Hostname: page-component-745bb68f8f-kw2vx Total loading time: 0 Render date: 2025-01-09T21:54:47.287Z Has data issue: false hasContentIssue false
  • English
  • Français

Cavitation in the rotational structures of a turbulent wake

Published online by Cambridge University Press:  26 April 2006

B. Belahadji ,
J. P. Franc  and
J. M. Michel
B. Belahadji
Affiliation:
Laboratoire des Écoulements Géophysiques et Industriels – Institut de Mécanique de Grenoble, Institut National Polytechnique de Grenoble et Université Joseph Fourier, BP 53, 38041 Grenoble Cedex 9, France
J. P. Franc
Affiliation:
Laboratoire des Écoulements Géophysiques et Industriels – Institut de Mécanique de Grenoble, Institut National Polytechnique de Grenoble et Université Joseph Fourier, BP 53, 38041 Grenoble Cedex 9, France
J. M. Michel
Affiliation:
Laboratoire des Écoulements Géophysiques et Industriels – Institut de Mécanique de Grenoble, Institut National Polytechnique de Grenoble et Université Joseph Fourier, BP 53, 38041 Grenoble Cedex 9, France
Get access Rights & Permissions [Opens in a new window]

Abstract

Experiments show that cavitation, if moderately developed, makes three kinds of vortical coherent structures visible inside the turbulent wake of a two-dimensional obstacle: Bénard–Kármán vortices, streamwise three-dimensional vortices and finally the vortices which appear on the borders of the very near wake. The latter, which are called here near-wake vortices, result by successive pairing in the first ones and there is some indication that they are also the origin of streamwise vortices. Cavitation is not a passive agent of visualization, as can be established on the basis of fundamental arguments, and it reacts with the flow as soon as it appears; when it is developed, it breaks the connection between the elongation rate and the vorticity rate of the vortex filaments. Then the subsequent evolution of a cavitating vortex and its final implosion are rather complicated. Despite its active character, cavitation in rotational structures, if properly interpreted, can give information of interest on the basic non-cavitating turbulent flow. By adapting a simple model due to Kermeen & Parkin (1957) and Arndt (1976), and counting near-wake vortices, it is possible to accurately predict the conditions of cavitation inception: consideration of coherent rotational structures is probably the best approach to explain, in an almost deterministic way, the large difference between the absolute value of the mean pressure coefficient at the obstacle base and the incipient cavitation number.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 287 , 25 March 1995 , pp. 383 - 403
Copyright
© 1995 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Arndt, R. E. A. 1976 Semi-empirical analysis of cavitation in the wake of a sharp-edged disk. Trans. ASME I: J. Fluids Engng 98, 560–562.Google Scholar
Arndt, R. E. A., Arakeri, V. H. & Higuchi, H. 1991 Some observations of tip-vortex cavitation. J. Fluid Mech. 229, 269–289.Google Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Belahadji, B. 1993 Cavitation dans le sillage turbulent d'un obstacle. PhD thesis, Université Joseph Fourier, Grenoble.
Belahadji, B., Franc, J. P. & Michel, J. M. 1993 Cavitation naissante dans un sillage turbulent et tourbillons de couche limite. Quatrième J. Hydrodyn. Nantes, Proc., pp. 117–120. Inst. Français du Pétrole.
Berger, E. & Wille, R. 1972 Periodic flow phenomena. Ann. Rev. Fluid Mech. 4, 313–340.Google Scholar
Bernal, L. P. & Roshko, A. 1986 Streamwise vortex structure in plane mixing layers. J. Fluid Mech. 170, 499–525.Google Scholar
Briançon-Marjollet, L., Franc, J. P. & Michel, J. M. 1990 Transient bubbles interacting with an attached cavity and the boundary layer. J. Fluid Mech. 218, 355–376.Google Scholar
Briançon-Marjollet, L. & Michel, J. M. 1990 The hydrodynamic tunnel of I.M.G.: former and recent equipment. Trans. ASME I: J. Fluids Engng 112, 338–342.Google Scholar
Comte, P., Lesieur, M. & Lamballais, E. 1992 Large- and small-scale stirring of vorticity and a passive scalar in a 3-D temporal mixing layer. Phys. Fluids A 4, 2761–2778.Google Scholar
