scholarly journals Numerical Simulation of Interaction Between Kr+ Ion and Rotating C60 Fullerene Towards for Nanoarchitectonics of Fullerene Materials

Crystals ◽  
2021 ◽  
Vol 11 (10) ◽  
pp. 1204
Author(s):  
Aleksandr V. Lun-Fu ◽  
Alexey M. Bubenchikov ◽  
Mikhail A. Bubenchikov ◽  
Vyacheslav A. Ovchinnikov
Keyword(s):  
Mathematical Model ◽  
Lattice Structure ◽  
Numerical Study ◽  
Equations Of Motion ◽  
Translational Motion ◽  
C60 Fullerene ◽  
Special Role ◽  
Centrally Symmetric ◽  
Centers Of Mass ◽  
Angular Oscillations

Dynamics of charged fullerene in a surface layer of fullerite is studied under the influence of neutral or charged particles of the gas phase surrounding the fullerite material. The translational displacements of the nodes of the crystal lattice structure are determined by the equations of motion of the centers of mass of fullerenes. Central fullerene, which is described as a discrete set of sixty carbon atoms, plays a special role in the presented mathematical model. Angular oscillations and rotations of the central fullerene are described by the dynamic Euler equations. All other fullerenes have a centrally symmetric field of the potential of interaction with the surrounding atoms and molecules. In this regard, we use the hybrid discrete–continuous mathematical model with four potentials that describe the interactions between the surrounding fullerenes, smoothed fullerene and an atom, a pair of atoms, and electric charges. The results of a numerical study of influence of the Coulomb interaction on the rotational and translational motion of the C60 fullerene are presented.

scholarly journals A Numerical Study of a Compressed Air Engine with Rotating Cylinders

2021 ◽  
Vol 11 (16) ◽  
pp. 7504
Author(s):  
Ján Dižo ◽  
Miroslav Blatnický ◽  
Milan Sága ◽  
Pavol Šťastniak
Keyword(s):  
Mathematical Model ◽  
Lateral Pressure ◽  
Numerical Study ◽  
Equations Of Motion ◽  
Combustion Engines ◽  
Connecting Rod ◽  
Conventional Combustion ◽  
Working Principle ◽  
Engine Components ◽  
The Mathematical Model

This article explores the possibility that, during the elimination of conventional combustion engines, the connecting rod becomes deflected. A larger connecting rod angle creates higher lateral pressure on the piston, also leading to greater loads on other engine components. This fact inspired us to develop an applied mechanism design that reduces the disadvantages of conventional combustion engines. The presented mathematical model that describes the designed engine working principle was created utilizing Lagrange’s equations of motion of the second kind and solved in MATLAB. This paper also includes a multibody simulation model of the engine mechanism created using the Simpack software. Based on a comparison of the two methods, the obtained waveforms of the selected kinematic quantities were found to yield minimal deviations. A real prototype was subsequently developed based on the mathematical model outputs. In this manner, we practically verified that the proposed theoretical solution for a non-conventional engine is fully functional.

scholarly journals NUMERICAL STUDY OF THE INFLUENCE OF DISPERSED INCLUSIONS SIZE ON THE GAS-SUSPENSION SPLITTING PROCESS IN VACUUM

2020 ◽  
pp. 109-119
Author(s):  
Д.А. Тукмаков ◽  
Н.А. Тукмакова
Keyword(s):  
Mathematical Model ◽  
Particle Size ◽  
Inhomogeneous Medium ◽  
Numerical Study ◽  
Equations Of Motion ◽  
Momentum Conservation ◽  
System Of Equations ◽  
Gas Suspension ◽  
Carrier Medium ◽  
The Mathematical Model

