Physics of Fluids
Feedback | Help | Exit
Search:
   
 
 
 
Previous Article
Absolute and convective instabilities of an inviscid compressible mixing layer: Theory and applications
This study aims to examine the effect of compressibility on unbounded and parallel shear flow linear instabilities. This analysis is of interest for industrial, geophysical, and astrophysical flows. W...
Next Article
Centrifugal instabilities in curved compressible wakes
This investigation is concerned with the linear development of Görtler vortices in the high-Reynolds-number laminar compressible wake behind a flat plate which is aligned with the centerline of a...

Absolute and convective instability of cylindrical Couette flow with axial and radial flows

Phys. Fluids 21, 104102 (2009); doi:10.1063/1.3243976

Published 7 October 2009

You are not logged in to this journal. Log in

Denis Martinand,1 Eric Serre,1 and Richard M. Lueptow2
1LM2P2 UMR 6181, CNRS, Universités d'Aix-Marseille, IMT, La Jeté-Technopôle de Château-Gombert, 38 rue Frédéric Joliot-Curie, 13451 Marseille Cedex 20, France
2Department of Mechanical Engineering, Northwestern University, Evanston, Illinois 60208, USA
Imposing axial flow in the annulus and/or radial flow through the cylindrical walls in a Taylor–Couette system alters the stability of the flow. Theoretical methods and numerical simulations were used to determine the impact of imposed axial and radial flows, homogeneous in the axial direction, on the first transition of Taylor–Couette flow in the framework of convective and absolute instabilities. At low axial Reynolds numbers the convective instability is axisymmetric, but convective helical modes with an increasing number of helices having a helicity opposite that of the base flow dominate as the axial flow increases. The number of helices and the critical Taylor number are affected only slightly by the radial flow. The flow becomes absolutely unstable at higher Taylor numbers. Absolutely unstable axisymmetric modes occur for inward radial flows, while helical absolute instability modes having a helicity identical to that of the base flow occur at high enough axial Reynolds numbers for outward radial flow. ©2009 American Institute of Physics
History: Received 19 March 2009; accepted 8 September 2009; published 7 October 2009
Permalink: http://link.aip.org/link/?PHFLE6/21/104102/1
BUY THIS ARTICLE   (US$24)
Download PDF (1043 kB) View Cart

KEYWORDS and PACS

Keywords
PACS
  • 47.11.-j
    Computational methods in fluid dynamics
  • 47.20.-k
    Flow instabilities
  • 47.20.Qr
    Centrifugal flow instabilities
  • 47.27.te
    Turbulent convective heat transfer
  • 47.55.P-
    Buoyancy-driven flows; convection
  • YEAR: 2009

RELATED DATABASES


To view database links for this article,
you need to log in.
To view database links for this article,
you need to log in.

PUBLICATION DATA

ISSN:
1070-6631 (print)   1089-7666 (online)
Publisher:
AIP is a member of CrossRef AIP

