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Solution of the 3-D, Incompressible Navier-Stokes Equations for the Simulation of Vortex Breakdown

  • M. Breuer
  • D. Hänel
Part of the Notes on Numerical Fluid Mechanics (NNFM) book series (NNFM, volume 29)

Summary

A method of solution is presented for the threedimensional, unsteady Navier - Stokes equations of an incompressible fluid. The method is based on the principle of artificial compressibility, extended to time-dependent solutions by the concept of dual time stepping. Higher order upwinding (Quick interpolation, and Roe-type splitting) is used for the spatial discretization. The properties of the method were tested by means of different validated flow problems. Present computations concern with the unsteady, and three-dimensional problem of the breakdown of an isolated vortex. The temporal evolution and the internal structure of the breakdown bubble is investigated and compared with experimental observations.

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References

  1. [1]
    Grabowski, W.J., Berger, S.A.: Solutions of the Navier-Stokes equations for vortex breakdown, J. Fluid Mech., vol.75, part 3, pp.525–544, (1976).ADSzbMATHCrossRefGoogle Scholar
  2. [2]
    Menne, S.: Rotationssymmetrische Wirbel in achsparalleler Strömung, Diss. RWTH Aachen, (1986).Google Scholar
  3. [3]
    Hafez, M., Ahmad, J., Kuruvila, G., Salas, M.D.: Vortex breakdown simulation, Part I, AIAA Paper 87-1343., (1987).Google Scholar
  4. [4]
    Menne, S.: Vortex breakdown in an axisymmeiric flow, AIAA 26th Aerospace Sciences Meeting, Reno, Nevada, Jan. 11-14, (1988).Google Scholar
  5. [5]
    Menne, S.: Simulation of vortex breakdown in tubes, AIAA-Paper 88-3575, 1st National Fluid Dynamics Congress, Cincinatti, Ohio, July 25-28, (1988).Google Scholar
  6. [6]
    Spall, R.E., Gatski, T.B.: A Numerical Simulation of Vortex breakdown, Forum on Unst. Flow Sep., ASME Fluids Eng. Conf., June 1987.Google Scholar
  7. [7]
    Leibovich, S., Ma, H.Y.: Phys. Fluids, vol. 26, 3173 (1983).MathSciNetADSzbMATHCrossRefGoogle Scholar
  8. [8]
    Chorin, A.J.: J. Comput. Phys. 2, 12–26, (1967).ADSzbMATHCrossRefGoogle Scholar
  9. [9]
    Leonard, B.P.: Proceedings of the 2nd National Sym. on Numerical Properties and Methologies in Heat Transfer, Univ. of Maryland, 211, (1983).Google Scholar
  10. [10]
    Leonard, B.P.: Proceedings of the 1983 Int. Conf. on Computational Techniques and Applications, Univ. of Sydney, Australia, 106, (1984).Google Scholar
  11. [11]
    Roe, P.L.: Approximate Rieman solvers, parameter vectors and difference schemes, J. Comp. Phys., vol 22, pp 357, (1981).CrossRefGoogle Scholar
  12. [12]
    Spall, R.E., Gatski, T.B., Grosch C.E.: A Criterion for vortex breakdown, Phys. Fluids 30, (11), (Nov. 1987).Google Scholar
  13. [13]
    Sarpkaya, T.: On stationary and travelling vortex breakdowns, J. Fluid Mech., vol.45, part 3, pp.545–559, (1971).ADSCrossRefGoogle Scholar
  14. [14]
    Escudier, M.: Vortex breakdown: Observation and Explanations, Progress in Aerospace Sciences, vol.25, No.2, pp.189–229, (1988).ADSCrossRefGoogle Scholar
  15. [15]
    Leibovich, S.: The structure of vortex breakdown, Ann. Rev. of Fluid Mechanics, vol.10, pp.221–246, (1978).ADSCrossRefGoogle Scholar

Copyright information

© Springer Fachmedien Wiesbaden 1990

Authors and Affiliations

  • M. Breuer
    • 1
  • D. Hänel
    • 1
  1. 1.Aerodynamisches InstitutRWTH AachenAachenGermany

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