The study of a thin, incompressible Newtonian fluid layer trapped between two almost parallel, sliding surfaces has been actively pursued in the last decades. This subject includes lubrication applications such as slider bearings or the sealing of non-pressurized fluids with rotary lip seals. When a viscous lubricant flows between an elastic body and a rigid surface, the contact geometry may undergo substantial deformation affecting the flow field of the lubricant. Therefore, a coupled model between an elastic ring and the fluid film underneath it is proposed. Initially, a linear stability analysis is performed. Then, non-linear calculations are presented showing that the system deformations are able to induce mixing of lubricant throughout the sealed region. In the second part of this work, the flow of lubricant fluid through the micro-gap of rotary lip seals is analyzed theoretically and numerically from a different perspective. The study is carried out assuming that a 'small-gap' parameter δ attains an extreme value in the Navier-Stokes equations. The precise meaning of small-gap is achieved by the limit δ = 0, and the numerical solution of the resulting set of equations predicts transport of lubricant through the contact region due to centrifugal instabilities. Numerical results obtained with the finite element method are presented. In particular, the influence of inflow and outflow boundary conditions, and their importance in the simulated flow are discussed. To this aim, the penalty method for incompressible flows in presence of variable body forces is re-examined with the help of well-known examples, yielding a corrected formulation that is more accurate and faster than standard finite element methods found in the literature.
展开▼
