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TECHNICAL PAPERS: Gas Turbines: CFD Modeling and Simulation

# Rayleigh-Bénard Convection in Open and Closed Rotating Cavities

[+] Author and Article Information
Martin P. King

Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, Trieste, Italy

Michael Wilson

Department of Mechanical Engineering, University of Bath, Bath BA2 7AY, UK

J. Michael Owen

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

J. Eng. Gas Turbines Power 129(2), 305-311 (Nov 15, 2005) (7 pages) doi:10.1115/1.2432898 History: Received October 31, 2005; Revised November 15, 2005

## Abstract

Buoyancy effects can be significant in the rotating annular cavities found between compressor discs in gas-turbine engines, where Rayleigh numbers above $1012$ are common. In some engines, the cavity is “closed” so that the air is confined between four rotating surfaces: two discs and inner and outer cylinders. In most engines, however, the cavity is “open” and there is an axial throughflow of cooling air at the center. For open rotating cavities, a review of the published evidence suggests a Rayleigh–Bénard type of flow structure, in which, at the larger radii, there are pairs of cyclonic and anti-cyclonic vortices. The toroidal circulation created by the axial throughflow is usually restricted to the smaller radii in the cavity. For a closed rotating annulus, solution of the unsteady Navier–Stokes equations, for Rayleigh numbers up to $109$, show Rayleigh–Bénard convection similar to that found in stationary enclosures. The computed streamlines in the $r$-$θ$ plane show pairs of cyclonic and anti-cyclonic vortices; but, at the larger Rayleigh numbers, the computed isotherms suggest that the flow in the annulus is thermally mixed. At the higher Rayleigh numbers, the computed instantaneous Nusselt numbers are unsteady and tend to oscillate with time. The computed time-averaged Nusselt numbers are in good agreement with the correlations for Rayleigh–Bénard convection in a stationary enclosure, but they are significantly higher than the published empirical correlations for a closed rotating annulus.

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## Figures

Figure 1

Simplified diagram of high-pressure compressor rotor with axial throughflow

Figure 2

Schematic diagram of open and closed rotating cavities

Figure 3

Rayleigh–Bénard convection in a horizontal stationary enclosure

Figure 4

Computed 2D streamlines and isotherms for a∕b=0.5

Figure 5

Computed 3D flow structure at z¯=0.25 and for Ra3=103.9, a∕b=0.5, G=0.5

Figure 6

2D computations of variation of Nu3,av with t¯ for a∕b=0.5

Figure 7

2D computations of variation of Nu¯3,av with Ra3 for a∕b=0.5

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