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

Planetary Exploration Using Biomimetics
An Entomopter for Flight on Mars
From the plots, we notice that the thin airfoil generates a higher lift coefficient than the thick airfoil.
Also, beyond an angle of attack of about 2 o , the drag coefficient begins to reduce.
3.3.1.4 Refined Case Studies
With the knowledge gained from the previous case studies, a new airfoil section was created for
further simulations. A thin cambered airfoil has the necessary low Reynolds number characteristics
that can be used to advantage in MAVs. A circular arc airfoil with negligible thickness and a
thin airfoil with an elliptical leading edge and a gradually tapering trailing edge, having the same
camber as the first airfoil, were modeled. The choice of these two airfoil shapes, differing in
thickness but identical in other respects, provided a means to evaluating further the effect of
thickness on the low Reynolds number, unsteady flow field. The chord length (C) of the airfoils
is 36.5 cm, and the maximum thickness of Airfoil 1 is 1.825 cm (0.05C).
Seven cases were run with angle of attack ranging from 8.3 o to 45.79 o . CFD simulations were
done at the conditions of the Mars environment, assumed to consist of CO 2 as given in
Table 3-5.
Lift and drag coefficients were determined from the simulations. C L values from the small-α
simulations were compared to those from “lifting-line theory.” The close agreement between the
C L values from the steady state simulations and the “lifting-line theory” served to validate the
CFD procedure.
Figures 3-63 and 3-64 show results from α = 8.31 o and Reynolds number = 9,600 simulations.
Figures 3-63 and 3-64 show C L and c d variations, respectively, vs. time. The present-time accurate
simulations, using a fine grid optimized for the geometry and flow conditions, capture the
cyclical nature of lift and drag. The frequency of the force oscillations is related to the frequency of
the LEV dynamics.
Figure 3-65 shows velocity vector plot, and Figure 3-66 shows the static pressure contours.
These results are based on a time-accurate solution with a step size of 0.001 s. Several interesting
features were observed for this case. At regular intervals, the vortex formed at the leading
edge stayed attached to the top surface, grew, and convected downstream. The lift showed a
cyclical variation depending on the phase of the LEV. Results from several other cases not
included in this report showed that the behavior of the LEV depends strongly on the Reynolds
number.
Table 3-6: Lift and Drag Coefficient Values
Case Flow Time(s) C L C d
1 1.5 2.44 0.486
2 1.6 2.55 0.366
3 1.7 2.80 0.360
4 1.8 4.01 0.560
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Phase II Final Report