Near-wall turbulence modulation using textured surfaces for drag control

Abstract

To evaluate finite-width textured regions as a passive drag control strategy, numerical simulations are performed to understand the modulation of turbulent boundary layer (TBL) by cubical surface texture elements placed in a staggered configuration over a zero-pressure-gradient surface. The roughness Reynolds number ( 𝑘 + = 𝑘 ⁢ 𝑈 𝜏 / 𝜈 ) is varied from 22 to 46, while the aspect ratio (inter-element distance to element height) lies around 7, representing a transitionally rough regime with the intermediate-type aspect ratio. By shifting the textured region in the streamwise direction, the effect of the relative height of the texture element with respect to the boundary-layer thickness (blockage ratio, 𝑘 𝑏 ) is investigated. This strategy creates a test matrix combining the effects of 𝑘 + and 𝑘 𝑏 . In the wake region, inner-normalized mean velocity profiles show a higher velocity defect with an increase in 𝑘 + , indicating the skin friction drag reduction. For cases with similar 𝑘 + , highest 𝑘 𝑏 shows the maximum deviation. Analysis of the Reynolds stresses shows a wall-normal shift in its peak with element height, with its streamwise component showing a second peak. The characteristic spanwise wavelength for smooth TBL lies around 𝜆 + 𝑧 ≈ 1 0 0 , the staggered distribution excites its harmonics, and rapidly recovers within 1 unit downstream of the textured region. The spatio-temporal analysis using Fourier and modal approaches shows the strengthening of high-frequency varicose and mid-frequency sinusoidal modes with increasing element height. It further shows that the mid-frequency sinusoidal modes are excited and sustained both within upstream and downstream regions due to the staggered configuration. In-phase and anti-phase low-frequency modes are identified as well, which corresponds to streamwise streak structures, and oblique structures generated by the inter-element motion induced by the staggered configuration. A budget analysis of mean turbulent skin friction coefficient identifies viscous-generated drag as the dominant term in the baseline, which is significantly reduced in the wake of the textured region. Presence of recirculation and stagnation regions in the leeward and windward sides of the texture elements induces lower viscous forces in the exposed bottom wall, leading to a 7 − 1 4 % reduction in overall drag force. Although an order of magnitude lower, owing to the increase in surface area and pressure differences, the side viscous and form drag increase in the textured cases with element height, which are also quantified.