doi: 10.18698/2309-3684-2021-3-2441
The paper considers a numerical model of flow in a porous medium containing particles of a melting component (polymer). When heated, these particles swell, deform and fill the pore spaces, as a result of which the permeability is significantly reduced. The relationship between porosity and permeability is described by a simple Kozeny-Karman formula. Then, near the lower (inlet) boundary, a region with low permeability (i.e.agglomerate) is formed, the growth of which is determined by the conditions at the side wall and inlet boundaries. As a result of calculations, typical scenarios of porous medium blocking at different heating temperatures were obtained. It is shown that when heated through the wall, the polymer may decompose, so the porous medium partially restores its permeability. When heated by the inlet gas, agglomerate is much more stable, since it blocks the heating source.
Донской И.Г. Численное моделирование процессов образования, роста и разложения агломератов в пористой среде при разных режимах нагрева. Математическое моделирование и численные методы, 2021, № 3, с. 24–41.
doi: 10.18698/2309-3684-2025-1-4456
The objective of the work is to theoretically determine the ignition conditions of a reacting gas flowing near an inert metal wire heated with a constant intensity (for example, by an electric current). This problem corresponds to typical conditions of the reactivity tests of combustible gases. Approximate mass and energy balance equations are written for stationary conditions. The key parameters are reactivity, heat and mass transfer coefficients, and wire heating flux. The resulting system of equations is numerically solved for a wide range of conditions (heating intensity, domain size, radiative heat loss intensity). It is known that equations systems of this type may have several stationary solutions: the low-temperature, slow reaction solution; and the high-temperature solution (combustion mode). Stable ignition is realized when the low-temperature branch becomes unstable. Using the bisection method, the critical values of the reactivity parameter corresponding to stable ignition are determined. The dependence of the ignition conditions on the heat transfer conditions is discussed.
Донской И.Г. Моделирование влияния лучистых теплопотерь на условия зажигания газа накаленной проволокой. Математическое моделирование и численные методы, 2025, № 1, с. 44–56.