scholarly journals The mathematical model and numerical approach based on ENO schemes for the flows in variable cross-section channels with combustion

2016 ◽  
pp. 1-20
Author(s):  
Ekaterina Vladimirovna Borovik ◽  
Mikhail Mikhailovich Krasnov ◽  
Yuri Germanovich Rykov ◽  
Dmitriy Konstantinovich Shalyga
Keyword(s):  
Mathematical Model ◽  
Cross Section ◽  
Numerical Approach ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Eno Schemes ◽  
The Mathematical Model

Three-Dimensional Force and Deflection Analysis of a Variable Cross Section Drill String

1977 ◽  
Vol 99 (2) ◽  
pp. 367-373 ◽  
Author(s):  
B. H. Walker ◽  
M. B. Friedman
Keyword(s):  
Mechanical Properties ◽  
Mathematical Model ◽  
Cross Section ◽  
Three Dimensional ◽  
Variable Cross Section ◽  
Drill String ◽  
Oil Field ◽  
Variable Cross ◽  
Deflection Curve ◽  
Deflection Analysis

A mathematical model of an oil field drill string which includes the effect of torque has been developed. The drill string can include arbitrary members with known mechanical properties. The solution gives the three-dimensional deflection curve, forces on the borehole wall, the magnitude and direction of the resultant force and slope of the deflection curve at the bit.

scholarly journals A mathematical model of the aerodynamics of drying chambers with vertical transverse circulation

2015 ◽  
Vol 5 (2) ◽  
pp. 131-137
Author(s):  
Земцовский ◽  
Aleksey Zemtsovskiy ◽  
Мануковский ◽  
Andrey Manukovskiy
Keyword(s):  
Mathematical Model ◽  
Cross Section ◽  
Air Flow ◽  
Variable Cross Section ◽  
Side Channel ◽  
Variable Cross ◽  
Factors Affecting ◽  
Lateral Channel ◽  
Drying Chamber ◽  
Transverse Circulation

In the article, from the standpoint of aerodynamics considered the concept of a mathematical model of the circulation channels marketing chambers of variable cross section with a vertically transverse circulation. Factors affecting the uniformity of the air flow in the pile of lumber. Developed analytical mathematical model of the motion of drying agent on the side channel of variable cross section. Revealed that the parameters of the lateral channel of the drying chamber of variable cross section does not depend on the temperature and humidity of the circulating air, and hence from the "rigidity" of the drying mode.

Mathematical Model of the Damped Variable Cross Section Beam in Transportation

2013 ◽  
Vol 837 ◽  
pp. 517-522
Author(s):  
Sławomir Zolkiewski ◽  
Leszek Dziczkowski
Keyword(s):  
Mathematical Model ◽  
Cross Section ◽  
High Speed ◽  
Equations Of Motion ◽  
Variable Cross Section ◽  
Resonance Phenomenon ◽  
Dynamic State ◽  
Variable Cross ◽  
Wide Range ◽  
Simple Systems

The paper concerns the problem of vibrations of beamlike system with variable cross section. The beam is treated as the movable system in transportation. The considered problem focuses on modelling and dynamic analysis of geometrically nonlinear beam systems in rotational motion within the context of damping. The major scientific purpose of the paper is to elaborate the mathematical model of such a system. Additionally, the main motion impact on the local vibrations due to the mathematical sense is determined. Moreover, it is necessary to remember the interactions between damping forces of the above mentioned mechanisms and the transportation effect. The main motion of the system is treated as transportation, whereas the vibrations of the system are treated as relative motion. There are two types of systems considered: simple vibrating longitudinally and simple vibrating transversally in the plane transportation. The most interesting elements of the analysis determine the dynamic state of the system and present the mutual coupling of vibration amplitudes, natural frequency, and transportation velocity. Analysis of systems moving with low velocities or vibrating only locally treats the systems as already known models in literature. There are many scientific articles where the forms of vibrations of these systems have been described. Due to the obtained results it will be possible to confront mathematical models with the known stationary and non-stationary systems. As regards complex and simple systems running at high speed, the resonance phenomenon can be noticed, and depending on the amplitude and frequency of vibrations, we consider the following cases: when the amplitude reaches theoretical infinity leading in practice to permanent damage of the mechanism or when the amplitude of vibration reaches a certain speed which can cause the decrease of durability of the whole system. The adequate practical usage of the above mentioned researches is justified by its wide range of applications. In the majority of technical cases, further analysis of the systems is considered to be far too much simplified when we ignore the elements of flexibility, damping, or the nonlinear geometry of the beam. All the mentioned influences are presented in the derived mathematical model in form of equations of motion.

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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