IMPROVEMENT OF APPROACHES AND METHODS OF TURBULENT FLOW THEORY IN THE PIPES

Abstract

Abstract. The article consideres the analysis of the literature about the development of the water turbulent flow theory in the pipes. According to the results of analysis and theoretical studies, we obtained mathematical models. These models described the kinematic structure of the water turbulent flow in the pipes for different regions of turbulence. For the first time, the hypothesis was accepted that the dependence obtained from the Navier-Stokes differential equation for constructing the velocity profile in the laminar regime is suitable for calculating the average velocities in the turbulent regime of flow, but for this, it is necessary to replace the molecular kinematic viscosity with the total turbulent kinematic viscosity, which includes kinematic viscosity on the inner surface of the pipe and turbulent kinematic viscosity , which occurs due to the movement of masses from one layer into another, as recommended in J.V. Boussinesq. Based on experimental data I. Nikuradze and F.O. Shevelev, we obtained a distribution of the total kinematic viscosity in the pipes, including the kinematic viscosity on the pipe inner surface and the kinematic turbulent viscosity. For the first time, we used the kinematic viscosity distribution equation in the pipes and obtained the averaged velocity profile equation. This equation corresponds to the boundary conditions on the pipe inner surface and on the axis of the pipe. The equation of maximum averaged velocity, the equation of distance from the axis of the pipe to the points having average velocity, the equation of the ratio of maximum velocity to average velocity was obtained. For the first time, the equation of the tangent stresses components ( , ) and the tangent stresses equation in radial coordinates ( ) were obtained. The equation of the maximum value of the tangent stresses located on the inner surface of the pipe was obtained. The tangent stresses assume a zero value on the pipe axis. The equation of the vortex components ( , ) was obtained. We have shown that vortex lines are concentric circles whose centers are located on the pipe axis. The equation of angular velocity of flow particles rotation relative to the vortex lines was obtained. The maximum value of the particle rotation angular velocity on the pipe inner surface is determined. It decreases monotonically to zero on the axis of the pipeline. It is zero on the pipe axis. In this article, all equations reveal the kinematic structure of the water flow. We described these equations by the Reynolds number and the pipe friction factor. Such equations are adopted to show the dependencies between the regimes and the flow kinematic structure. These equations make it possible to calculate the distribution profile of the total kinematic viscosity, averaged velocity, tangential stresses and angular velocity of flow particle rotation.