Issue 2

JTAM, Sofia, vol. 23 Issue 2 (1992)

FOREWARD

S. Slavtchev


JTAM, Sofia, vol. 23 Issue 2 pp. 015-015 (1992), [Full Article]


Numerical and Experimental Study of Hydrodynamic Effects in Crystal Growth from Melts

G. Muller, M. Peric
Universitat Erlangen-Nurnberg, Erlangen, Germany

Crystal growth from the melt is the key technology for producing the starting materialsfor micro- and opto-electronics. The properties of the growing crystals arestrongly influenced by the transport processes occurring in the melt. Buoyancy, thermocapillary and forced convections interact in a complex manner in determining the growth rate, crystal erfection, incorporation of dopants and homogeneity of all relevant crystal properties. This will be demonstrated by selected experimental results. It is also discussed to what extent a numerical modelling of the melt growth process is possible and what results can presently be obtained. Finally a perspective is given on the future use of advanced numerical solution techniques.

JTAM, Sofia, vol. 23 Issue 2 pp. 016-029 (1992), [Full Article]


Fixed Grid Solution of Phase Change Problem

V.Voller, C. Swaminathan
University of Minnesota, Minneapolis, USA

In general, phase change problems involve moving boundaries at which heat and mass balance conditions need to be satisfied. In such well defined problems it is possible to develop a numerical solution based on a grid that adapts with the movement of the boundaries. In this approach the heat and mass balance constraints at the moving boundaries are absorbed into the governing equations so that a fixed numerical space grid can be used throughout the calculation. Three test examples are considered. Two of them are conduction driven solidification problems while the third example involves the solution of the coupled Navier-Stokes and the energy equation during the melting of pure gallium.

JTAM, Sofia, vol. 23 Issue 2 pp. 030-040 (1992), [Full Article]


Mathematical Modelling of Heat Transfer in Silicon Czochralski Growth

S. Kobayashi, Sh. Miyahara, T. Fujiwara, T. Kubo, H. Fujiwara, Sh. Inami
Sumitomo Metal Industries, Ltd. Amagaski, Japan

This paper describes two topics on computer modeling of heat transfer in Czochralski (CZ) crystal growth. A global thermal model of a whole CZ puller has been developed to predict the temperature distribution accurately. Computer simulation of heat transfer based on reasonable boundary conditions and actual input parameters has been carried out and typical model results on thermal history are discussed. Convective heat transfer in the melt is studied by comparing three different computer models: conduction dominated model, 2D laminar convection model, and 2D k-epsilon convection model, and 2D k-epsilon.

JTAM, Sofia, vol. 23 Issue 2 pp. 041-046 (1992), [Full Article]


Thin Filament and Thin Film Theories of Hydrodynamics and Rheology

S. Kase
Kyoto Institute of Technology, Kyoto, Japan

The purpose of the paper is to demonstrate the simplicity of thin filament and thin film equations by discussing the case of isothermal Newtonian fluids with the effects of surface air drag, gravity and surface tension neglected. This simplification reduces the problem to that in the hydrodynamics of creeping viscous flow. All conceivable aspects of the simplest thin film and filament theories are discussed.

JTAM, Sofia, vol. 23 Issue 2 pp. 047-071 (1992), [Full Article]


Hydrodynamical Aspects of Melt Spinning

V. Entov, Kh. Kestenboim
Institute for Problems in Mechanics, Moscow, Russia

The objective of this paper is to discuss . some basic aspects of melt spinning as a mechanical phenomenon. The discussion is focussed on the possible elastic effects, their manifestations and theoretical description.

JTAM, Sofia, vol. 23 Issue 2 pp. 072-078 (1992), [Full Article]


Determination of the Activation Energy during Drawing of Glass Microcapillaries

St. Radev1, P. Gospodinov1, Vl. Roussinov2, A. Yarin2
1Institute of Mechanics and Biomechanics, Bulg. Acad. Sci., Sofia
2Institute for Problems in Mechanics, Moscow, Russia

The study is based on a recently obtained analytical solution, considering a steady one dimensional model for the fabrication of micro capillaries from glass tubes. However, these relations allow for an experimental determination of the activation energy which takes part in the viscosity relation of the vitreous mass. A direct determination of the activation energy is given by performing experiments on a real technological installation for drawing of glass fibers and capillaries. In order to describe adequately the process the analytical solution is compared to the experimental data.

