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Research Papers

# Thermodynamic Analysis of Buoyancy-Induced Flow in Rotating Cavities

[+] Author and Article Information
J. Michael Owen

Department of Mechanical Engineering, University of Bath, BA2 7AY, UKensjmo@bath.ac.uk

J. Turbomach 132(3), 031006 (Mar 24, 2010) (7 pages) doi:10.1115/1.2988170 History: Received January 25, 2008; Revised January 30, 2008; Published March 24, 2010; Online March 24, 2010

## Abstract

Buoyancy-induced flow occurs in the rotating cavities between the adjacent disks of a gas-turbine compressor rotor. In some cases, the cavity is sealed, creating a closed system; in others, there is an axial throughflow of cooling air at the center of the cavity, creating an open system. For the closed system, Rayleigh–Bénard (RB) flow can occur in which a series of counter-rotating vortices, with cyclonic and anticyclonic circulation, form in the $r-ϕ$ plane of the cavity. For the open system, the RB flow can occur in the outer part of the cavity, and the core of the fluid containing the vortices rotates at a slower speed than the disks: that is, the rotating core “slips” relative to the disks. 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 were observed in rotating cavities, and expressions for the entropy production were derived for both open and closed systems. For the closed system, MEP corresponds to the maximization of the heat transfer to the cavity; for the open system, it corresponds to the maximization 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.

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## Figures

Figure 1

Simplified diagram of the high-pressure compressor rotor with an axial throughflow of cooling air

Figure 2

Schematic of the flow structure in the core of the heated rotating cavity with an axial throughflow of cooling air (1)

Figure 3

Computations of the flow structure in the core of the heated rotating cavity with an axial throughflow of cooling air (3)

Figure 4

Computed temperature contours in the core of the heated rotating cavity with an axial throughflow of cooling air (4). Expt. 2 on the left and Expt. 5 on the right (rotation of the cavity is clockwise).

Figure 5

Computed 2D Rayleigh–Bénard vortices in a sealed rotating annulus (6)

Figure 6

“Attractor landscape” with three valleys

Figure 7

Thermodynamic model of a closed rotating cavity

Figure 8

Transient 2D computed isotherms for a sealed rotating annulus (19): a/b=0.5 and Ra=4×106

Figure 9

Effect of n on computed Nusselt numbers for a sealed rotating annulus (19): a/b=0.5 and Ra=106

Figure 10

Variation of the number of vortex pairs, N, with the radius ratio, a/b, of the closed cavity. Solid symbols, Eq. 33; x, computations of Lewis (19); and Δ, computations of King (21).

Figure 11

Simplified diagram of the open rotating cavity

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