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Research Papers: Gas Turbines: Turbomachinery

Direct Numerical Simulation of Rotating Cavity Flows Using a Spectral Element-Fourier Method

[+] Author and Article Information
Diogo B. Pitz

Department of Mechanical Engineering Sciences,
Thermo-Fluid Systems University
Technology Centre,
University of Surrey,
Guildford, UK
e-mail: d.bertapitz@surrey.ac.uk

John W. Chew

Department of Mechanical Engineering Sciences,
Thermo-Fluid Systems University
Technology Centre,
University of Surrey,
Guildford, UK
e-mail: j.chew@surrey.ac.uk

Olaf Marxen

Department of Mechanical Engineering Sciences,
University of Surrey,
Guildford, UK

Nicholas J. Hills

Department of Mechanical Engineering Sciences,
Thermo-Fluid Systems University
Technology Centre,
University of Surrey,
Guildford, UK

1Corresponding author.

Contributed by the Turbomachinery Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received August 16, 2016; final manuscript received October 7, 2016; published online February 14, 2017. Editor: David Wisler.

J. Eng. Gas Turbines Power 139(7), 072602 (Feb 14, 2017) (10 pages) Paper No: GTP-16-1411; doi: 10.1115/1.4035593 History: Received August 16, 2016; Revised October 07, 2016

A high-order numerical method is employed to investigate flow in a rotor/stator cavity without heat transfer and buoyant flow in a rotor/rotor cavity. The numerical tool used employs a spectral element discretization in two dimensions and a Fourier expansion in the remaining direction, which is periodic and corresponds to the azimuthal coordinate in cylindrical coordinates. The spectral element approximation uses a Galerkin method to discretize the governing equations, but employs high-order polynomials within each element to obtain spectral accuracy. A second-order, semi-implicit, stiffly stable algorithm is used for the time discretization. Numerical results obtained for the rotor/stator cavity compare favorably with experimental results for Reynolds numbers up to Re1 = 106 in terms of velocities and Reynolds stresses. The buoyancy-driven flow is simulated using the Boussinesq approximation. Predictions are compared with previous computational and experimental results. Analysis of the present results shows close correspondence to natural convection in a gravitational field and consistency with experimentally observed flow structures in a water-filled rotating annulus. Predicted mean heat transfer levels are higher than the available measurements for an air-filled rotating annulus, but in agreement with correlations for natural convection under gravity.

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References

Figures

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Fig. 1

Annular geometry employed to model a sealed rotating cavity. In the rotor/stator case, the lower disk and the shaft rotate, while the upper disk and the shroud remain stationary.

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Fig. 2

Iso surfaces of the Q-criterion on the rotor disk for increasing Reynolds number, colored by the tangential velocity ranging from 0 to Ωro: (a) Re1 = 8 × 104, (b) Re1 = 4 × 105, and (c) Re1 = 106

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Fig. 3

Tangential and radial velocities and rms quantities for Re1 = 4 × 105 at r* = 0.5. Comparison with the experimental data from Ref. [5]: (a) tangential and radial velocities and (b) rms quantities.

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Fig. 4

Tangential and radial velocities and rms quantities for Re1 = 4 × 105 at r* = 0.7. Comparison with the experimental data from Ref. [5]: (a) tangential and radial velocities and (b) rms quantities.

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Fig. 5

Tangential and radial velocities and rms quantities for Re1 = 106 at r* = 0.5. Comparison with the experimental data from Ref. [5]: (a) tangential and radial velocities and (b) rms quantities.

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Fig. 6

Tangential and radial velocities and rms quantities for Re1 = 106 at r* = 0.7. Comparison with the experimental data from Ref. [5]: (a) tangential and radial velocities and (b) rms quantities.

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Fig. 7

Near-wall profile of the tangential velocity for Re1 = 106 at r* = 0.5 (rotor on the left, stator on the right). The dashed lines represent the law of the wall profiles.

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Fig. 8

Instantaneous temperature contours in the interval Ti≤T≤To for increasing Rayleigh number at the midaxial position. The cavity rotates in the counterclockwise direction. Traditional Boussinesq approximation: (a) Ra = 106, (b) Ra = 107, (c) Ra = 108, and (d) Ra = 109. Extended Boussinesq approximation: (e) Ra = 106, (f) Ra = 107, (g) Ra = 108, and (h) Ra = 109.

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Fig. 9

Space-time temperature plots for r* = 0.2 and x* = 0.5 at two different Rayleigh numbers, obtained using the traditional Boussinesq approximation: (a) Ra = 107 and (b) Ra = 108

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Fig. 10

Nusselt number as a function of the Rayleigh number for the rotating annulus. Comparison with the correlations given in Refs. [7,8,21].

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Fig. 11

Nusselt number as a function of the modified Rayleigh number Ra′. The numerical results are compared with correlations for a flat plate given by Eq. (9).

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