer has a dramatic effect on surface pressures,
closer to that of a separation streamline. This is demonstrated by considering the
inviscid and viscous pressure distributions on the NACA 0008 at zero angle of attack,
shown in Figure 3.1. Both the Re=6000 and Re=2000 cases are fully attached. As the
Reynolds number is reduced, the value of the minimum pressure and the slope of the
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