Spatial modes of combustion of the donor–acceptor system were numerically modelled. The discrete character of the combustion wave was determined by the unit cell size. The burning velocity of the sample depending on the unit cubic cell size was calculated. It was shown that as unit cell size grows, the average burning velocity of the sample increases, which is explained by a decrease in the specific area of the cell contact boundaries. Single-hot point spin modes of combustion of the parallelepiped sample with a discrete structure were found.

This work presents a two-dimensional mathematical model of self-propagating high-temperature synthesis (SHS) of a specimen consisting of three layers (copper foil - 5Ti + 3Si compacted mixture - steel substrate). A numerical study of the mathematical model is carried out using the finite-difference method. The limiting frontal SHS modes of a three-layer specimen of rectangular cross-section are determined, taking into account the copper layer melting and the thermocapillary wetting of Ti5Si3 synthesis products by the melt with the formation of a composite material during thermal interaction with the steel substrate. The critical minimum thickness of the main internal synthesis layer allowing one to obtain titanium silicides in the frontal combustion mode is calculated. The maximum temperature in the combustion front near the critical conditions is 1652 K. The depth of capillary wetting of the synthesis products with copper melt is in the range of 2-4 mm.

An inhomogeneous model of gas-free combustion of a mixture consisting of activated and non-activated cells was proposed. The structure of the combustion wave was studied to suit the scale of heterogeneity, reaction cell size. The influence of gas dispersed layers separating the reaction cells on the burning velocity of a combined mixture was analyzed. The burning velocity dependences at varying effective porosity, effective thermal conductivity, and external heat transfer parameters were constructed.

A theoretical study of the critical conditions of forced solid-phase ignition in Ti-Al, Ni-Al systems was carried out. Based on the analysis of the non-stationary diffusion equation with moving boundaries, the critical powers of the heating source and the corresponding critical temperatures were determined during the formation of NiAl, TiAl3 intermetallic compounds using the state diagrams of these binary systems. The diffusion activation energies, frequency factors, particle sizes, and heat removal conditions were considered as variable parameters. The diagrams of critical parameters which relate the corresponding specific heating powers with the indicated values were constructed. It has been established that for the same values of the parameters and under identical synthesis conditions, the critical temperatures in these systems differ by more than one hundred degrees. The latter is associated with a significant difference in the width of the solubility region for the corresponding compounds of the composition NiAl, TiAl3. The performed analysis allows separating the modes of isothermal sintering and thermal explosion which makes it possible to control the thermal and diffusion modes of synthesis. The comparison of the calculation results with the experimental data showed their satisfactory agreement.

The passage of a high-temperature synthesis wave through a perforated metal plate mounted inside a cylindrical sample of a Ni + Al powder mixture was studied experimentally and theoretically. Copper and steel plates of different thickness were used. The propagation of the exothermic reaction front through a hole in the barrier was investigated for different thermophysical characteristics of the plate and different geometric dimensions of the hole. The minimum critical diameter of the hole required for the propagation of the combustion wave in the sample was determined as a function of plate parameters.

A discrete 2D model of combustion process in donor–acceptor mixture consisting of activated and non-activated reaction cells was proposed. The influence of the activated composition fraction and cell size on the burning velocity of a combined mixture was analyzed. Calculations showed that an increase in the activated composition fraction elevates the average burning velocity. It was found that burning velocity vs cell size dependence passes through a maximum.

Unsteady spatial modes of gasless combustion in parallelepiped-shaped sample containing two powder mixtures separated by low-melting inert layer were numerically modelled. Samples with square cross section were found to burn both in stationary and in unsteady periodic modes depending on the thermal conductivity of the inert inner layer. Combustion of sample with an active inner layer in quasi-stationary control modes when the average burning velocities of the donor and acceptor mixtures are the same were studied.

