0
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
Your Session has timed out. Please sign back in to continue.

References

Dörfler, P. , Sick, M. , and Coutu, A. , 2013, Flow-Induced Pulsations and Vibration in Hydraulic Machinery, Springer-Verlag, London.
Wu, Y. L. , Li, S. C. , Liu, S. H. , Dou, H.-S. , and Qian, Z. D. , 2013, Vibration of Hydraulic Machinery, Vol. 11, Springer, Dordrecht, The Netherlands.
Frunzaverde, D. , Muntean, S. , Marginean, G. , Campian, V. , Marsavina, L. , Terzi, R. , and Serban, V. , 2010, “ Failure Analysis of a Francis Turbine Runner,” IOP Conf. Ser.: Earth Environ. Sci., 12(1), p. 012115. [CrossRef]
Thicke, R. H. , 1981, “ Practical Solutions for Draft Tube Instability,” Int. Water Power Dam Constr., 33(2), pp. 31–37.
Nishi, M. , Wang, X. M. , Yoshida, K. , Takahashi, T. , and Tsukamoto, T. , 1996, “ An Experimental Study on Fins, Their Role in Control of the Draft Tube Surging,” 18th IAHR Symposium on Hydraulic Machinery and Cavitation (IAHR), E. Cabrera , V. Espert , and F. Martínex , eds., Valencia, Spain, Sept. 16–19, Kluwer Academic Publishers, Dordrecht, The Netherlands, pp. 905–914.
Miyagawa, K. , Sano, T. , Kunimatsu, N. , Aki, T. , and Nishi, M. , 2006, “ Flow Instability With Auxiliary Parts in High Head Pump–Turbines,” 23rd IAHR Symposium on Hydraulic Machinery and Systems, Yokohama, Japan, Oct. 17–21, Paper No. F307.
Vevke, T. , 2004, “ An Experimental Investigation of Draft Tube Flow,” Ph.D. thesis, Norwegian University of Science and Technology, Trondheim, Norway.
Qian, Z. D. , Li, W. , Huai, W. X. , and Wu, Y. L. , 2012, “ The Effect of the Runner Cone Design on Pressure Oscillation Characteristics in a Francis Hydraulic Turbine,” Proc. Inst. Mech. Eng., Part A, 226(1), pp. 137–150. [CrossRef]
Kurokawa, J. , Kajigaya, A. , Matusi, J. , and Imamura, H. , 2000, “ Suppression of Swirl in a Conical Diffuser by Use of J-Groove,” 20th IAHR Symposium on Hydraulic Machinery and Systems (IAHR), Charlotte, NC, Aug. 6–9, Paper No. DY-01.
Kurokawa, J. , Imamura, H. , and Choi, Y.-D. , 2010, “ Effect of J-Groove on the Suppression of Swirl Flow in a Conical Diffuser,” ASME J. Fluids Eng., 132(7), p. 071101. [CrossRef]
Pappilon, B. , Sabourin, M. , Couston, M. , and Deschenes, C. , 2002, “ Methods for Air Admission in Hydro Turbines,” 21st IAHR Symposium on Hydraulic Machinery and Systems (IAHR), F. Avellan, G. D. Ciocan, and S. Kvicinsky, eds., Lausanne, Switzerland, Sept. 9–12, pp. 1–6.
Kjeldsen, M. , Olsen, K. , Nielsen, T. , and Dahlhaug, O. , 2006, “ Water Injection for the Mitigation of Draft Tube Pressure Pulsations,” 1st IAHR International Meeting of Working Group on Cavitation and Dynamic Problems in Hydraulic Machinery and Systems, Barcelona, Spain, pp. 1–11.
Susan-Resiga, R. , Vu, T. C. , Muntean, S. , Ciocan, G. D. , and Nennemann, B. , 2006, “ Jet Control of the Draft Tube in Francis Turbines at Partial Discharge,” 23rd IAHR Symposium on Hydraulic Machinery and Systems (IAHR), Yokohama, Japan, Oct. 17–21, Paper No. F192.
Kirschner, O. , Schmidt, H. , Ruprecht, A. , Mader, R. , and Meusburger, P. , 2010, “ Experimental Investigation of Vortex Control With an Axial Jet in the Draft Tube of a Model Pump-Turbine,” IOP Conf. Ser.: Earth Environ. Sci., 12(1), p. 012092. [CrossRef]
Oberleithner, K. , Terhaar, S. , Rukes, L. , and Paschereit, C. O. , 2013, “ Why Non-Uniformity Density Suppresses the Precessing Vortex Core,” ASME J. Eng. Gas Turbines Power, 135(12), p. 121506. [CrossRef]
