Calculation of the clearances between the blades and casing of the high-pressure-compressor rotors in aeroengines involves calculating the radial growth of the corotating compressor discs. This requires the calculation of the thermal growth of the discs, which in turn requires a knowledge of their temperatures and of the Nusselt numbers and the flow structure in the cavity between the discs. The authors have recently published a theoretical model of the buoyancy-induced flow in rotating cavities, and approximate solutions were obtained for laminar Ekman-layer flow on the discs; the equation for the Nusselt numbers, which includes two empirical constants, depends strongly on the Grashof number and on the radial distribution of disc temperature.
In this paper, Nusselt numbers and disc temperatures predicted by the buoyancy model are compared with values obtained from published experimental data. For most of the 19 test cases, with Grashof numbers up to nearly 1012, mainly good agreement was achieved between the theoretical and experimental distributions of Nusselt numbers and disc temperatures. This suggests that, owing to Coriolis effects, the laminar model of buoyancy-induced rotating flow could be valid even at the high Grashof numbers found in the compressor rotors of aeroengines. As predicted by the model, for a constant Grashof number increasing the rotational Reynolds number can cause a decrease in the Nusselt number.
This is the first time a theoretical model (rather than CFD) has been used to predict the temperatures of a compressor disc, and the model takes only seconds to predict disc temperatures that would take days or even weeks to predict using CFD. More experimental data is required if the model is to be used by the designers of compressor rotors, and suggestions for future research are given in the paper.