Corcos, G. M. & Lin, S. J. 1984 The mixing layer: deterministic models of a turbulent flow. Part 2. The origin of the three-dimensional motion. J. Fluid Mech. 139, 67–95.Google Scholar
Douady, S., Couder, Y. & Brachet, M. E. 1991 Direct observation of the intermittency of intense vorticity filaments in turbulence. Phys. Rev. Lett. 67, 983–986.Google Scholar
Drazin, P. G. & Reid, W. H. 1981 Hydrodynamic Stability. Cambridge University Press.
Filali, E. G. 1993 Analyse des tourbillons cavitants formés dans le sillage d'un coin. Institut National Polytechnique de Grenoble, DEA Rep.
Franc, J. P. 1982 Étude de cavitation, tome 2: Sillage cavitant d'obstacles épais. PhD thesis, Institut National Polytechnique de Grenoble, pp. 66–121.
Franc, J. P., Michel, J. M. & Lesieur, M. 1982 Structures rotationnelles bi et tri-dimensionnelles dans un sillage cavitant. C.R. Acad. Sci. Paris 295, 773–777.Google Scholar
Fruman, D. H., Dugué, C., Pauchet, A., Cerrutti, P. & Briançon-marjollet, L. 1992 Tip vortex roll-up and cavitation. Proc. ONR Cong. Seoul, Korea. ONR.
Genoux, P. & Chahine, G. L. 1983 Équilibre statique et dynamique d'un tore de vapeur tourbillonnaire. J. Méc. Théor. Appl. 2, 829–857.Google Scholar
Jimenez, J., Wray, A. A., Saffman, P. G. & Rogallo, R. S. 1993 The structure of intense vorticity in isotropic turbulence. J. Fluid Mech. 255, 65–90.Google Scholar
Katz, J. & O'Hern, T. J. 1986 Cavitation in large scale shear flows. Trans. ASME I: J. Fluids Engng 108, 373–376.Google Scholar
Kermeen, R. W. & Parkin, B. R. 1957 Incipient cavitation and wake flow behind sharp-edged disks. Calif. Inst. of Tech. Engng Div. Rep. 85-4.
Knapp, R. T., Daily, J. W. & Hammitt, F. G. 1970 Cavitation. McGraw Hill.
Kourta, A., Boisson, H. C., Chassaing, P. & Ha Minh, H. 1987 Nonlinear interaction and the transition to turbulence in the wake of a circular cylinder. J. Fluid Mech. 181, 141–161.Google Scholar
Lasheras, J. C., Cho, J. S. & Maxworthy, T. 1986 On the origin and evolution of streamwise vortical structures in a plane, free shear layer. J. Fluid Mech. 172, 231–258.Google Scholar
Lasheras, J. C. & Choi, H. 1988 Three-dimensional instability of a plane free shear layer: an experimental study of the formation and evolution of streamwise vortices. J. Fluid Mech. 189, 53–86.Google Scholar
Lesieur, M. 1993 Turbulence in Fluids, 2nd edn. Kluwer.
Liepman, D. & Gharib, M. 1992 The role of streamwise vorticity in the near-field entrainment of round jets. J. Fluid Mech. 245, 643–668.Google Scholar
Ligneul, P. 1989 Theoretical tip vortex cavitation inception threshold. Eur. J. Mech. B Fluids 8, 495–521.Google Scholar
Lin, S. J. & Corcos, G. M. 1984 The mixing layer: deterministic models of a turbulent flow. Part 3. The effect of a plane strain on the dynamics of streamwise vortices. J. Fluid Mech. 141, 139–178.Google Scholar
Meiburg, E. & Lasheras, J. C. 1988 Experimental and numerical investigation of the three-dimensional transition in plane wakes. J. Fluid Mech. 190, 1–37.Google Scholar
Méatais, O. & Lesieur, M. 1992 Spectral large-eddy simulation of isotropic and stably stratified turbulence. J. Fluid Mech. 239, 157–194.Google Scholar
Milne-Thomson, L. M. 1968 Theoretical Hydrodynamic, 5th edn, pp. 377–380. Macmillan.
Pauchet, J., Retailleau, A. & Woillez, J. 1992 The prediction of cavitation inception in turbulent water jets. Cavitation and Multiphase Flow Forum, ASME FED, vol. 135, pp. 149–158.Google Scholar
Ramamurthy, A. S. & Balachandar, R. 1990 The near wake characteristics of cavitating bluff sources. Trans. ASME I: J. Fluids Engng 112, 492–495.Google Scholar
Roshko, A. 1954 On the development of turbulent wakes from vortex streets. NACA Rep. 1191.
Schlichting, H. 1987 Boundary layer Theory. McGraw-Hill.
Silvestrini, J. H., Comte, P. & Lesieur, M. 1994 Large-eddy simulation of periodic incompressible mixing layers. Preprint LEGI-IMG (to be submitted to Eur. J. Mech.).
Soyama, H., Kato, H. & Oba, R. 1992 Cavitation observations of severely erosive vortex arising in a centrifugal pump. Proc. Intl Conf. on Cavitation, I. Mech. E., Cambridge, pp. 103–110.
Young, A. J. & Holl, W. J. 1966 Effects of cavitation on periodic wakes behind symmetric wedges. Trans. ASME D: J. Basic Engng, 163–176.