Numerical modeling of turbulent-transfer processes in a mixing zone

  • A. F. Kurbatskii
Article
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Abstract

The series of moments of the velocity field in a two-dimensional zone of mixing is calculated in this article by numerically solving a system of turbulent-transfer differential equations derived from an equation for a single-point distribution function of the velocity pulsation field [1] and simplified to an approximation of the boundary layer. The closed form of the transfer equation is obtained at the level of the third moments using the Millionshchikov hypothesis [2]. The differential operator of the system under this closure turns out to be weakly hyperbolic [3], and not parabolic. A difference scheme is proposed that realizes the method of matrix fitting [4]. A comparison is carried out with an experiment [5, 6].

Keywords

Differential Equation Boundary Layer Distribution Function Mechanical Engineer Numerical Modeling 
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Literature cited

  1. 1.
    A. T. Onufriev, “Equations in the semiempirical theory of turbulent transfer,” Zh. Prikl. Mekh. Tekh. Fiz., No. 2, 62–71 (1970).Google Scholar
  2. 2.
    M. D. Millionshchikov, “Theory of homogeneous isotropic turbulence,” Dokl. Akad. Nauk SSSR,32, No. 9, 611–617 (1941).Google Scholar
  3. 3.
    G. Flaschke and G. Streng, “Correctness of boundary-value problem,” in: Matematika [Periodic collection of translations of foreign articles], No. 72/2, pp. 74–97 (1973).Google Scholar
  4. 4.
    I. M. Gel'fand and O. V. Lokutsievskii, “Fitting method for solving difference equations,” in: S. K. Godunov and V. S. Ryaben'kii, Introduction to the Theory of Difference Schemes [in Russian], Fizmatgiz, Moscow (1972), Appendix II.Google Scholar
  5. 5.
    H. W. Liepmann and J. Laufer, “Investigations of free turbulent mixing,” NASA Report No. 1257 (1947).Google Scholar
  6. 6.
    I. Wygnanski and H. E. Fiedler, “The two-dimensional mixing region,” J. Fluid Mech.,41, Part. 2, 327–361 (1970).Google Scholar
  7. 7.
    K. Rotta, “Statistiche theorie nichttogener turbulenz,” Z. Phys.129, No. 5, 547–572 (1951);131, No. 1, 51–77 (1951).Google Scholar
  8. 8.
    W. Rodi and D. B. Spalding, “Two-parameter model of turbulence and its application to free jets,” in: Warme und Stoffubertragung, Vol. 3, Springer-Verlag, Berlin (1970), pp. 85–95.Google Scholar
  9. 9.
    K. Hanjalic and B. E. Launder, “A Reynold's stress model of turbulence and its application to thin shear flows,” J. Fluid Mech.,52, Part. 4, 609–638 (1972).Google Scholar
  10. 10.
    R. Courant, Partial Differential Equations [Russian translation], Mir, Moscow (1964).Google Scholar
  11. 11.
    P. Bradshaw, D. H. Ferris, and P. N. Atwell, “Calculation of boundary layer development using turbulent energy equations,” J. Fluid Mech.,28, Part. 3, 593–616 (1967).Google Scholar
  12. 12.
    S. K. Godunov, “Difference method for numerically calculating discontinuous solutions of hydrodynamics equations,” Mat. Sb.,47, No. 3, 271 (1959).Google Scholar
  13. 13.
    G. B. Alalykin, S. K. Godunov, I. L. Kireeva, and L. A. Pliner, Solution of One-dimensional Gasdynamics Problems in Stationary Networks [in Russian], Nauka, Moscow (1970).Google Scholar
  14. 14.
    R. G. Batt, T. Kubota, and J. Laufer, “Experimental investigation of effective shear-flow turbulence on a chemical reaction,” in: AIAA Reacting turbulent flows conference, San Diego, California, June 17–18 (1970), Paper 70-721.Google Scholar
  15. 15.
    A. A. Townsend, Structure of Turbulent Shear Flow, Cambridge University Press.Google Scholar

Copyright information

© Plenum Publishing Corporation 1976

Authors and Affiliations

  • A. F. Kurbatskii
    • 1
  1. 1.Novosibirsk

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