A Local Adaptive Mesh Refinement for JFO Cavitation Model on Cartesian Meshes

Abstract

Nonuniform mesh is beneficial to reduce computational cost and improve the resolution of the interest area. In the paper, a cell-based adaptive mesh refinement (AMR) method was developed for bearing cavitation simulation. The bearing mesh can be optimized by local refinement and coarsening, allowing for a reasonable solution with special purpose. The AMR algorithm was constructed based on a quadtree data structure with a Z-order filling curve managing cells. The hybrids of interpolation schemes on hanging nodes were applied. A cell matching method was used to handle periodic boundary conditions. The difference schemes at the nonuniform mesh for the universal Reynolds equation were derived. Ausas’ cavitation algorithm was integrated into the AMR algorithm. The Richardson extrapolation method was employed as an a posteriori error estimation to guide the areas where they need to be refined. The cases of a journal bearing and a thrust bearing were studied. The results showed that the AMR method provided nearly the same accuracy results compared with the uniform mesh, while the number of mesh was reduced to 50–60% of the number of the uniform mesh. The computational efficiency was effectively improved. The AMR method is suggested to be a potential tool for bearing cavitation simulation.

A decoupled approach to enhance the Elrod algorithm

“…High residuals can be seen at some nodes close to the film reformation boundary, as shown by the white lines. 38 Although these residuals are limited to only the local 2 ∼ 6 nodes, the maximum value is as high as the level of 1 × 10 −3 . The accuracy of the resulting pressure must be reduced.…”

Reynolds Model versus JFO Theory in Steadily Loaded Journal Bearings

“…The JFO theory is well accepted because it obeys the law of conservation of mass, and had been validated by experiments [6,7]. A variety of algorithms [10,[13][14][15][16][17] have been developed for implementing the JFO theory, such as the well-known Elrod algorithm [13]. Although the complexity of the algorithm is higher than the Christopherson's method, it was largely used in studying cavitation and its effect on bearing characteristics [18,19].…”