Numerical investigations on the enhanced thrust and lift coefficient characteristics of the tubercle flapping wing compared to the baseline flapping wing

Inspired by the leading-edge profile of the humpback whale, the impact of the leading-edge tubercles on the thrust (C_T) and lift (C_L) coefficients of high-aspect ratio flapping wings is examined in the present study. These wings are designed with a rectangular planform, featuring a mean chord (c) of 0.04 m and a span (b) of 10c. The Reynolds number is set at 5000, while the Strouhal number (St) ranges from 0.2 to 0.6, with the maximum effective angle of attack (α₀) capped at 15°. The amplitudes (a) of the sinusoidal tubercles are explored at 0.05c and 0.15c, and the wavelengths (λ) are examined at 0.15c and 0.45c. The numerical simulation results indicate that the baseline wing produces higher time-averaged C_T and C_L at St = 0.5 compared to all tested tubercle wings. However, at the lower St of 0.3, the tubercle flapping wing (with a = 0.05c and λ = 0.15c) exhibits time-averaged C_T and C_L values that are 12.80% and 28.27% higher, respectively, than those of the baseline wing. These results suggest that appropriately tuning the shape and size of the tubercles can significantly enhance the propulsive characteristics (C_T and C_L) of a flapping wing relative to the baseline wing. The presentation will further explore the intricacies of the associated flow physics.