Hydrodynamic instability of premixed flame propagating in narrow planar channel in the presence of gas flow

The paper analyses the hydrodynamic instability of a flame propagating in the space between two parallel plates in the presence of gas flow. The linear analysis was performed in the framework of a two-dimensional model that describes the averaged gas flow in the space between the plates and the perturbations development of two-dimensional combustion wave. The model includes the parametric dependences of the flame front propagation velocity on its local curvature and on the combustible gas velocity averaged along the height of the channel. It is assumed that the viscous gas flow changes the surface area of the flame front and thereby affects the propagation velocity of the two-dimensional combustion wave. In the absence of the influence of the channel walls on the gas flow, the model transforms into the Darrieus–Landau model of flame hydrodynamic instability. The dependences of the instability growth rate on the wave vector of disturbances, the velocity of the unperturbed gas flow, the viscous friction coefficients and other parameters of the problem are obtained. It is shown that the viscous gas flow in the channel can lead, in some cases, to a significant increase in instability compared with a flame propagating in free space. In particular, the instability increment depends on the direction of the gas flow with respect direction of the flame propagation. In the case when the gas flow moves in the opposite direction to the direction of the flame propagation, the pulsating instability can appear.     

Filtration combustion of a porous structure in a multicomponent gas environment

A mathematical model for describing the quasi-isobaric filtration combustion of porous materials with the formation of condensed reaction products in a multicomponent gas is developed. Two-stage combustion waves (control modes) at the counter filtration of gas mixture are examined. The effect of inert gas component on the structure of a two-stage filtration combustion wave is studied, and the critical conditions of the changeover between filtration combustion modes caused by inert gas concentration variation are determined. It is demonstrated the characteristics of the two-stage combustion front propagating in the control mode in a multicomponent gas flow depends on the porosity of the heterogeneous system.     

Intensification of shock-induced combustion by electric-discharge-excited oxygen molecules: numerical study

Mechanisms of combustion enhancement in a supersonic H₂–O₂ reactive flow behind an oblique shock wave front are investigated when vibrational and electronic states of O₂ molecule are excited by an electric discharge. The analysis is carried out on the base of updated thermally nonequilibrium kinetic model for the H₂–O₂ mixture combustion. The presence of vibrationally and electronically excited O₂ molecules in the discharge-activated oxygen flow allows to intensify the chain mechanism and to shorten significantly the induction zone length at shock-induced combustion. It makes possible, for example, to ignite the atmospheric pressure H₂–O₂ mixture at the distance shorter than 1 m behind the weak oblique shock wave at a small energy E_s = 1.2 × 10^–2 J · cm^–3 input to O₂ molecules. At higher pressure it is needed to put greater specific energy into the gas in order to ignite the mixture at appropriate distances. It is shown that excitation of O₂ molecules by electric discharge is much more effective for accelerating the hydrogen–oxygen mixture combustion than mere heating the gas.     

One-dimensional model of steady filtration combustion front

The stability of the front of a steady combustion wave propagating through a porous medium was examined. It was assumed that the inflow of the gaseous reactant from outside into the reaction zone is determined by the chemical interaction mechanism. Changes in the mass of the products and in the thermophysical parameters of the condensed component during combustion were taken into account. The wave structure arising during the exothermic conversion of such systems was studied, the boundary of steady combustion was determined, and the character of loss of stability with respect to one-dimensional spatial perturbations was examined.     

Mathematical combustion model of nanoaluminum-air suspension

This paper presents a combustion model of a nano-aluminum-air (nAl-air) suspension. The special feature of the model is performing a local mathematical model of the oxidant diffusion through an aluminum oxide layer on the particle surface taking into account the aluminum-oxidant reaction to simulate the combustion of nano-size aluminum (nAl) particles. The oxidation rate of the aluminum particles and the associated with this process the rate of heat release are determined from the solution of the local combustion problems for the entire set of nAl particles in the suspension. To obtain the suspension state parameters we solve the equation system, which includes the energy conservation equations for the gas and particles, the mass-conservation equation for the gas-dispersed mixture and the motion equations for the gas and particles controlling for the particle velocity lag. The model considers gas expansion and thus gas and particle motion. The developed model does not require setting the ignition temperature of nAl particles. The study provides the calculated propagation rate of the combustion front in the nAl-air suspension depending on the nAl mass concentration and on the initial temperature of the suspension.     

