Erlangen pipe flow: the concept and DNS results for microflow control of near-wall turbulence

The concept of a micropatterned surface morphology capable of producing self-stabilization of turbulence in wall-bounded flows is considered in pipes of non-circular cross-sections which act to restructure fluctuations towards the limiting state where these must be entirely suppressed. Direct numerical simulations of turbulence in pipes of polygon-shaped cross-sections with straight and profiled sides were performed at a Reynolds number \(Re_\tau \simeq {\mathrm 300}\) based on the wall shear velocity and the hydraulic diameter. Using the lattice Boltzmann numerical algorithm, turbulence was resolved with up to \({\mathrm 540\times 10^6}\) grid points (\({\mathrm 8,192\times 257 \times 256}\) in the x 1, x 2 and x 3 directions). The DNS results show a decrease in the viscous drag around corners, resulting in a reduction of the skin-friction coefficient compared with expectations based on the well-established concept of hydraulic diameter and the use of the Blasius correlation. These findings support the conjecture that turbulence might be completely suppressed if the pipe cross-section is a polygon consisting of a sufficient number of profiled sides of the same length which intersect at right angles at the corners.