Cellular and heterogeneous filtration combustion modes of titanium in the gravitational force field

The paper describes the formation of the combustion zone structure of a titanium powder layer in inclined rectangular air channels with natural gas filtration. It is shown that heterogeneous combustion near the critical conditions of its existence with limited supply of gaseous reagent in the reaction zone and under the effect of gravitational forces is accompanied by rearrangement of the plane homogeneous front into more complex wave structures: cellular, cross-cellular, and heterogeneous. The features of the process under study is the presence of gaseous impurities affecting the gas exchange in the reaction zone, the destabilization of the plane front, and the formation and propagation of heterogeneous and cellular wave structures.     

Emergence of Spatial Structures during Filtration Combustion

The front of filtration combustion and the possibility of its structuring are studied. Cellular structures of the front are demonstrated to form under conditions of instability of a plane combustion front, large filtration coefficients, and insufficient mass of the active gaseous reagent inside the pores. These cellular structures are similar to cellular flames in the case of combustion of gas mixtures. In such systems, the concentration fields of condensed products of filtration combustion form frontal structures that were called fingering instabilities.     

To the theory of filtration combustion at high pressures of gas reagent

The model of filtration combustion (FC) at high pressures of gas reagent has been analyzed in terms of the analytical method giving explicit expressions for pressure profile and thus removing some inconsistence existed in the theory of FC. Approximate analytical solutions were analyzed for two cases distinguished by whether gas or solid reactant is a deficient component of reaction. For each case, existence domains for combustion modes with different pressure profiles have been outlined. For typical gas-solid SHS systems, model parameters were evaluated and the range of initial pressures ensuring combustion modes with a pressure peak ahead of the combustion front has been determined.      

Effect of gas pressure on the laws of propagation of spinning waves during filtration combustion

A three-dimensional mathematical model of filtration combustion with the combustion front propagating over a cylindrical specimen pressed from a powdered solid reagent and placed into an oxidizing medium is considered. Characteristics of spinning waves are studied for different pressures of the ambient gas. Steady waves of surface combustion are demonstrated to propagate over the specimen at low ambient pressures. For spinning waves formed at higher pressures, the characteristics may change nonmonotonically with increasing pressure, and the point with the maximum temperature may be located in the depth of the specimen.     

Diffusion-thermal stability of gas filtration combustion waves in an inert porous medium

A mathematical model for the filtration gas combustion taking into account thermal conductivity, diffusion, and intense interfacial heat transfer is presented. The temperature dependence of the chemical reaction rate is approximated by a δ-function and the thermal-expansion coefficient of gases behind the combustion front is taken into account. Unsteady combustion regimes are analyzed using the method of small perturbations. The boundaries of the longitudinal and spatial stability for steady regimes of the filtration combustion wave are obtained. The dependence of the Lewis number on the thermal-expansion coefficient of the gas mixture along the boundary of stability is derived, along with other relations.     

Model for filtration combustion of carbon: Approximation of a thermodynamically equilibrium composition of combustion products

A model for stationary filtration combustion of mixtures of carbon with a solid incombustible material in a counterflow a gas containing oxygen and a chemically inert gas is proposed. If the rates of chemical reactions in the combustion zone are sufficiently high, the ratio of carbon monoxide and dioxide in combustion products is assumed to be thermodynamically equilibrium at the combustion temperature. This assumption provides a closure for the balance equations for carbon, oxygen, and energy in the combustion front and gives explicit analytical expressions for the combustion temperature and composition of the products as functions of the composition of the carbon/inert mixture and of the gaseous oxidizer in stoichiometric regimes. Combustion modes are numerically calculated for a wide variation of the compositions. The upper limit of the reagent supply rate until which equilibrium relations can be used is found. A comparison of model predictions with experimental results shows their reasonable qualitative agreement.     

Unsteady Modes of Filtration Combustion

Unsteady modes of filtration combustion are studied with the use of a three-dimensional mathematical model. The model describes exothermic chemical interaction of condensed systems with active gases and formation of solid products. Unsteadiness of the filtration combustion modes is caused by instability of the plane combustion front. Formation of the periodic structure of the front of combustion of porous cylindrical samples with different cross-sectional shapes is studied. It is demonstrated that different periodic regimes of combustion-front propagation can occur under conditions of instability of the plane combustion front and deficit of the active gas mass inside the pores, depending on the cross-sectional shape of cylindrical samples and various methods of heat and mass transfer between the sample and the ambient gas medium. Periodic regimes of oscillatory (volume and surface) combustion for samples with a circular cross section, spinning mode for samples with a ring-shaped cross section, and complicated periodic regimes for samples with a rectangular cross section are obtained.     

