Mathematical modeling of the wall oil film in the bearing chamber of the GTE

Abstract

The most preferable result of modeling the flow in the BC is the determination of the heat transfer coefficient to the inner wall. The complexity of solving this problem is due to both the complex geometry of the BC and the presence of a two-phase flow, the structure of which changes from air-droplet in the core to a nearly liquid in the wall oil film. Available research results show that even three-dimensional CFD modeling of such a flow does not completely solve the problem. At the same time, the calculation time is long, and the results require, at a minimum, selective experimental validation. At the same time, it can be considered proven that the main mechanism of heat transfer from the core to the wall region of the BC is related to the radial flow of droplets, and the thermal resistance of the wall oil film has a decisive effect on the value of the internal heat transfer coefficient. It is advisable to model these media on the basis of a two-dimensional problem with the averaging of phase parameters along the axis. Considering the small volume fraction of droplets, the Lagrangian approach can be used to model the two-phase flow in the core of the BC. This allows consideration of not only the polydispersity of the droplets, but also the creation and movement of secondary droplets during the formation of the wall oil film. One of the main problems in the modeling of the wall film is the definition of its flow regime and the corresponding criterion equations for calculating the coefficients of friction and heat transfer. Most of the equations use the longitudinal coordinate of the plate as a geometric parameter and cannot be applied to the bearing chamber. In this study, the possibility of converting the film flow into a flow similar to that occurring in a flat pipe is substantiated. This allows not only to consider the geometric features of the BC, but also to use the corresponding Reynolds numbers and similarity equations for the equivalent flow. Along with the use of a two-layer model for the boundary region and the concept of the analogy of transfer processes, this made it possible to form a mathematical model of the film, which considers all the components that determine the formation, movement, and heat transfer of the wall oil film. In addition, the model does not contain restrictions on the appearance of the parameters transverse profile, which are, for example, for the EWF model of the oil film in ANSYS FLUENT. The obtained results along with the previously developed air-droplet flow model in the core provide a complete two-dimensional model of the gas-liquid flow in the GTE bearing chamber, which allows the main geometric and all mode parameters to be used to determine the heat transfer coefficient to the inner wall of the chamber. Given the short calculation time, the proposed model allows for a detailed investigation of each factor’s contribution and element-by-element identification of the model based on the results of more detailed modeling and by comparing calculated and experimental data.