Aerodynamics of wings at low Reynolds numbers: boundary layer separation and reattachment

Unrestricted Due to advances in electronics technology, it is now possible to build small scale flying and swimming vehicles. These vehicles will have size and velocity scales similar to small birds and fish, and their characteristic Reynolds number will be between 104 and 10^5. Currently, these flying and swimming vehicles do not perform well, and very little research has been done to characterize them, or to explain why they perform so poorly. This dissertation documents three basic investigations into the performance of small scale lifting surfaces, with Reynolds numbers near 10^4.; Part I. Low Reynolds number aerodynamics. Three airfoil shapes were studied at Reynolds numbers of 1 and 2 x 10^4: a flat plate airfoil, a circular arc cambered airfoil, and the Eppler 387 airfoil. Lift and drag force measurements were made on both 2D and 3D conditions, with the 3D wings having an aspect ratio of 6, and the 2D condition being approximated by placing end plates at the wing tips.; Comparisons to the limited number of previous measurements show adequate agreement. Previous studies have been inconclusive on whether lifting line theory can be applied to this range of Re, but this study shows that lifting line theory can be applied when there are no sudden changes in the slope of the force curves. This is highly dependent on the airfoil shape of the wing, and explains why previous studies have been inconclusive.; Part II. The laminar separation bubble. The Eppler 387 airfoil was studied at two higher Reynolds numbers: 3 and 6 x 10^4. Previous studies at a Reynolds number of 6 x 10^4 had shown this airfoil experiences a drag increase at moderate lift, and a subsequent drag decrease at high lift. Previous studies suggested that the drag increase is caused by a laminar separation bubble, but the experiments used to show this were conducted at higher Reynolds numbers and extrapolated down.; Force measurements were combined with flow field measurements at Reynolds numbers 3 and 6 x 10^4 to determine whether the drag increase is really caused by the formation of a laminar separation bubble. The results clearly indicate that the reverse is true, and that the subsequent drag decrease is caused by the laminar separation bubble.; Part III. The leading edge vortex. Four wings with different sweep angles were studied at Reynolds number 5 x 10^4: sweep angles of 0deg, 20deg, 40deg, and 60deg. The wings had a simple cambered plate airfoil similar to the cambered airfoil of part I above. Each wing was built to have the same aspect ratio, wing area, and streamwise airfoil shape. Previous studies on bird wings speculate that simply sweeping the wings can cause a leading edge vortex to form, which could cause substantial improvements in performance. However, these studies were not well controlled, and were conducted from a biological perspective.; Qualitative and quantitative flow field measurements were combined with force measurements to conduct a well controlled engineering experiment on the formation and effect of a leading edge vortex on simple swept wings. A stable vortex was found to form over the 60deg swept wing at one particular angle of attack, but it was not similar to the traditional notion of a leading edge vortex. The vortex has a small radius, and extends over little of the span. Force measurements indicate that the vortex has no significant impact on the forces measured. Thus, simply sweeping a wing is not sufficient to form a significant leading edge vortex, and other effects must be considered.得益于电子技术的进步，如今已可研制小型飞行与水下航行载具。此类载具的尺寸与速度尺度接近小型鸟类与鱼类，其特征雷诺数（Reynolds number）介于10⁴与10^5之间。当前此类飞行与水下航行载具的性能表现欠佳，且相关表征研究与性能不佳成因的阐释工作均较为匮乏。本学位论文针对雷诺数接近10^4的小型升力面性能开展三项基础研究，具体内容如下： 第一部分 低雷诺数空气动力学 针对雷诺数为1×10^4与2×10^4的工况，研究了三种翼型：平板翼型、圆弧弯扭翼型以及Eppler 387翼型。分别在二维与三维条件下开展升力与阻力测量实验：三维机翼的展弦比（aspect ratio）为6，二维工况则通过在机翼翼尖加装端板（end plates）近似实现。 将本次实验结果与既往有限的测量数据对比后，二者吻合度良好。既往研究对于升力线理论（lifting line theory）是否适用于该雷诺数范围尚未得出定论，但本研究表明，当力曲线斜率无突变时，升力线理论可应用于此场景。该结论高度依赖机翼的翼型设计，这也解释了既往研究结论不一致的原因。 第二部分 层流分离泡（laminar separation bubble） 针对雷诺数为3×10^4与6×10^4的工况，研究了Eppler 387翼型。既往在雷诺数6×10^4下的研究表明，该翼型在中等升力条件下会出现阻力上升，在高升力条件下随后出现阻力下降。既往研究推测该阻力上升现象由层流分离泡引发，但相关验证实验均在更高雷诺数下开展，并通过外推得到该结论。 本研究将测力实验与雷诺数3×10^4、6×10^4下的流场测量相结合，以验证阻力上升是否确由层流分离泡形成引发。实验结果清晰表明事实恰好相反，而后续的阻力下降现象才由层流分离泡导致。 第三部分 前缘涡（leading edge vortex） 针对雷诺数5×10^4的工况，研究了四种不同后掠角的机翼：后掠角分别为0°、20°、40°与60°。机翼采用与第一部分中弯扭翼型相似的简易弯板翼型。所有机翼均保持相同的展弦比、机翼面积与弦向翼型外形。既往针对鸟类翅膀的研究推测，仅通过后掠机翼即可引发前缘涡形成，从而大幅提升性能，但此类研究未设置良好的控制变量，且从生物学视角开展。 本研究结合定性与定量流场测量与测力实验，针对简单后掠机翼上前缘涡的形成与影响开展了控制严谨的工程实验。实验发现，在特定攻角下，60°后掠机翼上方会形成稳定涡旋，但该涡旋与传统认知中的前缘涡并不一致：其半径较小，且展向覆盖范围有限。测力实验表明，该涡旋对测得的力值无显著影响。因此，仅通过后掠机翼不足以形成具有显著影响的前缘涡，还需考虑其他效应。