T HE aerodynamic efficiency of an aircraft, or the ratio of the coefficient of lift to the coefficient of drag, is the most important parameter affecting the range and endurance of subsonic aircraft. For aircraft designed for the maximum range or endurance possible, it is therefore critical to achieve the highest possible lift-to-drag ratio. Unmanned aerial vehicles (UAV) are often designed for these types of long endurance/maximum range missions, including military surveillance UAVs requiring long loiter times or unpowered sailplanes looking for a long range or glide distance. Although there has been much research done on designing airfoils with very low coefficients of drag at transonic speeds [1–3] and at Reynolds numbers commonly encountered by lighter general aviation aircraft [4], there have been few research projects aimed at producing highly efficient airfoils for much smaller aircraft. Therefore, this Note uses numerical optimization in an attempt to design highly efficient airfoils for use on aircraft with spans of 2 to 3m and operating around 10–40 mph, roughly at Reynolds numbers between 1 10 and 4 10. The resulting airfoils were then examined to determine their potential usefulness as wings and to explore what shapes and characteristics are most efficient at these low Reynolds numbers. Other investigations into numerical optimization of airfoils for this Reynolds number range have been conducted by Secanell et al. [5], although their efforts concentrated on Reynolds numbers from 5 10 to 1:4 10. Secanell et al. also limited the maximum thicknessto-chord ratio to be 1%. Another investigation by Secanell and Suleman [6] used three different gradient-based optimization techniques to determine which would produce an airfoil with the lowest drag from a common starting airfoil. The Reynolds number in this case was 5 10, closer to this Note’s target Reynolds numbers, although the thickness ratio was again constrained to 1%. This very low maximum thickness vale meant all the optimized airfoils that Secanell et al. [5,6] produced had a thickness-to-chord ratio of 1%, making them impractical airfoils for use in a real wing. Amore recent effort by Secanell et al. [7] focused on the design of airfoils for a small reconnaissance UAV; several airfoils were designed using optimization methods for all of the flight regions the UAV was expected to encounter, including takeoff, climb, cruise, loiter, and stall. This extended the Reynolds number region from 5 10 to 1:5 10. The gradient-based optimization routine used by Secanell et al. performed very similarly to the optimization routine used in this paper; both were given a fixed Cl and Reynolds number value and told to minimize drag. In response, the optimization routine minimized the airfoil’s thickness and increased the camber. Secanell et al. concluded the optimization program was cutting thickness to reduce pressure drag. Unlike their earlier papers, Secanell et al. limited thickness to 5%. Interestingly, although this paper used a higher minimum thickness value, the resulting airfoils have higher aerodynamic efficiency values. Another paper dealing with optimization of airfoils in low Reynolds numbers with direct implications on this paper is Lutz et al. [8], which optimized airfoils at Reynolds numbers of 2, 3, and 4 10. A hybrid genetic algorithm/gradient-based method using inverse airfoil design was used to minimize the drag coefficient at various coefficients of lift from 0.0 to 0.6. These values are very close to the target Cl and Reynolds number used in this investigation; however, different optimization and airfoil design methods are used in this Note, one of the suggestions for further researchmade by Lutz et al.
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Jul 1, 2015
Moumen Idres + 4
Open Access