REFERENCES (67)
View in Separate Window/Tab
For access to fully linked references, you need to log in. For access to fully linked references, you need to Log in.
  1. G. Beaudoin and M. Y. Jaffrin, “Plasma filtration in Couette flow membrane devices,” Artif. Organs 13, 43 (1989).
  2. R. M. Lueptow and A. Hajiloo, “Flow in a rotating membrane plasma separator,” Trans. Am. Soc. Artif. Intern. Organs 41, 182 (1995).
  3. K. Ohashi, K. Tashiro, F. Kushiya, T. Matsumoto, S. Yoshida, M. Endo, T. Horio, K. Osawa, and K. Sakai, “Rotation-induced Taylor vortex enhances filtrate flux in plasma separation,” Trans. Am. Soc. Artif. Intern. Organs 34, 300 (1988).
  4. G. Belfort, P. Mikulasek, J. M. Pimbley, and K. Y. Chung, “Diagnosis of membrane fouling using a rotating annular filter. 2. Dilute particule suspension of known particle size,” J. Membr. Sci. 77, 23 (1993).
  5. G. Belfort, J. M. Pimbley, A. Greiner, and K. Y. Chung, “Diagnosis of membrane fouling using a rotating annular filter. 1. Cell culture media,” J. Membr. Sci. 77, 1 (1993).
  6. B. Hallström and M. Lopez-Leiva, “Description of a rotating ultrafiltration module,” Desalination 24, 273 (1978).
  7. K. H. Kroner and V. Nissinen, “Dynamic filtration of microbial suspension using an axially rotating filter,” J. Membr. Sci. 36, 85 (1988).
  8. A. Margaritis and C. R. Wilke, “The rotor fermentor. I. Description of the apparatus power requirements and mass transfer characteristics,” Biotechnol. Bioeng. 20, 709 (1978).
  9. S. T. Wereley, A. Akonur, and R. M. Lueptow, “Particle-fluid velocities and fouling in rotating filtration of a suspension,” J. Membr. Sci. 209, 469 (2002).
  10. J. A. Schwille, D. Mitra, and R. M. Lueptow, “Design parameters for rotating filtration,” J. Membr. Sci. 204, 53 (2002).
  11. J. Kaye and E. C. Elgar, “Modes of adiabatic and diabatic fluid flow in an annulus with an inner rotating cylinder,” Trans. ASME 80, 753 (1958).
  12. S. Chandrasekhar, “The hydrodynamic instability of viscid flow between coaxial cylinders,” Proc. Natl. Acad. Sci. U.S.A. 46, 141 (1960).
  13. R. C. DiPrima, “The stability of a viscous fluid between rotating cylinders with an axial flow,” J. Fluid Mech. 9, 621 (1960).
  14. R. J. Donnelly and D. Fultz, “Experiments on the stability of spiral flow between rotating cylinders,” Proc. Natl. Acad. Sci. U.S.A. 46, 1150 (1960).
  15. K. W. Schwarz, B. E. Springlett, and R. J. Donnelly, “Modes of instability in spiral flow between rotating cylinders,” J. Fluid Mech. 20, 281 (1964).
  16. K. C. Chung and K. N. Astill, “Hydrodynamic instability of viscous flow between rotating coaxial cylinders with fully developed axial flow,” J. Fluid Mech. 81, 641 (1977).
  17. M. A. Hasoon and B. W. Martin, “The stability of a viscous axial flow in an annulus with a rotating inner cylinder,” Proc. R. Soc. London, Ser. A 352, 351 (1977).
  18. N. Gravas and B. W. Martin, “Instability of viscous axial flow in annuli having a rotating inner cylinder,” J. Fluid Mech. 86, 385 (1978).
  19. B. S. Ng and E. R. Turner, “On the linear stability of spiral flow between rotating cylinders,” Proc. R. Soc. London, Ser. A 382, 83 (1982).
  20. K. L. Babcock, G. Ahlers, and D. S. Cannell, “Noise-sustained structure in Taylor–Couette flow with through-flow,” Phys. Rev. Lett. 67, 3388 (1991).
  21. A. Recktenwald, M. Lücke, and H. W. Müller, “Taylor vortex formation in axial through-flow: Linear and weakly nonlinear analysis,” Phys. Rev. E 48, 4444 (1993).
  22. E. C. Johnson and R. M. Lueptow, “Hydrodynamic stability of flow between rotating porous cylinders with radial and axial flow,” Phys. Fluids 9, 3687 (1997).
