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

The present work deals with the flow characteristics induced by a two-dimensional textured surface. The texture 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 flow 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 emphasized by the momentum balance performed for the computational cell. The peculiar effect of the groove is also shown by the rotor and the stator shear stresses variations. Finally, it is shown that despite the presence of fluid inertia forces, cell-averaged rotor, and stator shear stresses obtained for pure Couette or Poiseuille flows can be added or subtracted to obtain with good accuracy the characteristics of combined shear and pressure driven flows.