Propagation and quenching of premixed flames in narrow channels

The shape and propagation of unsteady premixed flames in narrow channels with adiabatic and isothermal walls are numerically investigated in the present study. The flame chemistry is modelled by an one-step overall reaction, which simulates the reaction of a stoichiometric acetylene-air mixture. The numerical results show that both ignition methods and thermal boundary conditions affect flame formation and its shape. The flame keeps a single tulip shape in the whole process of propagating through the channel if plane ignition is used and a single mushroom shape if spark ignition is used. For isothermal cold walls, the flame cannot keep a single tulip shape or mushroom shape all the time. Under plane ignition, a transition from a tulip-shaped flame to a mushroom-shaped flame occurs as flames propagate from one end of channel to the other. Under spark ignition, the process is just the contrary. It is also shown that the heat loss at the cold walls has a dual effect on the formation of a tulip-shaped flame. Flame propagation and quenching in narrow channels of different heights are analyzed systematically, and a criterion is proposed to judge the flame states of partial extinction and total extinction. It is called the criterion of flame propagation and quenching in narrow channels. __________ Translated from Fizika Goreniya i Vzryva, Vol. 42, No. 3, pp. 27–36, May–June, 2006.     

Splitting flames in a narrow channel with a temperature gradient in the walls

A possibility of simultaneous formation of two chemical reaction fronts during nonstationary combustion of a gas in a microchannel with a temperature gradient in the walls is demonstrated. Combustion in a straight tube and in a gap between two disks with radial fuel injection is considered. In both cases, the characteristic transverse size of the channel is smaller than the critical diameter determined for the ambient temperature, and gas combustion occurs in the region where the wall temperature is higher than the ambient temperature. A numerical study of flame repetitive extinction/ignition (FREI) demonstrated a possibility of simultaneous formation of two chemical reaction fronts in the hot region of the channel. One front corresponds to conventional flame propagating upstream from the hot to the cold part of the channel, and the other front moves in the downstream direction and decays as the fuel burns out. Based on this study, a new mechanism of ignition and incomplete combustion of the combustible mixture in microsystems is proposed. __________ Translated from Fizika Goreniya i Vzryva, Vol. 45, No. 2, pp. 12–19, March–April, 2008.     

Stable and critical heat- and mass-transfer regimes of a traveling carbon particle

We consider the effect of the relative velocity of a carbon particle on the specific features of the time dependences of the temperature and dimater of the particle at given temperatures of air and the wall of a reaction device and at a specified oxygen concentration in the medium. The stable and critical values of the temperature and combustion rate of the particle versus the initial particle diameter at its given velocity and the relative velocity of a particle of given size are studied. The effect of the diameter and velocity of the particle on the critical values of its initial temperature, which determine ignition inside hysteresis loops, is analyzed. The dependences of the critical particle diameter at which the thermal regime changes (ignition and extinction) on the relative particle velocity are derived. Translated fromFizika Goreniya i Vzryva, Vol. 34, No. 1, pp. 25–30, January–February, 1998.     

Ignition of porous, solid radiation source

Asymptotic analysis of the ignition of a semiinfinite porous body by a radiant heat flux yields a critical condition dividing ignition from inert heating. For the case of ignition, the temperature field in the body prior to ignition and the time characteristics of the process are determined. The dependence of the ignition time on the system parameters is analyzed. Tomsk State University, Tomsk. Translated from Fizika Goreniya i Vzryva, Vol. 31, No. 6, pp. 5–13, November–December, 1995.     

Mathematical study of thermal explosion of a magnesium particle with allowance for metal evaporation

A catastrophe/ignition manifold for a model of thermal explosion of a magnesium particle is constructed. The model takes into account the chemical oxidation reaction, metal evaporation, and convective heat exchange with the ambient gas. This made it possible to determine the types of heat dynamics of the particle in the plane of bifurcation parameters of the model (to locate ignition, extinction, and regular-heating regions), to find the kinetic constants in the empirical law of ignition on the basis of experimental data, and to show the stability of the integral parameter of the ignition delay in relation to sets of kinetic constants determined for mathematical models with and without account for metal evaporation. Translated fromFizika Goreniya i Vzryva, Vol. 34, No. 2, pp. 39–46, March–April, 1998.     

