Phase II Final Report - NASA's Institute for Advanced Concepts

Planetary Exploration Using Biomimetics
An Entomopter for Flight on Mars
St = fC
U
Equation 3-31
where C is the airfoil chord length and U is the free stream velocity, has been calculated. For
Karman vortex shedding, the established value of St ~ 0.2 and the Strouhal numbers shown for
Cases A and D in Table 3-7 are close to this value. Therefore, the flow in the present low Reynolds
number high-α simulations is closely related to flow over bluff bodies at low Reynolds
numbers. Some questions remain as to the characteristic length to be used in Equation 3-31.
Depending on the value of α the thickness or the chord length may be appropriate, or projected
length normal to the free stream might provide a better correlation. Due to the exploratory nature
of the current work, we plan to address such details in the future. Another important observation
is that the cases in the Reynolds number range above do not yield a steady state solution, indicating
that such a solution will violate the flow physics. A similar observation has also been made
by Kunz and Kroo [146, 149].
If the wing were to flap at the LEV-shedding frequency, the low C L phase can be avoided, and
the airfoil can always stay in the high C L (and high C L /c d ) phase. Note that the C L /c d ratio varies
over the range ~3.273-20.8, indicating the benefits of tailoring the flapping frequency to the
LEV-shedding frequency.
Table 3-7: Lift and Drag Summary for Reynolds Number =
510-5,100 Range
Case A
(Rec = 510)
Case B
(Rec = 5100)
C L (max) 4.5 5.2
C L (min) 2.7 1.95
∆cl 1.8 3.25
C L (average) 3.6 3.575
cd (max) 0.825 0.77
cd (min) 0.45 0.25
∆cd 0.375 0.52
cd (average) 0.636 0.51
C L (max)/cd (min) 10 20.8
C L (min)/cd (max) 3.273 2.53
Strouhal number (St) 0.237 0.2
92
Phase II Final Report