Plume model for buoyancy-induced flow and heat transfer in closed rotating cavities

Hui Tang, Mike Owen

Research output: Chapter or section in a book/report/conference proceedingChapter in a published conference proceeding

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 buoyancy-induced flow and heat transfer in the air-filled 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 quasi-axisymmetric core of rotating fluid. The fluid 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 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 languageEnglish
Title of host publicationHeat Transfer - General Interest/Additive Manufacturing Impacts on Heat Transfer; Internal Air Systems; Internal Cooling
PublisherAmerican Society of Mechanical Engineers (ASME)
ISBN (Electronic)9780791886045
DOIs
Publication statusPublished - 28 Oct 2022
EventASME Turbo Expo 2022 - Rotterdam, Netherlands
Duration: 13 Jun 202217 Jun 2022

Publication series

NameProceedings of the ASME Turbo Expo
Volume6-B

Conference

ConferenceASME Turbo Expo 2022
Country/TerritoryNetherlands
CityRotterdam
Period13/06/2217/06/22

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