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Research Papers

Theoretical Model of Buoyancy-Induced Flow in Rotating Cavities

[+] Author and Article Information
J. Michael Owen, Hui Tang

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

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received March 3, 2015; final manuscript received July 29, 2015; published online September 16, 2015. Assoc. Editor: Ardeshir (Ardy) Riahi.

J. Turbomach 137(11), 111005 (Sep 16, 2015) (7 pages) Paper No: TURBO-15-1037; doi: 10.1115/1.4031353 History: Received March 03, 2015; Revised July 29, 2015

The Ekman-layer equations, which have previously been solved for isothermal source–sink flow in a rotating cavity, are derived for buoyancy-induced flow. Although the flow in the inviscid core is three-dimensional and unsteady, it is assumed that the flow in the Ekman layers is axisymmetric and steady; and, as for source–sink flow, the average mass flow rate in the Ekman layers is assumed to be invariant with radius. In addition, it is assumed that the flow in the core is adiabatic, and consequently the core temperature increases with radius and with rotational speed. Approximate solutions are obtained for laminar flow, and it is shown that the Nusselt numbers for the rotating disks and the mass flow rate in the Ekman layers are proportional to Grc1/4, where Grc is a Grashof number based on the rotational Reynolds number and the temperature difference between the disk and the core. The equation for the Nusselt numbers, which includes two empirical constants, depends strongly on the radial distribution of the temperature of the disks.

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Figures

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Fig. 1

Schematic of flow structure in heated rotating cavity with axial throughflow of cooling air [7]

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Fig. 2

Simplified diagram of axial throughflow in an isothermal rotating cavity

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Fig. 3

Assumed flow structure

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Fig. 4

Assumed shape of velocity distributions in Ekman layer

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