Behavior of the temperature and burnup of a reactive body at the surfacex=0 upon thermal ignition

Using the Laplace transform, we show that equations that govern the evolution with time of the temperature and burnup of areactive body in the cross sectionx=0 in the processes of thermal ignition can be derived. The equations for the temperature and burnup of a semibounded body at the ignition pointx=0 are obtained when the ignition is initiated by a radiation flux and in the case of thermal explosion, of a hot spot. An asymptotic analysis of the equations obtained is carried out, and the ignition times of bodies and the critical conditions for ignition of a hot spot are determined. Vilyunov's “adiabatic method” of obtaining the temporal ignition characteristics is justified. The results of the asymptotic analysis of the ignition of a hot-spot are supported. Translated fromFizika Goreniya i Vzryva, Vol. 35, No. 5, pp. 46–54, September–October 1999.     

Numerical study of heat waves in the oxidation of a magnesium wire

A mathematical model of ignition of magnesium samples is proposed based on the concept of the existence of thermal deceleration of a chemical reaction responsible for ignition. The model gives realistic values of temperatures after sample ignition and is in satisfactory agreement with experimental data on the dependence of the radius of a small particle on the limiting temperature of the ambient medium. It is shown that heat waves can be excited by heterogeneous oxidation of Mg wire located in the external flow. The range of parameters in which self-excited wave regimes are observed fits experimental data on oxidation of metal wires qualitatively and in order of magnitude. The problem of initiation of an ignition wave by the initial distributions of the sample temperature is solved numerically, and the stability of heat waves to small and finite perturbations is shown. Tranlated fromFizika Goreniya i Vzryva, Vol. 34, No. 6, pp. 29–38, November–December 1998.     

Hot-spot thermal explosion in deformed solids

A model for hot-spot thermal explosion is proposed taking into account the coherence of deformation and temperature fields and the dependence of the reaction rate on the work of the deformation force. The problem is considered in terms of thermal elasticity theory. The solution is performed using matched asymptotic expansions in various particular cases. The temperature, displacement, deformation and stress fields, the hot-spot radius corresponding to the boundary of ignition and extinction regimes, and the ignition time are determined under critical conditions.Tomsk. Translated from Fizika Goreniya i Vzryva, Vol. 29, No. 4, pp. 3–13, July–August, 1993.     

Heat and mass transfer correlations and bifurcation analysis of catalytic monoliths with developing flows

We review and compare the literature correlations for estimating the heat and mass transfer coefficients as well as pressure drop in catalytic monoliths with simultaneously developing velocity, concentration and temperature profiles. We present accurate correlations for estimating the local Nusselt and Sherwood numbers for developing flows with constant flux (slow reaction) and constant wall concentration or temperature (fast reaction) cases for a channel of arbitrary shape. These new correlations need only a single parameter, namely, the asymptotic value, which depends on the channel geometric shape. We establish the accuracy of the proposed correlations by comparing the predicted values with the exact numerical values available for a few cases. We use the new correlations to analyze the effect of flow conditions near the inlet of the channel on the ignition and extinction behavior of catalytic monoliths used in combustion and after-treatment applications as well as laboratory experiments. It is shown that the bifurcation behavior, such as the number and location of the ignition/extinction points, the number of stable steady-states and the hysteresis locus is sensitive to the flow conditions in the entry region, and hence the heat and mass transfer correlations used, especially for large values of the transverse Peclet number (high space velocities or very short monoliths) or adiabatic temperature rise or when the axial catalyst loading is not uniform.     

Hot-Spot Ignition of a Reactive Gas in an Inert Porous Medium

The main stages of development of hot-spot ignition of a reactive gas in a high-porous medium with high values of the Peclet number under conditions of natural gas filtration and limited internal heat transfer between the phases are determined. Gas ignition in a U-shaped hot spot is considered within the framework of an asymptotic analysis with high values of the temperature difference and Frank-Kamenetskii parameter. The critical relation of parameters separating the regimes of gas ignition and gradual cooling of the hot spot is determined. The dependence of the ignition time on parameters of the process is found and analyzed. A strong effect of interphase heat transfer on the ignition limit and time is demonstrated. An example of calculating the critical parameters of hot-spot ignition of methane in processed rocks is given. __________ Translated from Fizika Goreniya i Vzryva, Vol. 41, No. 5, pp. 41–48, September–October, 2005.     

