Simulation of fluid outflow from a channel with complex geometry

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.