Physics of Fluids
Feedback | Help | Exit
Search:
   
 
 
 
Previous Article
Formation and temporal evolution of the Lamb-dipole
The formation and dynamics of dipolar vortex structures in two-dimensional flows are studied. Localized initial structures possessing a finite linear momentum are found to develop into dipoles by dire...
Next Article
Instability of vortical and acoustic modes in supersonic round jets
The stability of "top-hat" and fully developed jet profiles is investigated by an inviscid linear stability theory for compressible flow. The study covers a wide range of the Mach number and...

The role of nonunique axisymmetric solutions in 3-D vortex breakdown

Phys. Fluids 9, 992 (1997); doi:10.1063/1.869194

Issue Date: April 1997

You are not logged in to this journal. Log in

J. C. Tromp and P. S. Beran
Department of Aeronautics and Astronautics, U.S. Air Force Institute of Technology, Wright-Patterson Air Force Base, Ohio 45433
The three-dimensional, compressible Navier–Stokes equations in primitive variables are solved numerically to simulate vortex breakdown in a constricted tube. Time integration is performed with an implicit Beam-Warming algorithm using fourth-order compact operators to discretize spatial derivatives. Initial conditions are obtained by solving the steady, compressible, and axisymmetric form of the Navier–Stokes equations with Newton's method. The effects of three-dimensionality on flows that are initially axisymmetric and stable to 2-D disturbances are examined. Stability of the axisymmetric base flow is assessed through 3-D time integration. Axisymmetric solutions at a Mach number of 0.3 and a Reynolds number of 1000 contain a region of nonuniqueness. Within this region, 3-D time integration reveals only unique solutions, with nonunique axisymmetric initial conditions converging to a unique solution that is steady and axisymmetric. Past the primary limit point, which approximately identifies the appearance of critical flow (a flow that can support an axisymmetric standing wave), the solutions bifurcate into 3-D time-periodic flows. Thus this numerical study shows that the vortex strength associated with the loss of stability to 3-D disturbances and that of the primary limit point are in close proximity. Additional numerical and theoretical studies of 3-D swirling flows are needed to determine the impact of various parameters on dynamic behavior. For example, it is possible that a different flow behavior, leading to a nearly axisymmetric vortex breakdown state, may develop with other inlet profiles and tube geometries.
History: Received 19 January 1996; accepted 11 December 1996
Permalink: http://link.aip.org/link/?PHFLE6/9/992/1
BUY THIS ARTICLE   (US$24)
Download PDF (314 kB) View Cart

KEYWORDS and PACS

Keywords
PACS
  • 47.32.Cc
    Fluid dynamics Rotational flow and vorticity Vortex dynamics
  • 47.40.-x
    Fluid dynamics Compressible flows; shock and detonation phenomena
  • 47.11.+j
    Fluid dynamics Computational methods in fluid dynamics
  • YEAR: 1996-97

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 (27)
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. J. H. Faler and S. Leibovich, "Disrupted states of vortex flow and vortex breakdown," Phys. Fluids 20, 1385 (1977).
  2. J. D. Buntine and P. G. Saffman, "Inviscid swirling flows and vortex breakdown," Proc. R. Soc. London Ser. A 449, 139 (1995).
  3. S. Wang and Z. Rusak, "On the stability of an axisymmetric rotating flow in a pipe," Phys. Fluids 8, 1007 (1996).
  4. S. Wang and Z. Rusak, "On the stability of non-columnar swirling flows," Phys. Fluids 8, 1017 (1996).
  5. J. M. Lopez, "On the bifurcation structure of axisymmetric vortex breakdown in a constricted pipe," Phys. Fluids 6, 3683 (1994).
  6. D. L. Darmofal and E. M. Murman, "On the trapped wave nature of axisymmetric vortex breakdown," AIAA Paper No. 94–2318, 1994.
  7. P. S. Beran and F. E. C. Culick, "The role of non-uniqueness in the development of vortex breakdown in tubes," J. Fluid Mech. 242, 491 (1992).
  8. M. Breuer and D. Hänel, "Solution of the 3-D incompressible Navier-Stokes equations for the simulation of vortex breakdown," 8th GAMM Conference, Delft, Netherlands, 1989.
  9. R. E. Spall, T. B. Gatski, and R. L. Ash, "The structure and dynamics of bubble-type vortex breakdown," Proc. R. Soc. London Ser. A 429, 613 (1990).
  10. R. E. Spall and T. B. Gatski, "A computational study of the topology of vortex breakdown," Proc. R. Soc. London Ser. A 435, 321 (1991).
  11. M. R. Visbal, "Computed unsteady structure of spiral vortex breakdown on delta wings," AIAA Paper No. 96–2074, 1996.
  12. S. Táasan, "Multigrid method for a vortex breakdown simulation," NASA CR-178106, 1986.
  13. S. Leibovich and A. Kribus, "Large-amplitude wavetrains and solitary waves in vortices," J. Fluid Mech. 216, 459 (1990).
  14. P. S. Beran, "The time-asymptotic behavior of vortex breakdown in tubes," Comput. Fluids 23, 913 (1994).
  15. Z. Rusak and S. Wang, "Review of theoretical approaches to the vortex breakdown phenomenon," AIAA Paper No. 96–2126, 1996.
  16. T. Sarpkaya, "On stationary and traveling vortex breakdowns," J. Fluid Mech. 45, 545 (1971).
  17. J. C. Tromp and P. S. Beran, "Temporal evolution of three-dimensional vortex breakdown from steady, axisymmetric solutions," AIAA J. 34, 632 (1996).
  18. T. B. Benjamin, "Theory of the vortex breakdown phenomenon," J. Fluid Mech. 14, 593 (1962).
  19. M. G. Hall, in Annual Review of Fluid Mechanics (Annual Review, Palo Alto, 1972), Vol. 4, p. 195.
  20. J. C. Tromp, "The dependence of the time-asymptotic structure of 3-D vortex breakdown on boundary and initial conditions," Ph.D. thesis, Air Force Institute of Technology (1995).
  21. J. P. Steinbrenner, J. R. Chawner, and C. L. Fouts, "The GRIDGEN 3D multiple block grid generation system," 1, (WRDC, Wright-Patterson AFB, OH, 1990), TR-90–3022.
  22. Z. Rusak, S. Wang, and C. Whiting, "Numerical computations of axisymmetric vortex breakdown in a pipe," AIAA Paper No. 96–0801, 1996.
  23. G. Iooss and D. D. Joseph, Elementary Stability and Bifurcation Theory, 2nd ed. (Springer-Verlag, New York, 1990).
  24. S. A. Morton and P. S. Beran, "Hopf-bifurcation analysis of airfoil flutter at transonic speeds," AIAA Paper No. 96–0060, 1996.
  25. R. M. Beam and R. F. Warming, "An implicit finite-difference algorithm for hyperbolic systems in conservation-law Form," J. Comput. Phys. 22, 87 (1976).
  26. S. K. Lele, "Compact finite difference schemes with spectral-like resolution," J. Comput. Phys. 103, 16 (1992).
  27. J. Désidéri, J. L. Steger, and J. C. Tannehill, "On improving the iterative convergence properties of an implicit approximate-factorization finite difference algorithm," NASA TM 78495, 1978.

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