Effect of wing mass on the free flight of a butterfly-like model using immersed boundary–lattice Boltzmann simulations

Abstract

The wings of butterflies are relatively heavier than those of other insects, and the inertial force and torque due to the wing mass are likely to have a significant effect on agility and manoeuvrability in the flapping flight of butterflies. In the present study, the effect of wing mass on the free flight of butterflies is investigated by numerical simulations based on an immersed boundary–lattice Boltzmann method. We use a butterfly-like model consisting of two square wings with mass connected by a rod-shaped body. We simulate the free flights of the model by changing the ratio of the wing mass to the total mass of the model and also changing the mass distributions of the wings. As a result, we find that the aerodynamic vertical and horizontal forces decrease as the wing-mass ratio increases, since for a large wing-mass ratio the body has large vertical and horizontal oscillations in each stroke and consequently the speeds of the wing tip and the leading edge relatively decrease. In addition, we find that the wing-mass ratio has a dominant effect on the rotational motion of the model, and a large wing-mass ratio reduces aerodynamic force and intensifies the time variation of the pitching angle. From the results of our free flight simulations, we clarify the critical wing-mass ratio between upward flight and downward flight and find that the critical wing-mass ratio is a function of the non-dimensional total mass and almost independent of the wing length. Then, we evaluate the effect of the wing-mass distribution on the critical wing-mass ratio. Finally, we discuss the limitations of the model.