Thermodynamic Analysis of Buoyancy-Induced Flow in Rotating Cavities

Abstract

Buoyancy-induced flow occurs in the rotating cavities between the adjacent discs of a gas-turbine compressor rotor. In some cases, the cavity is sealed, creating a closed system; in others, there is an axial through-flow of cooling air at the centre of the cavity, creating an open system. For the closed system, Rayleigh-Be´nard (R-B) flow can occur in which a series of counter-rotating vortices, with cyclonic and anti-cyclonic circulation, form in the r-φ plane of the cavity. For the open system, R-B flow can occur in the outer part of the cavity, and the core of fluid containing the vortices rotates at a slower speed than the discs: that is, the rotating core ‘slips’ relative to the discs. These flows are examples of self-organizing systems, which are found in the world of far-from-equilibrium thermodynamics and which are associated with the maximum entropy production (MEP) principle. In this paper, these thermodynamic concepts are used to explain the phenomena that have been observed in rotating cavities, and expressions for the entropy production have been derived for both open and closed systems. For the closed system, MEP corresponds to the maximisation of the heat transfer to the cavity; for the open system, it corresponds to the maximisation of the sum of the rates of heat and work transfer. Some suggestions, as yet untested, are made to show how the MEP principle could be used to simplify the computation of buoyancy-induced flows.