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Research Papers: Flows in Complex Systems

Proper Orthogonal Decomposition of Self-Induced Instabilities in Decelerated Swirling Flows and Their Mitigation Through Axial Water Injection

[+] Author and Article Information
David Štefan

Assistant Professor
Kaplan Department of Fluids Engineering,
Faculty of Mechanical Engineering,
Brno University of Technology,
Technická 2896/2,
Brno CZ-61669, Czech Republic
e-mail: david.steffan@gmail.com

Pavel Rudolf

Professor
Kaplan Department of Fluids Engineering,
Faculty of Mechanical Engineering,
Brno University of Technology,
Technická 2896/2,
Brno CZ-61669, Czech Republic
e-mail: rudolf@fme.vutbr.cz

Sebastian Muntean

Center for Advanced Research in
Engineering Sciences,
Romanian Academy—Timisoara Branch,
Boulevard Mihai Viteazu 24,
Timisoara RO-300223, Romania
e-mail: seby@acad-tim.tm.edu.ro

Romeo Susan-Resiga

Professor
Hydraulic Machinery Department,
Politehnica University Timişoara
Boulevard Mihai Viteazu 1,
Timisoara RO-300222, Romania
e-mail: romeo.resiga@upt.ro

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received June 20, 2016; final manuscript received February 17, 2017; published online May 17, 2017. Assoc. Editor: Oleg Schilling.

J. Fluids Eng 139(8), 081101 (May 17, 2017) (25 pages) Paper No: FE-16-1383; doi: 10.1115/1.4036244 History: Received June 20, 2016; Revised February 17, 2017

The swirling flow exiting the runner of a hydraulic turbine is further decelerated in the discharge cone of the draft tube to convert the excess of dynamic pressure into static pressure. When the turbine is operated far from the best efficiency regime, particularly at part load, the decelerated swirling flow develops a self-induced instability with a precessing helical vortex and the associated severe pressure fluctuations. This phenomenon is investigated numerically in this paper, for a swirl apparatus configuration. The unsteady three-dimensional (3D) flow field is analyzed using a proper orthogonal decomposition (POD), and within this framework we examine the effectiveness of an axial jet injection for mitigating the flow instability. It is shown that a limited number of modes can be used to reconstruct the flow field. Moreover, POD enables to reveal influence of the jet injection on the individual modes of the flow and illustrates continuous suppression of the modes from higher-order modes to lower-order modes as the jet discharge increases. Application of POD offers new view for the future control effort aimed on vortex rope mitigation because spatiotemporal description of the flow is provided. Thereby, POD enables better focus of the jets or other flow control devices.

Copyright © 2017 by ASME
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References

Figures

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Fig. 1

Cross-sectional view of the scheme of a hydraulic power plant

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Fig. 2

The swirl generator apparatus installed on the experimental test rig: (a) cross section and (b) general view

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Fig. 3

Three-dimensional computational domain of the convergent–divergent parts

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Fig. 4

Detailed views of the computational mesh: (a) longitudinal and (b) transversal

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Fig. 5

Spatial shapes of axial velocity modes 1–9 for a decelerated swirling flow with a vortex rope

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Fig. 6

(a) The eigenvalue magnitudes of axial velocity modes 0–9 and (b) the power spectra of the temporal modes for a decelerated swirling flow with a vortex rope

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Fig. 7

The spatial shapes of tangential velocity modes 1–9 for a decelerated swirling flow with a vortex rope

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Fig. 8

(a) The eigenvalue magnitudes of tangential velocity modes 0–9 and (b) the power spectra of the temporal modes for a decelerated swirling flow with a vortex rope

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Fig. 9

The spatial shapes of radial velocity modes 1–9 of a decelerated swirling flow with a vortex rope

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Fig. 10

(a) The eigenvalue magnitudes of radial velocity modes 0–9 and (b) the power spectra of the temporal modes for a decelerated swirling flow with a vortex rope

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Fig. 11

(a) The dimensionless eigenvalue magnitudes of the first ten static pressure modes and (b) the temporal power spectra for a decelerated swirling flow with a vortex rope

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Fig. 12

Spatial representation of static pressure modes (a) 1 to (i) 9 for a decelerated swirling flow with a vortex rope

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Fig. 13

(a) Visualization of the vortex rope in the test rig, (b) the original snapshot from CFD computation, and the reconstructed snapshots based on (c) four modes and (d) and ten modes

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Fig. 14

Strouhal number for different values of the jet discharge: numerical computation and experimental data

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Fig. 15

Dimensionless amplitudes: numerical computation and experimental data for different values of jet discharge

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Fig. 16

The dimensionless eigenvalue magnitude distribution of radial velocity (a) mode 0 and (b) mode 1 for all jet discharge values

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Fig. 17

The power spectra of radial velocity mode 1 for all jet discharge values

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Fig. 18

The dimensionless eigenvalue magnitude distribution of static pressure (a) mode 0 and (b) mode 1 for all jet discharge values

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Fig. 19

The power spectra of static pressure mode 1 for all jet discharge values

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Fig. 20

The dimensionless eigenvalue magnitudes of the first ten (a) static pressure modes and (b) radial velocity modes at 2% jet discharge

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Fig. 21

The power spectra of (a) static pressure modes and (b) radial velocity modes at 2% jet discharge

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Fig. 22

The spatial shapes of (a) static pressure and (b) radial velocity mode 1 at 2% jet discharge

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Fig. 23

The spatial shapes of (a) static pressure mode 3 and (b) radial velocity mode 7 at 2% jet discharge

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Fig. 24

(a) Visualization of the vortex rope in the test rig, (b) the original snapshot from CFD computation, and the reconstructed snapshots based on (c) four modes and (d) ten modes at 2% jet discharge

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Fig. 25

The dimensionless eigenvalue magnitudes of the first ten (a) static pressure modes and (b) radial velocity modes at 5% jet discharge

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Fig. 26

The power spectra of (a) static pressure modes and (b) radial velocity modes at 5% jet discharge

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Fig. 27

The spatial shapes of (a) static pressure and (b) radial velocity mode 1 at 5% jet discharge

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Fig. 28

(a) Visualization of the vortex rope in the test rig, (b) the original snapshot from CFD computation, and the reconstructed snapshots based on (c) four modes and (d) ten modes at 5% jet discharge

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Fig. 29

The dimensionless eigenvalue magnitudes of the first ten (a) static pressure modes and (b) radial velocity modes at 8% jet discharge

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Fig. 30

The power spectra of (a) static pressure modes and (b) radial velocity modes at 8% jet discharge

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Fig. 31

The spatial shapes of (a) static pressure and (b) radial velocity mode 1 at 8% jet discharge

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Fig. 32

The spatial shapes of (a) static pressure and (b) radial velocity mode 1 at 11% jet discharge

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Fig. 33

Computed and reconstructed pressure recovery factors with the experimental data for the case with the vortex rope (0% jet) and full water injection (14% jet)

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Fig. 34

The distribution of computed and reconstructed pressure recovery factors and experimental data for levels MG1, MG2, and MG3 during jet injection

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Fig. 35

Comparison of the computed and experimental dimensionless amplitudes for levels MG0, MG1, MG2, and MG3

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Fig. 36

The dimensionless eigenvalue magnitude of the first ten static pressure modes for (a) data sets with different sampling intervals and (b) different lengths of time

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Fig. 37

Mode 1 of the static pressure field: (a) original data set Δt = 0.92 s and dt = 0.001 s, (b) the data set with longer sampling period dt = 0.02 s, and (c) data set with shorter length of time Δt = 0.23 s and dt = 0.001 s

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