Influence of radiation on the critical heat-and mass-transfer conditions in parallel reactions at the surface of a particle

Analytical expressions are derived for the critical diameters bounding the region of high-temperature heat and mass transfer in parallel reactions at the surface of a particle. It is found that radiation with a large initial particle diameter leads to increase in the critical diameter of ignition with increase in the initial particle temperature. Formulas relating the combustion temperature and the particle diameter are derived. The influence of the prevailing conditions on the critical particle diameter at which spontaneous (induced) extinction and ignition occur is investigated in detail. An expression is obtained for the limiting gas temperature and oxidant content below which particle combustion is impossible. Degeneracy of the critical parameters of heterogeneous particle ignition and damping is investigated.State University, Odessa 270074. Translated from Fizika Goreniya i Vzryva, Vol. 30, No. 4, pp. 63–74, July–August, 1994.     

Mathematical model of magnesium ignition in an extended range of parameters

A mathematical model of ignition of a magnesium particle with allowance for a heterogeneous chemical reaction is proposed. The model allows the final particle temperature after its ignition to be found and takes into account the region of the thermal influence of the particle on the gas. A stationary solution is found, which makes it possible to propose a classification of the thermal history of the particle-gas system. The mathematical model is consistent with experimental data on the dependence of the ignition delay on the gas pressure and particle radius and on the dependence of the limiting temperature on the particle radius and the ambient pressure. The mathematical model also reveals the effect of the size of the gas layer around the particle on the integral parameters of ignition. __________ Translated from Fizika Goreniya i Vzryva, Vol. 44, No. 5, pp. 64–71, September–October, 2008.     

Thermal explosion in semi-batch reactors

The problem of thermal explosion in a semi-batch reactor is solved. The critical conditions for the thermal explosion are studied. It is shown that the ignition resulting from the chemical reaction is possible both during the stage of feeding of the second reactant solution and after its completion. The dynamic behavior of the reactor depending on the temperature of the heat exchanger and the volumetric feed rate of the second reactant is analyzed. It is shown that ignition at the feeding stage occurs at high temperature of the heat exchanger and involves two macroscopic stages. In the first stage, the temperature increases with increasing rate (thermal explosion regime), and in the second stage, its further increase occurs in the regime of combustion of the second reactant. The critical ignition conditions are found to be independent on the feed rate of the second reactant in a particular range of its values.     

Ignition of a system of hot spots in the presence of heat transfer through the side surface

An asymptotic analysis is used to study the ignition of a reactive cylindrical body in which, initially, there is a periodic system of hot spots. The effects of the heat transfer through the side surface of the cylinder and the adjacency of hot spots on the ignition regimes are studied. The solution shows that the critical ignition conditions depend considerably on the heat-transfer regime. The adjacency of the hot spots leads to finite changes in the parameters only if they are sufficiently close to each other. The results obtained for a heat-insulated side surface are compared with known solutions. Translated fromFizika Goreniya i Vzryva, Vol. 36, No. 2, pp. 17–21, March–April, 2000.     

Generalized Criteria of Volume Ignition for One‐Stage Exothermic Reations

A method of ignition conditions determination for any type of exothermic reaction is proposed. The method is based on the maximum temperatures equation for any kind of kinetic function, which was obtained using the integral equation for phase trajectories. In this case, the asymptotic ignition criterion is defined by the infinitely high sensitivity of maximum temperature to the change of parameters at the limit of ignition. Hence, the critical ignition conditions are determined by the presence of extreme points on the plane: parameter – maximal temperature. On the strength of these ideas, the universal algebraic set of equations for critical conditions calculation for arbitrary kinetic law of reaction product formation was obtained. The application of this method to calculation of the second order reactions allows to define the thermal explosion degeneration conditions and the regions of critical conditions existence. The maximum discrepancy between the results obtained with the results of numerical calculation does not exceed ten percent.     