Modeling of a self-excited pulse combustor and stability analysis

The major bottleneck for popularization and utilization of the conventional mechanical valve pulse combustors is the self-priming mode of gas supply. An aerodynamic valve (as against mechanical valve) self-excited pulse combustor of the Helmholtz-type with continuous supply of gas and air was designed and a mathematical model was established in this paper. The theoretical model employed well-stirred reactor model and a single step Arrhenius chemistry, and took those factors which might affect the combustion stability into account. The factors include the variation of the mass rate of the reactants affected by the pressure in the combustion chamber, the convective and radiation heat loss in the combustion chamber, and the heat transfer and wall friction in the tailpipe. The effect of wall temperature of combustion chamber, wall heat transfer coefficient, tailpipe length and friction coefficient on combustionstability were analyzed. The range of combustion oscillations can be predicted. It is theoretically and experimentally shown that combustion oscillations can be produced with a continuous supply of fuel and air without mechanical valves. The experimental data show qualitative agreement with predictions from the theoretical model. The theoretical model could be a tool for designing and optimizing the self-excited pulse combustor.     

Observation of droplet motion during flame spread on three-fuel-droplet array with a pendulum suspender

Flame spread on a fuel droplet array has been studied as a simple model of spray combustion. A three-fuel-droplet array with a pendulum suspender was employed to investigate interactions between flame spread and droplet motion in the axial direction. Initial droplet diameter was 0.8 mm, and fuel was n-heptane. A silicon carbide pendulum suspender of 15 μm in diameter and 30 mm in length was used for the third droplet. The first fixed droplet was ignited by electric spark. Behavior of the flame and the third droplet was observed using a high-speed video camera with an image intensifier. Particle tracking velocimetry (PTV) measurements were performed to explain the behavior of the third movable droplet. The dimensionless droplet span, which is the average of droplet-to-droplet distances divided by the average initial diameter of the three droplets, was varied from 2.5 to 8 for observing flame spread, and fixed at 5.5 for PTV measurements. It was observed that the third droplet moved away from the second droplet before the flame spread to the third droplet. The displacement of the third droplet is remarkable when the dimensionless droplet span is close to the limit of flame spread. This implies that the movement of the droplet decreases the dimensionless span of the flame spread limit and the flame spread speed near the flame spread limit. Results of PTV measurements suggest that the heat expansion wave, caused by ignition of the premixture which was accumulated around the second droplet, and the burned gas flow from the second droplet pushed away the third droplet; then natural convection, induced by the flames of the first and second droplets, drew the third droplet to the second droplet. The heat expansion wave and the burned gas flow of the second droplet reached nearly 12 in dimensionless span.     

Combustion waves in a model with chain branching reaction and their stability

In this paper the travelling wave solutions in the adiabatic model with the two-step chain branching reaction mechanism are investigated both numerically and analytically in the limit of equal diffusivity of reactant, radicals and heat. The properties of these solutions and their stability are investigated in detail. The behaviour of combustion waves are demonstrated to have similarities with the properties of non-adiabatic one-step combustion waves in that there is a residual amount of fuel left behind the travelling waves and the solutions can exhibit extinction. The difference between the non-adiabatic one-step and adiabatic two-step models is found in the behaviour of the combustion waves near the extinction condition. It is shown that the flame velocity drops down to zero as the extinction condition is reached. Prospects of further work are also discussed.     

Hydrodynamics of pulsed supersonic underexpanded jets: Spatiotemporal characteristics

The gasdynamic parameters of nonsteady expansion of He, Ar, N₂, and SiH₄ from a sonic nozzle into a space with reduced background gas pressure were experimentally studied for moderate values of n (10³–10⁶) and the Reynolds number (Re_L∼10⁰–10²). The jet set times necessary for the formation of pulsed jets of a given finite duration are determined. The results are generalized in terms of dimensionless similarity parameters. The laws of motion of the leading and trailing fronts in pulsed jets of various gases are established. The leading front of a pulsed jet propagates at a velocity significantly smaller than the limiting steady value. The jet expansion dynamics is determined by the ratio of the momentum of the expanding gas to that of the background gas displaced from the flow region. The length of the steady flow region in a pulsed jet monotonically decreases downstream from the source and drops with increasing background gas pressure because of the loss of jet particles in the trailing rarefaction wave; this length increases with the initial momentum because the background gas is more intensively displaced from the flow region.     

