Research Papers

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

[+] 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

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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Owen, J. M., 2007, “Modelling Internal Air Systems in Gas Turbine Engines,” J. Aerosp. Power, 22(4), pp. 505–521.
Farthing, P. R., Long, C. A., Owen, J. M., and Pincombe, J. R., 1992, “Rotating Cavity With Axial Throughflow of Cooling Air: Flow Structure,” ASME J. Turbomach., 114, pp. 237–246. [CrossRef]
Bohn, D., Deuker, E., Emunds, R., and Gorzelitz, V., 1995, “Experimental and Theoretical Investigations of Heat Transfer in Closed Gas Filled Rotating Annuli,” ASME J. Turbomach., 117, pp. 175–183. [CrossRef]
Owen, J. M., Abrahamsson, H., and Linblad, K., 2007, “Buoyancy-Induced Flow in Open Rotating Cavities,” ASME J. Eng. Gas Turb. Power, 129, pp. 893–900. [CrossRef]
Bohn, D., Ren, J., and Tümmers, C., 2006, “Investigation of the Unstable Flow Structure in a Rotating Cavity,” ASME Paper No. GT2006-90494. [CrossRef]
Owen, J. M., and Powell, J., 2006, “Buoyancy-Induced Flow in a Heated Rotating Cavity,” ASME J. Eng. Gas Turb. Power, 128, pp. 128–134. [CrossRef]
Tian, S., Tao, Z., Ding, S., and Xu, G., 2004, “Investigation of Flow and Heat Transfer Instabilities in a Rotating Cavity With Axial Throughflow of Cooling Air,” ASME Paper No. GT2004-53525. [CrossRef]
Bohn, D., Bouzidi, F., Kitanina, E. E., Ris, V. V., Smirnov, E. M., Burkhardt, C., and Wolff, M. W., 2002, “Numerical and Experimental Investigations of the Air Flow and Heat Transfer in Rotating Cavities,” Proceedings of the 9th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery (ISROMAC), Honolulu, HI, February 10-14, Paper No. HT-ABS-35.
Owen, J. M., 2010, “Thermodynamic Analysis of Buoyancy-Induced Flow in Rotating Cavities,” ASME J. Turbomach., 132, p. 031006. [CrossRef]
Bohn, D. and Ren, J., 2007, Influence of Laminar and Turbulent Viscosity on the Unstable Flow Pattern in a Rotating Cavity, Proceedings of the 7th European Turbomachinery Conference (ETC), Athens, Greece, March 5-7, Paper No. ETC7-135.
Bohn, D., Deutsch, G., Simon, B., and Burkhardt, C., 2000, “Flow Visualisation in a Rotating Cavity With Axial Throughflow,” ASME Paper No. 2000-GT-280.
Eberle, A., Schmatz, M. A., and Bissinger, N., 1990, “Generalized Flux Vectors for Hypersonic Shock-Capturing,” AIAA Paper No. 90-0390.
Schmatz, M. A., 1988, “Three-Dimensional Viscous Flow Simulations Using an Implicit Relaxation Scheme,” Numerical Simulation of Compressible Viscous-Flow Aerodynamics, W.Kordulla, ed., Vieweg, Brunswick, Germany, pp. 226–242.
Anderson, W. K., Thomas, J. L., and van Leer, B., 1985, “A Comparison of Finite Volume Flux Vector Splitting for the Euler Equations,” AIAA Paper No. 85-0122.
Owen, J. M., and Rogers, R. H., 1995, Flow and Heat Transfer in Rotating-Disc Systems, Vol. 2, Research Studies Press Ltd., Taunton, UK.
Long, C. A., and Childs, P. R. N., 2007, “The Effect of Inlet Conditions on the Flow and Heat Transfer in a Multiple Rotating Cavity With Axial Throughflow,” J. Aerosp. Power, 22(5), pp. 683–693.
Bohn, D., Bonhoff, B., Schönenborn, H., and Wilhelmi, H., 1995, “Validation of a Numerical Model for the Coupled Simulation of Fluid Flow and Diabatic Walls With Application to Film-Cooled Turbine Blades,” VDI-Berichte, 1186, pp. 259–272.
Bohn, D., Hötker, S., Tadesse, H., and Wolff, A., 2010, “Wärmeübergang in rotierenden Kammern (Teilprojekt 1.3.6),” Abschlussbericht zum COOREFF-T Forschungsvorhaben Strömungs- und Wärmeübergangsuntersuchungen in einem rotierenden Einkammermodell.
Long, C. A., and Tucker, P. G., 1994, “Shroud Heat Transfer Measurements From a Rotating Cavity With an Axial Throughflow of Air,” ASME J. Turbomach., 116, pp. 525–534. [CrossRef]
Farthing, P. R., Long, C. A., Owen, J. M., and Pincombe, J. R., 1992, “Rotating Cavity With Axial Throughflow of Cooling Air: Heat Transfer,” ASME J. Turbomach., 114, pp. 229–236. [CrossRef]


Grahic Jump Location
Fig. 1

Modular rotating cavity rig

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Fig. 2

Sketch of core component assembly

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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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Fig. 10

Total average Nusselt number on the disks



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