Autoignition of nonuniform mixtures in chambers of variable volume

Autoignition histories are considered under conditions such that the compression and heat release occur sufficiently rapidly that molecular transport is negligible during the ignition and propagation processes. The objective is to account for arbitrary spatial variations of temperature and composition that may be present when ignition begins. A one-step, Arrhenius reaction of large activation energy and arbitrary orders with respect to both fuel and oxidizer describes the chemistry. Expressions are obtained for the ignition time and for the rate of pressure buildup after ignition in terms of the temperature and species concentrations that exist in the nonreacting, multiphase, turbulent flow just prior to or shortly after ignition

Asymptotic analysis of n-heptane ignition and cool flames with a temperature-explicit model

An empirical four-step mechanism has previously been proposed for describing ignition of heptane-air mixtures. This mechanism captures the low-temperature and high-temperature ignition behavior as well as the intermediate-temperature behavior, between roughly 800 K and 1100 K, where a negative temperature dependence of the overall rate is observed. The present paper derives simplified overall rate formulas for ignition times from this four-step mechanism and uses those formulas to derive a temperature-explicit model whose simplicity facilitates analysis of more complex ignition phenomena. Methods of activation-energy asymptotics are employed for the temperature-explicit model to investigate ignition in homogeneous, adiabatic systems, ignition by compressional heating in homogeneous systems, and structures and quasisteady propagation velocities of cool flames in weakly strained mixing layers. It is shown that, in the range of negative temperature dependence, there is a plateau in the ignition time when the criterion of thermal runaway is employed. Near this plateau region, cool flames with three-zone structures can propagate at velocities that increase with increasing initial temperature. Besides providing qualitative descriptions of ignition processes for hydrocarbon-air mixtures, the results lead to quantitative predictions that can be compared with experiment

Note on ignition by a hot catalytic surface

In a previous paper [1], we applied asymptotic methods based on large values of the nondimensional activation temperature to study ignition of a reactive material, semi-infinite in extent, subjected to a step increase in temperature at its planar surface. In appendices of that paper, the analysis was extended to consider effects of reactant consumption and of surface catalysis, the latter involving catalytic removal of fuel by the surface at which the temperature increase is imposed. There appears to be increasing interest in this last problem, in connection with situations in which reactants are exposed to hot surfaces which possess the capability of consuming fuel. Therefore, additional considerations, reported herein, have been pursued

Ignition in an unsteady mixing layer subject to strain and variable pressure

A general formulation is given for ignition in nonpremixed systems involving time-dependent mixing of fuel and oxidizer streams that experience both strain and time-varying pressure, subject to one-step, Arrhenius chemistry. From this general formulation, a number of specific situations are identified that require separate ignition-stage analyses. These ignition-stage analyses are completed for those cases that appear to be of greatest relevance to autoignition in Diesel engines. The resulting ignition times may thus be employed in arriving at estimates of Diesel ignition

Asymptotic theory of diffusion-flame extinction with radiant loss from the flame zone

Laminar diffusion flames in counterflow configurations such as stagnation-point boundary layers are analyzed by methods of matched asymptotic expansions with large parameters being the temperature sensitivities of the rates of chemical heat generation and radiant heat loss. Formulas are derived defining critical conditions for flame extinction, including influences of radiant loss

Deflagration regimes of laminar flames modeled after the ozone decomposition flame

Methods of activation-energy asymptotics are employed to investigate regimes of combustion of steady, planar, adiabatic deflagrations involving a four-step kinetic mechanism modeled after that of the ozone decomposition flame. The analysis demonstrates the occurrence of previously known regimes having flame structures that involve a nonreactive preheat zone followed by a narrow reactive-diffusive zone, in which a steady-state approximation for the reaction intermediary may or may not apply and downstream from which a recombination zone may or may not exist. In addition, a new regime is identified having a two-zone flame structure in which the intermediary is generated in a downstream zone that obeys a steady-state approximation for temperature and diffuses into an upstream zone where the primary heat release occurs. In this regime convection, diffusion, and reaction all are important in both zones, and heat release persists in the preheat zone all the way to the cold boundary. For the ozone flame new results for burning velocities are given and regimes are identified as functions of pressure, initial temperature, and initial ozone concentration

