Combustion Wave Propagation Research Articles

The effect of ambient temperature on the propagation of nonadiabatic combustion waves

In this paper, we undertake an analytical and numerical investigation of the linear stability and properties of travelling nonadiabatic combustion wave for the case of nonzero ambient temperature. Here we consider premixed fuel with one-step exothermic reaction described by Arrhenius law. The speed of the front is estimated analytically by employing the matched asymptotic expansion approach and numerically using the shooting and relaxation methods. It is shown that increasing the ambient temperature results in the growth of both the flame speed and the region of existence of the travelling wave solutions in the parameter space. The linear stability of the travelling wave solution is investigated analytically by using the matched asymptotic expansion method and numerically by employing the Evans function approach. We demonstrate that by increasing the ambient temperature the stability of the propagating wave can also be increased.

The Application of Energetic SHS Reactions in the Synthesis of Multi-functional Bone Tissue Engineering and Drug Delivery Systems

AbstractThe term combustion synthesis, or self-propagating high temperature synthesis (SHS), refers to an exothermic chemical reaction process that utilizes the heat generated by the exothermic reaction to ignite and sustain a propagating combustion wave through the reactants to produce the desired product(s). The products of combustion synthesis normally are extremely porous: typically 50 percent of theoretical densityAdvantages of combustion synthesis over traditional processing routes, e.g., sintering, in the production of advanced materials such as ceramics, intermetallic compounds and composites include process economics, simplicity of operation, and low energy requirements. However, the high exothermicity and rapid combustion propagation rates necessitate a high degree of control of these reactions.One research area being conducted in the Institute for Space Resources (ISR) at the Colorado School of Mines (CSM) is the application of combustion synthesis (SHS) to synthesize advanced, engineered porous multiphase/heterogeneous calcium phosphate (HCaP), NiTi, NiTi-TiC, TiB-Ti, TiC-Ti for bone tissue engineering and drug delivery systems. Such material systems require a complex combination of properties that can be truly classified as multi-functional materials. The range of properties includes: an overall porosity of 40-60% with a pore size of 200-500 μm; mechanical properties (compression strength and Young’s modulus) that match those of natural bone to avoid ‘stress shielding’; and a surface chemistry that is capable of facilitating bone growth and mineralization.The paper will discuss the synthesis of porous multiphase/heterogeneous calcium phosphate (HCaP), NiTi, NiTi-TiC, TiB-Ti, TiC-Ti for bone tissue engineering and drug delivery systems.

Mathematical modelling of hybrid combustion waves

Mathematical models for investigating the formation and propagation of hybrid combustion waves in the stationary layer of a catalyst are developed. In spherical and cylindrical symmetry reactors, the linear velocity of a flow is a radial variable. Therefore, the heat and mass transfer coefficients and the heat conductivity coefficient of the charge, which vary with the reactor radius, are taken into account in the mathematical model. The nonlinear dependence of the heat conductivity coefficient on reemission is also taken into account. To numerically calculate these regimes a special algorithm with an adaptive space-time grid in the gas-phase combustion zone is developed. The proposed algorithm allows us to effectively carry out the numerical investigation of the dynamical characteristics of hybrid waves in the combustion zone. We simulate the process of reaching the stationary mode in a spherical reactor and obtain the dependence of the position of the standing wave on the gas flow rate.

Microstructural correlations between reaction medium and combustion wave propagation in heterogeneous systems

The combustion synthesis (CS) of materials is an advanced approach in powder metallurgy. Our previous studies of various CS systems have shown that at small time scales ( 10 - 3 – 10 - 4 s ), the behavior of self-propagating high-temperature reaction waves in heterogeneous mixtures follows two modes, classified according to their microstructures: quasihomogeneous and scintillating reaction waves. The latter is a novel phenomenon where the reaction propagates in a form of short and high-temperature flashes, so-called scintillations, which randomly arise in vicinity of the combustion front and promote its local movement. Using Ti–Si mixture as an example, this work is aimed to find quantitative relationship between reactant particle size and microstructural characteristics of the reaction front, including scintillation size and its distribution, as well as lifetime. It was shown that, for coarse powders ( > 40 μ m ) , specific number of Ti particles approximately equals the number of hot spots observed during the combustion process. This means that essentially every Ti particle forms a hot spot. However, for finer Ti particles, average hot spot is formed by several (3–5) such particles. Since size of scintillation decreases to a lesser extent than Ti particle size, the scintillation regime does not vanish when using finer Ti powders. These results confirm the general assumption of the relay-race model that the limiting factor of combustion wave propagation is heat transfer between reaction cells rather than reaction within the cell itself.

