A new model for textured surface lubrication based on a modified Reynolds equation including inertia effects

Abstract

For textured surface lubrication problems, a small texture aspect ratio and a large Reynolds number can lead to strong recirculation in the textures and significant convective inertia effects. When these effects cannot be neglected, the Stokes system and the Reynolds equation are unsuitable and the Navier-Stokes equations should be considered instead. Particularly compared with the Reynolds equation, solving the Navier-Stokes system is computationally much more demanding due to its higher spatial dimension and nonlinearity. In this work, a new model is presented based on a modified Reynolds equation taking into account convective inertia and recirculation effects while so far neglecting cavitation. The model provides an accurate and considerably less expensive alternative to Navier-Stokes, demonstrated for two- and three-dimensional numerical configurations.