Free hovering of hummingbird hawkmoth and effects of wing mass and wing elevation

Abstract This paper presents a computational study on the free hovering flight of an insect-like flapping-wing flyer modelled after the hummingbird hawkmoth ( Macroglossum stellatarum ), with a Reynold number Re ≈ 3000. The numerical model integrated a Navier-Stokes solver with the Newtonian free-body dynamics of the model insect. The primary cyclic kinematics of wings were assumed to be sinusoidal for simplicity here. A generic PID-based kinematics controller was used to achieve stable quasi-steady hovering flights. Hovering flight with zero wing mass was first simulated and served as a reference for subsequent study into the effects of wing mass. The translational inertia of wings, which was proportional to the longitudinal acceleration and the mass of the wings, accentuated the longitudinal and pitching oscillations of the model hawkmoth. The inertial wing force and torque were dominant over the aerodynamic ones at the morphological wing mass (4.67%) of the hawkmoth. The cyclic pitching oscillation may, however, be significantly suppressed by a suitable adjustment of wing elevation, subject to a small penalty on the aerodynamic power. The flow created by a flapping wing comprised a connected system of vortices, emanating from the leading edge, the inner edge, the trailing edge and the wing tip of the wing – these were shed downwards during stroke reversal to form a vortical wake below each of the wings. The results obtained show good consistency and agreement with available results in the literature.