Effects of boundary layer displacement and separation on opposed-flow flame spread

An analysis is presented of the viscous-inviscid Interaction region around the tip of a flame spreading over the surface of a solid fuel in a forced laminar high reynolds number air stream that opposes the flame propagation. Through the interaction, the vaporization of the solid and the thermal expansion of the gas originate an adverse pressure gradient upstream of the flame tip, which leads to a decrease of the shear acting on the small region controlling the flame spread rate. Under certain realistic conditions this adverse pressure gradient may separate the boundary layer upstream of the vaporizing region of the solid, leading to a new mode of flame spread with a higher spread rate determined by the flow in the whole interaction region

The ignition and anchoring of diffusion flames by triple flames

The enhancement effects of thermal expansion on the propagation velocity of triple flames in mixing layers have been evaluated by direct numerical simulation of the Process. Numerical calculations have been used for the description of the flow, concentration and temperature field in the diffusion flame attachment region in the near wake of the injector. The numerical analysis provides the criterium for lift-off of the flames

An asymptotic analysis of chain-branching ignition in the laminar wake of a splitter plate separating streams of hydrogen and oxygen

Abstract. The chain-branching process leading to ignition in the high-temperature laminar wake that forms at the trailing edge of a thin splitter plate separating a stream of hydrogen from a stream of oxygen is investigated with a reduced chemistry description that employs H as the only chain-branching radical not in steady state. The analysis presented covers ignition events occurring in the Rott-Hakkinen and Goldstein regions, where self-similar solutions for the different flow variables are available. It is found that the initiation reactions, which create the first radicals, are only important in a relatively small initial region, becoming negligible downstream as the radical mole fractions increase to values larger than the ratio of the characteristic branching time to the characteristic initiation time, a very small quantity at temperatures of practical interest. As a result, most of the ignition history is controlled by the autocatalytic branching reactions, giving rise to a radical pool that increases exponentially with distance in a process that is described by using as a large parameter the ratio of the streamwise distance to the downstream extent of the initial region where initiation reactions are significant. Comparisons of the asymptotic results with numerical integrations of the conservation equations reveal that a three-term expansion for the H-atom profile is necessary in this case to provide an accurate prediction for the ignition distance

Large-activation-energy analysis of gaseous reacting flow in pipes

This paper analyzes the exothermic reaction of an initially cold gaseous mixture flowing with a moderately large Reynolds number along a cylindrical pipe with constant wall temperature. An overall irreversible reaction with an Arrhenius rate having a large activation energy is used for the chemistry description. The flow is chemically frozen in the cold entrance region, where the velocity evolves towards the Poiseuille profile as the gas temperature increases towards the wall value, ushering in a reaction stage during which the rate of heat transfer from the wall changes from positive to negative. The subsequent downstream evolution of the flow depends critically on the competition between the heat released by the chemical reaction and the heat-conduction losses to the wall, as measured by the Damkohler number 8, first introduced by Frank-Kamenetskii in his seminal analysis of thermal explosions in cylindrical vessels. For values of delta below the critical value delta &#61; 2 corresponding to the quasi-steady explosion limit, heat losses to the wall keep the gas temperature close to the wall value, so that the chemical reaction occurs slowly along the pipe in a flameless mode, which is analyzed to give an implicit expression for the streamwise reactant distribution. By way of contrast, for delta > 2 the slow reaction rates occur only in an initial ignition region, which ends abruptly when very large reaction rates cause a temperature runaway, or thermal explosion, at a well-defined location, whose computation must account for the temperature found at the end of the entrance region. The predictions of the large-activation-energy analyses, including ignition distances for delta > 2 and flameless reactant consumption rates for delta < 2, show good agreement with numerical computations of the reactive pipe flow for finite values of the activation energy.This work was supported by the Spanish MCINN through project # CSD2010-00011