  23. H. A. Snyder, “Experiments on the stability of spiral flow at low axial Reynolds numbers,” Proc. R. Soc. London, Ser. A 265, 198 (1962).
  24. M. M. Sorour and J. E. R. Coney, “The characteristics of spiral vortex flow at high Taylor numbers,” J. Mech. Eng. Sci. 21, 65 (1979).
  25. R. C. DiPrima and A. Pridor, “The stability of viscous flow between rotating concentric cylinders with an axial flow,” Proc. R. Soc. London, Ser. A 366, 555 (1979).
  26. R. M. Lueptow, A. Docter, and K. Min, “Stability of axial flow in an annulus with a rotating inner cylinder,” Phys. Fluids A 4, 2446 (1992).
  27. D. I. Takeuchi and D. F. Jankowski, “A numerical and experimental investigation of the stability of spiral Poiseuille flow,” J. Fluid Mech. 102, 101 (1981).
  28. S. T. Wereley and R. M. Lueptow, “Velocity field for Taylor–Couette flow with an axial flow,” Phys. Fluids 11, 3637 (1999).
  29. K. Bühler, “Instabilitaten spiralformiger Strömungen im Zylinderspalt,” Z. Angew. Math. Mech. 64, 180 (1984).
  30. K. Bühler, “Symmetric and asymmetric Taylor vortex flow in spherical gaps,” Acta Mech. 81, 3 (1990).
  31. K. Min and R. M. Lueptow, “Circular Couette flow with pressure-driven axial flow and a porous inner cylinder,” Exp. Fluids 17, 190 (1994).
  32. A. Kolyshkin and R. Vaillancourt, “Convective instability boundary of Couette flow between rotating porous cylinder with axial and radial flow,” Phys. Fluids 9, 910 (1997).
  33. A. Meseguer and F. Marques, “On the competition between centrifugal and shear instability in spiral Poiseuille flow,” J. Fluid Mech. 455, 129 (2002).
  34. D. L. Cotrell and A. J. Pearlstein, “The connection between centrifugal instability and Tollmien–Schlichting-like instability for spiral Poiseuille flow,” J. Fluid Mech. 509, 331 (2004).
  35. D. L. Cotrell, S. L. Rani, and A. J. Pearlstein, “Computational assessment of subcritical and delayed onset in spiral Poiseuille flow experiments,” J. Fluid Mech. 509, 353 (2004).
  36. A. Meseguer and F. Marques, “On the stability of medium gap corotating spiral Poiseuille flow,” Phys. Fluids 17, 094104 (2005).
  37. C. J. Heaton, “Optimal linear growth in spiral Poiseuille flow,” J. Fluid Mech. 607, 141 (2008).
  38. S. K. Bahl, “Stability of viscous flow between two concentric rotating porous cylinders,” Def. Sci. J. 20, 89 (1970).
  39. K. Bühler, in Ordered and Turbulent Patterns in Taylor–Couette Flow, edited by E. D. Andereck and F. Hayot (Plenum, New York, 1992), pp. 197–203.
  40. T. S. Chang and W. K. Sartory, “Hydromagnetic stability of dissipative flow between rotating permeable cylinders,” J. Fluid Mech. 27, 65 (1967).
  41. T. S. Chang and W. K. Sartory, “Hydromagnetic stability of dissipative flow between rotating permeable cylinders. Part 2. Oscillatory critical modes and asymptotic results,” J. Fluid Mech. 36, 193 (1969).
  42. K. Min and R. M. Lueptow, “Hydrodynamic stability of viscous flow between rotating porous cylinders with radial flow,” Phys. Fluids 6, 144 (1994).
  43. E. Serre, M. A. Sprague, and R. M. Lueptow, “Stability of Taylor–Couette flow in a finite-length cavity with radial through-flow,” Phys. Fluids 20, 034106 (2008).
  44. S. Lee and R. M. Lueptow, “Rotating membrane filtration and rotating reverse osmosis,” J. Chem. Eng. Jpn. 37, 471 (2004).
  45. S. K. Bahl and K. M. Kapur, “The stability of a viscous flow between two concentric rotating porous cylinders with an axial flow,” Def. Sci. J. 25, 139 (1975).
  46. P. Huerre and P. A. Monkewitz, “Absolute and convective instabilities in free shear layers,” J. Fluid Mech. 159, 151 (1985).
