Chiarini, A.

Cipelli, S.

Gattere, F.

Gatti, D.

Luchini, P.

Quadrio, M.

English

Archivio istituzionale della ricerca - Politecnico di Milano

Accurate and efficient direct numerical simulationof turbulent drag reduction via ribletsD. Gatti*, S. Cipelli, F. Gattere†, A. Chiarini, P. Luchini§ & M. Quadrio†Riblets, two-dimensional surface protrusions capable of reducing skin-friction drag inturbulent flows, have been extensively studied over the past 50 years, particularlyin experimental works1. Triangular or trapezoidal ridges aligned with the flow yield∼8% of drag reduction and have been found particularly effective. The correspondingnumerical verification of riblet drag reduction is extremely challenging but wouldenable the detailed analysis of the riblet physics and the optimisation of their shape,both necessary steps for their success. The challenge lies in the need for high-fidelitydirect numerical simulation (DNS) combined with the geometric singularity at theriblet tip. Such singularity is known to be directly responsible for the drag reductioneffect but is difficult to represent numerically even at the unreasonable cost of anextremely fine resolution around the riblet tip.In this contribution, we enable the accurate and efficient simulation of turbulentdrag reduction via riblets by introducing an analytical correction of the instantaneousflow solution around the riblet tip and embedding it into an immersed boundarymethod. The correction exploits the fact that the flow in the very vicinity of thesingularity behaves as the analytically-known Stokes flow around a sharp corner2.We include the corner correction into a staggered-grid, second-order solver of theincompressible Navier–Stokes equations3. At the conference, we describe the cornercorrection, its necessity, and demonstrate fidelity and performance of our approach byperforming DNSs of full-size turbulent channels flows with various riblet geometries,such as the sawtooth riblets with 60◦ tip angle and various sizes, whose drag reductionas relaive change in Cf with the respect to the flat channel is shown in the figure belowat Reτ = 200. Most datapoints required approximately 39·103 CPU hours each, sincethe spatial resolution was only marginally finer than a standard DNS.0 2 4 6 8 10 12 14 16 18−6−30369l+g∆Cf%w. correction (finer grid)w. correction (standard grid)no correction*Institute of Fluid Mechanics, Karlsruhe Institute of Technology, Karlsruhe, GermanyDepartment of Aerospace Science and Technologies, Politecnico di Milano, Milano, ItalyComplex Fluids and Flows Unit, Okinawa Institute of Science and Technology, Okinawa, Japan§Dipartimento di Ingegneria Industriale, Università di Salerno, Fisciano, Italy1Bechert et al., J. Fluid Mech. 338:59–87 (1997)2Luchini, J. Comp. Phys. 92:349–368 (1991)3Luchini, J. Mech. B/Fluids 55:340–347 (2016)

Accurate and Efficient Direct Numerical Simulation of Turbulent Drag Reduction via Riblets

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Accurate and Efficient Direct Numerical Simulation of Turbulent Drag Reduction via Riblets

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Archivio istituzionale della ricerca - Politecnico di Milano