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

TLDR: In this article, the effect of frontal gust on the force patterns of an insect-sized flapping wing in the inclined-stroke plane was assessed using global recurrence plots and windowed recurrence quantification analysis (WRQA).

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 $$ \frac{{{\text{u}}_{\text{G}} }}{{{\text{u}}_{\text{w}} }} = \frac{{{\text{u}}_{\infty } }}{{{\text{u}}_{\text{w}} }} + \left( {\frac{{{\text{u}}_{\text{g}} }}{{{\text{u}}_{\text{w}} }}} \right)\sin \left( {2\uppi\frac{{{\text{f}}_{\text{g}} }}{{{\text{f}}_{\text{w}} }}{\text{t}}} \right) $$ 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, fg/fw = 0.1, 0.5 and 1 and ratio of gust velocity amplitude to root mean square averaged flapping velocity, ug/uw = 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 fg/fw = 0.1 and ug/uw = 1. The onset of unstable behaviour was prominently captured by WRQA of the vertical force coefficient based on determinism (DET) and laminarity (LAM) series.