Skip to main content
SpringerLink
Log in

Turbulent flows. Models and numerical investigations. A review

  • Published:
Fluid Dynamics Aims and scope Submit manuscript

Abstract

Russian papers on differential models of turbulence and numerical simulation of nonequilibrium turbulent flows of liquids, gases, and conducting media, published for the most part in this journal over the last 10–15 years, are reviewed.

The turbulence models considered in this review are based on Kolmogorov's ideas, which generated a new approach to the mathematical modeling of turbulent flows consisting in the use of transport equations for the turbulence properties. The subsequent development of these models was due to the emergence of computers which made it possible to change over from a qualitative analysis in particular regions to obtaining quantitative results with the influence of viscosity, and also such effects as diffusion and convection, taken directly into account in the mathematical simulation of turbulent flows.

In this review the models are selected in accordance with the following criteria.

1. Only differential models are considered, that is models in which transport equations are used for the main turbulence properties: the turbulence energy, shear stress or the turbulent viscosity and a parameter involving the integral turbulence scale. According to the number of the transport equations the models are classified as one-, two-, or three-parameter. The application of the models is restricted to flows for which the boundary layer approximation holds true.

2. The models must have been put to practical use in the analysis of particular flows, and their most efficient areas of application specified. The models must have been tested by comparison with the most reliable experimental data. The models must be highly universal, thus making it possible, without adjusting the constants entering into the model, to take into account the inlet and boundary conditions, the variations of the physical properties of the medium, and external influences.

The review aims to demonstrate the potential of the turbulence models considered in relation to a wide variety of flows in boundary layers and channels, and also to draw them to the attention of users and researchers developing scientific and applied computational programs for the description and control of devices with complicated working processes in aviation and space technology, and other areas.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Computation of Turbulent Boundary Layers. AFOSR - IFP - Stanford Conf. Stanford, 1968. Proc. Stanford (1969).

  2. S. J. Kline, B. J. Cantwell and G. M. Lilley (Eds.), 1980–81AFOSR - HTTM - Stanford Conf. on Complex Turbulent Flows, Mech. Eng. Dept. Stanford Univ. (1981).

  3. P. Bradshaw,Turbulence: the chief outstanding difficulty of our subject, The third Stewartson lecture Sympos. on Numer. and Phys. Aspects Aerodynam. Flows, Long Beach, CA (1992).

  4. P. Bradshaw,Final Report on AFOSR 90-0154 “Collaborative Testing of Turbulence Models”, Mech. Eng. Dept., Stanford Univ. (1992).

  5. A. N. Kolmogorov, “Equations of turbulent flow of an incompressible fluid,” Izv. Akad. Nauk SSSR, Ser. fiz.,6, No. 1–2, 56–58 (1942).

    Google Scholar 

  6. A. A. Pavel'ev, “Development of lattice turbulence in a system with a constant velocity gradient,” Fluid Dynamics,9, No. 1, 28–34 (1974).

    Google Scholar 

  7. V. G. Lushchik, A. A. Pavel'ev, and A. E. Yakubenko, “Three-parameter model of shear turbulence,” Fluid Dynamics,13, No. 3, 350–359 (1978).

    Google Scholar 

  8. V. G. Lushchik, A. A. Pavel'ev, and A. E. Yakubenko, “Three-parameter model of turbulence: heat transfer calculations,” Fluid Dynamics,21, No. 2, 200–211 (1986).

    Google Scholar 

  9. V. G. Lushchik, A. A. Pavel'ev, and A. E. Yakubenko, “Transfer equation for turbulent heat flux. Calculation of heat exchange in a pipe,” bd23, No. 6, 835-842 1988.

  10. V. G. Lushchik, A. A. Pavel'ev, and A. E. Yakubenko, “A study of the transition to turbulence in a boundary layer at high external perturbation level using a three-parameter model,” in: Problems of Modern Mechanics. Pt. 1 [in Russian], 127–138, Izd. MGU, Moscow (1983)

    Google Scholar 

  11. V. G. Lushchik, A. E. Yakubenko, “A three-parameter model of turbulence: calculation of the flow in a longitudinal magnetic field,”Magn. Gidrodin., No. 3, 30–38 (1987).

    Google Scholar 

  12. V. G. Lushchik, A. A. Pavel'ev, and A. E. Yakubenko, “Control of turbulent boundary layers: experimental results and numerical models,” in:Mechanics and Progress in Science and Technology, V. 2, Fluid Mechanics [in Russian], 67–89, Nauka, Moscow (1987).

