1_c034415

virtually unchanged. Over the same Reynolds number range, the peak lift coefficient more than doubles for the NACA 0012 and Clark-Y, increasing from 0.55 to 1.3 for the NACA 0012 and from 0.72 to 1.63 for the Clark-Y.

The largest change in performance between the four airfoils occurs higher than a Reynolds number of 105. At Reynolds numbers of 2 × 104 and 4 × 104, the thin flat and cambered plates clearly outperform the conventional airfoils in terms of lift and drag. But at a Reynolds number of 1.2 × 105, the lift generated by the Clark-Y is comparable to that of the 6% cambered plate, and the lift of the NACA 0012 is greater than that of the flat plate for a given drag coefficient. These performance margins increase further at a higher Reynolds number of 106. It should also be noted that the Reynolds number appears to have an uniform effect on the drag coefficient of each of the four airfoils. Figure 16 shows that as the Reynolds number increases, the drag polars gradually shift to the left, indicating a decrease in drag. The minimum drag appears to decrease by approximately the same amount for all four airfoils. Because the geometric characteristics of the four airfoils are vastly different, the similar decrease in their minimum drag is likely attributed to decreasing viscous drag effects as the Reynolds number increases.

Figure 17 shows the effect of the Reynolds number on each airfoil (2% t∕c flat plate, 6% cambered plate, NACA 0012, and Clark-Y) separately in terms of lift-to-drag (cl∕cd) as a function of the angle of attack. Similarly to the results observed in Fig. 16, the conventional NACA 0012 and Clark-Y performance is shown to be more sensitive to the Reynolds number compared with the plate-type airfoils. Surprisingly, the 6% cambered plate appears to achieve the same peak lift-to-drag as the Clark-Y at a Reynolds number of 106, as seen in Fig. 17b. However, the Clark-Y maintains a larger envelope of a higher lift-to-drag ratio for a broader range of angles of attack. The primary implications for the design drawn from these results are as follows: 1) below the Reynolds number of 105, cambered plate airfoils demonstrate better lift-to-drag characteristics than conventional airfoils; 2) above the Reynolds number of 105, thicker airfoils have better lift-to-drag characteristics than thin flat or cambered plates; 3) below the Reynolds number of 106, lift-to-drag characteristics for most airfoils cannot be assumed to be constant with the Reynolds number; 4) zero-cambered flat plate performance is generally invariant to the Reynolds number.

VI. Conclusions

The goal of the present work was to use TURNS2D (a structured RANS solver with laminar-turbulent transition model) as a means to understand the low-Reynolds-number aerodynamics and, therefore, to provide guidelines for MAV and low-Reynolds-number designs. The results from TURNS2D were compared with available experimental lift, drag, pitching moment, and surface pressure data as means of validation. Overall, the calculated values from TURNS2D agree quite well with the experimental measurements at low Reynolds numbers. It was also observed from previous works that the uncertainty and error bounds in experimental results were higher for low-Reynolds-number flows, which could also contribute to certain misalignments between experimental observations and numerical predictions. The current work also identified the need for further assessment of turbulence models for low-Reynolds-number flows. The following specific conclusions were drawn from this study:

1)The results from TURNS2D show the extreme sensitivity of airfoil performance to changing the Reynolds number below 105, particularly for conventional airfoils such as the NACA 0012. As the Reynolds number decreases there is an increase in drag, particularly because of premature flow separation and failure to reattach, resulting in a reduced drag bucket and a large decrease in lift with the maximum lift coefficient decreases by approximately 46% between the Reynolds number of 105 and 104. Below a Reynolds number of 105, the lift curves are highly nonlinear, particularly for α < 5°, and a single lift-curve-slope value may not be appropriate.

2)As flat plate thickness-to-chord (t∕c) decreases (from 5 to 1%),

lift and drag characteristics improved, with the 1% flat plate being the most efficient at a Reynolds number of 104, a consequence of lower

form drag. An increase in camber (from 3 to 9%) on thin plate airfoils (t∕c of 1%) resulted in an increase in both the lift and the lift-to-drag ratio compared with flat plate airfoils of the same thickness. For a low-Reynolds-number wing design to achieve high lift-to-drag, a 6% camber appeared optimum. However, a 9% camber could be used if a maximum lift is a stronger design factor.