A study of the characteristics of the combustion of Ti + <Emphasis Type="Italic">x</Emphasis>C (<Emphasis Type="Italic">x</Emphasis> &gt; 0.5) powder and granular compositions in a gas coflow

The characteristics of the combustion of Ti + 0.5C, Ti + 0.75C, and Ti + C powder and granular mixtures in a flow of inert (argon) and reactive (nitrogen) gases at various pressure differences are studied. It is shown that the influence of the pressure difference on the burning velocity of the powder mixture decreases with increasing fraction of carbon in it, but a pressure difference of 1 atm producing practically no effect on the burning rate of the Ti + C mixture. The data obtained are indicative of a nonequilibrium mechanism of the combustion of Ti + xC granular mixtures in a nitrogen coflow, in which case the sequence of chemical reactions in the combustion wave is determined by the kinetic characteristics of the interaction of titanium with nitrogen and carbon. It is concluded that the reactive gas flow ignites the surface of the granules and thereby leads the propagation of the combustion wave. It is established that, for all the mixtures studied, the mechanism of the combustion of a granular charge in a nitrogen flow is fundamentally different from the combustion of a powder charge under the same condition.     

Characteristic regimes of premixed gas combustion in high-porosity micro-fibrous porous media

Dynamical behaviour of the premixed flame propagating in the inert high-porosity micro-fibrous porous media has been studied numerically. Effects of mixture filtration velocity, equivalence ratio and burner transverse size on the flame structure have been investigated and the regions of existence of different combustion regimes have been determined. It was found that the influence of the hydrodynamic instability on the flame dynamics is significant in the case of the moderate and high filtration velocities and this effect is negligible at the low velocities. At the moderate filtration velocities the effect of hydrodynamic instability manifests in the flame front deformation and in particular in the flame inclination. It was found that the flame can be stabilized within the whole interval of the filtration gas velocity, whereas in the ordinary porous media the standing wave is settled only at fixed value of gas filtration velocity. This finding is in line with recent experimental results on combustion in micro-fibrous porous media (Yang et al., Combust. Sci. Tech. 181 (2009), 1–16). Possible physical interpretation of the flame anchoring effect may be given on the base of present numerical analysis. At the high filtration velocities the hydrodynamic instability manifests itself in periodical appearance of the moving wrinkles on the flame front surface which forms non stationary high temperature trailing spots behind the leading part of the flame front. Such dynamics may be associated with splitting wave structures which were revealed in previous experiments (Yang et al., Combust. Sci. Tech. 181 (2009), 1–16).     

Shock waves and formation of carbon dioxide hydrate at an increased pressure in the gas-liquid medium

The processes of breaking, solution, and formation of hydrates behind a shock wave of moderate amplitude were studied experimentally in water with carbon dioxide bubbles under different initial static pressures. It is shown that an increase in the static pressure in a gas-liquid medium leads to reduction of critical relative amplitude of the shock wave, corresponding to starting development of Kelvin — Helmholtz instability and bubble splitting into small gas inclusions behind the shock wave front. It is shown that the rates of carbon dioxide solution and hydrate formation behind the shock wave front are close by the value; their dependences on medium and wave parameters are determined. Calculations by the model of gas hydration behind the shock wave are presented. The work was financially supported by the Russian Foundation for Basic Research (grants Nos. 06-01-00142 and 06-08-00657).     

Numerical model of two-dimensional heterogeneous combustion in porous media under natural convection or forced filtration

A novel mathematical model and original numerical method for investigating the two-dimensional waves of heterogeneous combustion in porous media are proposed and described in detail. The mathematical model is constructed within the framework of the model of interacting interpenetrating continua and includes equations of state, continuity, momentum conservation and energy for solid and gas phases. Combustion, considered in the paper, is due to the exothermic reaction between fuel in the porous solid medium and oxidiser contained in the gas flowing through the porous object. The original numerical method is based on a combination of explicit and implicit finite-difference schemes. A distinctive feature of the proposed model is that the gas velocity at the open boundaries (inlet and outlet) of the porous object is unknown and has to be found from the solution of the problem, i.e. the flow rate of the gas regulates itself. This approach allows processes to be modelled not only under forced filtration, but also under free convection, when there is no forced gas input in porous objects, which is typical for many natural or anthropogenic disasters (burning of peatlands, coal dumps, landfills, grain elevators). Some two-dimensional time-dependent problems of heterogeneous combustion in porous objects have been solved using the proposed numerical method. It is shown that two-dimensional waves of heterogeneous combustion in porous media can propagate in two modes with different characteristics, as in the case of one-dimensional combustion, but the combustion front can move in a complex manner, and gas dynamics within the porous objects can be complicated. When natural convection takes place, self-sustaining combustion waves can go through the all parts of the object regardless of where an ignition zone was located, so the all combustible material in each part of the object is burned out, in contrast to forced filtration.     

