Numerical Analysis of Heat Transfer and Flow Stability in an Open Rotating Cavity Using the Maximum Entropy Production Principle

D. Bohn; R. Krewinkel; A. Wolff

doi:10.1115/1.4007613

Journal of Turbomachinery | Volume 135 | Issue 4 | research-article

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Research Papers

Numerical Analysis of Heat Transfer and Flow Stability in an Open Rotating Cavity Using the Maximum Entropy Production Principle

D. Bohn, R. Krewinkel and A. Wolff

[+] Author and Article Information

A. Wolff

Institute of Power Plant Technology,
Steam and Gas Turbines,
RWTH Aachen University,
Templergraben 55,
D-52056 Aachen, Germany
e-mail: office@ikdg.rwth-aachen.de

¹Full professor, retired.

²Present address: BorgWarner Turbo Systems Engineering GmbH, Marnheimerstrasse 85/87, 67292 Kirchheimbolanden, Germany.

³Present address: RWE Power AG, Opernplatz 1, 45128 Essen, Germany.

Contributed by International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received August 15, 2012; final manuscript received August 29, 2012; published online June 5, 2013. Assoc. Editor: David Wisler.

J. Turbomach 135(4), 041023 (Jun 05, 2013) (7 pages) Paper No: TURBO-12-1173; doi: 10.1115/1.4007613 History: Received August 15, 2012; Revised August 29, 2012

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Abstract

The flow field and heat transfer in the internal cooling system of gas turbines can be modeled using rotating-disk systems with axial throughflow. Because of the complexity of these flows, in which buoyancy-induced phenomena are of the utmost importance, numerical studies are notoriously difficult to perform and need extensive experimental validation. J.M. Owen proposed using the maximum entropy production (MEP) principle as a possible means of simplifying numerical computations for these complex flows since this would enable us to use stationary numerical calculations to predict the flow field. Simply said, this theory is based on the heat flux out of the cavity. In this numerical study, the computed Nusselt numbers on the disk walls inside an open rotating cavity with a Rayleigh number of approximately 4.97 × 10⁸. This is representative of the lower values encountered in the flow inside rotating cavities. It is shown that, as predicted by Owen, the flow is stable when the heat transfer out of the cavity is maximized, or, conversely, the system is unstable when the heat transfer is minimized. Furthermore, it is proven that the level of the Nusselt number plays an important role for the change between the number of vortex pairs in the flow as well.

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Fig. 2

Sketch of core component assembly

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Fig. 1

Modular rotating cavity rig

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Fig. 3

Solution domain

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Fig. 10

Total average Nusselt number on the disks

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Fig. 4

Calculation of the Nusselt number

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Fig. 5

Variation of local Nusselt number over radius for the upstream disk

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Fig. 6

Variation of local Nusselt number over radius for the downstream disk

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Fig. 7

Variation of local Nusselt number over radius

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Fig. 8

Nusselt number on the downstream disk

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Fig. 9

Nusselt number on the upstream disk

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Bohn DD, Krewinkel RR, Wolff AA. Numerical Analysis of Heat Transfer and Flow Stability in an Open Rotating Cavity Using the Maximum Entropy Production Principle. ASME. J. Turbomach. 2013;135(4):041023-041023-7. doi:10.1115/1.4007613.

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Numerical Analysis of Heat Transfer and Flow Stability in an Open Rotating Cavity Using the Maximum Entropy Production Principle

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