Porous TiNi Biomaterial by Self‐Propagating High‐Temperature Synthesis

AbstractPorous TiNi shape‐memory alloy (TiNi SMA) bodies with controlled pore structure were produced from the (Ti+Ni) powder mixture by self‐propagating high‐temperature synthesis (SHS) method. The effect of processing variables such as the kind of starting powders, ignition temperature and preheating schedule on the behavior of combustion wave propagation, the formation of phases and pore structure was investigated. The relationship between pore structure and mechanical properties was also investigated. An in vivo test was performed to evaluate bone tissue response and histocompatibility of porous TiNi SMA using 15 New Zealand white rabbits. No apparent adverse reactions such as inflammation and foreign body reaction were noted on or around all implanted porous TiNi SMA blocks. Bone ingrowth was found in the pore space of all implanted blocks.

The transition from spinning to radial solid flame waves

We describe computations of various propagating wave modes in a cylinder of radius R modeled by an array of interacting 1D rods in a reaction-diffusion model of solid flames. For sufficiently small and sufficiently large R, the model exhibits planar uniformly propagating combustion waves. Spin modes, characterized by hot spots spinning periodically around the cylinder, occur for small R, and radial modes, periodically oscillating solutions independent of the cylindrical angle occur for larger R. We describe the transition from spin to radial modes via a family of quasi-periodic modes.

An exact solution to the problem of combustion wave propagation

An exact solution to the problem of combustion wave propagation

Mathematical modelling of hybrid combustion waves

Mathematical models for investigating the formation and propagation of hybrid combustion waves in the stationary layer of a catalyst are developed. In spherical and cylindrical symmetry reactors, the linear velocity of a flow is a radial variable. Therefore, the heat and mass transfer coefficients and the heat conductivity coefficient of the charge, which vary with the reactor radius, are taken into account in the mathematical model. The nonlinear dependence of the heat conductivity coefficient on reemission is also taken into account. To numerically calculate these regimes a special algorithm with an adaptive space-time grid in the gas-phase combustion zone is developed. The proposed algorithm allows us to effectively carry out the numerical investigation of the dynamical characteristics of hybrid waves in the combustion zone. We simulate the process of reaching the stationary mode in a spherical reactor and obtain the dependence of the position of the standing wave on the gas flow rate.

A simple model of two-dimensional solid flame microstructure

In Beck and Volpert (2003 Physica D 182 86), we presented a model of condensed phase combustion that attempts to elucidate the effects of spatially localized reaction sites on the propagation of a combustion wave. Heat transfer was assumed to be uniform but the exothermic reactions are allowed to occur only at evenly distributed locations. Under certain simplifying assumptions we showed that the propagation of a one-dimensional combustion wave through such a medium may be described by a history dependent iterative map that relates the times of all previous particle ignitions to the time of the next ignition. In this paper, we consider the propagation of a two-dimensional wave through a channel. For a propagating wave which is semi-planar, we show that the dynamics of the continuous system may be represented by a history dependent map similar to . Iteration of this map demonstrates the existence of a wide variety of travelling waves. Furthermore, a linear stability analysis similar to that of Beck and Volpert shows that steady planar waves undergo a period doubling bifurcation as the system transitions to a region of bi-stability in which chaotic behaviour is observed. Stochastic perturbations to particle location are also discussed.

IFC: Editorial board

Self-propagating high-temperature synthesis (SHS) of compacted blends of nano-size TiO2 and micron-size Al powders was used to fabricate in situ alumina–TiAl/Ti3Al interpenetrating phase composites. Combustion wave propagation and pressureless or pressure-assisted thermal explosion (TE) modes have been investigated, and samples' temperature in the course of combustion synthesis has been accurately monitored. The ignition of self-sustained reaction in the system studied occurred at temperatures well above the melting point of Al, and temperature evolution in the samples was affected by interfacial barriers and by heat transfer to the surrounding ambience. The application of a moderate pressure (∼ 50 MPa) during thermal explosion at 950 °C yielded near fully dense (up to 98% TD) Al2O3–TiAl/Ti3Al composites with fine micron size interpenetrating ceramic and intermetallic networks. The aluminide component had a very fine submicron γ+α2 lamellar microstructure. The TE procedure performed under uni-axial pressure between press rams (reactive forging) seems especially attractive due to the extremely short processing cycle (several minutes) and near-net-shape capability. This approach is compared with reactive hot pressing (RHP) where only partial conversion of reagents into products was observed after one hour exposure at 950 °C.