JTAM, Sofia, vol. 23 Issue 2 pp. 079-084 (1992), [Full Article]


Thermocapillary Convection in a Rectangular Cavity at Minimum of Surface Tension

S. Slavtchev, K. Dubovik
1Institute of Mechanics and Biomechanics, Bulg. Acad. Sci., Sofia
2Institute for problems in Mechanics, Moscow, Russia

Thermocapillary flow of a viscous incompressible liquid is examined in a rectangular two-dimensional cavity with adiabatic free surface, isolated bottom and differentially heated side walls. Numerical solutions of the Navier-Stokes and heat equations for moderate Reynolds and Prandtl numbers are obtained in case of non-linear dependence of the surface tension on temperature. Some features of the flow pattern are discussed comparing the results to the self-similar solution of the same equations obtained for an infinite liquid layer with a free surface along which the temperature changes linearly.

JTAM, Sofia, vol. 23 Issue 2 pp. 085-090 (1992), [Full Article]


Influence of Surface Tension Minimum on Thermocapillary Flow in Thin Liquid Layer

Zh. Kozhoukharova
Institute of Mechanics and Biomechanics, Bulg. Acad. Sci., Sofia

Thermocapillary convection, arising in small-depth layers with deformable free surface subjected to a horizontal temperature gradient is studied analytically. The investigated liquids are characterized with the existence of a surface tension minimum. An explicit analytical form is obtained for describing the steady-state free liquid surface.

JTAM, Sofia, vol. 23 Issue 2 pp. 091-097 (1992), [Full Article]


Modelling Technological Process of Plastics Moulding under Pressure

V. Belikov1, V. GoIoviznin1, J. Katyschkov2, P. Vabishchevich2
1Institute of Nuclear Safety, Moscow, Russia
2Institute of Mathematical Modelling, Moscow, Russia

Simplified quasi-3D mathematical model was proposed for processes of plastic moulding of thin-walled constructions. A feature of the filling stage is the free boundary of the liquid polymer. In the condensation and cooling stages the principal question is to take into account compressibility of the polymer that is considered as a reologically complex liquid. Numerical algorithms for solving obtained system of PDE's are developed. The system PLASTIC for the automation of the projection of casts from plastics is created.

JTAM, Sofia, vol. 23 Issue 2 pp. 098-102 (1992), [Full Article]


Mathematical and Numerical Modelling of a Casting Formation in Complicated Forms

I. Katzarov, J. Popov
Institute of Meta Science and Technology, Bulg. Acad. Sci., Sofia

Based on a method for construction of boundary fitted coordinate systems, two problems of heat and mass transfer, and crystallization of a body with complex geometry are numerically solved. First, laminar filling of a liquid metal into three-dimensional form with small deviations from axial symmetry is considered. The second problem is a filling of a mould with metal, which simultaneously crystallizes and forms a crust upon the walls, thus changing the geometry of the cavity.

JTAM, Sofia, vol. 23 Issue 2 pp. 103-107 (1992), [Full Article]


Mathematical Modelling of Non-Stationary Flow of Liquid Metal through Vertical Sprue Tubes

N. Andreev1, O. Iliev1, G. Simeonov2, V. Videnova2
1Institute of Mathematics, Bulg. Acad. Sci., Sofia
2Institute of Mechanics and Biomechanics, Bulg. Acad. Sci., Sofia

A mould steel casting process is considered. A real casting machine realizing the technological process is described. The casting process under consideration is devided into three stages and a specific mathematical model is developed for each stage. Parabolized convection - diffussion heat equation and parabolized Navier-Stokes equations in Boussinesq approximation are used for describing heat transfer and liquid metal flow through vertical sprue tubes. Finite differences method is used for solving the obtained system of PDE's. Results from the numerical experiments are shown too.

JTAM, Sofia, vol. 23 Issue 2 pp. 108-113 (1992), [Full Article]


Numerical Simulatiion of Opposite Currents

Ch. Boyadjiev1, P. Vabishchevich
1Institute for Chemical Engineering, Bulg. Acad. Sci., Sofia
2Institute for Mathematical Modelling, Moscow, Russia

The mathematical model for description of hydrodynamic processes in opposite current reactor in approximation of boundary layer for two immiscible liquids is proposed. An algorithm for an approximate solution of the corresponding boundary value problem is developed. The algorithm is based on decomposition of calculated domain to two subdomains with iterative satisfying conditions at the boundaries of the subdomains.

JTAM, Sofia, vol. 23 Issue 2 pp. 114-119 (1992), [Full Article]


Mathematical Modelling of Complex Flow Phenomena in Vertical Chemical Vapour Decomposition Reactors

A. Chourbanov
Institute for Mathematical Modelling, Moscow, Russia

The flow structures in chemical vapor deposition reactors are investigated and their influence on crystal growth is numerically studied. The transport of heat and momentum for axisymmetric incompressible flow is governed by 2D Navier-Stokes equations in the vorticity – stream function formulation with Boussinesq approximation for the buoyancy. Code NEPTUNE is used for solving the obtained system of PDE's. The presented numerical results demonstrate the influence of different technological parameters on the considered process.

