Analytical correction of corner singularity for the turbulent flow over riblets

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Andrea Rossi

A corner correction method designed to avoid the loss of computational efficiency when DNS is applied for cases with bodies with geometric singularities is presented, and applied to the V-shaped riblets to measure turbulent drag reduction.

The strategy proposed by Luchini, IJNMF 1991 to correct the solution near the edge for the cavity problem, is tailored to a V-shaped riblet. Once the Stokes equations are solved for stream function and vorticity in a polar coordinate system centered at the corner, the spanwise and wall-normal components are substituted into the momentum equation. Pressure is obtained by integration. The velocity component parallel to the edge results from a Laplace equation.

The correction is then used within into a DNS solver of the incompressible Navier- Stokes equations developed by Luchini and based on the immersed-boundary concept. First a validation is carried out by computing the protrusion heights at different resolutions and aspect ratios of the computational grid, with the corresponding analytical quantities reported in Luchini et al. [17]. An improvement of almost an order of magnitude, quantified by the number of points per riblet necessary to achieve a comparable error is observed. In a turbulent channel flow at a friction Reynolds number of Re = 200 for the two lowest resolution cases, riblets drag reduction is measured. The code with corner correction approaches the experimental results with an error of about 2%, while the uncorrected code, at corresponding resolutions, measures a drag increase.

Lastly, an extension of the method is proposed and tested to deal with three-dimensional geometries like sinusoidal riblets.