STUDY OF CHANGES IN HYDRODYNAMIC PARAMETERS PATTERNS OF VISCOUS FLUID FLOW IN A FLAT DIFFUSER

Abstract

The relevance. Diffusers, either as nozzles or constituent elements, are frequently used in many mechanisms and machines. In this regard, the study of viscous fluid flow in diffusers aims to discover patterns of changes in the flow's hydrodynamic parameters, allowing better understanding of the nature of flow as a function of Reynolds number. Following the results of the analysis of the study, conditions for the proper construction of the mechanism unit, ensuring its reliable and durable operation will be revealed. The main aim of this study is to determine the velocity profiles in the flat diffuser for a viscous incompressible fluid by integrating the simplified Navier–Stokes differential equations under the established initial and boundary conditions, as well as the bifurcation point's dependence on the opening angle and Reynolds number of the diffuser. Objects: a flat diffuser in which viscous incompressible fluid moves. At the same time, revealing the patterns of changes of the hydrodynamic parameters of the flow is of defining value when choosing the structural dimension of devices and mechanisms, the main part of which is the flat diffuser. Methods. To reveal the patterns of changes of the hydrodynamic parameters of the flow in a flat diffuser, the study is based on the fundamental nonlinear differential equations of viscous fluid mechanics, which in a general case are not subject to an exact mathematical solution. For integration in the nonlinear differential equations, due to the smallness, the nonlinear-convective terms are neglected, and the inertial terms are also partially simplified. Such a simplification is justified if the velocities are very small or if the dynamic coefficient of viscosity of the fluid is very large. A method for solving the boundary value problem was developed, and regularities for changing the flow parameters were obtained. According to the derived regularities, graphs of the change in velocity, pressure and shear stresses on the wall of the fixed channel were plotted and the coordinates of the separation point were determined. Results. Depending on the angle of the diffuser opening and the Reynolds number, a general solution of the approximating Navier–Stokes equations was given. In accordance with the nature of the motion, the boundary conditions of the problem were established and the boundary value problem was stated. A method for integrating a boundary value problem was developed, and regularities for the change in velocities along the length of the diffuser were obtained for a parabolic distribution of velocities in the inlet sections. Graphs of the change in radial velocities along the length and at a fixed value of the opening angle were constructed, a flow pattern and the transition of a single-mode flow to multimode operation were obtained. For a fixed opening angle and Reynolds number, the conditions for flow separation from a fixed wall were derived, where the flow velocity changes the sign.

Keywords

• diffuser
• velocity profile
• pressure distribution
• breaking point
• viscous fluid
• fluid flow