    Google Scholar 

  13. V. G. Lushchik, A. A. Pavel'ev, and A. E. Yakubenko, “Transport equation for turbulence properties: models and numerical results,”Itogi nauki i tekhniki. VINITI. MZhG,22, 3–61 (1988).

    MathSciNet  Google Scholar 

  14. V. I. Kovalev, V. G. Lushchik, V. I. Sizov, and A. E. Yakubenko, “Three-parameter turbulence model: numerical investigation of the boundary layer in a nozzle with gas-film wall cooling,” Fluid Dynamics, No. 1, 35–42 (1992).

  15. V. G. Lushchik, V. I. Sizov, L. E. Stermin, and A. E. Yakubenko, “Specific impulse losses due to friction and dispersion in a gas-film cooled liquid rocket engine nozzle,” Fluid Dynamics,28, No. 4, 495–503 (1993).

    Google Scholar 

  16. G. S. Glushko, “Turbulent boundary layer on a flat plate in an incompressible fluid,”Izv. Akad Nauk SSSR, Mekhanika, No. 4, 13–23 (1965).

    Google Scholar 

  17. J. C. Rotta, “Statistische Theorie nichthomogener Turbulenz,”Z. Phys., 1 Mitt.,129, No. 6, 547–572; 2 Mitt.,131, No. 1, 51–77 (1951).

    MATH  MathSciNet  Google Scholar 

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

    Google Scholar 

  19. G. S. Glushko, A differential equation for the turbulence scale and calculation of the turbulent boundary layer on a flat plate,” in:Turbulent Flows [in Russian], 37–44, Nauka, Moscow (1970).

    Google Scholar 

  20. G. S. Glushko, “Some distinctive features of the turbulent flow of an incompressible liquid with transverse drift,” Fluid Dynamics,6, No. 4, 662–669 (1971).

    Google Scholar 

  21. G. S. Glushko, “Transition to the turbulent flow mode in the boundary layer on a flat plate for different free-stream turbulence scales,” Fluid Dynamics, No. 3, 424–425 (1972).

  22. G. S. Glushko and V. A. Solopov, “Heat transfer process in turbulent flows,” Fluid Dynamics,7, No. 4, 551–556 (1972).

    Google Scholar 

  23. A. N. Sekundov, “Application of a differential equation for turbulent viscosity to the analysis of plane non-self-similar flows,” Fluid Dynamics,6, No. 5, 828–840 (1971).

    Google Scholar 

  24. G. N. Abramovich, V. B. Kuz'mich, A. N. Sekundov, and I. P. Smirnova, “Investigation by experiment and calculation of a supersonic stream adjacent to a wall in an accompanying supersonic flow,” Fluid Dynamics,7, No. 4, 557–563 (1972).

    Google Scholar 

  25. A. B. Lebedev and A. N. Sekundov, “Use of the equation for turbulent viscosity to describe the flow near a rough surface,” Fluid Dynamics, No. 5, 741–744 (1975).

  26. V. B. Kuz'mich, A. N. Sekundov, and I. P. Smirnova, “Investigation of a compressible turbulent boundary layer in the presence of tangential blowing and a positive pressure gradient,” Fluid Dynamics, No. 6, 903–907 (1975).

  27. G. N. Abramovich, S. Yu. Krasheninnikov, and A. N. Sekundov,Turbulent Flows under the Action of Volume Forces and Non-similarity, Mashinostroenie, Moscow (1975).

    Google Scholar 

  28. V. R. Kuznetsov, A. B. Lebedev, A. N. Sekundov, and I. P. Smirnova, “Calculation of a turbulent diffusion combustion flame core, taking account of concentration pulsations and Archimedean forces,” Fluid Dynamics,12, No. 1, 24–33 (1977).

    Google Scholar 

  29. V. E. Kozlov, A. N. Sekundov, and I. P. Smirnova, “Models of turbulence for the description of a flow in a jet of compressible gas,” Fluid Dynamics,21, No. 6, 875–881 (1986).

    Google Scholar 

  30. C. S. Wells, “Effects of freestream turbulence on boundary layer transition,”AIAA Journal,5, No. 1, 172–174 (1967).

    MathSciNet  Google Scholar 

  31. E. K. Kholshchevnikova, “Investigation of developed flow of an incompressible conductive fluid in a circular pipe by using the equation for the turbulent viscosity,” Fluid Dynamics,10, No. 5, 757–764 (1975).

