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Stefano Cipelli
The present thesis presents a finite-difference Direct Numerical Simulation (DNS) code designed to assess the turbulent drag reduction produced by riblets of arbitrary shape. The code’s strength lies in its efficiency, achieved through the implementation of an immersed boundary method that incorporates a corner correction for the riblets’ edges. The idea hinges on the observation that, near geometrical singularities, convection terms are negligible: the analytical steady Stokes solution is used to correct the immersed boundary terms. As a result, extremely fine grids are not required to properly resolve the riblet tip.The computationally efficient code enabled a comprehensive parametric study, in which longitudinally straight and sinusoidal triangular riblets with a 60-degree tip angle were tested for a wide range of riblet sizes to measure the drag reduction curve. The corner correction was found to be crucial in properly computing both the laminar and turbulent solutions. Results are presented in terms of the friction coefficient and shift in the mean velocity profile. Additionally, results for turbulence statistics such as Reynolds stresses, mean velocity profiles, and Quasi-Streamwise-Vortices position and intensity are also provided. The study focuses particularly on the advantages that sinusoidal riblets provide in comparison to their straight counterparts.