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ON THE EVOLUTION OF LAMINAR TO TURBULENT TRANSITION AND BREAKDOWN TO TURBULENCE

ABSTRACT
Starting from the basic conservation laws of fluid flow, we investigated transition and breakdown to turbulence of a laminar flat plate boundary layer exposed to small, statistically stationary, two-component, three-dimensional disturbances. The derived equations for the statistical properties of the disturbances are closed using the two-point correlation technique and invariant theory. By considering the equilibrium solutions of the modeled equations, the transition criterion is formulated in terms of a Reynolds number based on the intensity and the length scale of the disturbances. The deduced transition criterion determines conditions that guarantee maintenance of the local equilibrium between the production and the viscous dissipation of the disturbances and therefore the laminar flow regime in the flat plate boundary layer. The experimental and numerical databases for fully developed turbulent channel and pipe flows at different Reynolds numbers were utilized to demonstrate the validity of the derived transition criterion for the estimation of the onset of turbulence in wall-bounded flows.
KEYWORDS
PAPER SUBMITTED: 2003-08-25
PAPER REVISED: 2003-09-05
PAPER ACCEPTED: 2003-09-15
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THERMAL SCIENCE YEAR 2003, VOLUME 7, ISSUE Issue 2, PAGES [59 - 75]
REFERENCES
  1. J.O. HINZE, Turbulence, 2nd ed., McGraw-Hill, New York, 1975.
  2. S.J. KLINE, W.C. REYNOLDS, F.A. SCHRAUB AND W.P. RUNSTADLET, The structure of turbulent boundary layers, J. Fluid Mech. 30, 741-773 (1967).
  3. H.T. KIM, S.J. KLINE AND W.C. REYNOLDS, The production of turbulence near smooth wall in a turbulent boundary layer, J. Fluid Mech. 50, 133-160 (1971).
  4. R.E. FALCO, The role of outer flow coherent motions in the production of turbulence near a wall, In Coherent Structure of Turbulent Boundary Layer (ed. C.R. Smith and D.E. Abbott). AFOSR/Lehigh University, 448-461 (1978).
  5. J. LAUFER, New trends in experimental turbulence research, Anu. Rev. Fluid Mech. 7, 307-326 (1975).
  6. J. LAUFER, Flow instability and turbulence, In Structure of Turbulence in Heat and Mass Transfer, Ed. by Z. Zarh~, Hemisphere, 1982.
  7. M. FISCHER, J. JOVANOVIC AND F. DURST, Near-wall behaviour of statistical properties in turbulent flows, Int. J. Heat and Fluid Flow, 21, 471-479, 2000.
  8. M. FISCHER, Turbulente wandbebundene Str6mungen bei kleinen Reynoldszhalen, Ph.D. Thesis, Universit䴠Erlangen-Niirnberg, 63-65, 1999.
  9. P.Y. CHOU, On the velocity correlation and the solution of the equation of turbulent fluctuation, Quart. Appi. Math. 3, 38-54 (1945).
  10. J.L. LUMLEY AND G. NEWMAN, The return to isotropy of homogeneous turbulence, J. Fluid Mech. 82, 161-178 (1977).
  11. J.L. LUMLEY, Computational modeling of turbulent flows, Adv. Appi. Mech. 18,123-176 (1978).
  12. B.A. KOLOVANDIN AND l.A. VATUTIN, Statistical transfer theory in non-homogeneous turbulence, Int. J. Heat. Mass Thansfer 15, 2371-2383 (1972).
  13. J. JOVANOVIC, Q.-Y. YE AND F. DURST, Statistical interpretation of the turbulent dissipation rate in wall-bounded flows, J. Fluid Mech. 293, 321-347 (1995).
  14. J. JOVANOVIC, Q.-Y. YE AND F. DURST, Refinement of the equation for the determination of turbulent micro-scale, Universit~t Erlangen-Niirnberg Rep., LSTM 349/T/92, (1992).
  15. J. JOVANOVIC, I. OTId AND P. BRADSHAW, On the anisotropy of axisymmetric strained turbulence in the dissipation range, J. Fluids Eng. (in press), (2003).
  16. H. TENNEKES AND J.L. LUMLEY, A First Course in Turbulence, MIT Press, Cambridge, MA 1972.
  17. M. FISCHER, J. JOVANOVIC AND F. DURST, Reynolds number effects in the near-wall region of turbulent channel flows, Phys. Fluids, 13, 1755-1767, 2001.
