INVESTIGATION OF HYDRODYNAMIC AND GAS DYNAMIC PROCESSES IN A CLOSED BYPASS CHANNEL WITH A RECTANGULAR CROSS-SECTION OF VARYING ASPECT RATIOS

Abstract

The article addresses a scientific and applied problem of determining the hydrodynamic and gas dynamic characteristics of flow in closed channels with a rectangular cross-section. It is substantiated that classical analytical relations based on the Hagen-Poiseuille law are valid exclusively for channels with a circular cross-section, whereas in real engineering systems, rectangular or more complex geometries are predominant. The study presents an analytical investigation of laminar flow of liquids and gases in a rectangular channel based on the Navier-Stokes equations. For the rectangular channel, the solution was constructed using the method of expansion in trigonometric series, which allows proper consideration of boundary conditions and the geometric characteristics of the flow domain. It was established that the flow capacity of the channel depends on the aspect ratio of its sides, with the extreme value of the corresponding coefficient being achieved for a square cross-section. The analytical results were verified through numerical simulations using MATLAB and SOLIDWORKS Flow Simulation. Functional dependencies of velocity and flow characteristics on the geometric parameters of the channel were constructed.