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PLUME MODEL FOR BUOYANCY-INDUCED FLOW AND HEAT TRANSFER IN CLOSED ROTATING CAVITIES


 The radial clearance between the rotating blades and stationary casing of a gas turbine compressor depends on the radial growth of the rotating discs, and this growth depends on the buoyancy-induced flow and heat transfer in the air-filled cavities between adjacent discs. A theoretical model has been developed to calculate the radial distribution of the temperature of the disc in a closed rotating cavity. The principal assumptions are that the convective heat transfer from the hot shroud to the cold hub of the cavity is via plumes of fluid in which the cold fluid moves radially outward, and the hot fluid inward, inside an inviscid quasi-axisymmetric core of rotating fluid. The core is surrounded by boundary layers on all rotating surfaces, with free-convection layers on the surfaces of the shroud and hub and laminar Ekman layers on the surface of the discs. In addition to the convection, heat is transferred by one-dimensional radial conduction in the rotating discs. Using the model, equations have been derived to calculate the radial distribution of temperature in the discs and fluid core. These equations reveal that the non-dimensional temperatures for the disc and core, θd and θc, are controlled by three independent non-dimensional parameters: ReΦ, βΔT and x, the rotational Reynolds number, the buoyancy parameter, and the compressibility parameter. The theoretical model predicts radial distributions of temperatures in the discs and fluid core that are in good agreement with the experimentally derived values in a companion paper.