Navier-Stokes Analysis of Two-Dimensional Roughness Pattern Under Turbulent Flow Regime

The present work deals with the flow characteristics induced by a two-dimensional roughness pattern. The roughness pattern consists of identical and equally spaced rectangles with characteristic lengths at least one order of magnitude larger than the clearance of the thin film. Periodic boundary conditions enable the analysis of a single groove and the complete Navier-Stokes analysis is carried on for turbulent Reynolds numbers. The analysis is performed for shear driven flows (Couette), pressure driven flows (Poiseuille) and combined Couette-Poiseuille flows. First, the presence of inertial forces generated by the groove is underlined by the momentum balance performed for the computational cell. The peculiar effect of the groove is also depicted by the rotor and the stator shear stresses variations. Finally, it is shown that despite the presence of inertial forces, cell-averaged rotor and stator shear stresses obtained for pure Couette or Poiseuille flows can be added or subtracted for approximately obtaining the characteristics of combined shear and pressure driven flows.