Simulations of starting gas jets at low mach numbers

The starting jet produced by the impulsively started discharge of a submerged gas stream of constant velocity through a circular orifice in a plane wall is investigated by integrating numerically the axisymmetric Navier-Stokes equations for moderately large values of the jet Reynolds number. The analysis is restricted to low-Mach-number jets, for which the jet-to-ambient temperature ratio gamma=T/sub j//T/sub o/ emerges as the most relevant parameter. It is seen that the leading vortex approaches a quasisteady structure propagating at an almost constant velocity, which is larger for smaller values of gamma. The action of the baroclinic torque in regions of nonuniform temperature leads to significant vorticity production, with a constant overall rate equal to that of an inviscid starting je

Numerical analyses of deflagration initiation by a hot jet

Numerical simulations of axisymmetric reactive jets with one-step Arrhenius kinetics are used to investigate the problem of deflagration initiation in a premixed fuel–air mixture by the sudden discharge of a hot jet of its adiabatic reaction products. For the moderately large values of the jet Reynolds number considered in the computations, chemical reaction is seen to occur initially in the thin mixing layer that separates the hot products from the cold reactants. This mixing layer is wrapped around by the starting vortex, thereby enhancingmixing at the jet head, which is followed by an annular mixing layer that trails behind, connecting the leading vortex with the orifice rim. A successful deflagration is seen to develop for values of the orifice radius larger than a critical value aϲ in the order of the flame thickness of the planar deflagration δL. Introduction of appropriate scales provides the dimensionless formulation of the problem, with flame initiation characterised in terms of a critical Damk¨ohler number ∆ϲ = (aϲ/δL)², whose parametric dependence is investigated. The numerical computations reveal that, while the jet Reynolds number exerts a limited influence on the criticality conditions, the effect of the reactant diffusivity on ignition is much more pronounced, with the value of ∆ϲ increasing significantly with increasing Lewis numbers Le. The reactant diffusivity affects also the way ignition takes place, so that for reactants with Le ≳ 1 the flame develops as a result of ignition in the annular mixing layer surrounding the developing jet stem, whereas for highly diffusive reactants with Lewis numbers sufficiently smaller than unity combustion is initiated in the mixed core formed around the starting vortex. The analysis provides increased understanding of deflagration initiation processes, including the effects of differential diffusion, and points to the need for further investigations incorporating detailed chemistry models for specific fuel–air mixtures.This work was supported by the SpanishMCINN through project numbers ENE2008-06515-C01 and CSD2010-00010 and by the Comunidad de Madrid through project number S2009/ENE-1597

Critical radius for hot-jet ignition of hydrogen-air mixtures

This study addresses deflagration initiation of lean and stoichiometric hydrogen–air mixtures by the sudden discharge of a hot jet of their adiabatic combustion products. The objective is to compute the minimum jet radius required for ignition, a relevant quantity of interest for safety and technological applications. For sufficiently small discharge velocities, the numerical solution of the problem requires integration of the axisymmetric Navier–Stokes equations for chemically reacting ideal-gas mixtures, supplemented by standard descriptions of the molecular transport terms and a suitably reduced chemical-kinetic mechanism for the chemistry description. The computations provide the variation of the critical radius for hot-jet ignition with both the jet velocity and the equivalence ratio of the mixture, giving values that vary between a few tens microns to a few hundred microns in the range of conditions explored. For a given equivalence ratio, the critical radius is found to increase with increasing injection velocities, although the increase is only moderately large. On the other hand, for a given injection velocity, the smallest critical radius is found at stoichiometric conditions.This work was partially supported by Project S-505/ENE/0229 of the Spanish Comunidad de Madrid, and by projects CSD2010-00011 (CONSOLIDER-INGENIO) and MTM2010-18079 of the Spanish Ministerio de Economía y Competitivida

