Antonio L. Sánchez

Hydrogen-oxygen induction times above crossover temperatures

Ignition in hydrogen–oxygen systems above crossover temperatures and under various conditions of pressure and composition is addressed computationally and by asymptotic methods. Different descriptions of the detailed chemistry are evaluated through comparison of computed and measured ignition times, and a balance between accuracy and simplicity is struck in selecting rate parameters to be used in investigating reduced chemistry. Through numerical calculations for isobaric, homogeneous, and adiabatic hydrogen–air mixtures it is shown that the detailed chemistry can be reduced to only six elementary steps for determining induction times over the range of conditions addressed. From these six steps, an analytical expression for ignition time is derived which agrees well with computational results concerning dependence on pressure, temperature, and composition. It is shown that O and OH maintain steady states during ignition for stoichiometric and fuel-rich mixtures, whereas H maintains, a steady state for sufficiently fuel-lean conditions. Simple asymptotic formulas for the induction times are derived for these two limits that demonstrate the limiting effect of O2 under rich conditions and of H2 under lean conditions. These formulas are combined in an approximate way to obtain an expression for the ignition time that can be used for all equivalence ratios.

Relationships between bifurcation and numerical analyses for ignition of hydrogen—air diffusion flames

Abstract Linear bifurcation and numerical techniques are employed to determine critical conditions for ignition in steady, counterflow, nonpremixed hydrogen-air systems, with varying degrees of nitrogen dilution of the fuel, at temperatures larger than the crossover temperature associated with the second explosion limit for hydrogen. Analysis of profiles of the radical pool at ignition reveals that, irrespective of the degree of dilution of the fuel or oxidizer streams, the O-atom steady state fails on the oxidizer side of the mixing layer. Therefore, at least three overall steps, with O and H atoms as the chain-branching species, are necessary to describe the ignition process. A simplified model with variable density, specific heat and transport properties, and with Stefan-Maxwell approximations for the diffusion velocities, is proposed to describe the structure of the H 2 O 2 N 2 weakly reactive mixing layer. Results of bifurcation analysis with this flow-field model and a three-step reduced chemical-kinetic scheme show excellent agreement with results of numerical integration of the full conservation equations with detailed chemistry for all degrees of dilution of the fuel feed.

The reduced kinetic description of lean premixed combustion

Lean premixed methane-air flames are investigated in an effort to facilitate the numerical description of CO and NO emissions in LPP (lean premixed prevaporized) combustion systems. As an initial step, the detailed mechanism describing the fuel oxidation process is reduced to a four-step reduced description that employs CO, H2 and OH as intermediates not following a steady-state approximation. It is seen that, under conditions typical of LPP combustion, the mechanism can be further simplified to give a two-step description, in which fuel is consumed and CO is produced according to the fast overall step CH4 + f 0 2 -*• CO + 2H20, while CO is slowly oxidized according to the overall step CO + | 0 a -*• CO2- Because of its associated fast rate, fuel consumption takes place in thin layers where CO, H2 and OH are all out of steady state, while CO oxidation occurs downstream in a distributed manner in a region where CO is the only intermediate not in steady state. In the proposed description, the rate of fuel consumption is assigned a heuristic Arrhenius dependence that adequately reproduces laminar burning velocities, whereas the rate of CO oxidation is extracted from the reduced chemistry analysis. Comparisons with results obtained with detailed chemistry indicate that the proposed kinetic description, not only reproduces well the structure of one-dimensionai flames, including profiles of CO, temperature and radicals, but can also be used to calculate NO emissions by appending an appropriate reduced chemistry description that includes both the thermal and the N20 production paths. Although methane is employed in the present study as a model fuel, the universal structure of the resulting CO oxidation region, independent of the fuel considered, enables the proposed formulation to be readily extended to other hydrocarbons.

The virtual origin as a first-order correction for the far-field description of laminar jets

The far-field velocity and composition fields of a submerged laminar jet are known to approach a self-similar solution corresponding to the flow induced by a point source of momentum and scalar. Previous efforts to improve this far-field description have introduced a virtual origin for the streamwise coordinate to remedy the singular behavior of the self-similar solution near the jet origin. The purpose of this note is to show, by means of a perturbative analysis of the point-source solution, that this virtual origin is in fact the first-order correction to the leading-order description. The perturbative analysis, which uses the ratio x of the streamwise distance to the length of jet development as an asymptotically large quantity, also indicates that the displaced point source provides the description in the far field with small relative errors of order x−3 for the round jet and of order x−10/3 for the plane jet. The values of the virtual origin are obtained by numerical integration of the boundary-layer...