Nonlinear dynamics in a simple model of solid flame microstructure

We present a model of condensed phase combustion which attempts to elucidate the effects of spatially localized reaction sites on the propagation of a combustion wave. Heat transfer is assumed to be uniform but exothermic reactions are allowed to occur only at evenly distributed locations, that we refer to as reactant particles. Thus, combustion wave propagation manifests itself as a process of sequential ignition and burning of particles. Green’s functions are used to show that “steady” wave speed is related to particle ignition temperature, particle geometry and the ratio of heat diffusion to reaction times through a single transcendental equation. Furthermore, for the one-dimensional case, the dynamics of this system can be related to a history dependent implicit map f → : R ∞→ R ∞ which determines time to the next ignition. Iteration of this map demonstrates that average wave speed undergoes a period doubling bifurcation to chaos and subsequent extinction. A linear stability analysis of this map is performed to determine the stability boundaries for period 2 n orbits. Additionally, temperature profiles are shown to be in qualitative agreement with experiments which describe a transition from the so-called quasi-homogeneous to relay-race regimes.

Surface Effect on Branching Chain Reactions In Filtration Combustion of Gases

The existence of lean and rich concentration limits of the low-velocity regime of flame propagation was shown experimentally under filtration of a combustible gas mixture in narrow tubes. The values of the limits depend on the inner diameter of the tube. Experiments with an inhibitor affecting the concentration limits of combustion-wave propagation in tubes in a low-velocity regime showed that branching chain reactions occur in the filtration combustion wave and the concentrations of active centers thus exceed the equilibrium values. In the low-velocity regime, the surface of the narrow quartz tube slightly decreases the role of active centers in combustion-wave propagation.

Chemistry reaction processes during combustion synthesis of B 2O 3–TiO 2–Mg system

In this paper, combustion synthesis method was used to synthesize TiB 2 ceramic powder from various oxides. Thermal analysis methods were employed to reveal the chemical reaction processes, a high-speed image recorder was used to monitor and analyze the features of combustion processes. Study results indicated that in B 2O 3–TiO 2–Mg system, B 2O 3 was reduced to elemental B and MgB 2 in one step and TiO 2 was reduced to element Ti through following steps: TiO 2→Ti 3O 5→Ti 2O→Ti, and then, TiB 2 was formed by reaction Ti+2B→TiB 2 and Ti+MgB 2→TiB 2+Mg. In synthesis processing, Mg plays a important role in controlling the mineral phase component of synthesized production and combustion processing. The propagating combustion wave model was found to become unstable with increasing diluent additive amount in raw mixture.

Pressure-assisted SHS synthesis of MgAl 2O 4–TiAl in situ composites with interpenetrating networks

Self-propagating high-temperature synthesis (SHS) of compacted 2TiO 2–Mg–4Al powder blends was used to fabricate in situ magnesium aluminate spinel–TiAl/Ti 3Al interpenetrating phase composites. The combustion wave propagation and thermal explosion modes of SHS, as well as thermal explosion under uniaxial pressure (reactive forging) were investigated, with the samples’ temperature closely monitored in the course of processing. SHS in 2TiO 2–Mg–4Al blend was found to proceed in two stages, the leading reaction being the reaction between Mg and TiO 2 with the formation of MgTiO 3. Wave-like propagation of both leading and lagging reactions was observed during thermal explosion. The application of a moderate 60–80 MPa pressure during reactive forging at 800–900 °C yielded near fully dense (up to 98% of the theoretical density) MgAl 2O 4 spinel–TiAl/Ti 3Al composites with fine micrometer/submicrometer scale interpenetrating ceramic and intermetallic networks. The aluminide component had a very fine γ+α 2 lamellar structure that should beneficially affect the toughness of the material synthesized.

In situ processing of dense Al2O3–Ti aluminide interpenetrating phase composites

Abstract Self-propagating high-temperature synthesis (SHS) of compacted blends of nano-size TiO 2 and micron-size Al powders was used to fabricate in situ alumina–TiAl/Ti 3 Al interpenetrating phase composites. Combustion wave propagation and pressureless or pressure-assisted thermal explosion (TE) modes have been investigated, and samples' temperature in the course of combustion synthesis has been accurately monitored. The ignition of self-sustained reaction in the system studied occurred at temperatures well above the melting point of Al, and temperature evolution in the samples was affected by interfacial barriers and by heat transfer to the surrounding ambience. The application of a moderate pressure (∼ 50 MPa) during thermal explosion at 950 °C yielded near fully dense (up to 98% TD) Al 2 O 3 –TiAl/Ti 3 Al composites with fine micron size interpenetrating ceramic and intermetallic networks. The aluminide component had a very fine submicron γ+α 2 lamellar microstructure. The TE procedure performed under uni-axial pressure between press rams (reactive forging) seems especially attractive due to the extremely short processing cycle (several minutes) and near-net-shape capability. This approach is compared with reactive hot pressing (RHP) where only partial conversion of reagents into products was observed after one hour exposure at 950 °C.

