Advertisement

Experiments in Fluids

, 55:1849 | Cite as

Mind the gap: a new insight into the tip leakage vortex using stereo-PIV

  • Matthieu DreyerEmail author
  • Jean Decaix
  • Cécile Münch-Alligné
  • Mohamed Farhat
Research Article

Abstract

The tip leakage vortex (TLV), which develops in the clearance between the rotor and the stator of axial hydro turbines, has been studied for decades. Yet, many associated phenomena are still not understood. For instance, it remains unclear how the clearance size is related to the occurrence of cavitation in the vortex, which can lead to severe erosion. Experiments are here carried out on the influence of the clearance size on the tip vortex structure in a simplified case study. A NACA0009 hydrofoil is used as a generic blade in a water tunnel while the clearance between the blade tip and the wall is varied. The 3D velocity fields are measured using Stereo Particle Image Velocimetry (SPIV) in three planes located downstream of the hydrofoil for different values of the upstream velocity, the incidence angle and a large number of tip clearances. The influence of the flow conditions on the structure of the TLV is described through changes in the vortex intensity, core axial flow, vortex center position and wandering motion amplitude. Moreover, high-speed visualizations are used to highlight the vortex core trajectory and clearance flow alteration, turning into a wall jet as the tip clearance is reduced. The measurements clearly reveal the existence of a specific tip clearance for which the vortex strength is maximum and most prone to generating cavitation.

Keywords

Vortex Cavitation Vortex Core Inlet Velocity Vortex Center 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols

\(c\)

Hydrofoil chord

\(h\)

Maximum foil thickness

\(W_{\infty }\)

Inlet velocity

\(p_{\infty }\)

Inlet pressure

\(x,y,z\)

Cartesian coordinates

\(u,v,w\)

Spanwise, transverse and axial velocity

\(x_\text {c}, y_\text {c}\)

Vortex center coordinates

\(r_{\rm c}\)

Vortex core radius

\(Re_\text {c}\)

Reynolds number \(({W_{\infty }c}/{\nu })\)

\(\alpha\)

Incidence angle

\(\tau\)

Normalized tip clearance \((gap/h)\)

\(\omega\)

Vorticity

\(\varGamma\)

Circulation

\(\varGamma ^*\)

Normalized circulation \((\varGamma /W_{\infty } r_{\rm c})\)

\(\varGamma ^*_{\infty }\)

\(\varGamma ^*\) at \(\tau\) = 2

\(C_{\rm p_{\rm min}}\)

Pressure coefficient in the vortex center \(\left(\frac{p(r\,=\,0)\,-\,p_{\infty }}{\frac{1}{2}\rho W_{\infty }^2}\right)\)

Notes

Acknowledgments

The present study was performed within the framework of the HydroNet project (hydronet.epfl.ch). The authors would like to thank the Competence Center of Energy and Mobility (CCEM) and swisselectric research for their financial support.

Supplementary material

348_2014_1849_MOESM1_ESM.mpg (1.5 mb)
Supplementary material 1 (mpg 1522 KB)
348_2014_1849_MOESM2_ESM.mpg (1.8 mb)
Supplementary material 2 (mpg 1840 KB)
348_2014_1849_MOESM3_ESM.mpg (2.4 mb)
Supplementary material 3 (mpg 2430 KB)
348_2014_1849_MOESM4_ESM.mpg (3 mb)
Supplementary material 4 (mpg 3104 KB)
348_2014_1849_MOESM5_ESM.mpg (2.7 mb)
Supplementary material 5 (mpg 2760 KB)
348_2014_1849_MOESM6_ESM.mpg (3.6 mb)
Supplementary material 6 (mpg 3720 KB)
348_2014_1849_MOESM7_ESM.mpg (3.6 mb)
Supplementary material 7 (mpg 3658 KB)
348_2014_1849_MOESM8_ESM.mpg (3.2 mb)
Supplementary material 8 (mpg 3260 KB)
348_2014_1849_MOESM9_ESM.mpg (3.3 mb)
Supplementary material 9 (mpg 3402 KB)

