Aerodynamic Characteristics at Low Reynolds Number for Wings of Various Planforms

Abstract

The aerodynamic characteristics of various wing planforms at low Reynolds numbers (about 1 10 4 ) were studied by conducting wind-tunnel tests. These low Reynolds numbers correspond to the flights of small creatures, such as insects. Elliptical, rectangular, and triangular planforms with various aspect ratios were used in this study, as well as a swept rectangular (parallelogram) wing with an aspect ratio of four. The wing sections of all models were thin rectangular airfoils. The aerodynamic forces (lift and drag) and the pitching moment acting on the wing were measured for a wide range of angles of attack (including the maximum of 90 deg). Nonlinear characteristics of the lift coefficient were obtained, even at low angles of attack for high-aspect-ratio wings, whereas a small lift slope and a large maximum lift coefficient were obtained for low-aspect-ratio wings. The drag and the pitching moment coefficients also exhibited nonlinear characteristics. The effect of the Reynolds number based on the wing chord was comparatively small, but a distinctive phenomenon in low-Reynolds-number flow was observed in flow visualization using oil-film and smoke-wire methods. Nomenclature AR = aspect ratio, b 2 =S a = lift slope b = span length c = chord length C = coefficient of forces and moment related to ( ) c = mean aerodynamic chord D = drag D i = induced drag D p = pressure drag D 0 = minimum drag e = span efficiency factor f = friction drag, frequency k = proportional constant defined by Eq. (9) K p = lift slope given by lifting surface theory K V = constant value given by leading-edge suction force K W = constant value about aspect ratio of wing in blockage correction factor L = lift M = pitching moment q, q c = dynamic pressure and its corrected value R = resultant aerodynamic force, L 2 D 2 p r = distance between feathering axis and center of gravity Re = Reynolds number based on c S = wing area St = Strouhal number S ts = cross-sectional area of test section t = wing thickness t= c = thickness ratio U = wind velocity = angle of attack = proportional constant defined by Eq. (9) x = chordwise distance between quarter-chord and measurement point z = thicknesswise model distance between measurement point and wing chord " = wall blockage correction factor = leading-edge sweep angle = air density Subscripts M = measured value max = maximum value min = minimum value ST = strut ts = test section

Aerodynamic Characteristics of Low-Aspect-Ratio Wings with Various Aspect Ratios in Low Reynolds Number Flows

“…7,9,19) The occurrence of stall hysteresis was observed for wings with an aspect ratio of 1.0, although the data for aspect ratios of 1.5 and 0.5 did not show any hysteresis. Okamoto and Azuma 6) and Shields and Mohseni 10) also reported similar results. Thus, several previous studies reported the occurrence of hysteresis only for wings with an aspect ratio of 1.0.…”

“…However, the present study finds that there is a narrow region of the aspect ratio in which stall hysteresis occurs. This is the reason why several studies 6,7,9,10,19) reported the occurrence of stall hysteresis only for an aspect ratio of 1.0, as stated previously. Moreover, Torres and Mueller 8) stated that hysteresis was not observed for an aspect ratio of 1.0 in their study.…”

“…Figures 10 and 11 include the data obtained by other researchers. 6,8) The reference data was obtained at Reynolds numbers of 1:1 Â 10 4 and 1:0 Â 10 5 . The results of the present study quantitatively agree with the reference data.…”

“…[1][2][3][4][5][6][7] Moreover, the aerodynamics of low-aspect-ratio wings has also been investigated in low Reynolds number flows because some unmanned air vehicles use low-aspect-ratio wings. [4][5][6][7][8][9][10] Aerodynamic hysteresis was frequently observed in the previous studies. Here, when the aerodynamic coefficients of a wing become multiple-valued with respect to the angle of attack, it is referred to as aerodynamic hysteresis.…”

An Engineering Education toward Sustainable Society through Manufacturing a Flying Toy "Taketombo"

“…As can be seen in Fig. 5, where AR is the aspect ratio of the wing (the ratio of its length to its breadth), the computational fluid dynamics (CFD) results [7] for the drag and lift coefficients with AR=∞ (ideal wings of infinite length), are not easy to obtain experimentally, for example in a wind tunnel [8]. The correctness of the CFD results can be assessed by comparing them to the experimental data, so that the theoretical and experimental approaches compliment each other.…”