Multiscale analysis and texture design for interfaces hydrodynamically lubricated by variable viscosity and density liquids

Abstract

Optimization is fundamental in lubrication, as it is utilized to minimize the energy and durability loss due to friction. To be able to analyze such systems, efficient and accurate mathematical and numerical techniques are required during the modeling and the computation process. Although direct analyses of smooth surfaces for both Newtonian and non-Newtonian flows are well documented in literature, analysis for rough surface textures can be challenging both in terms of modeling and solution. As severity of roughness increases, the accuracy of the available models decreases while the necessary computational cost increases substantially. In this work, a model is developed for piezoviscous, compressible and shear-thinning lubricants using the novel modified viscosity approach alongside homogenization as a mathematical technique for the solution of the Reynolds equation to alleviate the inherent computational difficulties to model roughness. Our results demonstrate good agreement between rough DNS and Reynolds and homogenized results. Furthermore, the developed numerical framework has been used in conjunction with topology optimization algorithm to acquire different surface textures dependent on the fluid rheology. The obtained textures are shown to (i) minimize energy dissipation, or (ii) increase the traction to amplify the grip between the surfaces depending on the respective lubrication application.