Determining a flow structure in the region of local obstacles of different types taking into account the hydrodynamic conditions for entering the initial section

Abstract

This paper investigates the influence of hydrodynamic conditions for entering the initial section of the channel located after local obstacles of various types. It is shown that the head losses in the valves and bends of pipelines and in various control elements can be several times higher than those in straight sections of the pipeline. It was established that the assumption about the rectangular shape of the velocity diagram at the entrance to the hydrodynamic initial section does not correspond to the flow pattern in real channels of technological equipment. It is proved that with the manifestation of inertia forces in the flow at the initial section of the channel, hydrodynamic energy losses usually increase, velocity and stress fields are significantly deformed. Given this, it seemed expedient to conduct a study into the processes of flow of viscous liquids in the initial section, located after local obstacles of various types. Experimental and analytical studies have confirmed that there is a significant influence of boundary conditions at the entrance to the initial section on the formation of velocity diagrams and energy loss along its length. The analytical-numerical solution to the system of differential equations describing such flow is given. While solving, the system of equations, by appropriate transformations, takes the form of a nonlinear integral-differential equation. This makes it possible to obtain correct dependences for determining the length of the velocity distribution and energy loss in the investigated section of the channel. The results of calculations of velocity fields in the region of local obstacles agree well with known ideas of the flow pattern, which is observed in physical experiments and the results of analytical solutions. The quantitative difference in results ranges within 12–20 % depending on the Reynolds number. Thus, there is reason to assert that the results of studies reported here could be the basis for devising a procedure of hydrodynamic calculation aimed at structural and operational improvement of existing and designed technological equipment.