Near wall flow topology at superhydrophobic surfaces in turbulent channel flow*

The effect of superhydrophobic surfaces on drag reduction and flow topology in turbulent channel flow is investigated at Re_τ = 180 and different wave length of the structure (pillars, 10 ≤ L⁺≤ 80) using direct numerical simulation. The gas-liquid interface and the interface between pillar tip and liquid are considered as one plane. The gas-liquid interface is modeled by a slip boundary condition. The ratio of no-slip / total area of the surface structure amounts to 1/4. The drag reduction increases under-proportionally with L⁺ from 11% at L⁺= 10 up to 37% at L⁺= 80. Fully developed flow in streamwise direction appears for wall-normal distances of y_d⁺ ≥ 4 (L⁺= 10) and y_d⁺ ≥ 28 (L⁺= 80). The region smaller y_d⁺ differs significantly from the typical velocity profile of a turbulent wall-bounded flow. Above the slip area velocity profiles with ∂u⁺/ ∂y⁺ ≈ 0 appear for y⁺≤ 0.2. Above the pillar tips almost linear velocity profiles arise with a minimum thickness at the leading edge and a maximum downstream at 0.55 times the pillar edge length (y⁺< 1.8 at L⁺ = 80). In both wall near domains, viscous momentum transfer dominates turbulent momentum transfer. Above, non-linear velocity profiles and growing turbulent momentum transfer arise. In this contribution a detailed description of governing transport phenomena related to drag reduction is given for the mentioned regions.