T. P. Ivleva

Three-dimensional modes of unsteady solid-flame combustion

Mathematical simulation is being widely used in modeling wave propagation in various physical, chemical, and biological processes, such as gasless combustion, frontal polymerization, etc. Numerical simulation is especially important in three-dimensional (3D) modeling of the spinning and chaotic waves propagating in nontransparent solids. In this paper, we analyze the system of equations that describes the propagation of a self-sustained wave through a cylindrical sample of combustible mixture. In this case, sample composition, sample radius, and heat loss from the sample surface will be used as variable parameters. We will describe (i) the combustion modes that give rise to periodic screw motion of one or several hot spots, (ii) inner wave structure, (iii) effect of parameters on the wave structure, (iv) some modes that have not yet been observed experimentally, (v) a loss of periodicity that leads to chaotic propagation of a 3D self-sustained wave.

Mathematical Simulation of Three-Dimensional Spin Regimes of Gasless Combustion

A three-dimensional mathematical model is constructed for the gasless combustion of a solid circular cylindrical specimen. The steady-stated spin regimes obtained were studied by numerical methods. The structure and mechanism of spin combustion are illustrated and discussed. It is shown how the space–time pattern of spin-wave propagation is complicated as the radius of the cylinder increases. Spin propagation of the front can proceed in a regime in which the structure of the front does not change (for small radii of the sample) or in an unsteady regime, in which the structure of the front undergoes numerous changes over a period. In the second case, a synchronous or alternate “flicker” of the sites is observed on the surface of the cylinder. The nonuniqueness of the combustion regimes is detected. It is shown that the average velocity of propagation of the spin-combustion front is of the order of the velocity of steady front propagation under adiabatic conditions.

Three-Dimensional Unsteady Solid Flame Combustion under Nonadiabatic Conditions

The effect of heat losses on solid flame combustion characteristics is considered. New steady-state three-dimensional periodic regimes are found that do not occur under adiabatic combustion conditions. The essence of these regimes is explained using as an example the regime with six spots moving on helical lines in the near-surface layers of a cylinder. The spots are localized in the near-surface layers of a cylinder and do not intersect the central (located along the axis) zone of the sample. The interior of the cylinder (core) burns in a steady-state regime; i.e., along the cylinder axis, the front propagates at a constant velocity. An explanation is given for the existence of such regimes.

TWO-DIMENSIONAL MODES OF FILTRATION COMBUSTION

A theoretical analysis is made of the possible modes of filtration combustion and the transitions between modes with changing system parameters are studied. The “initial pressure-filtration coefficient” plane is subdivided into regions where the various modes exist. It is shown that at superstoichiometric initial pressures, when there is enough gas in the pores for complete transformation of the solid reagent, there is a range of parameters where combustion proceeds in a surface mode. At still higher initial pressures a new, bimodal, combustion regime is observed, which combines the features of the layer-by-layer and surface modes.

Simulation of the hydrodynamic instability of a filtration combustion wave in a porous medium

This paper presents a two-dimensional model of the propagation of a filtration combustion wave in a flat channel with cocurrent flow of a gas containing an oxidizer. It is shown that the increase in the permeability of the porous medium with fuel burnup leads to instability of the flat front and the formation of a structure called a finger. The reasons for the occurrence of the finger are explained, and the dependences of its most important characteristics on the permeability ratio of the initial fuel and combustion products, the specific heat of the injected gas and the width of the channel in which the filtration combustion occurs are determined.