Limits of Existence of a Two-Dimensional Steady-State Structure of a Liquid Film in Combustion-Wave Propagation

A two-dimensional steady-state structure of a film flow of a combustible liquid on a heat-conducting substrate in the case of combustion-wave propagation is considered in the hydrodynamic formulation. The physical mechanism of formation of this structure is analyzed. It is shown that the thermocapillary effect plays an important role. The conclusion is justified that the existence of a two-dimensional regime is possible only for rather low values of the temperature gradient on the film surface. A critical condition is obtained, which determines the transition to a three-dimensional regime. This condition implies that the flow velocity is equal to the velocity induced by the thermocapillary force. If the temperature gradient is higher than a certain critical value, a zone with a reverse flow should appear, in accordance with the two-dimensional model. It is assumed that such a regime cannot exist due to its instability to three-dimensional perturbations. Experiments with a liquid film flowing down due to gravity in the presence of an immovable heat source (without the combustion wave) support the conclusion of the transition to a three-dimensional regular flow structure if the temperature gradient is rather high. The first part of the paper deals with simulation of the film structure for the critical condition satisfied. The second part deals with generalization of the problem to the case of a movable heat source moving with a constant velocity. This formulation of the problem includes the situation with combustion-wave propagation. The mathematical formulation of this problem allows us to assume that the existence of a two-dimensional steady-state regime in this case is limited by the same critical condition. If the temperature gradient on the film surface is higher than the critical value, the two-dimensional steady-state solution does not exist. This concept justified in the present work offers a generic explanation of phenomena observed in liquid films in the presence of local heat sources of various natures.

Combustion-Wave Propagation and Phase-Formation Mechanism in the “Molybdenum–Carbon-Active Additive” System

The combustion of a mixture of molybdenum and carbon activated by a high-energy magnesium–fluoroplastic mixture was studied. The adiabatic combustion temperature and the equilibrium compositions of the combustion products were calculated and, experimental dependences of the combustion temperature and rate on the main parameters of the process are obtained. It is shown that the activation of the formation of molybdenum carbides is of a thermal nature. The two observed mechanisms of formation of molybdenum carbides are found to differ in combustion temperature: at T 2470 K it proceeds by crystallization from a melt. The possibility of synthesis of single-phase Mo2C in the combustion regime is shown.

SIMULATION OF THE PROCESS OF CHROMIZING AND SILICONIZING UNDER THE CONDITIONS OF SELF-PROPAGATING HIGH-TEMPERATURE SYNTHESIS

Coatings deposited under the conditions of self-propagating high-temperature synthesis (SHS processes) accompanied by vapor-transport reactions have many peculiar properties. They consist of a film of the deposited product (as a result of vapor-phase precipitation) and a wide transition diffusion (gradient) zone (produced by diffusion saturation) [1]. The method for depositing vapor-transport SHS coatings has been suggested by E. A. Shtessel’ and E. P. Kostogorov [2] and studied in detail by the authors of [3 – 7]. The method is based on the occurrence of exothermic reactions in a mode of propagating combustion waves. In contrast to the known diffusion methods of chromizing and siliconizing [8] that are energy-intensive and long lasting, the SHS method can provide diffusion layers in a mode of combustion or thermal ignition in a short time (from several minutes to 1 – 2 h). The formed layer is from several microns to 1 – 2 mm thick. The thickness of the protective layer may be controlled by the time parameters of the process and the thermophysical characteristics of the SHS mixtures. In the present work we modeled the processes of chromizing and siliconizing under the conditions of SHS.

Using the Electromotive Force of Condensed System Combustion to Estimate the Parameters of Heat Transfer through an Obstacle

The paper describes a method for measuring the delay of combustion wave propagation through an obstacle and other heat-transfer parameters by continuous recording of electrical signals arising in a burning condensed system. This method is suitable for systems and obstacles that have marked electric conductivity. Results of investigation of combustion wave propagation through a tantalum obstacle in the 3Zr + 2WO3 system using the proposed method are presented. Key words: gas-free system, combustion, mechanical strains, obstacle, combustion e.m.f., heat transfer, thermal parameters.

The Role of Molecular Gas-Phase and Conduction Heat Transfer in Propagation of Combustion Wave

The Role of Molecular Gas-Phase and Conduction Heat Transfer in Propagation of Combustion Wave