On wave radiation induced by a fast shock wave in an oblique magnetic field

The corrugation stability of the flat surface of a fast magnetohydrodynamic shock wave in a perfect monoatomic gas with a constant heat capacity is studied with numerical techniques. The magnetic field makes an arbitrary angle with the plane of discontinuity. It is shown that the shock wave remains stable only if it is strictly perpendicular to the magnetic field. At any other angle between the fast shock wave and magnetic field, the former may spontaneously radiate outwardly propagating magnetohydrodynamic waves under certain conditions. Incoming flow characteristics at which these waves are induced are determined.     

Structure of a pressure driven flame in porous media

The model of a combustion wave driven by local elevation of pressure in inert porous media filled with flammable gas is investigated. The combustion wave structure is studied using the Zel'dovich approach. Analytical formulae for the combustion wave speed and for values of temperature and pressure behind the flame front are derived.     

Pulsating hydrodynamic instability and thermal coupling in an extended Landau/Levich model of liquid-propellant combustion: I. Inviscid analysis

Hydrodynamic (Landau) instability in combustion is typically associated with the onset of wrinkling of a flame surface, corresponding to the formation of steady cellular structures as the stability threshold is crossed. In the context of liquid-propellant combustion, such instability has recently been shown to occur for critical values of the pressure sensitivity of the burning rate and the disturbance wavenumber, significantly generalizing previous classical results for this problem that assumed a constant normal burning rate. Additionally, however, a pulsating form of hydrodynamic instability has been shown to occur as well, corresponding to the onset of temporal oscillations in the location of the liquid/gas interface. In the present work, we consider the realistic influence of a non-zero temperature sensitivity in the local burning rate on both types of stability thresholds. It is found that for sufficiently small values of this parameter, there exists a stable range of pressure sensitivities for steady, planar burning such that the classical cellular form of hydrodynamic instability and the more recent pulsating form of hydrodynamic instability can each occur as the corresponding stability threshold is crossed. For larger thermal sensitivities, however, the pulsating stability boundary evolves into a C-shaped curve in the (disturbance-wavenumber, pressure-sensitivity) plane, indicating loss of stability to pulsating perturbations for all sufficiently large disturbance wavelengths. It is thus concluded, based on characteristic parameter values, that an equally likely form of hydrodynamic instability in liquid-propellant combustion is of a non-steady, long-wave nature, distinct from the steady, cellular form originally predicted by Landau.     

Simulation of front motion in a reacting condensed two phase mixture

The computational technique is developed in order to provide the scale capturing for numerical simulation of the thermal processes. The thermal front motion and gas flow dynamics as well as the rate of particle growth during the Carbon Combustion Synthesis of Oxides (CCSO) were predicted using the numerical simulation. In CCSO the exothermic oxidation of carbon nanoparticles generates a self-sustained thermal reaction front that propagates through the solid reactant mixture converting it to the desired complex oxides. The combusted carbon is emitted from the sample as carbon dioxide and its high rate of release increases the product porosity and friability. It was shown that the complicated finger front instability can be developed during the carbon combustion synthesis. This phenomenon results from a vortex gas flow in the reaction zone fed by the carbon dioxide co-flow and oxygen counter-flow filtration.     

Erosive burning of a propellant in the field of a traveling acoustic wave

The response of the propellant burning rate to periodically varied pressure and the tangential mass flow of the combustion products is examined within the framework of the phenomenological theory of unsteady combustion. The effect of an elementary acoustic disturbance, a plane monochromatic traveling acoustic wave, is examined. The analytical and numerical results are obtained for the simplest propellant model with a minimum number of parameters. The roles of the steady and unsteady components of erosion at low and high values of the erosion ratio are established.     

Nonlinear Stability of Weak Detonation Waves¶for a Combustion Model

We show that the weak detonation waves for a combustion model of Rosales–Majda are nonlinearly stable. Because of the strongly nonlinear nature of the wave, usual stability analysis of weakly nonlinear nature does not apply. The chemical switch on-off is the main feature of nonlinearity. In particular, the propagation of the wave depends sensitively on the tail behaviour of the flow in front of it. Unlike the strong detonation waves, a weak detonation is supersonic and there is the separation of the gas waves from the reacting front. As a consequence, the reacting front needs to be traced. Received: 6 October 1998 / Accepted: 2 February 1999