Application of the space-time conservation element and solution element numerical method to flows in fluid films.

摘要

This work, situated at the confluence between CFD and tribology, is the first application of a relatively new numerical method, the space-time conservation element and solution element (CE/SE) method, to flows in thin films.; The general features of the numerical method are highlighted, and also the concept of fluid film bearings is presented. The formulations of the governing equations and boundary conditions for four main cases are shown: 1-D and 2-D cavitated bearings using Elrod's formulation, hybrid gas bearings, and gas bearings including inertial effects.; The numerical formulations applied on both uniform and non-uniform grids are presented, with emphasis on the important features of the method when used to solve these specific problems, including the formulation of the boundary conditions.; Based on the described formulations, numerical codes have been developed. The results obtained are compared with experimental values, theoretical results, and numerical results obtained by using other algorithms. In the case of cavitated bearings, because the algorithm developed is capable of capturing potential discontinuities, the differences between the results obtained with the CE/SE method and with previous methods are significant when the position of the full film reformation point is not imposed through the supply system (boundary conditions). Important differences have also been noted in the case of gas bearings including inertia effects. Results demonstrate that the inclusion of inertial effects becomes necessary when the bearing speed is very high and/or the film clearance is large. Flow discontinuities are shown to occur in a manner similar to that of shock waves in supersonic flows.; Comparisons prove that the space-time CE/SE method, when contrasted to previous numerical algorithms, can successfully predict the pressure distribution within bearings, including cases with discontinuities in the lubricant film. Moreover, the method accomplishes this without any special treatment and without introducing distortion and/or excessive dissipation into the solution. The method is thus a strong candidate in applications that require more precise results, such as accurate, robust computation of the cavitation boundaries, as well as to solve transient problems. The method is also a perfect candidate in more complex problems, such as flows at very high speeds with inertia effects.