3)The effect of camber on thin NACA airfoils (NACA 0003, 2403, 4403, 6403) was examined at Reynolds numbers of 2 × 104 and 105, and high-camber airfoils (NACA 4403 and 6403) were shown to have the highest lift-to-drag at both Reynolds numbers. Additionally, the lift-to-drag curves were similar at the lower Reynolds number and more differentiated at the higher Reynolds number. The symmetric NACA 0003 airfoil performance changes very little with an increase in the Reynolds number and behaves similar to a flat plate. As camber is increased, however, the Reynolds number has a profound effect on the lift-to-drag, which improves by a greater margin.

4)Examination of the boundary layer at a low Reynolds number shows significant differences between thin plate airfoils and thicker airfoils. The NACA 0012 is more susceptible to trailing edge separation at a low Reynolds number, whereas the flat plate trips the laminar boundary layer at the leading edge, allowing it to reattach further downstream. The reattachment of the upper boundary layer preserves lower surface pressure and, therefore, allows the flat plate

to provide more lift than the NNACA 0012 at Reynolds numbers lower than 5 × 104.

5)When the NACA 0012 is placed in a reversed configuration at a Reynolds number of 2 × 104, its lift qualities improve. This effect is because of the sharp leading edge, creating an early LSB similar to the flat plate. Despite the fact that the NACA 0012 has the same maximum thickness in either configuration, the result indicates that the distribution of the thickness along the chord, particularly at the leading edge, has an effect on airfoil performance at a low Reynolds number that is counter to what is expected at a high Reynolds number.

Acknowledgments

This work is supported by the U.S. Army/U.S. Navy/NASAVertical Lift Research Center of Excellence Grant Number W911W6-11-2- 0012 with Mahendra Bhagwat as technical monitor. The authors would like to thank Alex Moodie, AMRDEC, for useful discussions.

References

[1]Shrestha, R., Benedict, M., Hrishikeshavan, V., and Chopra, I., “Hover Performance of a Small-Scale Helicopter Rotor for Flying on Mars,” Journal of Aircraft, Vol. 53, No. 4, 2016, pp. 1160–1167. doi:10.2514/1.C033621

[2]McMasters, J. H., and Henderson, M. L., “Low Speed Single-Element Airfoil Synthesis,” Technical Soaring, Vol. 6, No. 2, 1980, pp. 1–21.

[3]Mueller, T. J., “Aerodynamic Measurements at Low Reynolds Numbers for Fixed Wing Micro-Air Vehicles,” RTO AVT/VKI Special Course on Development and Operation of UAVs for Military and Civil Applications, Von-Karman Inst., Brussels, Sept. 1999, http://www.dtic

.mil/docs/citations/ADP010760.

[4]Abbott, I. H., and von Doenhoff, A., Theory of Wing Sections, McGraw–Hill, New York, 1959, Chap. 5.

[5]Mueller, T. J., and DeLaurier, J. D., “Aerodynamics of Small Vehicles,”

Annual Review of Fluid Mechanics, Vol. 35, No. 1, 2003, pp. 89–111. doi:10.1146/annurev.fluid.35.101101.161102

[6]Tsuchiya, T., Numata, D., Suwa, T., and Asai, K., “Influence of Turbulence Intensity on Aerodynamic Characteristics of an NACA 0012 at Low Reynolds Numbers,” 51st AIAA Aerospace Sciences Meeting, AIAA Paper 2013-65, Jan. 2013.

doi:10.2514/6.2013-65

[7]Schmitz, F. W., “Aerodynamics of the Model Airfoil Part I,” Airfoil Measurements, Translated from German, Redstone Scientific Information Center RSIC-721, Nov. 1967.

[8]Hoerner, S. F., Fluid-Dynamic Lift, edited by L. A. Hoerner, 2nd ed., 1985, pp. 42–44.

[9]Selig, M. S., Donovan, J. F., and Fraser, D. B., Airfoils at Low Speeds, H. A. Stokely, Virginia Beach, VA, 1989, Chap. 12.

[10]Mueller, T. J., and Batill, S. M., “Experimental Studies of Separation on a Two-Dimensional Airfoil at Low Reynolds Numbers,” AIAA Journal, Vol. 20, No. 4, 1982, pp. 457–463.

doi:10.2514/3.51095