Bosioc, A. I. , Susan-Resiga, R. , Muntean, S. , and Tanasa, C. , 2012, “ Unsteady Pressure Analysis of a Swirling Flow With Vortex Rope and Axial Water Injection in a Discharge Cone,” ASME J. Fluids Eng., 134(8), p. 081104. [CrossRef]
Muntean, S. , Susan-Resiga, R. F. , and Bosioc, A. I. , 2009, “ Numerical Investigation of the Jet Control Method for Swirling Flow With Precessing Vortex Rope,” 3rd IAHR International Meeting of the Workgroup on Cavitation and Dynamic Problems in Hydraulic Machinery and Systems (IAHR), Brno, Czech Republic, Oct. 14–16, Paper No. B2.
Bosioc, A. , Tanasa, C. , Muntean, S. , and Susan-Resiga, R. , 2009, “ 2D LDV Measurements and Comparison With Axisymmetric Flow Analysis of Swirling Flow in a Simplified Draft Tube,” 3rd IAHR International Meeting of the Workgroup on Cavitation and Dynamic Problems in Hydraulic Machinery and Systems, Brno, Czech Republic, Paper No. P6.
Nishi, M. , Kubota, T. , Matsunaga, S. , and Senoo, Y. , 1980, “ Study on Swirl Flow and Surge in an Elbow Type Draft Tube,” 10th IAHR Symposium on Hydraulic Machinery, Equipment and Cavitation (IAHR), Tokyo, Japan, Vol. 1, pp. 557–568.
Nishi, M. , and Liu, S. H. , 2013, “ An Outlook on the Draft-Tube-Surge Study,” Int. J. Fluid Mach. Syst., 6(1), pp. 33–48. [CrossRef]
Bienkiewicz, B. , Ham, H. J. , Sun, Y. , 1993, “ Proper Orthogonal Decomposition of Roof Pressure,” J. Wind Eng. Ind. Aerodyn., 50, pp. 193–202. [CrossRef]
Lumley, J. L. , 1967, “ The Structure of Inhomogeneous Turbulence,” Atmospheric Turbulence and Wave Propagation, A. I. Yaglom and I. V. Tatarski , eds., Nauka, Moscow, Russia.
Berkooz, G. , Holmes, P. , and Lumley, J. L. , 1993, “ The Proper Orthogonal Decomposition in the Analysis of Turbulent Flows,” Annu. Rev. Fluid Mech., 25(1), pp. 539–575. [CrossRef]
Holmes, P. , Lumley, J. L. , Berkooz, G. , and Rowley, C. W. , 2012, Turbulence, Coherent Structures, Dynamical Systems and Symmetry, 2nd ed., Cambridge University Press, Cambridge, UK.
Grinberg, L. , Yakhot, A. , and Karniadakis, G. E. , 2009, “ Analyzing Transient Turbulence in a Stenosed Carotid Artery by Proper Orthogonal Decomposition,” Ann. Biomed. Eng., 37(11), pp. 2200–2217. [CrossRef] [PubMed]
Sirovich, L. , 1987, “ Turbulence and the Dynamics of Coherent Structures—Part I: Coherent Structures,” Q. Appl. Math., 45(3), pp. 561–571. [CrossRef]
Lumley, J. L. , 1970, Stochastic Tools in Turbulence, Academic Press, New York.
Anton, A. , Creţu, V. , Ruprecht, A. , and Muntean, S. , 2013, “ Traffic Replay Compression (TRC): A Highly Efficient Method for Handling Parallel Numerical Simulation Data,” Proc. Rom. Acad., Ser. A, 14(4), pp. 385–392.
Jerri, A. J. , 1977, “ The Shannon Sampling Theorem—Its Various Extensions and Applications: A Tutorial Review,” Proc. IEEE, 65(11), pp. 1565–1596. [CrossRef]
Susan-Resiga, R. , and Muntean, S. , 2008, “ Decelerated Swirling Flow Control in the Discharge Cone of Francis Turbines,” 4th International Symposium on Fluid Machinery and Fluid Mechanics (ISFMFE), Beijing, China, Nov. 24–27, Paper No. IL-18.
Susan-Resiga, R. , Muntean, S. , Tanasa, C. , and Bosioc, A. I. , 2008, “ Hydrodynamic Design and Analysis of a Swirling Flow Generator,” 4th German–Romanian Workshop on Turbomachinery Hydrodynamics (GRoWTH), Stuttgart, Germany, June 12–15, pp. 1–16.
Bosioc, A. , Susan-Resiga, R. F. , and Muntean, S. , 2008, “ Design and Manufacturing of a Convergent-Divergent Test Section for Swirling Flow Apparatus,” 4th German–Romanian Workshop on Turbomachinery Hydrodynamics (GRoWTH), Stuttgart, Germany, June 12–15, pp. 1–15.
