Research of Unsteady Turbulent Motion in a Flat-Parallel Pipe

This paper focuses on studying structural changes in the viscous fluid during turbulent unsteady plane-parallel pressure flow. This investigation analyzes how hydrodynamic parameters change in viscous fluid unsteady motion, particularly by calculating the turbulent viscosity coefficient. The study addresses the boundary problem that arises when there are axisymmetric changes in the flow. The selection of boundary conditions aligns with the patterns associated with the arbitrary distribution of pressure gradients and velocities within the section. Based on the initial and boundary conditions, the boundary value problem is formulated. The method for solving this boundary value problem was developed, and the regularities of the instantaneous speed change along the cross-section were obtained. The solution to the boundary value problem is derived by integrating partial differential equations, ensuring the satisfaction of all boundary conditions. Analytical solutions have been derived, enabling the determination of velocity patterns at any given moment. On the basis of the general solutions to the problem, solutions were obtained for the accelerating motion under the influence of a constant pressure gradient on a fluid at rest. The computer analysis generated composite graphs displaying average velocities across various time intervals. The provided solutions enable the visualization of average velocity changes within conditions of plane-parallel turbulent flow. These findings allow for the conclusion of the design of individual units within hydro-mechanical equipment.