The synthesis of an intermetallic compound from a powder mixture of Ni + Al + Al2O3 with an inner metal plate oriented in the direction of combustion wave propagation has been studied by experiments and theoretical calculations as applied to the problem of self-propagating high-temperature synthesis of functionally graded materials. Copper, titanium, and steel plates are considered. The propagation of the exothermic reaction front is analyzed for various thermophysical characteristics of the inner metal layer. In samples with a copper plate, the combustion front near the contact boundary is extended in the direction of the combustion wave. An increase in the average burning rate of the sample with the heat recovery effect is observed when using copper plates 1–3 mm thick. During combustion of samples with titanium and steel plates, there is a deceleration of combustion wave propagation along the contact boundary.

Одной из особенностей синтеза керамических материалов в режиме горения безгазовых порошковых компактов является плавление и растекание одного или нескольких компонентов гетерогенной системы в матрице тугоплавких компонентов и продуктов реакции. Термокапиллярный механизм течения расплава обусловлен действием сил поверхностного натяжения в пористой среде. В данной работе, наряду с диффузионно-капиллярным массообменом, учитывался конвективный механизм смешения компонентов системы. Было выявлено, что плавление реагента и смачивание расплавом тугоплавкого компонента смеси увеличивает скорость тепловыделения и повышает температуру во фронте горения. Проведены численные расчеты скорости горения бинарной смеси (А)+(В), как основной интегральной характеристики высокотемпературного синтеза. Расчетные зависимости скорости горения от начальной пористости качественно согласуются с экспериментальными данными.

This paper presents a three-dimensional mathematical model of self-propagating high-temperature synthesis (SHS) of a three-layer "sandwich" sample. The layers are formed from gasless mixtures with the addition of an inert fusible component. The mathematical model is studied numerically using the finite-difference method. The unsteady periodic regimes of gasless combustion of the three-layer sample with square cross-section are revealed with account for melting and thermocapillary flow of the melted inert component of the mixture. The unsteady periodic combustion regimes are specified depending on the relative calorific value of the mixture in the inner layer. High-temperature points move along the side faces of the sample. The velocity of the points' motion along the combustion surface is much higher than the average burning velocity of the sample. An increase in the melt flow velocity leads to the equalization of the temperature field and stabilization of the combustion regime. The quasi-stationary regimes of control and fusion are studied during the combustion of the sample with an active inner layer, when the intrinsic burning velocities of the donor and acceptor mixtures are close to each other.

The paper focuses on the theoretical and experimental study of the mechanisms of reaction mixture combustion in the ≪chemical oven≫ mode in a three-layer Ni–Al/Ti–Co/Ni–Al sample. Experimental studies were carried out in a reactor in an argon atmosphere at atmospheric pressure and an ambient temperature of 298 K on rectangular samples pressed from Ni–Al and Ti–Co powder mixtures in the form of a three-layer package. The Ti–Co acceptor layer was in the middle of the sample, and the Ni–Al donor layer was outside. The acceptor layer thickness was varied from 4.3 to 13 mm, while the donor layer thickness (4.7 mm) remained constant. It was found that as the acceptor layer thickness increases, the combustion wave front propagation velocity and reaction initiation temperature decrease, and the maximum temperature in the front remains constant and equal to the melting point of the final product. The time of acceptor layer heating before the reaction increases. The acceptor mixture reaction proceeds in the thermal explosion mode when the thickness of the acceptor layer exceeds that of the donor one. Maximum temperature in this case is higher than the melting point of the final product. The inner layer synthesis modes change with an increase in the acceptor layer thickness: stationary – pulsating – extinction. The mathematical model of the three-layer sample high-temperature synthesis in dimensional variables is constructed taking into account heat transfer with the environment. As a result of experimental studies and numerical calculations, the critical thickness of the inner layer was found to be 15 mm, at which the inner layer combustion becomes impossible at fixed sizes of donor layers. Critical conditions for the combustion wave propagation along the acceptor layer are weakly dependent on the external heating source. The experimental technique and mathematical model of the layered system combustion can be used to assess the critical conditions for the metal composite synthesis in the frontal combustion mode.

