Investigation of the thermoviscous liquid flow in a plane channel with a narrowing

2017 ◽  
Vol 12 (2) ◽  
pp. 157-162
Author(s):  
A.D. Nizamova ◽  
V.N. Kireev ◽  
S.F. Urmancheev
Keyword(s):  
Cross Section ◽  
Liquid Flow ◽  
Plane Channel ◽  
Thermal Action ◽  
Variable Cross Section ◽  
Resistance Coefficient ◽  
Channel Cross Section ◽  
Variable Cross ◽  
Local Resistance Coefficient ◽  
Inhomogeneous Temperature

In this paper, the problem of the possibility of regulating hydraulic resistance due to local thermal action is considered. The flow of an incompressible liquid with a temperature dependence of the viscosity in a plane channel with a variable cross section and an inhomogeneous temperature field is investigated. The flow velocities profiles of a thermoviscous liquid for a narrowed channel are obtained numerically. Using the example of a thermoviscous liquid flow in a plane channel with a sharp expansion, it is shown that the temperature factor exerts a significant influence on the value of the local resistance coefficient for the variable channel cross-section.

Mathematical Model Of Liquid Flow Through The Pipe Of Curcular Cross-Section

2016 ◽  
Vol 11 (4) ◽  
pp. 61-67
Author(s):  
Eduard Arinstein ◽  
Denis Tokarev
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Liquid Flow ◽  
Analytical Approach ◽  
Variable Cross Section ◽  
Cylindrical Symmetry ◽  
Variable Cross ◽  
Current Line ◽  
Flow Velocity Profile ◽  
Flow Through

This article analyses the properties of homogeneous viscous liquid flow in the pipe with variable cross-section characterized by cylindrical symmetry. The analytical approach is proposed in order to determine the flow velocity profile in the pipe’s extremium cross-sections. The conditions when dead spaces emerge in neighborhood of the maximum cross-section are identified. The particular case of problem-solving allowing prime presentation is examined for the set of current line allowing prime presentation.

Boundary element method in numerical study of three-dimensional Stokes flows in channels of arbitrary shape

2012 ◽  
Vol 9 (1) ◽  
pp. 94-97
Author(s):  
Yu.A. Itkulova
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Cross Section ◽  
Numerical Study ◽  
Three Dimensional ◽  
Cylindrical Tube ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Periodic Flows ◽  
Element Method

In the present work creeping three-dimensional flows of a viscous liquid in a cylindrical tube and a channel of variable cross-section are studied. A qualitative triangulation of the surface of a cylindrical tube, a smoothed and experimental channel of a variable cross section is constructed. The problem is solved numerically using boundary element method in several modifications for a periodic and non-periodic flows. The obtained numerical results are compared with the analytical solution for the Poiseuille flow.

Longitudinal oscillation of a rod with a variable cross section

2019 ◽  
Vol 14 (2) ◽  
pp. 138-141
Author(s):  
I.M. Utyashev
Keyword(s):  
Cross Section ◽  
Natural Frequencies ◽  
Liouville Problem ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Longitudinal Vibrations ◽  
Cross Sectional ◽  
Independent Functions ◽  
The Cross ◽  
The Right

Variable cross-section rods are used in many parts and mechanisms. For example, conical rods are widely used in percussion mechanisms. The strength of such parts directly depends on the natural frequencies of longitudinal vibrations. The paper presents a method that allows numerically finding the natural frequencies of longitudinal vibrations of an elastic rod with a variable cross section. This method is based on representing the cross-sectional area as an exponential function of a polynomial of degree n. Based on this idea, it was possible to formulate the Sturm-Liouville problem with boundary conditions of the third kind. The linearly independent functions of the general solution have the form of a power series in the variables x and λ, as a result of which the order of the characteristic equation depends on the choice of the number of terms in the series. The presented approach differs from the works of other authors both in the formulation and in the solution method. In the work, a rod with a rigidly fixed left end is considered, fixing on the right end can be either free, or elastic or rigid. The first three natural frequencies for various cross-sectional profiles are given. From the analysis of the numerical results it follows that in a rigidly fixed rod with thinning in the middle part, the first natural frequency is noticeably higher than that of a conical rod. It is shown that with an increase in the rigidity of fixation at the right end, the natural frequencies increase for all cross section profiles. The results of the study can be used to solve inverse problems of restoring the cross-sectional profile from a finite set of natural frequencies.

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