Recurrence studies of insect-sized flapping wings in inclined-stroke plane under gusty conditions

Abstract

Global recurrence plots (GRPs) and windowed recurrence quantification analysis (WRQA) are two recurrence paradigms which find wide applications to detect the onset of instability in a dynamic system. The present work reports the attempt to employ these recurrence paradigms to assess the effect of frontal gust on the force patterns of an insect-sized flapping wing in the inclined-stroke plane. Horizontal and vertical forces generated by the flapping wing in the presence of gusts of the form u G u w ¼ u 1 u w þ u g u w sin 2p f g f w t were numerically estimated in the 2D reference frame for Re = 150. Nine gusts with combinations of the ratio of gust frequency to wing's flapping frequency, f g /f w = 0.1, 0.5 and 1 and ratio of gust velocity amplitude to root mean square averaged flapping velocity, u g /u w = 0.1, 0.5 and 1 were considered. Recurrence studies of the forces were carried out to find out the gusty condition, which would trigger an onset of unstable behaviour. Studies indicated a possible onset of instability in the force patterns for gust with f g /f w = 0.1 and u g /u w = 1. The onset of unstable behaviour was prominently captured by WRQA of the vertical force coefficient based on determinism (DET) and laminarity (LAM) series.