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Research Papers: Gas Turbines: Turbomachinery

Theoretical Model of Buoyancy-Induced Heat Transfer in Closed Compressor Rotors

[+] Author and Article Information
Hui Tang

Department of Mechanical Engineering,
University of Bath,
Bath BA2 7AY, UK
e-mail: h.tang2@bath.ac.uk

J. Michael Owen

Department of Mechanical Engineering,
University of Bath,
Bath BA2 7AY, UK
e-mail: ensjmo@bath.ac.uk

Contributed by the Turbomachinery Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received July 11, 2017; final manuscript received July 24, 2017; published online October 17, 2017. Editor: David Wisler.

J. Eng. Gas Turbines Power 140(3), 032605 (Oct 17, 2017) (7 pages) Paper No: GTP-17-1344; doi: 10.1115/1.4037926 History: Received July 11, 2017; Revised July 24, 2017

The cavities between the rotating compressor disks in aero-engines are open, and there is an axial throughflow of cooling air in the annular space between the center of the disks and the central rotating compressor shaft. Buoyancy-induced flow occurs inside these open rotating cavities, with an exchange of heat and momentum between the axial throughflow and the air inside the cavity. However, even where there is no opening at the center of the compressor disks—as is the case in some industrial gas turbines—buoyancy-induced flow can still occur inside the closed rotating cavities. The closed cavity also provides a limiting case for an open cavity when the axial clearance between the cobs—the bulbous hubs at the center of compressor disks—is reduced to zero. Bohn and his co-workers at the University of Aachen have studied three different closed-cavity geometries, and they have published experimental data for the case where the outer cylindrical surface is heated and the inner surface is cooled. In this paper, a buoyancy model is developed in which it is assumed that the heat transfer from the cylindrical surfaces is analogous to laminar free convection from horizontal plates, with the gravitational acceleration replaced by the centripetal acceleration. The resulting equations, which have been solved analytically, show how the Nusselt numbers depend on both the geometry of the cavity and its rotational speed. The theoretical solutions show that compressibility effects in the core attenuate the Nusselt numbers, and there is a critical Reynolds number at which the Nusselt number will be a maximum. For the three cavities tested, the predicted Nusselt numbers are in generally good agreement with the measured values of Bohn et al. over a large range of Raleigh numbers up to values approaching 1012. The fact that the flow remains laminar even at these high Rayleigh numbers is attributed to the Coriolis accelerations suppressing turbulence in the cavity, which is consistent with recently published results for open rotating cavities.

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References

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(1), pp. 237–246. [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(1), pp. 229–236. [CrossRef]
Owen, J. M. , and Tang, H. , 2015, “ Theoretical Model of Buoyancy-Induced Flow in Rotating Cavities,” ASME J. Turbomach., 137(11), p. 111005. [CrossRef]
Tang, H. , and Owen, J. M. , 2017, “ Effect of Buoyancy-Induced Rotating Flow on Temperature of Compressor Discs,” ASME J. Eng. Gas Turbines Power, 139(6), p. 062506. [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(1), pp. 175–183. [CrossRef]
Owen, J. M. , and Long, C. A. , 2015, “ Review of Buoyancy-Induced Flow in Rotating Cavities,” ASME J. Turbomach., 137(11), p. 111001. [CrossRef]
King, M. P. , Wilson, M. , and Owen, J. M. , 2007, “ Rayleigh-Benard Convection in Open and Closed Rotating Cavities,” ASME J. Eng. Gas Turbines Power, 129(2), pp. 305–311. [CrossRef]
Lewis, T. W. , 1999, “ Numerical Simulation of Buoyancy-Induced Flow in a Sealed Rotating Cavity,” Ph.D. thesis, University of Bath, Bath, UK. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.285311
Owen, J. M. , 2010, “ Thermodynamic Analysis of Buoyancy-Induced Flow in Rotating Cavities,” ASME J. Turbomach., 132(3), p. 031006. [CrossRef]
King, M. P. , 2003, “ Convective Heat Transfer in a Rotating Annulus,” Ph.D. thesis, University of Bath, Bath, UK. http://opus.bath.ac.uk/53228/1/king_2003_phdthesis_universityofbath.pdf
Grossmann, S. , and Lohse, D. , 2000, “ Scaling in Thermal Convection: A Unifying Theory,” J. Fluid Mech., 407, pp. 27–56. [CrossRef]
Holland, K. G. T. , Raithby, G. D. , and Konicek, L. , 1975, “ Correlation Equations for Free Convection Heat Transfer in Horizontal Layers of Air and Water,” Int. J. Heat Mass Transfer, 18(7–8), pp. 879–884. [CrossRef]
Sun, Z. , Kifoil, A. , Chew, J. W. , and Hills, N. J. , 2004, “ Numerical Simulation of Natural Convection in Stationary and Rotating Cavities,” ASME Paper No. GT2004-53528.
Pitz, D. B. , Chew, J. W. , Marxen, O. , and Hills, N. J. , 2016, “ Direct Numerical Simulation of Rotating Cavity Flows Using a Spectral Element-Fourier Method,” ASME Paper No. GT2016-56486.
Incropera, F. P. , and DeWitt, D. P. , 1996, Fundamentals of Heat and Mass Transfer, Wiley, New York.
Tang, H. , Puttock, M. , and Owen, J. M. , 2017, “ Buoyancy-Induced Flow and Heat Transfer in Compressor Rotors,” ASME J. Eng. Gas Turbines Power (under review).

Figures

Grahic Jump Location
Fig. 1

Open high-pressure compressor rotor for aero-engine

Grahic Jump Location
Fig. 2

Aachen closed cavity rig [5]

Grahic Jump Location
Fig. 3

Simplified diagram of temperature distribution inside cavity

Grahic Jump Location
Fig. 4

Theoretical effect (for ΔT constant) of increasing pressure on variation of Nu with Ra. Broken line corresponds to Nu∝Ra1/4.

Grahic Jump Location
Fig. 5

Variation of βΔT with Ra for experiments of Bohn et al. [5]

Grahic Jump Location
Fig. 6

Variation of Nu with Ra for three cavities (symbols denote experimental data [5], solid curves denote theoretical solutions, and broken curves denote empirical correlations [5]): (a) variation of Nu with Ra for cavity A (p = 4 bar), (b) variation of Nu with Ra for cavity B (p = 2 bar), and (c) variation of Nu with Ra for cavity C (p = 1 bar)

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