Numerical simulation of deflagration in hydrogen-air gas mixes

Verification of validity of different manifolds of chemical reactions and coefficients in Arrhenius formulae was made for numerical simulation of deflagration appearing in hydrogen-air gas mixes. Kinetic model of branching chain reaction was tested for initial stage of detonation of this kind of mixes. One dimensional numerical simulations of deflagration initiation where provided for small closed heat isolated region. The next problem was solved numerically:in small closed volume, initially filled by hydrogen-air mix with atmospheric meanings of gas dynamics parameters at moment t=0 temperature rising till meaning, at which reaction of deflagration should begin. Numerical experiment consist of calculation of thermodynamics parameters of gas mix in small isolated volume. Meanings of molar concentration of components of gas mix where calculated by implicit numerical method of Gir for numerical decision. Calculation where provided till zero concentration of hydrogen or not appearing of deflagration at all. Characteristic feature of hydrogen-air gas mix deflagration is appearance of sudden explosion after long period of induction. In this induction period grows of radicals H, O and OH appears. Mass of radicals, nevertheless stay small, and one radical component transverse to the others. This explosion mechanism is branching chain reaction introduced by N.N.Semenov. In agreement with branching chain reaction theory during process of branching chain reaction radicals H, O, OH many times initiates reaction with other components of the mix. Nevertheless mass of radical components preserve small during the reaction, them almost fully disappeared in every time of the process. That’s why method of “quasi - stationary concentration” is treated to components O, OH (velocity of changing of this components concentration is equal to zero). For concentration of component H one simplified differential equation is treated. Speed of changing H essentially grater then speed of changing “slow” components H2, O2, H2O, that’s why equation for H should be solved separately. Algorithm was developed for numerical simulation of hydrogen-air mixes on the basis of theory branching chain reactions. Calculations provided demonstrate applicability of developed algorithm for numerical simulations of initial stage of deflagration of hydrogen-air mixes.

Numerical modelling of agglomeration process in a granular bed containing melting particles

The paper considers a numerical model of a flow in a porous medium containing particles of a melting component (polymer). For this, an implicit numerical method of splitting in directions is used. Calculations are carried out for two heating methods (through the side wall, or by the input gas). The simulation results qualitatively reproduce some of the experimentally observed features of the thermal decomposition of polymer-containing mixtures. The results obtained are of interest in the study of low-grade fuels processing, often accompanied by agglomeration, as well as in the development of methods by which agglomeration can be prevented.

Numerical algorithm for fractional order population dynamics model with delay

For a fractional-diffusion equation with nonlinearity in the differentiation operator and with the effect of functional delay, an implicit numerical method is constructed based on the approximation of the fractional derivative and the use of interpolation and extrapolation of discrete history. The source of this problem is a generalized model from population theory. Using a fractional discrete analogue of Gronwall's lemma, the convergence of the method is proved under certain conditions. The resulting system of nonlinear equations using Newton's method is reduced to a sequence of linear systems with tridiagonal matrices. Numerical results are given for a test example with distributed delay and a model example from the theory of population with concentrated constant delay.

Numerical method for fractional diffusion-wave equations with functional delay

For a fractional diffusion-wave equation with a nonlinear effect of functional delay, an implicit numerical method is constructed. The scheme is based on the L2-method of approximation of the fractional derivative of the order from 1 to 2, interpolation and extrapolation with the given properties of discrete prehistory and an analogue of the Crank-Nicolson method. The order of convergence of the method is investigated using the ideas of the general theory of difference schemes with heredity. The order of convergence of the method is more significant than in previously known methods, depending on the order of the starting values. The main point of the proof is the use of the stability of the L2-method. The results of comparing numerical experiments with other schemes are presented: a purely implicit method and a purely explicit method, these results showed, in general, the advantages of the proposed scheme.