Хлапук, М. М. та Безусяк, О. В. та Волк, Л. Р. та Khlapuk, M. М. та BezusіaK, O. V. та Volk, L. R. (2021) ДО ТЕОРІЇ ТУРБУЛЕНТНОСТІ ПОТОКУ В ТРУБОПРОВОДАХ. Вісник Національного університету водного господарства та природокористування (1(93)). с. 76-92.

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Анотація

В статті приведено результати теоретичних досліджень та отримано математичні моделі, які розкривають гідродинамічну структуру потоку при турбулентному режимі руху в трубопроводах.

Title in English

TO THE THEORY OF TURBULENCE OF FLOW IN PIPES

English abstract

The article presents the results of theoretical research and obtained mathematical models. These models describe the hydrodynamic structure of turbulent flow in pipes. A two-layer model is adopted, which includes a turbulent layer with a power distribution of the translational velocity of vortex lines and a boundary layer with a linear velocity distribution in the direction of the 0х axis. We hypothesized that in the equation of tangential stresses of turbulent flow, the kinematic viscosity between the layers is replaced by circulation. For the turbulent layer, the differential equation of velocity distribution in pipes is obtained. The equation of the profile of the translational velocity of vortex lines, which corresponds to the boundary conditions, is also obtained. The adequacy of the velocity profile equation was also checked on the basis of experimental data obtained by many well-known authors on hydraulic and aerodynamic installations with different experimental conditions. The equation of the relative position of the average velocity for the turbulent layer is obtained. It is proved that this position is not constant. It depends on the hydrodynamic slope and the inner surface of the pipes, the action of which in the equation is taken into account by the exponent m . The equation of distribution of the radius of the vortex tube from the radius of its vortex line is obtained. The value of the radius of the vortex line at which the vortex tube has the maximum diameter is determined. The equation of distribution of the angular velocity of the vortex tube and the equation of circulation of the velocity vector and pulsation velocities х u  and r u  are obtained. The pulsation component of L. Prandtl’s friction forces is also determined. For the boundary layer, the equation of the radius of the vortex tube on the inner surface of the pipe is obtained. The equation of the angular velocity of the vortex tube on the inner surface of the pipe is also obtained. The equation of velocity distribution of the fluid particle velocity points of the boundary layer is determined. The obtained hydrodynamic parameters are the basis for the development of the turbulence theory. It should be noted that the mathematical models presented in the article make it possible to determine only the averaged hydrodynamic parameters of the turbulent flow structure, and the real picture of turbulence is much more complex. However, the proposed mathematical models are obtained for the first time and describe the regularities of turbulent flow in pipes.

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