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 γ=Tj∕To 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 γ. 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 jet.

One-dimensional overdriven detonations with branched-chain kinetics

The dynamics of time-dependent, planar propagation of gaseous detonations is addressed on the basis of a three-step chemistry model that describes branched-chain processes. Relevant nondimensional parameters are the ratio of the heat release to the thermal enthalpy at the Neumann state, the nondimensional activation energies for the initiation and branching steps, the ratio of the branching time to the initiation time and the ratio of the branching time to the recombination time. The limit of strong overdrive is considered, in which pressure remains constant downstream from the leading shock in the first approximation, and the ratio of specific heats γ is taken to be near unity. A two-term expansion in the strong overdrive factor is introduced, and an integral equation is derived describing the nonlinear dynamics and exhibiting a bifurcation parameter, the reciprocal of the product of (γ−1), the nondimensional heat release and the nondimensional branching activation energy, with an acoustic correction. A stability analysis shows that, depending on values of the parameters, either the mode of lowest frequency or a mode of higher frequency may be most unstable. Numerical integrations exhibit different conditions under which oscillations die, low-frequency oscillations prevail, high-frequency oscillations prevail, highly nonlinear oscillations persist, or detonation failure occurs. This type of parametric analysis is feasible because of the relative simplicity of the model, which still is more realistic than a one-step, Arrhenius chemical approximation. In particular, by addressing the limit of slow radical recombination compared with branching, explicit results are derived for the critical value of the bifurcation parameter, involving the ratio of the recombination time to the induction time. The results help to clarify the general nature of one-dimensional detonation instability and provide simplifications that can be employed in efficiently relating gaseous detonation behavior to the true underlying chemistry.

The hydrogen–air burning rate near the lean flammability limit

This paper investigates the inner structure of the thin reactive layer of hydrogen–air fuel-lean deflagrations close to the flammability limit. The analysis, which employs seven elementary reactions for the chemistry description, uses the ratio of the characteristic radical and fuel concentrations as a small asymptotic parameter, enabling an accurate analytic expression for the resulting burning rate to be derived. The analysis reveals that the steady-state assumption for chemical intermediaries, applicable on the hot side of the reactive layer, fails, however, as the crossover temperature is approached, providing a nonnegligible higher-order correction to the burning rate. The results can be useful, for instance, in future investigations of hydrogen deflagration instabilities near the lean flammability limit.

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 enhancing mixing 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 a c 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 Damköhler number Δc=(a c/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 Δc increasing significantly with increasing Lewis numbers . The reactant diffusivity affects also the way ignition takes place, so that for reactants with 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.

A WKB analysis of radical growth in the hydrogen-air mixing layer

The chain-branching process leading to ignition in the hydrogen-air mixing layer is studied by application of a novel WKB-like method with a four-step reduced scheme adopted for the chemistry description. Attention is restricted to initial free-stream temperatures above the crossover temperature corresponding to the second explosion limit of H2-O2 mixtures, thereby causing three-body recombination reactions to be negligible in the ignition process. It is shown that the initiation reactions, responsible for the early radical buildup, cease being important when the radical mass fractions reach values of the order of the ratio of the characteristic branching time to the characteristic initiation time, a very small quantity at temperatures of practical interest. The autocatalytic character of the chain-branching reactions causes the radical concentrations to grow exponentially with downstream distance in the process that follows. It is shown that, because of the effect of radical diffusion, the radical growth rate is uniform across the mixing layer in the first approximation, with an exponent given by that of a premixed branching explosion evaluated at the location where the effective Damköhler number based on the flow velocity is maximum. This exponent, as well as the leading-order representation of the radical profiles, are easily obtained by the imposition of a bounded, nonoscillatory behavior on the solution.

LIFTED LAMINAR JET DIFFUSION FLAMES

ABSTRACT This paper addresses the numerical description of lifted flames in axisymmetric laminar coflow jets. The analysis considers moderately large values of the Reynolds number, when the boundary-layer approximation can be used to describe the slender mixing region that extends between the jet exit and the flame, providing the profiles of velocity and mixture fraction that exist immediately upstream from the flame front region. The description of the nonslender flame front region, which provides the front propagation velocity as an eigenvalue, requires integration of the Navier-Stokes Equations with account taken of the reaction and thermal expansion effects. The limiting formulations corresponding to cases of practical interest, including large values of the air-to-fuel stoichiometric ratio, are briefly discussed. Illustrative numerical results are given for flames lifted or propagating at distances small compared with the jet development length, where the mixing layer is nearly planar.