Strained premixed laminar flames with nonunity Lewis numbers

The method of activation energy asymptotics is used to study the effects of Lewis numbers different from unity on nonadiabatic flamelets in counterflowing streams of reactants and products. A sequence of analyses parallels those reported earlier for such flamelets having Lewis number unity. Thus initial results relate to nearly adiabatic flows with Lewis numbers close to unity. It is found that the effect of nonunity Lewis numbers is accentuated in flamelets subjected to low rates of strain and that Lewis numbers greater than unity tend to promote extinction. Thus abrupt extinction and ignition events can occur even under adiabatic conditions. Next fully nonadiabatic flamelets with Lewis numbers near unity are treated in order to consider cases involving relatively large degrees of product heating and cooling. These results relate to reaction zones as they arise under conditions of low-to-moderate rates of strain with the customary diffusive-reactive balance. We also treat flamelets subjected to such high rates of strain that the reaction zone is extended and located far into the product stream. In this case a diffusive-convective-reactive balance prevails. Realistic density variations are considered in the numerical examples and are shown to tend to retard extinction

New results on q-positivity

In this paper we discuss symmetrically self-dual spaces, which are simply real vector spaces with a symmetric bilinear form. Certain subsets of the space will be called q-positive, where q is the quadratic form induced by the original bilinear form. The notion of q-positivity generalizes the classical notion of the monotonicity of a subset of a product of a Banach space and its dual. Maximal q-positivity then generalizes maximal monotonicity. We discuss concepts generalizing the representations of monotone sets by convex functions, as well as the number of maximally q-positive extensions of a q-positive set. We also discuss symmetrically self-dual Banach spaces, in which we add a Banach space structure, giving new characterizations of maximal q-positivity. The paper finishes with two new examples.Comment: 18 page

A generalized burke-schumann formulation for hydrogen-oxygen diffusion flames maintaining partial equilibrium of the shuffle reactions

Under a wide range of conditions of ambient pressures, temperatures, dilutions and strain rates, nonpremixed combustion in hydrogen-oxygen systems maintains partial equilibrium of the four two-body chain-carrying reactions while experiencing finite rates of the three-body radical-recombination reactions H + 03 + M -+ HOa + M and H + H + M -+ H2 + M. There then exists a three-step reduced mechanism, with H as the only intermediate species and concentrations of the radicals O, OH and H02 related to that of H through steady states. The conservation equations corresponding to this chemical description are formulated here in terms of generalized coupling functions that account for species diffusivities that differ from the thermal diffusivity, providing a set of equations that describe the flame structure for strain conditions ranging from near extinction to weakly strained flames. As a model example, the formulation is applied to the analysis of flame development in the hydrogen-air laminar mixing layer with free-stream temperatures above the crossover temperature corresponding to the second explosion limit. The formulation can be used for many other model problems as well as for computational studies of nonpremixed combustion in complex configurations involving both laminar and turbulent flows

Chain-branching explosions in mixing layers

The chain-branching process leading to ignition in the high-temperature hydrogen-oxygen mixing layer is studied by application of a novel WKB-like method when, as is typically the case, two branching radicals cannot be assumed to maintain steady state. 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 the transverse radical profiles that emerge can be described by exponential series of the WKB type in inverse powers of the streamwise coordinate. The analysis reveals that, because of the effect of radical diffusion, the rate of radical growth is uniform across the mixing layer in the first approximation, with the exponential growth in distance having the same nondimensional streamwise variation as that of a premixed branching explosion evaluated at the transverse location where the effective Damkoher number based on the flow velocity and branching rate is maximum. This functional streamwise variation, as well as the leading-order representation of the radical profiles, is obtained by imposing a condition of bounded, nonoscillatory behavior on the solution. The resulting radical profiles peak at the location of maximum local Damkohler number and decay exponentially to the sides. Analysis of the solution in the vicinity of the maximum, which is a turning point of second order in the WKB expansion, yields the second-order correction to the growth rate as an eigenvalue in a linear eigenvalue problem. The method developed can be extended to the analysis of chain-branching explosions in laminar, self-similar mixing layers with an arbitrary number of branching steps adopted for describing the chemistry