Abstract
Calculation of a mixing layer-a classical problem in the theory of jet flows-is usually performed with a boundary-layer approximation. If the velocity of one of the flows is small, then even in the case of an incompressible fluid the angle of expansion of the mixing layer reaches 20‡, and in the case of flows with different densities this angle is even larger. Therefore, there is some doubt about the smallness of the neglected terms which refer to differentiation in the flow direction. In the present paper the problem of the mixing of two semiinfinite flows is solved both with a boundary-layer approximation and by using a complete system of Reynolds equations (the molecular viscosity is assumed small compared to the turbulent viscosity; Re→∞).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
J. Rotta, “Statistische Theorie Nichthomogener Turbulenz”, Z. Phys.,129, No. 6 (1951);131, No. 1 (1951).
K. Hanjalic and B. E. Launder, “Reynolds stress model of turbulence and its application to thin shear flows”, J. Fluid Mech.,52, Pt. 4 (1972).
B. J. Daly and F. H. Harlow, “Transport equations in turbulence”, Phys. Fluids,13, No. 11 (1970).
M. L. Koosinlin and F. C. Lockwood, “The prediction of axisymmetric turbulent swirling boundary layers”, AIAA J.,12, No. 4 (1974).
J. O. Hinze, Turbulence, McGraw-Hill, New York (1959).
I. Wygnanski and H. E. Fiedler, “The two-dimensional mixing region”, J. Fluid Mech.,41, Pt. 2 (1970).
H. W. Liepman and J. Laufer, “Investigation of free turbulent mixing”, NACA Tech. Note No. 1257 (1947).
E. V. Vlasov, “Investigation of turbulence with regard to the determination of the acoustic characteristics of a jet”, Inzh.-Fiz. Zh.,8, No. 5 (1965).
L. J. S. Bradbury, “The structure of a self-preserving turbulent plane jet”, J. Fluid Mech.,23, Pt. 1 (1965).
E. V. Vlasov and A. S. Ginevskii, “Acoustic effect on the aerodynamic characteristics of a turbulent jet”, Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 4 (1967).
P. Bradshaw, D. H. Ferriss, and R. F. Johnson, “Turbulence in noise-producing region of a circular jet”, J. Fluid Mech.,19, Pt. 4 (1964).
P. T. Harsha and S. C. Lee, “Correlation between turbulent shear stress and turbulent kinetic energy”, AIAA J.,8, 1508 (1970).
G. N. Abramovich, S. Yu. Krasheninnikov, and A. N. Sekundov, Turbulent Flows Subjected to Body Forces and Non-Self-Similarity [in Russian], Mashinostroenie, Moscow (1975).
L. D. Landau and E. M. Lifshitz, Mechanics of Continuous Media [in Russian], Gostekhizdat, Moscow (1953).
Lu Ting, “On the mixing of two parallel streams”, J. Math. Phys.38, No. 3 (1959).
Ya. B. Zel'dovich and A. S. Kompaneets, “Theory of heat propagation with the thermal conductivity dependent on the temperature”, in: Collection Honoring the 70th Birthday of Academician A. F. Ioffe [in Russian], Izd. Akad. Nauk SSSR, Moscow (1950).
J. C. Laurence, “Intensity scale and spectra of turbulence in the mixing region of a free subsonic jet”, NACA Rept. 1292 (1956).
D. R. Miller and E. W. Comings, “Static pressure distribution in the free turbulent jet”, J. Fluid Mech.,3, Pt. 1 (1957).
M. M. Barat, “Variations de pression statique dans jet libre subsonique”, Compt. Rend. Acad. Sci.,238, No. 4.
Author information
Authors and Affiliations
Additional information
Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 35–42, September–October, 1976.
The authors thank G. G. Chernyi and V. R. Kuznetsov for useful discussions, and G. Yu. Stepanov for reading the article in manuscript and making a number of useful suggestions.
Rights and permissions
About this article
Cite this article
Rasshchupkin, V.I., Sekundov, A.N. Applicability of the boundary-layer approximation to the calculation of a plane turbulent mixing layer. Fluid Dyn 11, 683–688 (1976). https://doi.org/10.1007/BF01012957
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01012957