The effective slip length and vortex formation in laminar flow over a rough surface

TL;DR

This study numerically investigates how surface roughness and slip conditions affect flow behavior, vortex formation, and effective slip length in laminar flow over corrugated surfaces, revealing the influence of boundary conditions and inertial effects.

Contribution

It introduces a detailed numerical analysis of the impact of local slip and no-slip boundary conditions on effective slip length and vortex formation over rough surfaces.

Findings

Effective slip length decreases with increased roughness amplitude.

Vortex formation occurs under no-slip conditions but is suppressed with slip boundary conditions.

Inertial effects enhance vortex formation and reduce slip length.

Abstract

The flow of viscous incompressible fluid over a periodically corrugated surface is investigated numerically by solving the Navier-Stokes equation with the local slip and no-slip boundary conditions. We consider the effective slip length which is defined with respect to the level of the mean height of the surface roughness. With increasing corrugation amplitude the effective no-slip boundary plane is shifted towards the bulk of the fluid, which implies a negative effective slip length. The analysis of the wall shear stress indicates that a flow circulation is developed in the grooves of the rough surface provided that the local boundary condition is no-slip. By applying a local slip boundary condition, the center of the vortex is displaced towards the bottom the grooves and the effective slip length increases. When the intrinsic slip length is larger than the corrugation amplitude, the flow streamlines near the surface are deformed to follow the boundary curvature, the vortex vanishes, and the effective slip length saturates to a constant value. Inertial effects promote vortex flow formation in the grooves and reduce the effective slip length.