Abstract
Topic of the paper is the simulation of fluid outflow from a channel with complex geometry. Subject of the study is the outflow of fluid from a channel with an arbitrary section, in particular, consisting of a parabolic inlet, cylindrical middle and hyperbolic outlet sections. The paper considers the integral form of determining the pressure and the average flow rate of the fluid in a channel with an arbitrary cross section. From the obtained expression for the pressure and from the equation of conservation of mass, given in integral form, it is necessary to determine the pressure and the average flow rate in successively located channels with a parabolic, cylindrical and hyperbolic section. Research methods are based on: Newton’s rheological law; the continuity equation and the Navier-Stokes equation, which are the basic equations of fluid motion; the method of mathematical modeling and the analytical method for their solution. The paper contains integral expressions for the hydrodynamic characteristics of a fluid flow in a channel with an arbitrary section. The pressure and average flow rate in the channel of successively located parabolic, cylindrical, hyperbolic segments are determined. Analytical expressions are obtained for the pressure and average flow rate of the liquid in a channel with an arbitrary cross section. As an example, the pressures and the average flow rate in the channel from the parabolic inlet, cylindrical middle and hyperbolic outlet sections are determined. In perspective, by substituting in them an arbitrary arithmetic expression of the channel cross-section, it is possible to determine the hydrodynamic characteristics of the flow with any geometry of the flow channel.
Highlights
Anti-vibration baffles in pipeline transport improve flow characteristics and are the reason for flow establishment
Analyzing numerous studies aimed at improving the hydrodynamic characteristics by changing the geometry of a segment in a pipeline, segments with a circular and elliptical section were proposed [1]
The object of the study is the outflow of fluid from a channel of arbitrary shape, in particular, from a channel with a parabolic inlet, cylindrical middle and hyperbolic outlet sections
Summary
Anti-vibration baffles in pipeline transport improve flow characteristics and are the reason for flow establishment. In this case, the determination of the velocity and pressure of the liquid in this area plays an important role. The determination of the flow parameters depending on the geometry [1,2,3,4,5], external factors [6], internal factors [7,8,9] are solved using numerical [2,5,8] and analytical [9,10] methods In many works, such studies are carried out by numerical methods using modern information and communication systems. The problem relates to a segmental section of pipeline transport and is solved by the analytical method
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