A numerical algorithm to model wall slip and cavitation in two-dimensional hydrodynamically lubricated contacts

Hydrodynamic lubrication takes a fundamental role in mechanical systems to reduce energy losses and prevent mechanical breakdown. The analytic instrument usually adopted to describe hydrodynamic lubrication is the Reynolds equation, which in its simplest statement for monophase lubricants and with assuming no fluid slip at the walls, is a linear equation in the hydrodynamic pressure. However, this classical linear Reynolds equation cannot reflect all the lubricant characteristics in engineered surfaces (e.g. superhydro(oleo)phobic surfaces and textured surfaces). In these cases, the effect of two critical factors, such as wall slip and cavitation, need to be considered, introducing non-linearities in the system. In order to tackle this issue, a modified two-dimensional Reynolds equation is introduced, able to capture both the cavitation presence, via a complementary mass-conserving model, and wall slippage, starting from the multi-linearity description introduced by Ma et al. (2007). In addition, an alternative model for the slippage at the wall is proposed by modifying the multi-linearity wall slip model to improve accuracy and computational cost. In this new model, the possible slip directions are limited to three, separated by equal angles, with the slip occurring only along the first direction, and the other directions, then, used to iteratively adjust the direction of slippage, until a suitable convergence criterion is satisfied. The proposed mathematical model is validated versus results available in literature with tests performed on (i) journal bearings, (ii) slider bearings, (iii) squeeze dampers, and (iv) surface textured bearings. By conducting these tests, the proposed alternative wall slip model is proved to be up to one order of magnitude more computational efficient than the original multi-linearity wall slip model.