A Model of Mass and Heat Transfer for Disc Temperature Prediction in Open Compressor Cavities

Accurate prediction of heat transfer in compressor cavities is crucial to the design of efficient and reliable aircraft engines. The heat transfer affects the thermal expansion of the compressor rotor and, in turn, the tip clearance of the compressor blades. This paper presents a novel, physically-based predictive theoretical model of heat transfer and flow structure in an open compressor cavity, which can be used to accurately calculate disc temperatures. The radially higher region of the cavity is dominated by buoyancy effects created by the temperature difference between the hot mainstream flow and the axial throughflow used to cool the turbine. Strong interaction between the air in the cavity and this throughflow creates a mixing region at low radius. For a given geometry, the heat transfer and flow physics are governed by four parameters: the rotational Reynolds number Reϕ, the buoyancy parameter βΔT, the compressibility parameter χ, and the Rossby number Ro. The model quantifies both the buoyancy- and throughflow-induced mass and heat transfer, producing a reliable prediction of the disc and air temperatures. The model takes into account a two-fold effect of the throughflow: being entrained into the cold radial plumes directly and creating a toroidal vortex in the radially lower region of the cavity. The exchange of mass between the cavity and throughflow is related to the mass flow rate in the radial plumes in the buoyancy-induced region, considering the effect of flow reversal at low Ro. The model is validated using data collected in the Bath Compressor Cavity Rig and can be incorporated in engine design codes to robustly compute the thermal stress and expansion of the compressor rotor, contributing to more efficient engine designs.