Viscosity effects at low Reynolds number in lubrication systems : a study based on Navier-Stokes equations

Abstract

The Navier–Stokes equations are crucial in fluid dynamics as they govern the motion of viscous fluid substances. In creeping flow, where inertia is insignificant, the Reynolds equation may be derived from the Navier-Stokes equations, allowing it to be numerically solved using a boundary-value problem method. This condition is fulfilled in hydrodynamic lubrication, which is crucial in energy technology applications with the potential to reduce friction and increase machine efficiency as well.

This paper studies the effect of viscosity on lubrication pressure buildup distribution by modelling a wedge-shaped thin-film system to compare various ISO viscosity grades. The practical simplification of the Navier-Stokes equations into a one-dimensional form is the main focus of the study, thereby demonstrating the lubrication theory in real-world applications.

The results depict that pressure buildup distribution rises from the inlet, reaches a peak, and then gradually falls to zero at the outlet. Moreover, a nonlinear relationship between viscosity and peak pressure buildup is illustrated, which explains how variations in film thickness contribute to pressure buildup in this analytical model. These findings may be used in practical implications, such as turbine bearings, hydropower plants, and high-load gear systems.