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Three-parameter model of shear turbulence

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Abstract

A model of shear turbulence is proposed in which transport equations are used for three flow chracteristics: the energy E, the friction stress — (u′v′), and the function F, whose dimensionality coincides with that of the quantity EmLn. Well-known equations are used for the first two quantities, while a special analysis is required to construct the third equation. The constants in the equations are determined by analyzing the flow behind a grid with constant shear and the behavior of the solutions in different flow regions in the channel. The results of a numerical solution for a flow in a channel are given, and the results are compared with the known experimental data.

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Literature cited

  1. A. S. Monin and A. M. Yalgom, Statistical Hydromechanics [in Russian], Part. 1, Nauka, Moscow (1965).

    Google Scholar 

  2. P. Bradshaw, “The understanding and prediction of turbulent flow,” Aeron, J.,76, No. 739 (1972).

  3. B. E. Launder and D. B. Spalding, Lectures in Mathematical Models of Turbulence, Academic Press, New York. (1972).

    Google Scholar 

  4. G. L. Mellor and H. J. Herring, “A survey of the mean turbulent field closure models,” AIAA J.,11, No. 5 (1973).

  5. V. M. Ievlev, Turbulent Motion of High-Temperature Continuous Media [in Russian], Nauka, Moscow (1975).

    Google Scholar 

  6. G. N. Abramovich, S. Yu. Krasheninnikov, and A. N. Sekundov, Turbulent Flows under Bulk Forces and Non-self-similarity [in Russian], Mashinostroenie, Moscow (1975).

    Google Scholar 

  7. A. A. Pavel'ev, “Development of grid-generated turbulence in a flow with a constant velocity gradient,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 1 (1974).

  8. A. N. Komogorov, “Equations for the turublent motion of an incompressible fluid,” Izv. Akad. Nauk SSSR, Ser. Fiz.,6, Nos. 1 and 2 (1942).

  9. L. Pradtl., “Über ein penes Formelsystem für die ausgebildete Turbulenz,” Nachr. Ges. Gottingen Math. Phys.,6, (1945).

  10. G. S. Glushko, “Turbulent boundary layer on a flat plate in an incompressible fluid,” Izv. Akad. Nauk SSSR, Mekh., No. 4 (1965).

  11. G. S. Glushko, “Some features of turbulent flows of an incompressible fluid with transverse shear,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 4 1974.

  12. J. Rotta, “Statistische Theorie nichthomogener Turbulenz,” Z. Phys.,129, No. 5;131, No. 1 (1951).

  13. B. I. Davydov, “Statistical dynamics of an incompressible turbulent fluid,” Dokl. Akad. Nauk SSSR,127, No. 4 (1959).

  14. G. K. Batchelor and A. A. Townsend, “Decay of turbulence in the final period,” Proc. Roy. Soc. London.,194, No. 1039 (1948).

  15. G. K. Batchelor and A. A. Townsend, “Decay of isotropic turbulnce in the initial period,” Proc. Roy, Soc. London.,193, No. 1035 (1948).

  16. M. S. Uberoi, “Equipartition of energy and local isotropy in turbulent flows,” J. Appl. Phys.28, No. 10 (1957).

  17. H. K. Richards and J. B. Morton, “Experimental investigation of turbulent shear flow with quedratic mean-velocity profiles,” J. Fluid Mech.,73, Pt. 1 (1976).

  18. J. Laufer, “The structure of turbulence in fully developed pipe flow,” NACA Rept., No. 1174 (1954).

  19. E. M. Khabakhnasheva, E. S. Mikhailova, B. V. Perepemiza, and G. I. Efimenko, “Experimental investigation of the structure of turbulence near the wall,” in: Turbulent Near-Wall flow [in Russian], Pt. 2, Inst. Teplofiz Sibirsk. Otd. Akd. Nauk SSSR, Novosibirsk (1975).

    Google Scholar 

  20. G. Comte-Bellot, Turbulent Flow in a channel with Parallel Walls [Russian translation], Mir, Moscow (1968).

    Google Scholar 

  21. J. O. Hinze, Turbulence, McGraw-Hill, New York (1959).

    Google Scholar 

  22. K. Hanjalic and B. E. Launder, “A Reynolds stress model of turbulence and its application to thin shear flows,” J. Fluid Mech.,52, Pt. 4 (1972).

  23. A. N. Sekundov, “Application of a differential equation for turbulent viscosity to the analysis of plane nonself-similar flows,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 5 (1971).

  24. V. G. Lushchik, A. A. Pavel'ev, and A. E. Yakubenko, “Shear turbulence model,” Abstracts of Papers of the Fourth All-Union Congress on Theoretical and Applied Mechanics [in Russian], Naukova Dumka, Kiev (1976).

    Google Scholar 

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Authors and Affiliations

  1. Moscow

    V. G. Lushchik, A. A. Pavel'ev & A. E. Yakubenko

Authors
  1. V. G. Lushchik
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  2. A. A. Pavel'ev
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  3. A. E. Yakubenko
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Additional information

Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 13–25, May–June, 1978.

The authors thank V. M. Ievlev and the participants of the seminars run by G. N. Abramovich and G. A. Lyubimov for discussions of the work.

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Lushchik, V.G., Pavel'ev, A.A. & Yakubenko, A.E. Three-parameter model of shear turbulence. Fluid Dyn 13, 350–360 (1978). https://doi.org/10.1007/BF01050525

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