Hydrodynamic instability of the coflow filtration combustion: Numerical simulation

The stability of the front to infinitely small distor� tions was analyzed under the assumption that the reac� tor channel width is infinitely large in comparison with the combustion zone thickness (5). It was concluded that the plane filtration combustion wave may be unstable. The experimental investigation of the filtra� tion combustion wave stability confirmed (6) that the propagation of a plane filtration combustion front may be unstable and may be accompanied by the formation of structures similar to Saffman-Taylor fingers, which were observed as a highviscosity liquid was displaced by a lowviscosity liquid (7). In this work, for the first time, we made mathemat� ical modeling of twodimensional unsteady filtration combustion during the forced oxidant filtration in the combustion wave direction. The purposes of the study was to determine the conditions for the occurrence of filtration combustion with a stable plane front in chan� nels of finite width and investigate the filtration com� bustion wave propagation modes in the range of insta� bility of the plane reaction front. The physical formulation of the problem is the fol� lowing. A gas mixture with oxidant concentration a0 is fed to a reactor filled with a porous mixture containing a fuel component. The gas flow rate at the inlet (x = 0) is maintained constant (G0). Reaction initiation with a hightemperature source leads to reaction front prop� agation in the х direction at rate u. As the fuel is burned out, the structure of the porous medium changes, because of which the porosity, thermal diffusivity, and permeability of the combustion products may differ from the respective characteristics of the initial reac� tion mixture. The problem is considered in the plane geometry under the assumption that the reactor is shaped as a thin slitlike channel. If the reaction front propagation velocities are low, which is characteristic of filtration combustion waves, the difference between the temperatures of the parti� cles and the gas can be ignored and the porous medium can be considered locally uniform in temper� ature and concentration. Under this assumption, the dimensionless system of equations describing filtra� tion combustion has the form (1, 2)

Macrokinetic Analysis of Passivation of Pyrophoric Powders

A model of ignition and passivation of a layer of a pyrophoric nanopowder was proposed and studied by analytical and numerical methods. Under the assumption that the passivation wave propagation is controlled by the oxidant diffusion, the dependence of the maximum nanopowder temperature on governing parameters was characterized. Passivation was proposed to be performed in two stages with increasing oxidant concentration in the gas phase, which makes it possible to reach the complete passivation of a sample several times faster at permissible temperature rise and opens up new opportunities for improving nanopowder production performance.

Changes in the composition of synthesis products upon transitioning from self-ignition to combustion

Changes in the chemical composition of condensed products upon switching from synthesis in the self-ignition mode to combustion synthesis is studied by approximate analytical and numerical means for condensed substances that react via competing reaction pathways. It is shown that these different modes of synthesis produce different compositions of the reaction products. The conditions required for transitioning from one mode of combustion initiation (thermal explosion) to another (ignition) are determined. It is found that this transition can occur upon changing the temperature of a heater by just two characteristic intervals. A scaling procedure that allows the calculation results obtained at zero dimensionless temperature of the heater to be used to determine the effect its non-zero dimensionless temperature has on the ignition mode and the composition of the obtained products is proposed. Calculations show that materials with different distributions of the chemical composition along the sample can be obtained by deliberately changing the temperature of the heater.

Spinning waves of infiltration-mediated combustion

Infiltration-mediated combustion of powder compact with gas reagent was mathematically modeled in 3D formulation. The parameters of spinning waves were obtained as a function of ambient gas reactant pressure. At low gas pressures, combustion was found to propagate over the sample surface in the form of steady waves. At higher gas pressures, the onset of spinning waves was observed. With increasing gas pressure, parameters of these waves were found to change non-monotonically, a hot spot with a maximal temperature being inside the sample body. The results of modeling were found to qualitatively agree with the relevant experimental data.

Mathematical Modeling of Chemical Conversion in Thin‐Layer Exothermic Mixtures under Periodic Electric‐Spark Discharges

The dynamics of coating production using a reaction mixture with thermoreactive electric‐spark strengthening is studied numerically. It is shown that the main parameter that determines the thermal regime of coating is the initial thickness of the mixture layer. The parameter ranges for the process in a combustion regime and in a quasivolume conversion regime are determined. The effect of discharge frequency and the thermal characteristics of the reaction mixture and the substrate being strengthened on coating time is investigated. It is established that for a particular reaction mixture, the characteristic conversion temperature can be controlled by varying the electric discharge power and, hence, the heat flux at the active stage of the process, and for coating formation at this characteristic temperature, it is necessary that the thickness of the active layer be lower than a certain critical value.