Abstract
—A new explicit form of the Navier—Stokes equations is obtained by means of the Reynoldsaveraging of these equations within the framework of the generally accepted model of spectrum-averaged fluctuations. The equations thus obtained contain some new terms caused by density fluctuations, while certain their terms included earlier on the intuitive level are now physically validated. The equations of the k—ω model are derived using the method of moments. A new equation for the vortex fluctuations, written earlier on the intuitive and analogue level, is obtained from the general momentum equation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
O. Reynolds, “An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels,” Trans. Roy. Phil. Soc. 174, 935 (1883).
O. Reynolds, “On the dynamical theory of incompressible viscous fluids and the determination of the criterion,” Trans. Roy. Phil. Soc. 186, 123 (1895).
Problems of Turbulence (ONTI, Moscow, 1936) [in Russian].
N. E. Kochin, I. A. Kibel’, and N. V. Roze, Theoretical Hydromechanics (Wiley Interscience, 1964).
H. Schlichting, Boundary Layer Theory (McGraw-Hill, New York, 1968).
L. G. Loitsyanskii, Mechanics of Liquids and Gases (Pergamon, Oxford, 1966).
V. V. Lunev, Real Gas Flows with High Velocities (CRC, Boca Raton, 2009).
G. G. Stokes, “On the theories of the internal friction of fluids in motion,” Trans. Cambridge Phil. Soc. (1845).
J. V. Boussinesq, Théorie de l’écoulement tourbillonnant (Gauthier-Villais, Paris, 1897).
L. Prandtl, “Untersuchungen zur ausgebildete turbulenz,” Z. Angew. Math. Mech., No. 5 (1925).
H. Oertel Jr. (ed.), Prandtl - Fuhrer durch Stromungslehre (Teubner, 1931, 2008).
A. N. Kolmogorov, “Equations of the turbulent motion of an incompressible fluid,” Dokl. Akad. Nauk SSSR. Ser. Fizika 6(12), 56–58 (1942).
S. G. Kovasznay, “The Turbulent boundary layer,” Annu. Rev. Fluid. Mech. 2, 95–112 (1970).
P. G. Saffman, “A model for inhomogeneous turbulent flow,” Proc. Roy. Soc. London. A 317, 417–433 (1970).
D. C. Wilcox, Turbulence Modeling for CFD (DCW Industries Inc. 1998).
F. R. Menter, “Two-equation eddy-viscosity turbulence models for engineering application,” AIAA J. 32(8), 1598–1605 (1994).
A. N. Secundov, V. Kh. Strelets, and A. K. Travin. “Two-equation vt-L turbulence model. Account for elliptic mechanism of turbulent transport,” ASME J. Fluid Engineering. 123, 11–15 (2000).
G. S. Glushko, “Turbulent boundary layer on a flat plate in an incompressible fluid,” Izv. Akad. Nauk SSSR, Mekhanika, No. 4, 13–23 (1965).
A. N. Gulyaev, V. E. Kozlov, and A. N. Sekundov, “A universal one-equation model for turbulent viscosity,” Fluid Dynamics 28 (4), 485–494 (1993).
P. R. Spalart and S. R. Allmaras, “A one-equation turbulence model for aerodynamic flows,” AIAA Paper No. 0439 (1992).
A. V. Garbaruk, M. Kh. Strelets, and M. L. Shur, Modeling of Turbulence in the Calculations of Complicated Flows (St. Petersburg, 2012) [in Russian].
O. I. Khintse, Turbulence, Its Mechanism and Theory (Fizmatgiz, Moscow, 1963) [in Russian].
Yu. V. Lapin, Turbulent Boundary Layer in Supersonic Gas Flows (Nauka, Moscow, 1982) [in Russian].
A. Favre, “Equations des gaz turbulents compressibles,” J. Mecanique No. 3, 361–390 (1965).
D. C. Wilcox, “Formulation of the k-turbulence model revisited,” AIAA J. 46(11), 2823–2838 (2008).
Author information
Authors and Affiliations
Corresponding author
Additional information
Russian Text © The Author(s), 2019, published in Izvestiya RAN. Mekhanika Zhidkosti i Gaza, 2019, No. 2, pp. 134–144.
Rights and permissions
About this article
Cite this article
Lunev, V.V. Modified Version of the Averaged Navier—Stokes Equations. Fluid Dyn 54, 279–289 (2019). https://doi.org/10.1134/S0015462819020083
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0015462819020083