Abstract
Nonstationary flows in laminar and turbulent regimes in differently shaped channels have been investigated theoretically. An approach has been used which is based on the properties of the symmetry of differential equations (Lie groups) that describe the process of an accelerated channel flow. A way in which the self-similar forms of one-dimensional and two-dimensional flow can be obtained on the basis of symmetries is shown. The self-similar equations of the process and their analytical and numerical solutions are given.
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REFERENCES
N. A. Slezkin, Dynamics of Viscous Incompressible Fluid [in Russian], Moscow (1955).
A. A. Avramenko, Dokl. Nats. Akad. Nauk Ukrainy, No. 8, 76-80 (1999).
A. A. Avramenko, Teplofiz. Vys. Temp., 38, No. 3, 452-457 (2000).
P. J. Olver, Applications of Lie Groups to Differential Equations [Russian translation], Moscow (1989).
B. P. Ustimenko, Processes of Turbulent Transfer in Rotating Flows [in Russian], Alma-Ata (1977).
P. Nee and L. S. G. Kovasznay, Phys. Fluids, 12, No. 3, 473-484 (1969).
A. J. Reynolds, Turbulent Flows in Engineering [Russian translation], Moscow (1979).
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Avramenko, A.A. Analysis of Nonstationary Incompressible Flows in Differently Shaped Channels on the Basis of Symmetries. Journal of Engineering Physics and Thermophysics 74, 1137–1153 (2001). https://doi.org/10.1023/A:1012967830740
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DOI: https://doi.org/10.1023/A:1012967830740