Increasing pressures in gas-turbine compressors, particularly in aeroengines where the pressure ratios can be above 50:1, require smaller compressor blades and an increasing focus on blade-clearance control. The blade clearance depends on the radial growth of the compressor discs, which in turn depends on the temperature and stress in the discs. As the flow inside the disc cavities is buoyancy-driven, calculation of the disc temperature is a conjugate problem: the heat transfer from the disc is coupled with the air temperature inside the cavity. The flow inside the cavity is three-dimensional, unsteady and unstable, so computational fluid dynamics is not only expensive and time-consuming, it is also unable to achieve accurate solutions at the high Grashof numbers found in modern compressors. Many designers rely on empirical equations based on inappropriate physical models, and recently the authors have produced a series of papers on physically-based theoretical modelling of buoyancy-induced heat transfer in the rotating cavities found inside compressor rotors. Predictions from these models, all of which are for laminar flow, have been validated using measurements made in open and closed compressor rigs for a range of flow parameters representative of those found inside compressor rotors. (The fact that laminar buoyancy models can be used for large Grashof numbers (up to
), where most engineers expect the flow to be turbulent, is attributed to the large Coriolis accelerations in the fluid core and to the fact that there is only a small difference between the rotational speed of the core and that of the discs.) As many as 223 separate tests were analysed in the validation of the models, and good agreement between the predictions and measurements was achieved for most of these cases. This overview paper has collected together the equations from these papers, which should be helpful to designers and research workers. The paper also points out the limitations of the models, all of which are for steady flow, and shows where further experimental evidence is needed.
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