Tubercles on flippers of a humpback whale offer a hydrodynamic advantage. Previously, multiple attempts were made to employ them on airplane wings to get an aerodynamic advantage. The effects of the airfoil thickness, the wing planform, the Reynolds number Re, and the wavelength and amplitude are actively investigated to understand their impact on the wavy wing aerodynamic performance and the flow mechanism. However, the effect of varying wavelength along the span of the finite wing and its flow physics is yet to be explored. This research work aims at investigating the effect of varying waviness wavelength along the finite wingspan and its underlying flow mechanism in the pre-stall and post-stall regimes. The wavy wing models are designed using the NACA0021 airfoil and the simulation results are compared with the smooth leading edge (named as baseline model) at Reynolds number Re = 1.2 × 10⁵. The simulation results were validated against experimental results from the literature. Two different wavy wing models, i.e., with increasing wavelength from root to tip of the wing (λ0305h1) and decreasing wavelength from root to tip of the wing (λ0503h1) were simulated. From the aerodynamic force behavior it is estimated that in the pre-stall regime the maximum reduction in the lift-to-drag (L/D) ratio is 16.89% and 4.22% for λ0503h1 and λ0305h1, respectively. However, in the post-stall regime the maximum increase in the L/D ratio is estimated as 2.97% and 19.18% for λ0503h1 and λ0305h1, respectively, at 20^o angle of attack. It is observed that the λ0503h1 model has a lower L/D ratio in the post-stall regime due to the vortices produced on the wing surface. These vortices create a flow recirculation zone over the wing which causes an increase in the pressure at the upper surface of the wing. On the basis of the obtained results, it is concluded that the spanwise waviness on aircraft wing is only beneficial in the post-stall regime. It is also concluded that an increase in the waviness wavelength from the root to the tip provides higher aerodynamic advantage than for the case with decreasing waviness wavelength toward the tip.

Tubercles at the leading edge (LE) of airfoils are used in maintaining the lift coefficient at the higher angle of attack (AoA) and delay stall. Previous research has documented the impact of varying the wavelength and amplitude of sinusoidal tubercles on the aerodynamic efficiency of various airfoil models, with a particular focus on changes at the leading edge. This study introduces a novel approach to tubercle design by analyzing the aerodynamic efficiency of a sinusoidal leading edge airfoil featuring a single, high-amplitude tubercle, offering a more realistic estimate of its effects. The research involves the development of three wing models – first, a baseline with a smooth leading edge; second, an airfoil with a tubercle labeled A3λ11; and third, an airfoil featuring a high-amplitude tubercle (A311λ11) on a sinusoidal leading edge. All airfoil models are developed using the NACA0021 airfoil profile and simulated at the 20° angle of attack. Large eddy simulations (LES) are conducted at a chord-based Reynolds number Re_c = 1.2 × 10⁵, and the results are validated against experimental data reported in the literature. Compared with the baseline airfoil, both tubercle airfoils show a substantial increase in the lift coefficient and a reduction in the drag coefficient. For the A3λ11 and A311λ11 airfoil models the lift coefficients increase by 34.8 and 12%, respectively. Moreover, reduction in the drag coefficient of about 10.3 and 23.6% are noticed for the A3λ11 and A311λ11 airfoil models, respectively. Additionally, the results reveal that the A311λ11 airfoil model exhibits a 14.9% reduction in the drag coefficient as compared to that of the sinusoidal A3λ11 airfoil model.