В работе моделируется течение однородного газа и неоднородной среды. Целью работы является изучение влияния размера частиц дисперсной компоненты смеси на истечение дисперсной среды в вакуум и выявление отличий от процесса истечения в вакуум однородного газа. Математическая модель, примененная в данной работе, реализует континуальную методологию моделирования течения неоднородной среды, такого рода методика моделирования движения смеси предполагает решение полной гидродинамической системы уравнений движения для каждой из компонент смеси, системы уравнений движения компонент смеси связаны слагаемыми, отвечающими за межфазное силовое и тепловое взаимодействие. Система уравнений включает уравнения непрерывности для плотности несущей среды и средней плотности дисперсной компоненты смеси. Для описания сохранения импульса несущей среды решалось уравнение Навье-Стокса, для дисперсной компоненты смеси также записывалось уравнение сохранения импульса с учетом слагаемых отвечающих за межкомпонентное взаимодействие. Уравнения сохранения энергии компонент смеси решались с учётом межкомпонентного теплообмена. Система уравнений математической модели дополненная краевыми условиями решалась явным конечно-разностным методом второго порядка точности. В результате моделирования выявлены отличия в распределении параметров сплошной среды при распространении в вакуум чистого газа и газовой взвеси частиц. Также выявлено влияние размера частиц дисперсной фазы на процесс истечение несущей среды и дисперсной компоненты газовзвеси в вакуум. The work simulates the flow of a homogeneous gas and an inhomogeneous medium. The aim of the work is to study the influence of the particle size of the dispersed component of the mixture on the outflow of the dispersed medium into vacuum and to identify differences from the process of outflow of a homogeneous gas into the vacuum. The mathematical model used in this work implements a continuous methodology for modeling the flow of an inhomogeneous medium, this kind of methodology for modeling the mixture motion involves solving the complete hydrodynamic system of equations of motion for each of the components of the mixture, the systems of equations of motion of the components of the mixture are connected by terms responsible for the interphase force and thermal interaction. The system of equations includes continuity equations for the density of the carrier medium and the average density of the dispersed component of the mixture. To describe the momentum conservation of the carrier medium, the Navier-Stokes equation was solved for the dispersed component of the mixture, the equation of momentum conservation was also written taking into account the terms responsible for the intercomponent interaction. The energy conservation equations for the mixture components were solved taking into account inter-component heat transfer. The system of equations of the mathematical model supplemented by boundary conditions was solved by an explicit finite-difference method of the second order of accuracy. As a result of the simulation, differences in the distribution of the parameters of a continuous medium during the propagation of pure gas and gas suspension of particles into a vacuum are revealed. The effect of the particle size of the dispersed phase on the process of the outflow of the carrier medium and the dispersed component of the gas suspension into vacuum was also revealed.

NUMERICAL STUDY FOR THAILAND: MATHEMATICAL MODEL OF PRODUCTION AND LOGISTIC PLANNING FOR SUGARCANES USED IN BIOFUEL PRODUCTION

2013 ◽  
Author(s):  
Pancheewa Benjamasutin ◽  
◽  
Ponthong Rijana ◽  
Phongchayont Srisuwan ◽  
Aussadavut Dumrongsiri
Keyword(s):  
Mathematical Model ◽  
Numerical Study ◽  
Biofuel Production ◽  
Logistic Planning

A Numerical Study of Unsteady Natural Convection in a Rectangular Enclosure: The Effect of Compressibility

2004 ◽  
Author(s):  
K. M. Akyuzlu ◽  
Y. Pavri ◽  
A. Antoniou
Keyword(s):  
Mathematical Model ◽  
Stokes Equations ◽  
Numerical Study ◽  
Vertical Wall ◽  
Ideal Gas ◽  
Working Fluid ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
Rectangular Enclosure ◽  
Circulation Patterns

A two-dimensional, mathematical model is adopted to investigate the development of buoyancy driven circulation patterns and temperature contours inside a rectangular enclosure filled with a compressible fluid (Pr=1.0). One of the vertical walls of the enclosure is kept at a higher temperature then the opposing vertical wall. The top and the bottom of the enclosure are assumed insulated. The physics based mathematical model for this problem consists of conservation of mass, momentum (two-dimensional Navier-Stokes equations) and energy equations for the enclosed fluid subjected to appropriate boundary conditions. The working fluid is assumed to be compressible through a simple ideal gas relation. The governing equations are discretized using second order accurate central differencing for spatial derivatives and first order forward finite differencing for time derivatives where the computation domain is represented by a uniform orthogonal mesh. The resulting nonlinear equations are then linearized using Newton’s linearization method. The set of algebraic equations that result from this process are then put into a matrix form and solved using a Coupled Modified Strongly Implicit Procedure (CMSIP) for the unknowns (primitive variables) of the problem. A numerical experiment is carried out for a benchmark case (driven cavity flow) to verify the accuracy of the proposed solution procedure. Numerical experiments are then carried out using the proposed compressible flow model to simulate the development of the buoyancy driven circulation patterns for Rayleigh numbers between 103 and 105. Finally, an attempt is made to determine the effect of compressibility of the working fluid by comparing the results of the proposed model to that of models that use incompressible flow assumptions together with Boussinesq approximation.

Numerical modelling of swirling momentumless turbulent wake dynamics

2018 ◽  
pp. 37-48
Author(s):  
Андрей Геннадьевич Деменков ◽  
Геннадий Георгиевич Черных
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Mathematical Models ◽  
Equations Of Motion ◽  
Turbulent Wake ◽  
The Body ◽  
Jet Flows ◽  
Reynolds Stresses ◽  
Bodies Of Revolution ◽  
Averaged Equations

