The role of advance ratio and aspect ratio in determining leading-edge vortex stability for flapping flight

Abstract The effects of advance ratio and the wing’s aspect ratio on the structure of the leading-edge vortex (LEV) that forms on flapping and rotating wings under insect-like flight conditions are not well understood. However, recent studies have indicated that they could play a role in determining the stable attachment of the LEV. In this study, a numerical model of a flapping wing at insect Reynolds numbers is used to explore the effects of these parameters on the characteristics and stability of the LEV. The word ‘stability’ is used here to describe whether the LEV was attached throughout the stroke or if it was shed. It is demonstrated that increasing the advance ratio enhances vorticity production at the leading edge during the downstroke, and this results in more rapid growth of the LEV for non-zero advance ratios. Increasing the wing aspect ratio was found to have the effect of shortening the wing’s chord length relative to the LEV’s size. These two effects combined determine the stability of the LEV. For high advance ratios and large aspect ratios, the LEV was observed to quickly grow to envelop the entire wing during the early stages of the downstroke. Continued rotation of the wing resulted in the LEV being eventually shed as part of a vortex loop that peels away from the wing’s tip. The shedding of the LEV for high-aspect-ratio wings at non-zero advance ratios leads to reduced aerodynamic performance of these wings, which helps to explain why a number of insect species have evolved to have low-aspect-ratio wings.