The influence of a coupled formulation on the fluid dynamics in a large scale journal bearing

Abstract

In the pursuit of more accurate diagnostics of turbo machinery sophisticated rotor and bearing models are to be developed in order to better understand the dynamics of the rotor-bearing system. This study is concerned with such bearing models. Four distinct fluid models are developed: The first two have a viscous fluid formulation, where fluid dependencies enter the momentum equations primarily through the viscosity of the fluid. The last two have a viscoelastic fluid formulation where dependencies enter the equations through an additional differential constitutive relation. This constitutive relation is strongly coupled with the momentum equation. The dependencies included in the formulation of the fluid are: pressure, shear rate and temperature. The coupling of the fluid models is subject to the dependencies present in the formulation. Uncoupled, weakly coupled and strongly coupled formulations are compared in this work. The formulated models are solved numerically using the Finite Volume Method in the open source program OpenFOAM. These models were newly implemented in OpenFOAM as part of this study. The models are validated by comparing results with various known analytical solutions. A region of the bearing is subsequently analysed, where the dependencies of the lubricant are most prominent. In this region the influence of a weak and strong coupled formulation of the fluid dynamics in the oil film was considered. In this study it is shown that both weak and strong couplings influenced the fluid behaviour significantly. It is shown that when these dependencies are no longer isolated in the mere adjustment of fluid properties is inadequate to account for the influence of dependencies. The weak coupled formulation shows the difference between the coupled and uncoupled formulations. The weak coupling influence the fluid dynamics to the same extent as the pressure dependency in the region considered. The departure from the classical formulation is however observed to be uniform in the case of a weak coupling. The difference between the uncoupled and strongly coupled formulation was not as great as in the weakly coupled case. Although the difference was less, it was seen that the presence of the strong coupling was about 40% of that of the temperature dependency in the region considered. The change in flow, for the strong coupled formulation, was non-homogenous compared to the classical formulation. The influence of the coupling is therefore different in nature. The weak coupling changes the flow more than the strong coupling compared to the classical formulation. The strong coupling introduce a new characteristic to the fluid behaviour not seen with the weak coupled formulation. Lastly it is shown that in order to model the bearing adequately, the fluid model and the coupling of the governing equations are not trivial. Great care must be taken in both the fluid model used as well as the formulation of the coupled equations.