  47. P. Huerre and P. A. Monkewitz, “Local and global instabilities in spatially developing flows,” Annu. Rev. Fluid Mech. 22, 473 (1990).
  48. A. Tsameret, G. Goldner, and V. Steinberg, “Experimental evaluation of the intrinsic noise in the Couette–Taylor system with an axial flow,” Phys. Rev. E 49, 1309 (1994).
  49. A. Tsameret and V. Steinberg, “Noise-modulated propagating pattern in a convectively unstable system,” Phys. Rev. Lett. 67, 3392 (1991).
  50. F. Marques, J. Sanchez, and P. D. Weidman, “Generalized Couette–Poiseuille flow with boundary mass transfer,” J. Fluid Mech. 374, 221 (1998).
  51. O. Czarny and R. M. Lueptow, “Time scales for transition in Taylor–Couette flow,” Phys. Fluids 19, 054103 (2007).
  52. O. Czarny, E. Serre, P. Bontoux, and R. M. Lueptow, “Spiral and wavy vortex flows in short counter-rotating Taylor–Couette cells,” Theor. Comput. Fluid Dyn. 16, 5 (2002).
  53. O. Czarny, E. Serre, P. Bontoux, and R. M. Lueptow, “Interaction between Ekman pumping and the centrifugal instability in Taylor–Couette flow,” Phys. Fluids 15, 467 (2003).
  54. O. Czarny, E. Serre, P. Bontoux, and R. M. Lueptow, “Ekman vortices and the centrifugal instability in counter-rotating cylindrical Couette flow,” Theor. Comput. Fluid Dyn. 18, 151 (2004).
  55. E. Serre, E. C. del Arco, and P. Bontoux, “Annular and spiral patterns in flows between rotating and stationary discs,” J. Fluid Mech. 434, 65 (2001).
  56. J. M. Vanel, R. Peyret, and P. Bontoux, in Numerical Methods for Fluid Dynamics II, edited by K. W. Morton and M. J. Baines (Clarendon, Oxford, 1986), pp. 463–475.
  57. I. Raspo, S. Hughes, E. Serre, A. Randriamampianina, and P. Bontoux, “A spectral projection method for the simulation of complex three-dimensional rotating flows,” Comput. Fluids 31, 745 (2002).
  58. V. Sobolik, B. Izrar, F. Lusseyran, and S. Skali, “Interaction between the Ekman layer and the Couette–Taylor instability,” Int. J. Heat Mass Transfer 43, 4381 (2000).
  59. H. A. Snyder, “Experiments on the stability of two types of spiral flow,” Ann. Phys. 31, 292 (1965).
  60. S. Leibovich and K. Stewartson, “A sufficient condition for the instability of columnar vortices,” J. Fluid Mech. 126, 335 (1983).
  61. P. Büchel, M. Lücke, D. Roth, and R. Schmitz, “Pattern selection in the absolutely unstable regime as a nonlinear eigenvalue problem: Taylor vortices in axial flow,” Phys. Rev. E 53, 4764 (1996).
  62. I. Delbende and J. -M. Chomaz, “Nonlinear convective/absolute instabilities in parallel two-dimensional wakes,” Phys. Fluids 10, 2724 (1998).
  63. A. Couairon and J. -M. Chomaz, “Absolute and convective instabilities, front velocities, and global modes in nonlinear systems,” Physica D 108, 236 (1997).
  64. P. A. Monkewitz, P. Huerre, and J. -M. Chomaz, “Global linear stability analysis of weakly nonparallel shear flows,” J. Fluid Mech. 288, 1 (1993).
  65. P. Carrière and P. A. Monkewitz, “Transverse-roll global modes in a Rayleigh–Bénard–Poiseuille convection,” Eur. J. Mech. B/Fluids 20, 751 (2001).
  66. D. Martinand, P. Carrière, and P. A. Monkewitz, “Three-dimensional global instability modes associated with a localized hot spot in Rayleigh–Bénard–Poiseuille convection,” J. Fluid Mech. 551, 275 (2006).
  67. J. -M. Chomaz, “Global instabilities in spatially developing flows: Non-normality and nonlinearity,” Annu. Rev. Fluid Mech. 37, 357 (2005).

CITING ARTICLES
For access to citing articles, you need to log in.
For access to citing articles, you need to Log in.


Copyright © American Institute of Physics