Optimization of mesh density for numerical simulations of hydrodynamic lubrication considering textured surfaces

Abstract

In this work, a parametric study of a lubricated textured contact is carried out using a numerical model. The model solves the Reynolds equation coupled with a mass-conserving cavitation algorithm, and addresses the hydrodynamic lubrication of a mechanical seal with textured surfaces. Three shapes of texture (square, spherical cap, and triangle) are used, and the effect of the aspect ratio is also discussed for the case involving a triangular dimple. In order to estimate quantitatively the discretization error, the grid convergence index method is applied, considering several operating parameters (leakage, cavitation, load-carrying capacity) and using three grid levels: coarse (100 × 100), medium (200 × 200), and fine (400 × 400). As could be expected, grid convergence index analysis showed that there was a reduction in the discretization error when the grid system was refined. However, the study also showed that medium grid (200 × 200) solution has a grid convergence index of <6%. Comparison between fine and medium mesh densities, with regard to accuracy and computational time requirements, indicated that a medium mesh density was appropriate in the case of the present program, since the computational time is reduced by a factor of 9 when compared with the highest mesh density. Moreover, the size of the optimal mesh also depends on the operating conditions. The higher the lubrication number, the higher the number of nodes.