Fundamental Model for Compressor Cavity Heat Transfer: Theory and Validation

Abstract The buoyancy-driven flow inside compressor cavities is three-dimensional, unsteady and features a large range of time- and length-scales. The temperature and rotation of the fluid core of the cavity are influenced by an exchange (and recirculation) of enthalpy and momentum with an axial throughflow of cooling air at low radius. The complexity of the flow and conjugate nature of the heat transfer to the discs creates a challenge for the aero-engine designer when calculating thermal stresses, radial expansion, and blade-tip clearances. This paper presents a low-order model to predict the radial variation of disc and fluid-core temperatures, and the mass exchange (entrainment) to the rotating cavity. Fundamental physical principles and experimental data are used to create a single set of Rayleigh-Grashof correlations for heat transfer and radial mass flow of buoyant plumes. The model is applied to eleven test cases from experimental rigs at Bath, Dresden and Sussex, each with unique instrumentation, thermal boundary conditions, geometries and throughflow swirl. Empirical correlations for exchange and recirculation mass flow were determined for each rig using a common theoretical methodology. The model captures the heat and mass transfer characteristics with accuracy quantified relative to experimental data. New experimental data from the Bath Compressor Cavity Rig is used to validate the model under conditions of asymmetrical heating, demonstrating the effects associated with the axial gradient of temperature in the compressor are captured appropriately. The consistent agreement with experimental data and correlation methodology demonstrates a robust framework appropriate for application to thermo-mechanical design codes in the aero-engine.