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Research Papers

Efficient Computational Model for Nonaxisymmetric Flow and Heat Transfer in Rotating Cavity

[+] Author and Article Information
L. He

Department of Engineering Science, Osney Laboratory, Oxford University, Oxford OX1 3PJ, UK

J. Turbomach 133(2), 021018 (Oct 25, 2010) (9 pages) doi:10.1115/1.4000551 History: Received July 14, 2009; Revised August 04, 2009; Published October 25, 2010; Online October 25, 2010

Existence of large scale unsteady flow structures manifested in contrarotating vortex pairs has been previously identified in rotor disk cavities. The nonaxisymmetric nature with an unknown number of vortices presents a computational challenge, as a full 360 deg circumferential domain will be needed, requiring significant computational resources. A novel circumferential spatial Fourier spectral technique is adopted in the present work to facilitate efficient computational predictions of the nonaxisymmetric flows. Given that the flow nonuniformities in the circumferential direction are of large length scales, only a few circumferential Fourier harmonics would be needed, resulting in a drastic reduction in number of circumferential mesh points to be required. The modeling formulations and implementation aspects will be described. Computational examples will be presented to demonstrate the validity and effectiveness of the present modeling approach. The computational results show that the nonaxisymmetric flow patterns, in terms of the number of vortex pairs, are sensitive to small scale external disturbances. It is also indicated that the occurrence of a nonaxisymmetric flow might be captured by the present Fourier solution with even one harmonic.

Copyright © 2011 by American Society of Mechanical Engineers
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References

Figures

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Figure 6

Time history of convection heat transfer coefficient at cavity outer casing (shroud)

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Figure 7

Unsteady radial velocity contours and velocity perturbation vectors at midaxial plane

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Figure 8

Unsteady radial velocity contours and velocity perturbation vectors at midaxial plane (Fourier solution, reconstructed): Direct solution of (a) 14 harmonics and (b) 10 harmonics

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Figure 9

Unsteady radial velocity contours and velocity perturbation vectors at midaxial plane, constant inlet distortion amplitude for all harmonics (Fourier solution with 14 harmonics)

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Figure 10

Unsteady radial velocity contours and velocity perturbation vectors at midaxial plane, constant inlet distortion amplitude for all harmonics (Fourier solution with 10 harmonics)

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Figure 11

Unsteady radial velocity contours and velocity perturbation vectors at midaxial plane, constant amplitude of inlet disturbance for all harmonics; direct solution, time=30 rotor revolutions

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Figure 12

Unsteady radial velocity contours and velocity perturbation vectors at midaxial plane, constant amplitude of inlet disturbance for all harmonics; direct solution, time=40 rotor revolutions

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Figure 13

Unsteady radial velocity contours and velocity perturbation vectors at midaxial plane, constant amplitude of inlet disturbance for all harmonics; direct solution, time=70 rotor revolutions

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Figure 14

Unsteady radial velocity contours and velocity perturbation vectors at midaxial plane, constant amplitude of inlet disturbance for all harmonics; direct solution, time=95 rotor revolutions

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Figure 15

Unsteady radial velocity contours and velocity perturbation vectors at midaxial plane, constant amplitude of inlet disturbance for all harmonics; direct solution, time=120 rotor revolutions

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Figure 16

Unsteady radial velocity contours and velocity perturbation vectors at midaxial plane, constant amplitude of rotating inlet disturbances; direct solution, time=100 rotor revolutions

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Figure 17

Time history of convection heat transfer coefficient at cavity outer casing (shroud); constant inlet distortion amplitude for all harmonics

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Figure 18

Time history of shroud heat transfer coefficient (Fourier solutions with different numbers of harmonics)

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Figure 1

Rotating disk cavity configuration

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Figure 2

Nonaxisymmetrical flow pattern with two pairs of contrarotating vortices with associated high pressure (P+) and low pressure (P−) regions

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Figure 3

Number of circumferential mesh cells for Fourier modeling: (a) one harmonic (2N+1=3 mesh cells) and (b) two harmonics (2N+1=5 mesh cells)

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Figure 4

Circumferential Fourier transform as implemented in explicit time-marching solver

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Figure 5

Mesh cell center and circumferential dummy points for a second order finite volume scheme

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