Susan-Resiga, R. , Muntean, S. , Bosioc, A. , Stuparu, A. , Miloş, T. , Baya, A. , Bernad, S. , and Anton, L. E. , 2007, “ Swirling Flow Apparatus and Test Rig for Flow Control in Hydraulic Turbines Discharge Cone,” 2nd IAHR International Meeting of the Workgroup on Cavitation and Dynamics Problems in Hydraulic Machinery and Systems (IAHR), Timisoara, Romania, Oct. 24–26, pp. 203–216.
Tanasa, C. , Susan-Resiga, R. , Bosioc, A. , and Muntean, S. , 2010, “ Mitigation of Pressure Fluctuations in the Discharge Cone of Hydraulic Turbines Using Flow-Feedback,” IOP Conf. Ser.: Earth Environ. Sci., 12(1), p. 012067. [CrossRef]
Tanasa, C. , Susan-Resiga, R. , Muntean, S. , and Bosioc, A. I. , 2013, “ Flow-Feedback Method for Mitigating the Vortex Rope in Decelerated Swirling Flows,” ASME J. Fluids Eng., 135(6), p. 061304. [CrossRef]
Muntean, S. , Nilsson, H. , and Susan-Resiga, R. , 2009, “ 3D Numerical Analysis of the Unsteady Turbulent Swirling Flow in a Conical Diffuser Using FLUENT and OpenFOAM,” 3rd IAHR International Meeting of the Workgroup on Cavitation and Dynamic Problems in Hydraulic Machinery and Systems, Brno, Czech Republic, Oct. 14–16, Paper No. C4.
Petit, O. , Bosioc, A. I. , Nilsson, H. , Muntean, S. , and Susan-Resiga, R. , 2011, “ Unsteady Simulations of the Flow in a Swirl Generator Using OpenFOAM,” Int. J. Fluid Mach. Syst., 4(1), pp. 199–208. [CrossRef]
Bergman, O. , 2010, “ Numerical Investigation of the Flow in a Swirl Generator Using OpenFOAM,” M.S. thesis, Chalmers University of Technology, Gothenburg, Sweden.
Petit, O. , 2012, “ Towards Full Predictions of the Unsteady Incompressible Flow in Rotating Machines Using OpenFOAM,” Ph.D. thesis, Chalmers University of Technology, Gothenburg, Sweden.
Ojima, A. , and Kamemoto, K. , 2010, “ Vortex Method Simulation of Three-Dimensional and Unsteady Vortices in a Swirling Flow Apparatus Experimented in Politehnica University of Timisoara,” IOP Conf. Ser.: Earth Environ. Sci., 12(1), p. 012065. [CrossRef]
Stefan, D. , Rudolf, P. , Muntean, S. , and Susan-Resiga, R. F. , 2012, “ Structure of Flow Fields Downstream of Two Different Swirl Generators,” 18th International Conference of Engineering Mechanics (ICEM), Svratka, Czech Republic, May 14–17, pp. 1331–1342.
Fluent, 2006, “ Gambit 2.0 User's Guide,” Fluent Inc., Lebanon, NH.
Ansys, 2011, “ ANSYS FLUENT 14.0 User's Guide,” Ansys Inc., Canonsburg, PA.
Jawarneh, A. M. , and Vatistas, G. H. , 2006, “ Reynolds Stress Model in the Prediction of Confined Turbulent Swirling Flows,” ASME J. Fluids Eng., 128(6), pp. 1377–1382. [CrossRef]
Rudolf, P. , and Skoták, A. , 2001, “ Unsteady Flow in the Draft Tube With Elbow—Part B: Numerical Investigation,” 10th International Meeting of IAHR Workgroup on Cavitation and Dynamic Problems in Hydraulic Machinery and Systems, Trondheim, Norway, pp. 52–62.
Gibson, M. M. , and Launder, B. E. , 1978, “ Ground Effects on Pressure Fluctuations in the Atmospheric Boundary Layer,” J. Fluid Mech., 86(3), pp. 491–511. [CrossRef]
Fu, S. , Launder, B. E. , and Leschziner, M. A. , 1987, “ Modeling Strongly Swirling Recirculating Jet Flow With Reynolds-Stress Transport Closures,” Sixth Symposium on Turbulent Shear Flows, Toulouse, France, Sept. 7–9, pp. 1–6.
Launder, B. E. , 1989, “ Second-Moment Closure and Its Use in Modeling Turbulent Industrial Flows,” Int. J. Numer. Methods Fluids, 9(8), pp. 963–985. [CrossRef]
Muntean, S. , Ruprecht, A. , and Susan-Resiga, R. , 2005, “ A Numerical Investigation of the 3D Swirling Flow in a Pipe With Constant Diameter—Part 1: Inviscid Computation,” Sci. Bull. Politeh. Univ. Timisoara, Trans. Mech., 50(64), pp. 77–86.
