Spanwise twisting optimises flapping wing propulsive efficiency through force reallocation and the leading-edge vortex growth regulation

This work investigates how spanwise twisting modulates aerodynamic performance and leading-edge vortex (LEV) dynamics of a low aspect-ratio (AR) flapping wing through variations in effective angle of attack ( alpha Subscript italic eff α eff α eff ). Spanwise twisting primarily redistributes force between the streamwise and spanwise directions for a low-AR flapping wing – reallocating force orientation rather than altering total force magnitude – thereby directly governing the thrust-to-resultant-force ratio and hence propulsive efficiency. At low Strouhal number, excessive alpha Subscript italic eff α eff α eff induces stall, while at medium-to-high Strouhal number, resultant force remains insensitive to alpha Subscript italic eff α eff α eff as increasing twist enhances thrust at the expense of side force. Maximum propulsive efficiency of 0.36 occurs at Strouhal number = 0.6 and alpha Subscript italic eff comma max Baseline equals 27 Superscript ring α eff,max = 27 ∘ α eff,max = 27∘ , where the resultant force is optimally oriented in the streamwise direction, maximising the thrust-to-resultant-force ratio. Circulation analysis reveals that peak efficiency corresponds to a circulation plateau during late downstroke, sustained by a secondary structure, a lambda-shaped positive vortical structure beneath the LEV, that regulates the LEV growth. This mechanism is absent at both excessively low and high alpha Subscript italic eff comma max α eff,max α eff,max . Spanwise vortex variations indicate functional differentiation: inboard regions maintain attached flow for lift, while outboard regions exploit LEV dynamics for thrust. Moreover, late twisting in a flapping cycle enhances efficiency by promoting vortex shedding before the stroke reversal, whereas early twisting in a flapping cycle amplifies thrust.