    Google Scholar 

  32. O. I. Navoznov and A. A. Pavel'ev, “Influence of the initial conditions on axisymmetric jets in a parallel flow,” Fluid Dynamics,15, No. 4, 488–492 (1980).

    Google Scholar 

  33. R. L. Simpson, R. J. Moffat, and W. M. Kays, “The turbulent boundary layer on a porous plate: experimental skin friction with variable injection and suction,”Int. J. Heat and Mass Transfer,12, No. 7, 771–789 (1969).

    Google Scholar 

  34. H. L. Julien, W. M. Kays, and R. J. Moffat, “Experimental hydrodynamics of the accelerated turbulent boundary layer with and without mass injection,”Trans. ASME, J. Heat Transfer,93, No. 4, 373–379 (1971).

    Google Scholar 

  35. R. L. Simpson, J. H. Strickland, and P. W. Barr, “Features of a separating turbulent boundary layer in the vicinity of separation,”J. Fluid Mech.,79, No. 3, 553–594 (1977).

    ADS  Google Scholar 

  36. G. M. Bam-Zelikovich, “The calculation of boundary layer separation,”Izv. Akad. Nauk SSSR, OTN,12, 68–85 (1954).

    Google Scholar 

  37. A. S. Ginevskii, V. A. Ioselevich, A. V. Kolesnikovet al., “Method of calculating a turbulent boundary layer,”Itogi Nauki i Tekhniki. VINITI, MZhG,11, 155–304 (1978).

    Google Scholar 

  38. E. K. Kholshchevnikova, “Calculation of boundary layers in nozzles with heat exchange at high stagnation parameters,”Trudy TsIAM, No. 1252, 51–59 (1990).

    Google Scholar 

  39. A. Klein, “Review: Turbulent developing pipe flow,”Trans. ASME, J. Fluids Eng.,103, No. 2, 243–249 (1981).

    ADS  Google Scholar 

  40. L. P. Volnistova, B. N. Gabrianovich, Yu. D. Levchenko, and Yu. P. Trubakov, “Turbulent flow properties in the initial region of a circular tube,”Vopr. Atom. Nauki i Tekhniki, Ser. Reaktorostroenie, No. 4, 27–31 (1977).

  41. E. K. Kholshchevnikova, “Numerical investigation of the development of flow in the initial section of a circular tube in the presence of a transitional boundary layer,” Fluid Dynamics,17, No. 3, 403–408 (1982).

    MATH  Google Scholar 

  42. K. Hanjalic, B. E. Launder, “A Reynolds stress model of turbulence and its application to thin shear flows,”J. Fluid Mech.,52, No. 4, 609–638 (1972).

    ADS  Google Scholar 

  43. E. K. Kholshchevnikova, “Turbulent air flow in a round pipe at high temperatures,” Fluid Dynamics,13, No. 2, 294–298 (1978).

    MATH  Google Scholar 

  44. D. S. Kovner and V. G. Lushchik, “Turbulent flow of a conducting liquid in a longitudinal magnetic field,” Fluid Dynamics,5, No. 1, 7–13 (1970).

    Google Scholar 

  45. V. M. Ievlev and É. E. Son, “Semiempirical theory of turbulence of inhomogeneous flows with body forces,” Fluid Dynamics,20, No. 3, 363–368 (1985).

    Google Scholar 

  46. R. Chevray and L. S. G. Kovasznay, “Turbulence measurements in the wake of a thin flat plate,”AIAA Journal, No. 8, 1641–1643 (1969).

    Google Scholar 

  47. J. Andreopoulos and P. Bradshaw, “Measurement of interacting turbulent shear layers in the near wake of a flat plate,”J. Fluid Mech,100, No. 3, 639–668 (1980).

    ADS  Google Scholar 

  48. A. G. Gumilevskii, “Investigation of momentumless swirled wakes on the basis of a two-parameter turbulence model,” Fluid Dynamics, No. 3, 326–330 (1992).

  49. A. A. Vinberg, L. I. Zaichik, and V. A. Pershukov, “Calculation of the momentum and heat transfer in a turbulent gas-particle jet,” Fluid Dynamics, No. 3, 353–362 (1992).

Download references

Authors
  1. V. G. Luschik
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. A. Pavel'ev
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. E. Yakubenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 4–27, July–August, 1994.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Luschik, V.G., Pavel'ev, A.A. & Yakubenko, A.E. Turbulent flows. Models and numerical investigations. A review. Fluid Dyn 29, 440–457 (1994). https://doi.org/10.1007/BF02319065

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02319065

Keywords

Search

Navigation