In the present paper, a mathematical modeling of high-temperature synthesis process in powder system Ni+Al under linear heating conditions was carried out. A comparative analysis of numerical modeling results and experimental data which were obtained for mechanically activated powder mixtures is presented. The criterion for determining the characteristic ignition temperature in the case of forced ignition was proposed. This criterion makes it possible to establish a relationship between the thermokinetic parameters at the ignition limit. With the use of the model, the dependencies of the ignition temperature, the induction time, and the conversion degree on the effective activation energy were established. It was found that these dependencies are close to linear that allows making the predictive estimates. It was shown that the ignition temperature depends most significantly on the activation energy of the synthesis while its dependence on other kinetic parameters is of secondary importance. Based on the criterion proposed, an alternative method for determining the effective activation energy of synthesis was considered.

A mathematical model of gasless combustion in a “chemical furnace” mode was developed. The three-dimensional modeling of gasless combustion of a three-layer sample was performed. Numerical modeling was previously performed for non-stationary modes of gas-free combustion in homogeneous rectangular rods prepared from a mixture of two powder reagents with an admixture of low-melting inert metal powder. Further, the sample was considered as a combination of thermally coupled flat layers consisting of two mixtures of different chemical activity - the “chemical furnace” model. As a result of numerical modeling, various stationary and nonstationary combustion modes of the layered system were detected.

SHS of layered NiAl/Cu/NiAl composite was studied experimentally and by mathematical modeling with special emphasis on critical conditions for combustion synthesis in (Ni–Al)/Cu/(Ni–Al) compacts. Our results may turn interesting to those engaged in fabrication of functionally graded materials.

Abstract A macroscopic mathematical model has been developed for the gas-free combustion of a binary reaction mixture with allowance for thermocapillary convection of a low-melting reagent. The model includes equations as follows: mass balance of reaction substances, chemical transformation, melt motion, thermal conductivity. Melt formed during the melting of one of the components is believed to move in the porous carcass of the mixture due to thermocapillary forces. The dynamics of changes in temperature, chemical conversion depth, melt fraction and porosity are numerically calculated in a gasless combustion wave. Depending on the main parameters characterizing the process, conductive, convective, and mixed modes of synthesis front propagation are revealed. Analytical relationships are derived to estimate the combustion rate for these modes. An approximate criterion that reveals the synthesis mode from the structural and physicochemical parameters of the binary mixture is found.

A combustion model for a flat layered composition has been developed, where chemically active layers alternate with inert metallic layers with high thermal conductivity. The heat exchange between the layers was specified by the conjugate boundary conditions. A numerical study of gasless combustion of a multi-layer system with heat-conjugated layers of two types was performed. Optimal layer sizes and parameters of the layer system were obtained to provide the maximum burning rate of the layer package. The effect of increasing the burning rate was found to be associated with heat recovery and an increase in the effective thermal conductivity of the system. The concentration limits of combustion were determined depending on the volume content of the inert element. Replacing the system of inert layers with that of low-calorie mixture layers leads to a model for synthesis of inorganic materials in the "chemical furnace" mode.

A numerical investigation of the influence of the thermocapillary flow of a melt of an inert component of a gasless mixture on spin regimes of combustion in a strong-instability region has been carried out. New periodic regimes of spin combustion have been found. With increase in the velocity of melt flow, the stabilization of combustion, i.e., transition from spin regimes to a quasi-one-dimensional structure of the combustion wave, occurs.

Unsteady modes of gasless combustion in rectangular rods prepared from a mixture of two powdered reagents with an admixture of low-melting inert metal powder were explored by numerical modeling. Rods with square cross section were found to burn in a mode of spinning combustion. The number of spinning hot spots is defined by sample dimensions. On going to the configuration of long plates with the same cross area, a mode of spinning combustion gradually transformed to that of frontal one.