Vertical bending and aerodynamic performance in flying snake-inspired aerial undulation

This paper presents a numerical investigation into the aerodynamic characteristics and fluid dynamics of a flying snake-like model employing vertical bending locomotion during aerial undulation in steady gliding. In addition to its typical horizontal undulation, the modeled kinematics incorporates vertical undulations and dorsal-to-ventral bending movements while in motion. Using a computational approach with an incompressible flow solver based on the immersed-boundary method, this study employs topological local mesh refinement mesh blocks to ensure the high resolution of the grid around the moving body. Initially, we applied a vertical wave undulation to a snake model undulating horizontally, investigating the effects of vertical wave amplitudes (ψm). The vortex dynamics analysis unveiled alterations in leading-edge vortices formation within the midplane due to changes in the effective angle of attack resulting from vertical bending, directly influencing lift generation. Our findings highlighted peak lift production atψm=2.5∘and the highest lift-to-drag ratio (L/D) atψm=5∘, with aerodynamic performance declining beyond this threshold. Subsequently, we studied the effects of the dorsal-ventral bending amplitude (ψDV), showing that the tail-up/down body posture can result in different fore-aft body interactions. Compared to the baseline configuration, the lift generation is observed to increase by 17.3% atψDV= 5°, while a preferable L/D is found atψDV= -5°. This study explains the flow dynamics associated with vertical bending and uncovers fundamental mechanisms governing body-body interaction, contributing to the enhancement of lift production and efficiency of aerial undulation in snake-inspired gliding.