The paper presents a high Reynolds number experimental study of turbulent boundary layer separation control on a convex plate using the wavy-wall method, which was initially proposed for a flat plate by Dróżdż et al. 2021 (Exp Therm Fluid Sci 2021;121:110291). The application of this method increases the friction coefficient by up to 42.3%, resulting in a substantial delay in turbulent separation from the convex wall, while maintaining total momentum, quantified by changes in momentum-loss thickness. Other parameters indicating the high efficiency of the method are the invariant value of the friction Reynolds number along the flow and the thinner boundary layer. The above indicators demonstrate promising aerodynamic improvements in airfoils, similar to those achieved when active suction is applied to the suction side. The new insight into the physical mechanism of the wavy wall suggests that small-scale turbulent activity is the primary determinant of the effectiveness of the wavy wall in enhancing small-scale streamwise convection and the sweeping motion, resulting in superior momentum transport. However, when the wavy wall, due to poorly selected geometry, induces large-scale motions, such as separation in the trough, it counteracts the mechanism. Then this geometry has a detrimental effect on the efficiency of the method.
Most passive flow control strategies for aerofoils are based on reducing skin friction by attenuating large-scale streaks (Ricco et al. 2021). To mitigate skin friction reduction, which acts as a laminar-turbulent transition postponer, active methods are employed to counteract its detrimental effect on lift due to earlier separation. However, the use of active methods is limited in wind turbine blades due to a combination of practical, aerodynamic, and economic constraints. A commonly applied passive method in wind energy is the use of vortex generators. However, in large-scale wind turbine blades, vortex generators provide only minimal benefits (only about a 1% power increase on 5MW wind turbine blades). They may even lower efficiency at higher power levels (Bravo-Mosquera et al. 2022). Alternative passive flow control methods such as dimples (Tay et al. 2015;Gattere et al. 2022;Aoki et al. 2012;Bearman & Harvey 1976;Tay 2011Tay ), grooves (S. & H. 2016)), slotted airfoils (Belamadi et al. 2016;Coder & Somers 2020;Tanürün et al. 2026), or microcylinders (Wang et al. 2018;Mostafa et al. 2022;Wang et al. 2023) have been shown to reduce drag by speeding up the transition; however, their effectiveness diminishes in turbulent flows with high Reynolds numbers as shown by McMasters & Henderson (1979).
A promising alternative is the use of a streamwise wavy wall (WW) with appropriately selected geometry that yields an increase in friction coefficient downstream of WW of more than 35% at the friction Reynolds number 𝑅𝑒 𝜏 ≈ 4000 (Dróżdż et al. 2025). This is the highest reported gain for such a configuration to date, which highlights the practical potential of this method to delay separation. To be effective, the WW design must be carefully tailored to local flow conditions. The undulations should be placed where the Rotta-Clauser pressure gradient parameter 𝛽 = 𝛿 * 𝜏 -1 𝑤 𝑑𝑃 𝑒 , where 𝛿 * is displacement thickness, 𝜏 𝑤 is wall shear stress and 𝑑𝑃𝑒 is streamwise pressure gradient, remains below 10, with a maintained viscous scaled amplitude of 𝐴 + = 170, and a period adjusted so that flow troughs are held on the verge of separation (effective slope around 0.15). The wavy wall increases the momentum transport due to increased small-scale sweeping motions, in a mechanism similar to amplitude modulation in high-Reynolds wall-bounded flows (Mathis et al. 2009;Dróżdż et al. 2023). Simulations at about 𝑅𝑒 𝜏 ≈ 2500 by Kamiński et al. (2024) confirmed that the technique can enhance the wall-normal velocity gradient and wall shear stress downstream, although to a lesser extent. In turn, combined numerical LES and wind-tunnel studies by Elsner et al. (2022) at 𝑅𝑒 𝜏 ≈ 1400 did not show any improvements, suggesting the approach loses efficacy below a certain threshold Reynolds number.
The recent work of Dróżdż et al. (2025) aimed to test the single geometry of the WW selected in Dróżdż et al. (2021) on a range of Reynolds numbers (𝑅𝑒 𝜏 ≈ 2600, 4000, and 4500) and under varying pressure gradient conditions corresponding to large-scale pitchregulated wind turbine blades. For such turbines, the angle of attack varies from 3 • to 8 • Sayed et al. (2012) for different wind speeds, and even more due to the rotational position or torsional deflection of the blade. The results showed that when the Reynolds number varies, as when the wind speeds change from 5 to 40𝑚𝑠 -1 on a pitch-regulated wind turbine, the lowest increase in 𝐶 𝑓 was 30% for the lowest Reynolds number. Furthermore, when the pressure gradient was varied at a constant Reynolds number, mimicking unstable flow conditions resulting from changes in the rotational position of the blade or torsional deflection, the efficiency of the wavy wall was maintained, albeit at a lower level of 𝐶 𝑓 , about 27% on average. The tested pressure ranges and the Reynolds number variation showed that too low an amplitude limits the benefits. However, too high an amplitude leads to significant separation, which weakens the transport of momentum to the wall. However, as demonstrated, an overall effectiveness of approximately 23% was achieved, which can be considered high.
Recently, large-eddy simulations at 𝑅𝑒 𝜏 ≈ 2500 by Kamiński et al. (2025) was published as an extended work of Kamiński et al. (2024). They showed that the additional benefit can be achieved using the upstream tilted wavy wall (Kamiński et al. 2025). They report an increase in wall shear stress with respect to a sinusoidal type of wavy wall. However, the increase is at the level of 40% of that observed in Dróżdż et al. (2021) due to the lower Reynolds number. On the other hand, Kamiński et al. (2025) presented their observations on the physical interpretation of introducing a wavy wall on the curved surface of the NACA4412 wing section. They found that a sinusoidal wavy wall used at 𝑅𝑒 𝜏 ≈ 2500 causes increased energy across all scales in the outer region. In contrast, near the wall, only large-scale activity is enhanced, d
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