Combustion wave instability in the filtration combustion of gases

Theoretical and experimental approaches to the problem of combustion wave stability in gas filtration combustion are described. An approximate criterion of instability for an initially plane combustion wave front is suggested within the framework of a hydrodynamic model. It is shown that the wave instabiliry cannot be observed if the reactor diameter is under a critical value. The critical value of the diameter increases with increasing rate of gas filtration. A combustion wave propagating in the direction opposing the filtration flow is more stable than a cocurrent wave, which is consistant with experimental results.Institute of Chemical Kinetics and Combustion, Siberian Branch, Russian Academy of Sciences, 630090 Novosibirsk. Translated from Fizika Goreniya i Vzvyva, Vol. 30, No. 3, pp. 49–54, May–June, 1994.     

Structural transformations during combustion of a gasless mixture in a continuous reactor

A mathematical model is constructed for SHS with induced filtration of an inert gas counter to the gasless combustion front. Structural transformations are analyzed for a porous charge connected with liquid-phase sintering, the force effect of the filtering gas, and the change in condensed phase volume with chemical reaction. Conditions are determined for crack formation and for obtaining a uniform structure over the length of the products. Equations are obtained for product porosity and combustion rate.Institute of the Earth Cryosphere, Siberian Branch, Russian Academy of Sciences, Tyumen. Translated from Fizika Goreniya i Vzryva, Vol. 30, No. 1, pp. 36–44, January–February, 1994.     

Coflow filtration combustion in a slit-like reactor: Simultaneous manifestation of fluid-dynamic and thermal instability

A 2D model of coflow filtration combustion in a slit-like reactor was suggested. When the gas permeability of product is higher than that of fuel powder, this leads to the onset of fluid-dynamic instability and the planar front of filtration combustion may loose its planarity and acquire the shape of finger. Since combustion at the finger tip is kinetically controlled, this may lead to thermal instability giving rise to a mode of pulsating combustion. Simultaneous manifestation of fluid-dynamic and thermal instability in the system under study is reported.     

REACTION FRONT PROPAGATION CHARACTERISTICS IN NON-CATALYTIC EXOTHERMIC GAS-SOLID SYSTEMS

Synthesis of transition metal nitrides and hydrides can be accomplished in the self propagating high temperature regime. A one dimensional model is proposed to study the effects of various operating parameters on the stability of the combustion front, to which gaseous oxidizer is fed by a process of filtration through the permeable solid. Different propagation phenomena can exist depending on the pressure of the gaseous reactant. The stability criteria derived for solid-solid systems can be extended for gas-solid systems at high pressures. At very low pressures filtration combustion is always stable. Systems which show unstable front propagation under adiabatic conditions have been observed to become more unstable due to heat losses.     

Unsteady combustion of a binary gasless mixture ignited by a hot wall

The effect of phase-transition parameters and chemical conversion kinetics on unsteady combustion of gasless systems with a melting reagent is studied. It is found that the change in the kinetic law and in the chemical reaction rate constant resulting from the emergence of the liquid phase in the system destabilizes the combustion. The mean front velocity in the self-oscillatory mode with an adiabatic burning temperature close to the melting point exceeds the front velocity in the steady-state mode. In this case, the front stability improves with an increase in the rate of heat withdrawal from the system and with a decrease in the burning temperature.__________Translated from Fizika Goreniya i Vzryva, Vol. 41, No. 2, pp. 45–50, March–April, 2005.     

Dynamic modes of infiltration-mediated combustion in a tubular reactor

In this work, we analyzed some regularities of frontal steady-state filtration combustion in moving porous media in tubular reactors. We analyzed the profiles temperature, concentration, pressure, rate of heat release, and velocity of combustion front propagation. Analysis was carried out in terms of 1D model from the moment of reaction ignition until onset of steady-state frontal regime. Special emphasis was made on the processes of front stabilization, non-uniqueness of steady-state regimes, and stable periodical regimes. Analyzed is the stability on combustion waves arising in the reactor. The results can be expected to extend the applicability range for the theory of filtration combustion.      

