Aerodynamics and Design for Ultra-Low Reynolds Number Flight

The canonical pressure coefficient (C p’) may be expressed as a function of the edge
Chapter 3
velocities (U e ) yielding an expression having no Reynolds number dependence and a
dominant dependence on the pressure recovery gradient. In this instance, x represents the
distance from the location of minimum pressure.
Thwaites [20] laminar separation criteria takes the form:
This relation is also Reynolds number independent and dominated by the pressure
recovery gradient. This only become clear upon the substitution of Thwaites’s
formulation for the momentum thickness:
x 2 d
Cp' Cp ⎛ ⎞ '
⎠ dx
⎝ 2
≈ 0.0104
θ 2 dUe⎞ ---- ≈ – ⎛ 0.09
⎠ ⎝ ν dx
θ
x
2 0.45ν
=
6
Ue 0
------------- Ue d
Both of these formulations support the concept that the large growth in boundary layer
thickness that accompanies a reduction in Reynolds number is potentially beneficial to
lifting performance due to a reduction in the adverse pressure recovery gradient.
∫
5 x
(3.1)
(3.2)
(3.3)
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