Muntean, S. , Buntić, I. , Ruprecht, A. , and Susan-Resiga, R. , 2005, “ A Numerical Investigation of the 3D Swirling Flow in a Pipe With Constant Diameter—Part 2: Turbulent Computation,” Sci. Bull. Politeh. Univ. Timisoara, Trans. Mech., 50(64), pp. 87–96.
Celik, I. B. , Ghia, U. , Roache, P. J. , and Freitas, C. J. , 2008, “ Procedure for Estimation and Reporting of Uncertainty Due to Discretization in CFD Applications,” ASME J. Fluids Eng., 130(7), p. 078001. [CrossRef]
Roache, P. J. , 2003, “ Conservatism of the GCI in Finite Volume Computations on Steady State Fluid Flow and Heat Transfer,” ASME J. Fluids Eng., 125(4), pp. 731–732. [CrossRef]
Roache, P. J. , Ghia, K. N. , and White, F. M. , 1986, “ Editorial Policy Statement on the Control of Numerical Accuracy,” ASME J. Fluids Eng., 108(1), p. 2. [CrossRef]
MathWorks, 2010, “ MATLAB 7.10 User's Guide,” MathWorks Inc., Natick, MA.
Houde, S. , Iliescu, M. S. , Fraser, R. , Lemay, S. , Ciocan, G. D. , and Deschenes, C. , 2011, “ Experimental and Numerical Analysis of the Cavitating Part Load Vortex Dynamics of Low-Head Hydraulic Turbines,” ASME Paper No. AJK2011-33006.
Mayer, K. E. , Pedersen, J. M. , and Özcan, O. , 2007, “ A Turbulent Jet in Crossflow Analysed With Proper Orthogonal Decomposition,” J. Fluid Mech., 583, pp. 199–227. [CrossRef]
Andrianne, T. , Razak, N. A. , and Dimitriadis, G. , 2011, “ Flow Visualization and Proper Orthogonal Decomposition of Aeroelastic Phenomena,” Wind Tunnels, S. Okamoto , ed., InTech, Rijeka, Croatia.
Kellnerová, R. , Kukačka, L. , Juračková, K. , Uruba, V. , and Jaňour, Z. , 2012, “ PIV Measurement of Turbulent Flow Within a Street Canyon: Detection of Coherent Motion,” J. Wind Eng. Ind. Aerodyn., 104–106, pp. 302–313. [CrossRef]
Oberleithner, K. , Sieber, M. , Nayeri, C. N. , Paschereit, C. O. , Petz, C. , Hege, H.-C. , Noack, B. R. , and Wygnanski, I. , 2011, “ Three-Dimensional Coherent Structures in a Swirling Jet Undergoing Vortex Breakdown: Stability Analysis and Empirical Mode Construction,” J. Fluid Mech., 679, pp. 383–414. [CrossRef]
Perrin, R. , Braza, M. , Cid, E. , Cazin, S. , Barthet, A. , Servain, A. , Mockett, C. , and Thiele, F. , 2007, “ Obtaining Phase Averaged Turbulence Properties in the Near Wake of Circular Cylinder at High Reynolds Number Using POD,” Exp. Fluids, 43(2), pp. 341–355. [CrossRef]
Oberleithner, K. , Sieber, M. , Nayeri, C. N. , and Paschereit, C. O. , 2011, “ On the Control of Global Modes in Swirling Jet Experiments,” J. Phys.: Conf. Ser., 318(3), p. 032050. [CrossRef]
Tutkun, M. , Johansson, P. B. V. , and George, W. K. , 2008, “ Three-Component Vectorial Proper Orthogonal Decomposition of Axisymmetric Wake Behind a Disc,” AIAA J., 46(5), pp. 1118–1134. [CrossRef]
Citriniti, J. H. , and George, W. K. , 2000, “ Reconstruction of the Global Velocity Field in the Axisymmetric Mixing Layer Utilizing the Proper Orthogonal Decomposition,” J. Fluid Mech., 418, pp. 137–166. [CrossRef]
Rudolf, P. , and Štefan, D. , 2012, “ Decomposition of the Swirling Flow Field Downstream of Francis Turbine Runner,” IOP Conf. Ser.: Earth Environ. Sci., 15(6), p. 062008. [CrossRef]
Ciocan, G. D. , Iliescu, S. M. , Vu, T. C. , Nennemann, B. , and Avellan, F. , 2007, “ Experimental Study and Numerical Simulation of the FLINDT Draft Tube Rotating Vortex,” ASME J. Fluids Eng., 129(2), pp. 146–158. [CrossRef]
Stefan, D. , and Rudolf, P. , 2013, “ Computational Fluid Dynamic Study of the Flow Downstream of the Swirl Generator Using Large Eddy Simulation,” HPC-EUROPA 2, Stuttgart, Germany, pp. 1–2.

