Mathematical modelling of heat transfer in air-droplet flow of GTE bearing chamber

Abstract

The gas-liquid flow in the bearing chamber (BC) of the gas turbine engine is realized due to the interaction of the sealing air and oil supplied for lubrication and cooling of friction units. The complex nature of the flow movement is determined not only by the BC geometry but also by the presence of rotating elements and the manner of oil supply and flow removal. The most important result for the engineering practice of BC flow modelling is the determination of the heat transfer coefficient to the inner wall. The variety of influencing factors causes difficulties even at the stage of an integral mathematical model of the process formation, which makes it possible to determine this coefficient. As a result, significantly different approaches are used – from three-dimensional CFD modelling of a heterogeneous flow up to the use of a criterion equation that formally considers the effect of geometric and regime parameters on a heat transfer. The first approach requires significant computational resources, and certain difficulties arise in setting the initial and boundary conditions, especially in terms of droplet parameters. Homogeneous models somewhat simplify the problem, including when formulating the boundary conditions. However, all the effects of the influence of the droplet diameter are levelled. In both cases, the computation time is long, and the results of CFD simulations require selective experimental verification. Therefore, it is problematic to use this approach solely for engineering problems, as well as when generalizing experimental data in several regime parameters. When using the criterion equation, the calculation procedures are as simple as possible. However, dimensionless complexes do not ensue from the basic equations of heterogeneous media mechanics and do not consider the effects of interfacial interaction during heat transfer in the BC. Therefore, the possibility of the application of the proposed correlations for other BC geometries and oil and air supplying conditions also needs to be experimentally confirmed. This makes it problematic to use such correlations at the design stage of the BC and the oil system as a whole. The preferred approach for engineering practice is when the thermohydraulic processes in the BC are described on the basis of the proven equations of heterogeneous media mechanics with the transition to a two-dimensional problem by averaging the phase parameters along the axis. This averaging is justified by the fact that the main heat carrier from the core to the inner wall of the BC is the radial flow of droplets. In view of the low volume fraction of droplets, the Lagrange approach is used to simulate a two-phase flow in the BC core. The droplet parameters along the trajectory are calculated considering the interfacial interaction with the air. In this regard, the air velocity field is determined by considering the geometry of the BC, the flow through the seals and the shaft speed. Here, it is possible to consider not only the droplet polydispersity but also the effects of primary droplet reflection, the formation, and movement of secondary droplets during the formation of a near-wall oil film, the thermal resistance of which directly affects the value of the internal heat transfer coefficient.