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Abstract
The radial clearance between the rotating blades and stationary casing of a gas turbine compressor depends on the radial growth of the rotating discs to which the blades are attached, and this growth depends on the buoyancyinduced flow and heat transfer in the airfilled cavities between adjacent discs. In some engines, the cavities are sealed, which creates a closed rotating cavity. 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 quasiaxisymmetric core of rotating fluid. The fluid core is surrounded by boundary layers on all rotating surfaces, with freeconvection 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 onedimensional 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 nondimensional temperatures for the disc and core,θd and θc, are controlled by three independent nondimensional parameters: Reφ, βδT and x, the rotational Reynolds number, the buoyancy parameter, and the compressibility parameter, respectively. The compressibility parameter is defined as x def/= Ma2/βδT where Ma is a Mach number, and x is shown to strongly affect the radial distribution of the core temperatures. There will be a critical value of x at which the core temperature equals that of the heated shroud. For a closed cavity with adiabatic discs and xa = 0.5, the critical value is 6.7. Above this critical value, stratification is expected to occur and heat transfer from the shroud to the core will be by conduction rather than by convection. 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.
Original language  English 

Title of host publication  Heat Transfer  General Interest/Additive Manufacturing Impacts on Heat Transfer; Internal Air Systems; Internal Cooling 
Publisher  American Society of Mechanical Engineers (ASME) 
ISBN (Electronic)  9780791886045 
DOIs  
Publication status  Published  28 Oct 2022 
Event  ASME Turbo Expo 2022  Rotterdam, Netherlands Duration: 13 Jun 2022 → 17 Jun 2022 
Publication series
Name  Proceedings of the ASME Turbo Expo 

Volume  6B 
Conference
Conference  ASME Turbo Expo 2022 

Country/Territory  Netherlands 
City  Rotterdam 
Period  13/06/22 → 17/06/22 
Bibliographical note
Publisher Copyright:Copyright © 2022 by ASME.
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 1 Finished

Modelling of BuyancyInduced Flow in Compressor Rotors  Surrey/RR
Lock, G. (PI), Sangan, C. (CoI), Scobie, J. (CoI) & Wilson, M. (CoI)
Engineering and Physical Sciences Research Council
11/01/17 → 31/12/20
Project: Research council