Explosion of tetrafluoroethylene during nonisothermal polymerization

On the basis of dimerization kinetics and experimental data on thermal explosion we determine conditions for ignition of tetrafluoroethylene on a hot wall. A mathematical model of nonisothermal polymerization on a plane wall and in a cavity which takes into account heat removal to the wall and to the gas phase is proposed. The conditions for explosion hazard situations are established and expressions for the induction time are obtained. Saint Peterburg. Translated from Fizika Goreniya i Vzryva, Vol. 29, No. 5, pp. 56–62, September–October, 1993.     

Experimental studies of the ignition of a solid propellant in water

The ignition of a solid propellant in water by means of an unsealed system of ignition in the form of an open channel with a heating coil placed in the channel is considered. The ignition system operates according to the principle of creation of extreme conditions of water boiling in the channel with heat supply from an electrical heater. It was established visually that the heating of the walls is preceded by a preliminary period connected with the change in the state of aggregation of water. The system was tested on solid-propellant specimens. Translated fromFizika Goreniya i Vzryva, Vol. 35, No. 3, pp. 52–57, July–August 1999.     

Regimes of combustion of a premixed mixture of gases in a heated microchannel with the wall temperature smoothly increasing in the downstream direction

Specific features of the unsteady flame in a microchannel with a controlled wall temperature are theoretically studied within the framework of a one-dimensional diffusion-thermal model. The case with the channel wall temperature increasing in the gas flow direction and the channel size being smaller than the critical value determined on the basis of the ambient temperature is considered. Depending on the flow rate of the combustible mixture of gases through the channel, either flame stabilization or alternation of flame repetitive extinction/ignition is possible. The influence of the characteristic length of channel wall heating on the domains of existence of various combustion modes is studied for the first time. The theoretical study shows that there exists a critical value of the temperature gradient in the channel walls, below which the regime of flame repetitive extinction/ignition is no longer observed. At small values of the temperature gradient, a hysteresis phenomenon is found, which is associated with different changes in the flame position in the cases with increasing and decreasing flow rates of the gas.     

Characteristics of the boundary layer with hydrogen combustion with variations of thermal conditions on a permeable wall

The paper describes a numerical study of the influence of thermal and boundary conditions on the structure of laminar and turbulent diffusion flames in the cases with hydrogen injection through a porous surface and with hydrogen combustion in an air flow. Two types of boundary conditions are compared: with a given constant temperature T _w = const over the length of the porous surface for arbitrary intensities of fuel injection and with a constant temperature T′ = const of the fuel injected through the porous wall. The first case occurs during combustion of a liquid fuel whose burning surface temperature remains unchanged. Injection of gaseous fuel usually leads to the second case with T′ = const. Despite significant differences in velocity and temperature profiles, the skin friction coefficients in the laminar flow are close to each other in these two regimes. In the turbulent regime, the effect of the thermal boundary conditions on friction and heat transfer is more pronounced. Moreover, the heat flux to the wall as a function of fuel-injection intensity is characterized by a clearly expressed maximum. A principal difference of the effect of combustion on friction and heat transfer in the laminar and turbulent flow regimes is demonstrated. __________ Translated from Fizika Goreniya i Vzryva, Vol. 45, No. 3, pp. 3–11, May–June, 2009.     

Ignition of gaseous suspensions in an interacting continuum regime

A mathematical model is proposed for describing the flow of a mixture of gases and reactive solids including a heterogeneous chemical ignition reaction. The model is closed with an equation for the kinetics of oxide film growth. It is assumed that the heat of the chemical reaction can be released in both phases depending on the accommodation coefficients. The ignition of a motionless cloud of magnesium particles is studied in terms of this model. The model is tested with the use of experimental data on the maximum temperature of the medium as a function of the particle radius. Data on the dependence of the parameters of a heated particle cloud on the physical and chemical constants of the mixture and particles are presented. Translated fromFizika Goreniya i Vzryva, Vol. 34, No. 4, pp. 57–64, July–August 1998.