References

  1. Arndt RE (2002) Cavitation in vortical flows. Annu Rev Fluid Mech 34(1):143–175CrossRefMathSciNetGoogle Scholar
  2. Ausoni P, Zobeiri A, Avellan F, Farhat M (2012) The effects of a tripped turbulent boundary layer on vortex shedding from a blunt trailing edge hydrofoil. J Fluids Eng 134(5):051207–051207. doi: 10.1115/1.4006700 CrossRefGoogle Scholar
  3. Batchelor GK (1964) Axial flow in trailing line vortices. J Fluid Mech 20:645–658. doi: 10.1017/S0022112064001446 CrossRefzbMATHMathSciNetGoogle Scholar
  4. Bhagwat MJ, Leishman JG (2002) Generalized viscous vortex model for application to free-vortex wake and aeroacoustic calculations. In: Annual forum proceedings-American Helicopter Society. American Helicopter Society, Inc, vol 58, pp 2042–2057Google Scholar
  5. Bhagwat MJ, Ramasamy M (2012) Effect of tip vortex aperiodicity on measurement uncertainty. Exp Fluids 53(5):1191–1202CrossRefGoogle Scholar
  6. Bouillot P, Brina O, Ouared R, Lovblad K, Pereira VM, Farhat M (2014) Multi-time-lag PIV analysis of steady and pulsatile flows in a sidewall aneurysm. Exp Fluids 55(6):1–11CrossRefGoogle Scholar
  7. Boulon O, Callenaere M, Franc JP, Michel JM (1999) An experimental insight into the effect of confinement on tip vortex cavitation of an elliptical hydrofoil. J Fluid Mech 390:1–23CrossRefzbMATHGoogle Scholar
  8. Chang NA, Yakushiji R, Dowling DR, Ceccio SL (2007) Cavitation visualization of vorticity bridging during the merger of co-rotating line vortices. Phys Fluids (1994-present) 19(5):058106. doi: 10.1063/1.2732264 CrossRefGoogle Scholar
  9. Chen G, Marble F, Greitzer E, Tan C (1991) Similarity analysis of compressor tip clearance flow structure. J Turbomach 113(2):260–269CrossRefGoogle Scholar
  10. Del Pino C, Parras L, Felli M, Fernandez-Feria R (2011) Structure of trailing vortices: comparison between particle image velocimetry measurements and theoretical models. Phys Fluids 23(013):602Google Scholar
  11. Devenport WJ, Rife MC, Liapis SI, Follin GJ (1996) The structure and development of a wing-tip vortex. J Fluid Mech 312:67–106. doi: 10.1017/S0022112096001929 CrossRefMathSciNetGoogle Scholar
  12. Doligalski T, Smith C, Walker J (1994) Vortex interactions with walls. Annu Rev Fluid Mech 26(1):573–616CrossRefMathSciNetGoogle Scholar
  13. Fabre D, Fontane J, Brancher P, Le Dizes S, Roy C, Leweke T, Fernandez-Feria R, Parras L, del Pino C (2008) Synthesis on vortex meandering. Technical report, STREP project no. AST4-CT-2005-012238Google Scholar
  14. Farrell K, Billet M (1994) A correlation of leakage vortex cavitation in axial-flow pumps. J Fluids Eng 116(3):551–557CrossRefGoogle Scholar
  15. Gopalan S, Katz J, Liu HL (2002) Effect of gap size on tip leakage cavitation inception, associated noise and flow structure. J Fluids Eng 124(4):994–1004CrossRefGoogle Scholar
  16. Graftieaux L, Michard M, Grosjean N (2001) Combining PIV, POD and vortex identification algorithms for the study of unsteady turbulent swirling flows. Meas Sci Technol 12:1422–1429. doi: 10.1088/0957-0233/12/9/307 CrossRefGoogle Scholar
  17. Green SI (1995) Fluid vortices: fluid mechanics and its applications, vol 30. Springer, BerlinzbMATHGoogle Scholar