Critical radius for hot-jet ignition of hydrogen-air mixtures

This study addresses deflagration initiation of lean and stoichiometric hydrogen–air mixtures by the sudden discharge of a hot jet of their adiabatic combustion products. The objective is to compute the minimum jet radius required for ignition, a relevant quantity of interest for safety and technological applications. For sufficiently small discharge velocities, the numerical solution of the problem requires integration of the axisymmetric Navier–Stokes equations for chemically reacting ideal-gas mixtures, supplemented by standard descriptions of the molecular transport terms and a suitably reduced chemical-kinetic mechanism for the chemistry description. The computations provide the variation of the critical radius for hot-jet ignition with both the jet velocity and the equivalence ratio of the mixture, giving values that vary between a few tens microns to a few hundred microns in the range of conditions explored. For a given equivalence ratio, the critical radius is found to increase with increasing injection velocities, although the increase is only moderately large. On the other hand, for a given injection velocity, the smallest critical radius is found at stoichiometric conditions

The slowly reacting mode of combustion of gaseous mixtures in spherical vessels. Part 1: transient analysis and explosion limit

In this paper we revisit Frank-Kamenetskii’s analysis of thermal explosions, using also a single-reaction model with an Arrhenius rate having a large activation energy, to describe the transient combustion of initially cold gaseous mixtures enclosed in a spherical vessel with a constant wall temperature. The analysis shows two modes of combustion, including a flameless slowly reacting mode for low wall temperatures or small vessel sizes, when the temperature rise due to the reaction is kept small by the heat-conduction losses to the wall, so as not to change significantly the order of magnitude of the reaction rate. In the second mode of combustion the slow reaction rates occur only in the first ignition stage, which ends abruptly when very large reaction rates cause a temperature runaway, or thermal explosion, at a welldefined ignition time and location, which triggers a flame that propagates across the vessel to consume rapidly the reactant. We define the explosion limits, in agreement with FrankKamenetskii’s analysis, by the limiting conditions for existence of the slowly reacting mode of combustion. In this mode, a quasi-steady temperature distribution is established after a transient reaction stage with small reactant consumption. Most of the reactant is burnt, with nearly uniform mass fraction, in a second long stage, when the temperature follows a quasisteady balance between the rates of heat conduction to the wall and of chemical heat release. The changes in the explosion limits due to the enhanced heat transfer rates by the buoyant motion are described in an accompanying paper.This work was supported by the Spanish MCINN through project # CSD2010- 00010

The slowly reacting mode of combustion of gaseous mixtures in spherical vessels. Part 2: buoyancy-induced motion and its effect on the explosion limits

This paper investigates the effect of buoyancy-driven motion on the quasi-steady “slowly reacting” mode of combustion and on its thermal-explosion limits, for gaseous mixtures enclosed in a spherical vessel with a constant wall temperature. Following Frank-Kamenetskii’s seminal analysis of this problem, the strong temperature dependence of the effective overall reaction rate is taken into account by using a single-reaction model with an Arrhenius rate having a large activation energy, resulting in a critical value of the vessel radius above which the slowly reacting mode of combustion no longer exists. In his contant-density, convection-free analysis, the critical conditions were found to depend on the value of a Damk¨ohler number, defined as the ratio of the time for the heat released by the reaction to be conducted to the wall, to the homogeneous explosion time evaluated at the wall temperature. For gaseous mixtures under normal gravity, the critical Damk¨ohler number increases through the effect of buoyancy-induced motion on the rate of heat conduction to the wall, measured by an appropriate Rayleigh number Ra. In the present analysis, for small values of Ra, the temperature is given in the first approximation by the spherically symmetric Frank-Kamenetskii solution, used to calculate the accompanying gas motion, an axisymmetric annular vortex determined at leading order by the balance between viscous and buoyancy forces, which we call the FrankKamenetskii vortex. This flow is used in the equation for conservation of energy to evaluate the influence of convection on explosion limits for small Ra, resulting in predicted critical Damk¨ohler numbers that are accurate up to values of Ra on the order of a few hundred.This work was supported by the Spanish MCINN through project # CSD2010- 00010. FAW is supported by the US National Science Foundation through award #CBET-1404026