  18. J. JOVANOVIC, The Statistical Dynamics of Turbulence, Ongoing project at the Lehrstuhl fur Str6mungsmechanik-Erlangen, 2002.
  19. J. JOVANOVIC AND I. OTIC, On the constitutive relation for the Reynolds stresses and the PrandtlKolmogorov hypothesis of effective viscosity in a.xisymmetric strained turbulence, J. Fluids Eng. 122, 48-50 (2000).
  20. U. SCHUMANN, Realizability of Reynolds stress turbulence models, Phys. Fluids 20, 721-725 (1977).
  21. G.I. TAYLOR, Statistical theory of turbulence. Part V. Effects of turbulence on boundary layer. Theoretical discussion of relationship between scale of turbulence and critical resistence of spheres, Proc. Roy. Soc. Loud. A 156, 307-317 (1936).
  22. S. BECKER, personal communication (1999).
  23. A.N. KOLMOGOROV, On degeneration of isotropic turbulence in an incompressible viscous liquid, Dokl. Akad. Nauk SSSR 6, 538-540 (1941).
  24. J. KIM, P. MoIN AND R. MOSER, Turbulence statistics in a fully developed channel flow at low Reynolds numbers, J. Fluid Mech. 1, T7, 133-166 (1987).
  25. N. GILnERT AND L. KLEISER, Turbulence model testing with the aid of direct numerical simulation results, Proc. Eighth Symp. on Turbulent Shear Flows, Munich, 26.1.1-26.1.6 (1991).
  26. R.A. ANTONIA, M. TEITEL, J. KIM AND L.W.B. BROWNE, Low-Reynolds number effects in a fully developed channel flow, J. Fluid Mech. 236, 579-605 (1992).
  27. K. HORIUTI, Y. MIYAKE, T. MwAucHI, Y. NAGANO, AND N. KASAGI, Establishment of the DNS database of turbulent transport phenomena, Rep. Grants-in-aid for Scientific Research, No.
  28. 02302043 (1992).
  29. A. KURODA, N. KASAGI AND M. HIRATA, Direct numerical simulation of the turbulent plane Couette-Poiseulle flows: Effect of mean shear on the near wall turbulence structures, Proc. 9th Symp. on Turbulent Shear Flows, Kyoto, 8.4.1-8.4.6 (1993).
  30. F. DURST, M. FISCHER, J. JovANovId AND H. KIKURA, Methods to set-up and investigate low Reynolds number, fully developed turbulent plane channel flows, J. Fluids Eng. 120, 496-503 (1998).
  31. H. SCHLICHTING, Boundary-Layer Theory, 6th edn., McGraw-Hill, New York, 1968.
  32. S.A. ORSZAG AND C. KELLS, Transition to turbulence in plane Poiseuille and plane Couette flow, J. Fluid Mech. 96, 159-205 (1980).
  33. F. ALAVYQON, D.S. HENNINOSON AND P.H. ALFREDSSON, Turbulence spots in plane Poiseuille flow - flow visualization, Phys. Fluids 29, 1328-1331 (1986).
  34. D.R. CARLSON, S.E. WIDNALL AND M.F. PAETERS, A flow-visualization study of transition in plane Poiseuille flow, J. Fluid Mech. 121, 487-505 (1982).
  35. J.G.M. EGGELS, F. UNGER, M.H. WEIss, J. WESTERWEEL, R.J. ADRIAN, R. FRIEDRICH AND
  36. F.T.M. NIEUWSTADT, Fully developed turbulent pipe flow: A comparison between direct numerical simulation and experiment, J. Fluid Mech. 268, 175-209 (1994).
  37. J. LAUFER, The structure of turbulence fully developed pipe flow, NACA TN, 2954 (1953).
  38. F. DURST, J. JOVANOVId AND J. SENDER, LDA measurements in the near-wall region of a turbulent pipe flow, J. Fluid Mech. 295, 305-355 (1995).
  39. 0. REYNOLDS, An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and the law of resistance in parallel channels, Phil. Trans. Roy. Soc. 174, 935-982 (1883).
  40. A.S. MONIN AND A.M. YAGLOM, Statistical Fluid Mechanics - Mechanics of Turbulence, Vol. I, Chapter 2, CTR Monograph, Stanford University, Stanford, CA, 7-25 (1997).

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