С применением математической модели, включающей осредненные уравнения движения и дифференциальные уравнения переноса нормальных рейнольдсовых напряжений и скорости диссипации, выполнено численное моделирование эволюции безымпульсного закрученного турбулентного следа с ненулевым моментом количества движения за телом вращения. Получено, что начиная с расстояний порядка 1000 диаметров от тела течение становится автомодельным. На основе анализа результатов численных экспериментов построены упрощенные математические модели дальнего следа. Swirling turbulent jet flows are of interest in connection with the design and development of various energy and chemical-technological devices as well as both study of flow around bodies and solving problems of environmental hydrodynamics, etc. An interesting example of such a flow is a swirling turbulent wake behind bodies of revolution. Analysis of the known works on the numerical simulation of swirling turbulent wakes behind bodies of revolution indicates lack of knowledge on the dynamics of the momentumless swirling turbulent wake. A special case of the motion of a body with a propulsor whose thrust compensates the swirl is studied, but there is a nonzero integral swirl in the flow. In previous works with the participation of the authors, a numerical simulation of the initial stage of the evolution of a swirling momentumless turbulent wake based on a hierarchy of second-order mathematical models was performed. It is shown that a satisfactory agreement of the results of calculations with the available experimental data is possible only with the use of a mathematical model that includes the averaged equations of motion and differential equations for the transfer of normal Reynolds stresses along the rate of dissipation. In the present work, based on the above mentioned mathematical model, a numerical simulation of the evolution of a far momentumless swirling turbulent wake with a nonzero angular momentum behind the body of revolution is performed. It is shown that starting from distances of the order of 1000 diameters from the body the flow becomes self-similar. Based on the analysis of the results of numerical experiments, simplified mathematical models of the far wake are constructed. The authors dedicate this work to the blessed memory of Vladimir Alekseevich Kostomakha.

ROTATIONS AND VIBRATIONS OF FULLERENES IN THE MOLECULAR COMPLEX C20@C80

2021 ◽  
pp. 35-48
Author(s):  
M.A. Bubenchikov ◽  
◽  
A.M. Bubenchikov ◽  
D.V. Mamontov ◽  
◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Classical Mechanics ◽  
Rotation Frequency ◽  
Dynamic State ◽  
Large Molecules ◽  
Rotational Degrees Of Freedom ◽  
Rotational Motions ◽  
Centers Of Mass ◽  
The Moment

The aim of this work is to apply classical mechanics to a description of the dynamic state of C20@C80 diamond complex. Endohedral rotations of fullerenes are of great interest due to the ability of the materials created on the basis of onion complexes to accumulate energy at rotational degrees of freedom. For such systems, a concept of temperature is not specified. In this paper, a closed description of the rotation of large molecules arranged in diamond shells is obtained in the framework of the classical approach. This description is used for C20@C80 diamond complex. Two different problems of molecular dynamics, distinguished by a fixing method for an outer shell of the considered bimolecular complex, are solved. In all the cases, the fullerene rotation frequency is calculated. Since a class of possible motions for a single carbon body (molecule) consists of rotations and translational displacements, the paper presents the equations determining each of these groups of motions. Dynamic equations for rotational motions of molecules are obtained employing the moment of momentum theorem for relative motions of the system near the fullerenes’ centers of mass. These equations specify the operation of the complex as a molecular pendulum. The equations of motion of the fullerenes’ centers of mass determine vibrations in the system, i.e. the operation of the complex as a molecular oscillator.

scholarly journals Vibration and Instability of Rotating Composite Thin-Walled Shafts with Internal Damping

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Ren Yongsheng ◽  
Zhang Xingqi ◽  
Liu Yanghang ◽  
Chen Xiulong
Keyword(s):  
Virtual Work ◽  
Numerical Study ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Dynamical Analysis ◽  
Design Parameters ◽  
Internal Damping ◽  
Analysis Method ◽  
Governing Equations ◽  
Thin Walled

The dynamical analysis of a rotating thin-walled composite shaft with internal damping is carried out analytically. The equations of motion are derived using the thin-walled composite beam theory and the principle of virtual work. The internal damping of shafts is introduced by adopting the multiscale damping analysis method. Galerkin’s method is used to discretize and solve the governing equations. Numerical study shows the effect of design parameters on the natural frequencies, critical rotating speeds, and instability thresholds of shafts.

scholarly journals Steady and unsteady flow of non-newtonian fluid in curved pipe with triangular

2006 ◽  
Vol 3 (3) ◽  
pp. 470-480
Author(s):  
Baghdad Science Journal
Keyword(s):  
Unsteady Flow ◽  
Pressure Gradient ◽  
Secondary Flow ◽  
Cross Section ◽  
Numerical Study ◽  
Equations Of Motion ◽  
Curved Pipe ◽  
First Case ◽  
Stable Flow ◽  
Flow Cross

This paper deals with numerical study of the flow of stable and fluid Allamstqr Aniotina in an area surrounded by a right-angled triangle has touched particularly valuable secondary flow cross section resulting from the pressure gradient In the first case was analyzed stable flow where he found that the equations of motion that describe the movement of the fluid

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