Aerodynamics and Design for Ultra-Low Reynolds Number Flight

Chapter 4
Here, u is the constant downwash velocity predicted by actuator disk theory:
Using the downwash velocities (u’) calculated from the contracted wake model the
corrected value of BΓ may be expressed as:
The final expression for κ simplifies to:
The effectiveness of this model and its impact on both performance estimation and
design are assessed later in Chapter 6.
4.5 Higher-Order Modeling of 2-D Viscous Effects
70
u( u+ U∞) BΓ κΓ ∞ blades
------------
T
4ρπr
(4.45)
(4.46)
(4.47)
The commonly used simplifications of linear lift curve slopes and parabolic drag polars
become increasingly inaccurate as the Reynolds number drops into the region of interest.
The most attractive operating point, around the sectional maximum lift to drag ratio, is
also the area of greatest non-linearity in the lift curves; it is also typically very close to
the steady-state stall point. The necessary fidelity is attained by utilizing an database of
2-D section characteristics. The method, first implemented by Kunz [29], sequentially
generates spline fits across flap deflection and Reynolds number, resulting in final spline
curves for the geometric angle of attack and C d as a function of C l . This method was
developed for natural laminar flow airfoils used on high-performance sailplanes. These
sections also generally exhibit performance curves that differ significantly from the
=
4πru'( u' + U∞) = = ------------------------------------
( Ωr – v)
u'( u' + U∞) κ =
-------------------------uu
( + U∞)