Effect of buoyancy-induced rotating flow on temperatures of compressor disks

Calculation of the clearances between the blades and casing of the high-pressurecompressor rotors in aeroengines involves calculating the radial growth of the corotating compressor disks. This requires the calculation of the thermal growth of the disks, which in turn requires knowledge of their temperatures and of the Nusselt numbers and the flow structure in the cavity between the disks. 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 disks; the equation for the Nusselt numbers, which includes two empirical constants, depends strongly on the Grashof number and on the radial distribution of disk temperature. In this paper, Nusselt numbers and disk 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 disk 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 computational fluid dynamics (CFD)) has been used to predict the temperatures of a compressor disk, and the model takes only seconds to predict disk 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.