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 (TLMR) 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 (ψ_m). The vortex dynamics analysis unveiled alterations in leading-edge vortices (LEV) 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 at ψ_m=2.5° and the highest lift-to-drag ratio at ψ_m=5°, with aerodynamic performance declining beyond this threshold. Subsequently, we studied the effects of the dorsal-ventral bending amplitude (ψ_DV), 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% at ψ_DV = 5°, while a preferable lift-to-drag ratio is found at ψ_DV = -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.