Информационная система "Конференции"

Abstracts

The theoretical analysis of stability of operations regimes of the flat epitaxial reactor with asymmetrical heating of walls is executed in previous works [1,2]. In the present work the critical phenomena, the stability of steady states of chemical deposition from a gas phase in cylindrical epitaxial reactor of terminating length are investigated approximate - analytically and numerically.

It is supposed, that the gaseous mixture is not compressed, flow is laminar, dynamic viscosity, specific heat, the diffusion coefficient, heat-conductivity are constant. The limiting stages of exothermal chemical reactions in a gas phase and on a deposition surface are taken into account.

Mathematically, the problem is formulated by the system of two-dimensional equations of the continuity, the motion, the energy conversion, diffusion of reagent. Representation of the equations in dimensionless variables has resulted in revealing effective parameters describing mutual influence of chemical transformations and processes of transport.

The simplified model of process (dynamical system of the third order) is constructed. The model contains effective heat - transfer coefficient, overall mass transfer coefficient and nonlinearity of initial two-dimensional system of partial differential equations. On the basis of this dot model the coordinates, number, static and dynamic instability of modes of process are studied.

With the help of the bifurcation diagrams is shown, that depending on numerical values of parameters the process occurs without crisis or with a hysteresis, i.e. with critical conditions of «ignition» and «extinction».

The stability of steady states of multiparametric system is analyzed by the first Lyapunov`s metod on separate plane of two parameters while the numerical values of other parameters are fixed. With the help of Routh – Gurwitz criterion parametrical equations of four stability boundaries are received. One of them coincides with boundary of non-unique steady states (static instability). Three others - allocate parameters areas with asymptotically steady regimes and auto - oscillatory regimes (dynamically unstable regimes). The influence of Sherwood-, Damkohler-, Lewis-, Peclet - numbers, of heat of homogeneous reaction, relation of reactor radius to length, etc. on the form of stability boundaries, on their place on a plane is established.

The parametrical analysis is used for planning numerical experiment. The results of numerical and approximately -analytical solutions are coordinated on character of regimes, period of oscillations, stationary values of the temperature, concentration, the rate of the flow. The theoretical analysis can be used for management of epitaxial reactor operation.

References

1.Itskova P.G. Nonlinear dynamics of chemical deposition from gas phase. // Reports of III traditional Kazakhstan - Russian scientific - practical conference" Mathematical modeling of scientific and technical and ecological problems of the industry of extracting petroleum and gas. Almaty, October 19-20 2000, p.102-105.

2. Itskova P.G. Numerical modeling of stability of processes of transport with exothermal chemical reactions// On Materials of the International conference ”Computational Technologies and Mathematical Models for Research, Engineering and Education”. Almaty, Kazakhstan, September, 18-20, 2002, part 3. Computing technologies, 2002, v.7, p. 52-60.

Note. Abstracts are published in author's edition

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