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Description
This study investigates the effects of two-dimensional streamwise wall waviness (WW) on turbulent boundary layer (TBL) separation over a NACA 4412 airfoil surface under adverse pressure gradient conditions. Both regular sinusoidal and tilted WW configurations are analyzed to determine their effectiveness in delaying flow separation. The universality of the optimal WW design is evaluated across a range of Reynolds numbers. Large Eddy Simulation (LES) is used to analyze both instantaneous and time-averaged flow characteristics.
Initial investigations focus on sinusoidal WW at a friction Reynolds number Reτ = 2500. The effective slope (ES), which defines the waviness slope (Napoli et al., 2008), is found to significantly impact separation delay and wall shear stress. Separation is maximally delayed at ES ≈ 0.17, with a reversal of this trend at higher ES values. A strong correlation is observed between the wavelength (λ) of WW and the downstream shift of the separation point, with larger λ increasing wall shear stress, while amplitude (A) shows no consistent trend. The waviness crests are shown to influence turbulent structures and enhance sweep events, similarly to the amplitude modulation mechanism identified by Mathis et al. (2009). At lower Reτ, the beneficial effects of the optimal sinusoidal configuration diminish due to weaker momentum transfer from the outer layer and reduced amplitude modulation effects.
The tilted WW design demonstrates superior separation control, outperforming the optimal sinusoidal WW by 70% in delaying separation and maintaining effectiveness over a broader range of Reynolds numbers. Unlike the sinusoidal design, which performs well only at higher Reτ, the tilted configuration is effective even at lower Reτ.