JTAM, Sofia, vol. 23 Issue 2 pp. 120-126 (1992), [Full Article]


Investigation of the Pocess of Silicon Carbide Crystal Growth from Vapour Phase

S. Lilov, I. Janchev
Sofia University, Sofia

The purpose of the present, work is to determine the vapour concentration in the crystal growth zone during the growth of SiC monocrystals from vapour phase. The study is based on a solution of the Laplace equation in cylindrical coordinates. The results for the concentration distribution being a function of the axial temperature gradient agree very well with experimental data.

JTAM, Sofia, vol. 23 Issue 2 pp. 127-131 (1992), [Full Article]


Chemical Mass Transport and Epitaxial Growth of Semiconductor Materials

L. Hitova, E. Trifonova
Sofia University, Sofia

Some experimental results on the production and study of the structures InAs/GaAs, InAs/InAs and GaAs/GaAs obtained by the epitaxial growth are reported in the present work.

JTAM, Sofia, vol. 23 Issue 2 pp. 132-138 (1992), [Full Article]


An Effective Algorithm for Solving Convection - Diffusion Problem

N. Petrov, M. Mikrenska
Institute of Mechanics and Biomechanics, Bulg. Acad. Sci., Sofia

It is proposed an effective technique for solution of convection-diffussion problem in the case of incompressible fluid. A sufficient condition for the presented time-differencing scheme stability has been found and proved by the autors. This scheme allows to obtain the solution of the problem with arbitrary degree of approximation with respect to time. The main advantage of the proposed technique is the reduction of the computer memory required and the CPU time consumed.

JTAM, Sofia, vol. 23 Issue 2 pp. 139-143 (1992), [Full Article]


General Numerical Programme for Solving Plan-Parallel Flow Problems

D. VeIichkovich
University of Nis, Yugoslavia

A new numerical method, called the equivalent electrodes method (EEM) is used for solving plan-parallel flow problems. A general computer programme SHYDRO is developed for this purpose. In contrast to the existing numerical methods, the EEM application does not require a numerical integration. The obtained numerical results are compared to the corresponding existing exact or approximate solutions. It is concluded that the EEM results have a very good accuracy and convergence with respect to the number of the equivalent electrodes.

JTAM, Sofia, vol. 23 Issue 2 pp. 144-149 (1992), [Full Article]


Force Interaction between Two Equal Spheres in Tandem and Uniform at Infinity Flow

E. Toshev
Institute of Mechanics and Biomechanics, Bulg. Acad. Sci., Sofia

The purpose of the present investigation is to study the axisymmetrical flow past two solid spherical particles in tandem and to obtain the forces, inducted over the particles from the stream. The flow around the particles is induced by uniform at infinity stream, parallel to the central line of the particles. The model of the flow is based on the 2D incompressible Navier-Stokes equations in the terms of stream function-vorticity. By using the ADI scheme and the method of the fractional steps, the distribution of the stream function and vorticity have been obtained. The complete parametric analysis, based on numerous numerical experiments, gives the drag forces influence on the distance between the particles and Reynolds number.

JTAM, Sofia, vol. 23 Issue 2 pp. 150-154 (1992), [Full Article]


Numerical Study of the Axisymmetrical Flow Past a Hollow Cylinder

T. Petrova, E. Toshev
Institute of Mechanics and Biomechanics, Bulg. Acad. Sci., Sofia

The granulated catalysts are very important for many different chemical technologies. For such kind of catalysts the size of their surface is the main factor for the activity of the catalyst particles. In that reason the particles, having shape as a piece of a tube are often used in numerous chemical technologies and usually are called Rashig rings. The purpose of the present investigation is to study the axisymmetrical flow past a hollow solid cylinder with a finite length and thickness of the wall. The considered particle imitates a single Rashig ring. The model of the flow is based on the incompressible 2D Navier-Stokes equations in terms of stream function-vorticity. By using both the ADI and over relaxation methods, the distribution of the stream function and vorticity have been obtained. For several values of the Reynolds number the flow pattern and drag force induced over the particle are obtained.

JTAM, Sofia, vol. 23 Issue 2 pp. 155-160 (1992), [Full Article]


Application of the Theory of Explosion with Release of Mass and Energy

B. Srebrov
Institute of Geophysics, Bulg. Acad. Sci., Sofia

The work shows an application of the theory of point explosion with release of mass and energy for investigation of electrical discharges in extremely short gap in gas media.

JTAM, Sofia, vol. 23 Issue 2 pp. 161-164 (1992), [Full Article]