Figures

Grahic Jump Location
Fig. 1

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

Grahic Jump Location
Fig. 2

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

Grahic Jump Location
Fig. 3

Three-dimensional computational domain of the convergent–divergent parts

Grahic Jump Location
Fig. 4

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

Grahic Jump Location
Fig. 5

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

Grahic Jump Location
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

Grahic Jump Location
Fig. 7

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

Grahic Jump Location
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

Grahic Jump Location
Fig. 9

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

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
Fig. 12

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

Grahic Jump Location
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

Grahic Jump Location
Fig. 14

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

Grahic Jump Location
Fig. 15

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

Grahic Jump Location
Fig. 16

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

Grahic Jump Location
Fig. 17

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

Grahic Jump Location
Fig. 18

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

Grahic Jump Location
Fig. 19

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

Grahic Jump Location
Fig. 20

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

Grahic Jump Location
Fig. 21

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

Grahic Jump Location
Fig. 22

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

Grahic Jump Location
Fig. 23

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

Grahic Jump Location
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

Grahic Jump Location
Fig. 25

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

Grahic Jump Location
Fig. 26

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

Grahic Jump Location
Fig. 27

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

Grahic Jump Location
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

Grahic Jump Location
Fig. 29

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

Grahic Jump Location
Fig. 30

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

Grahic Jump Location
Fig. 31

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

Grahic Jump Location
Fig. 32

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

Grahic Jump Location
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)

Grahic Jump Location
Fig. 34

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

Grahic Jump Location
Fig. 35

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

Grahic Jump Location
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

Grahic Jump Location
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

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In