Dynamic combustion regimes of the Ti-(Ti+0.5C) layered system in a concurrent nitrogen flow

The filtration combustion of a layered porous fill consisting of alternating layers of a mixture of Ti + 0.5C a titanium powder with forced concurrent filtration of nitrogen was studied for the first time. The gas flow through the sample was provided by a vacuum pump attached to the lower end of the fill. The presence of the concurrent gas flow radically changes the character of propagation of the combustion front and the structure and composition of the products obtained. The layers consisting of carbonitride and titanium nitride make a single unit. The experiments provided scientific bases for the production of new laminated and composite ceramic materials by dynamic filtration combustion. __________ Translated from Fizika Goreniya i Vzryva, Vol. 44, No. 6, pp. 44–51, November–December, 2008.     

Modeling of unsteady filtration gas combustion

Unsteady filtration gas combustion with various gas flow parameters is studied by mathematical modeling. Transition processes due to a sudden change in the calorific value of the gas mixture, gas flow velocity, and flow direction are considered. Trends and mechanisms of change in the structure of the filtration gas combustion wave and its propagation velocity are analyzed for various types of transition processes. It is found that with a sudden change in gas flow parameters, the flame can abruptly move large distances in the porous medium. Subsequently, at the new flame localization, a wave of filtration gas combustion forms which corresponds to the changed parameters of the gas flow. If in the porous medium, the amount of heat is insufficient, the transition process ends with quenching. As the gas flow direction changes, the combustion wave continues to propagate in the former direction for some time, which can lead to the spread of the high-temperature zone in devices based on the reverse process with a homogeneous gas-phase reaction.     

Carbon combustion synthesis of oxides: Effect of Mach, Peclet, and Reynolds numbers on gas dynamics

Recent experimental and numerical studies on Carbon Combustion Synthesis of Oxides (CCSO) have revealed that the gas transport behavior is rather complex with respect to traditional SHS systems. It involves at least two gaseous components: oxygen (oxygenator) as the main and practically unique gaseous reagent in gas-solid SHS reactions and carbon dioxide which is released in the post-combustion zone in CCSO. The goal of this study is to develop Two Gas Flow (2GF) model of filtration combustion counting resistance distribution in a porous reacting media and enabling the numerical investigation of the complex gas dynamic behavior during CCSO. In contrast to classical filtration combustion (FC) models, the proposed 2GF model for CCSO is capable of considering and predicting potential gas motion as well as complex vortex flows.     

GAS ABSORPTION WITH INSTANTANEOUS CHEMICAL REACTION IN A FALLING FILM FOR PARALLEL AND COUNTERCURRENT FLOWS

A theoretical analysis is presented for the absorption of a gas accompanied by instantaneous chemical reaction with a dissolved reagent in a falling liquid film of liquid. The reaction occurs on a moving front inside the liquid film separating the zones containing either of the reactants. The governing equations are solved by using a coordinate transformation to immobilize the reaction front. The effects of the different system parameters on the reaction front profile, absorption rate and enhancement factor are presented for both cocurrent and countercurrent flow of the gas. In the former case the reaction front profile shows a maximum, but in the later case it is monotonic in the axial distance along the film. The enhancement factor plots exhibit maxima in both the cases.     

Experimental investigation of combustion of a gasless pelletized mixture of Ti + 0.5C in argon and nitrogen coflows

Combustion of a pelletized mixture of titanium and carbon black placed in a quartz tube and exposed to a flow of argon or nitrogen is studied. The gas flow (cocurrent filtration) is provided by a fixed pressure gradient at the inlet and outlet of the tube, which did not exceed 1 atm. The possible modes of combustion of pelletized mixtures related to the presence of a more complex hierarchy of scales (micro, macro, and meso) compared to that of powder mixtures (micro, macro) are analyzed. A comparison is made of the burning rates of powder and pelletized mixtures. An increase in the burning rate when using pelletized mixtures was found experimentally. It is shown that the gas coflow through the pelletized mixture of Ti + 0.5C leads to an increase in the burning rate. It is established that the propagation of the flame front of the pelletized mixture of Ti + 0.5C in flows of nitrogen and argon is controlled by different reactions. In contrast to combustion of powder mixtures of Ti + 0.5C, in combustion of pelletized mixtures of Ti + 0.5C in a nitrogen flow, only one front is observed. It is proved that radiation plays a significant role in the propagation of the combustion front in the pelletized mixture of Ti + 0.5C.     

Method of generating cold gases in solid-fuel gas generators

The principle of operation of a gas generator that is to burn a porous charge of a solid fuel in the filtration regime of gaseous combustion products toward the cold side, i.e., in the direction of displacement of the combustion front, is described. Translated fromFizika Goreniya i Vzryva, Vol. 35, No. 4, pp. 75–78, July–August 1999.