Ornithopters and entomopters should be insensitive to the gusty environment during outdoor operations. Hence, it becomes imperative to understand their behaviour under the influence of gust for ensuring stable flight. In light of this, the present numerical study focused on understanding the aerodynamics of flapping wings with five different planform shapes under the influence of a spatiotemporally varying frontal gust. 3D, unsteady, laminar, and incompressible Navier-Stokes equations were solved using finite volume formulation. A canonical case of asymmetric 1 degree of freedom (DoF) flapping kinematics was considered. Horizontal and vertical force patterns in constant and gusty inflow conditions were numerically computed and compared. Findings were analyzed quantitatively by comparing the differences in the instantaneous force patterns, ordinal scoring approach, and phase space plots. Qualitative comparisons were made based on plots of vortex structures and surface pressure contours for constant and gusty inflow conditions for wings with different planform shapes. Spanwise Lagrangian Coherent Structures (LCS) of all the five wings were also compared. Studies revealed that the elliptical wing exhibited low sensitivity and inverse semi-elliptical wing exhibited high sensitivity to the gusty inflow. Rectangular, triangular and semi-elliptical shaped wings were moderately sensitive to the gusty inflow. This finding, within the limitations of the flapping kinematics and simulation conditions considered for the present study, supported the fact that many natural flyers like forest raptors, non-migratory passerines, pheasants, and partridges have adopted elliptical wing planform for efficient flight.
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.
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