  18. Iungo G, Skinner P, Buresti G (2009) Correction of wandering smoothing effects on static measurements of a wing-tip vortex. Exp Fluids 46(3):435–452. doi: 10.1007/s00348-008-0569-2 CrossRefGoogle Scholar
  19. Laborde R, Mory M, Chantrel P (1997) Tip clearance and tip vortex cavitation in an axial flow pump. J Fluids Eng 119(3):680–685CrossRefGoogle Scholar
  20. Le Guen A, Viot X, Billard JY, Fruman D (1997) Fluctuations des vitesses et biais spatial dans le tourbillon marginal. Sixièmes Journées de l’Hydrodynamique 317–328Google Scholar
  21. Lee T, Pereira J (2010) Nature of wakelike and jetlike axial tip vortex flows. J Aircr 47(6):1946–1954CrossRefGoogle Scholar
  22. McCormick B (1962) On cavitation produced by a vortex trailing from a lifting surface. J Fluids Eng 84(3):369–378Google Scholar
  23. Miorini RL, Wu H, Katz J (2012) The internal structure of the tip leakage vortex within the rotor of an axial waterjet pump. J Turbomach 134(3):031,018CrossRefGoogle Scholar
  24. Moore DW, Saffman PG (1973) Axial flow in laminar trailing vortices. Proc R Soc Lond Ser A Math Phys Sci 333(1595):491–508CrossRefzbMATHGoogle Scholar
  25. Müller A, Dreyer M, Andreini N, Avellan F (2013) Draft tube discharge fluctuation during self-sustained pressure surge: fluorescent particle image velocimetry in two-phase flow. Exp Fluids 54(4):1–11. doi: 10.1007/s00348-013-1514-6 CrossRefGoogle Scholar
  26. Pasche S, Gallaire F, Dreyer M, Farhat M (2014) Obstacle-induced spiral vortex breakdown. Exp Fluids 55(8):1–11. doi: 10.1007/s00348-014-1784-7 CrossRefGoogle Scholar
  27. Prasad AK (2000) Stereoscopic particle image velocimetry. Exp Fluids 29(2):103–116. doi: 10.1007/s003480000143 CrossRefGoogle Scholar
  28. Roussopoulos K, Monkewitz PA (2000) Measurements of tip vortex characteristics and the effect of an anti-cavitation lip on a model Kaplan turbine blade. Flow Turbul Combust 64(2):119–144CrossRefzbMATHGoogle Scholar
  29. Spalart PR (1998) Airplane trailing vortices. Annu Rev Fluid Mech 30(1):107–138CrossRefMathSciNetGoogle Scholar
  30. Vatistas GH, Kozel V, Mih W (1991) A simpler model for concentrated vortices. Exp Fluids 11(1):73–76CrossRefGoogle Scholar
  31. van der Wall BG, Richard H (2006) Analysis methodology for 3C-PIV data of rotary wing vortices. Exp Fluids 40:798–812. doi: 10.1007/s00348-006-0117-x CrossRefGoogle Scholar
  32. Wang Y, Devenport WJ (2004) Wake of a compressor cascade with tip gap, part 2: effects of endwall motion. AIAA J 42(11):2332–2340CrossRefGoogle Scholar
  33. Westerweel J (2000) Theoretical analysis of the measurement precision in particle image velocimetry. Exp Fluids 29(1):S003–S012. doi: 10.1007/s003480070002 Google Scholar
  34. Wu H, Tan D, Miorini RL, Katz J (2011) Three-dimensional flow structures and associated turbulence in the tip region of a waterjet pump rotor blade. Exp Fluids 51(6):1721–1737. doi: 10.1007/s00348-011-1189-9 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Matthieu Dreyer
    • 1
    Email author
  • Jean Decaix
    • 2
  • Cécile Münch-Alligné
    • 2
  • Mohamed Farhat
    • 1
  1. 1.Laboratory for Hydraulic MachinesEcole polytechnique fédérale de LausanneLausanneSwitzerland
  2. 2.Institut Systèmes industrielsHES-SO Valais-WallisSionSwitzerland

Personalised recommendations