Computational Studies of Insect-Sized Flapping Wings In Inclined Stroke Plane Under the Influence Of Temporally Varying Shear Inflow

Abstract

2D computational studies on the effects of temporally varying shear inflow condition on forces generated by an insect-sized flapping wing in the inclined stroke plane have been carried out for Re = 150. Temporally varying shear inflow condition was represented by a combination of a mean wind speed term, a temporally fluctuating velocity term and a spatial velocity gradient term. The mathematical form followed the expression UG Uw = U∞ Uw +    Ug Uw    sin    2π fg fw t    ±    Vgrad Uw    y. Here, UG is the gusty inflow velocity in m/s, U∞ is mean free stream velocity in m/s, Ug is the amplitude of the temporally sinusoidal velocity fluctuation in m/s, Vgrad is the linear velocity gradient along the Y-axis in m/s per m, Uw is the root mean square average of the flapping cycle velocity of the wing in m/s, fg is the frequency of the temporally sinusoidal velocity fluctuation in Hz, fw is the wing’s flapping frequency in Hz, y is dimension along Y-axis in m and t is time in second. For the present studies Ug/Uw = 1 and fg/fw = 0.1 were chosen. Five cases with linear velocity gradient ratio along the Y-axis, Vgrad/Uw = ± 5, ± 2.5 and 0 were considered. Findings were analyzed by plots of instantaneous and cycle-averaged force coefficients, phase space plots, global recurrence plots and windowed recurrence quantification analysis. Numerical investigations revealed that negative Vgrad/Uw induced a considerable increase in vertical force and marginal decrease in the horizontal force. Positive Vgrad/Uw induced a marginal increment in horizontal force but caused a substantial decrement in vertical force.