Autoignition in nonpremixed flow

The objective of this investigation has been to improve understanding of autoignition processes in nonpremixed flow fields of the types encountered in Diesel-engine ignition, through theoretical analyses that employ asymptotic methods of applied mathematics. The work was intended to develop formulas and equations that can be used in activities of applied research, such as code development, aimed at providing tools useful for the design of Diesel engines. The formulas may also be used directly for ignition estimates.Characteristic time scales were identified for these ignition problems. Their relative magnitudes were employed to define different regimes of ignition and to obtain simplified partial differential equations that describe ignition in these regimes. Effects of turbulence on ignition were addressed. Special attention was devoted to unsteady mixing layers, involving both variable strain and variable pressure, for which ignition-time formulas were derived. In addition, ignition analyses were completed for variable-volume chambers with arbitrary initial spatial variations of temperature and composition, to determine pressure histories produced by ignition-front propagation. These studies were based on one-step, Arrhenius approximations for the chemical kinetics and were restricted to ignition stages that precede ordinary flame propagation. Additional work considered triple-flame propagation that can odcur in mixing layers after ignition, with this same chemical-kinetic description, and asymptotic analysis of n-heptane ignition on the basis of a four-step, semi-empirical model for the chemical kinetics. In this latter study, the region of negative effective overall activation energy, between 800 K and 1100 K, was identified as exhibiting unusual ignition dynamics, and the asymptotic ignition-time formulas were shown to give good agreement with predictions of numerical integrations. This research has helped to strengthen the foundations of ignition theory for nonuniform media. It provided simplified descriptions of ignition processes that can be employed in studies of Diesel combustion that are oriented more towards development than are the present investigations. The asymptotic methods employed in this work thus appear capable of providing quite useful results

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

Flamelet structures in spray ignition

In typical liquid-fueled burners the fuel is injected as a high-velocity liquid jet that breaks up to form the spray. The initial heating and vaporization of the liquid fuel rely on the relatively large temperatures of the sourrounding gas, which may include hot combustion products and preheated air. The heat exchange between the liquid and the gas phases is enhanced by droplet dispersion arising from the turbulent motion. Chemical reaction takes place once molecular mixing between the fuel vapor and the oxidizer has occurred in mixing layers separating the spray flow from the hot air stream. Since in most applications the injection velocities are much larger than the premixed-flame propagation velocity, combustion stabilization relies on autoignition of the fuel-oxygen mixture, with the combustion stand-off distance being controlled by the interaction of turbulent transport, droplet heating and vaporization, and gas-phase chemical reactions. In this study, conditions are identified under which analyses of laminar flamelets canshed light on aspects of turbulent spray ignition. This study extends earlier fundamental work by Liñan & Crespo (1976) on ignition in gaseous mixing layers to ignition of sprays. Studies of laminar mixing layers have been found to be instrumental in developing un-derstanding of turbulent combustion (Peters 2000), including the ignition of turbulent gaseous diffusion flames (Mastorakos 2009). For the spray problem at hand, the configuration selected, shown in Figure 1, involves a coflow mixing layer formed between a stream of hot air moving at velocity UA and a monodisperse spray moving at velocity USUA. The boundary-layer approximation will be used below to describe the resulting sl ender flow, which exhibits different igniting behaviors depending on the characteristics of t he fuel. In this approximation, consideration of the case U A = U S enables laminar ignition distances to be related to ignition times of unstrained spray flamelets, thereby pro viding quantitative information of direct applicability in regions of low scala r dissipation-rate in turbulent reactive flows (see the discussion in pp. 181–186 of Peters (2000)) . This report is organized as follows. Effects of droplet dispersion dynamics on ignition of sprays in turbulent mixing layers are discussed in Section 2. The formulation f or ignition in laminar mixing layers is outlined in Sections 3 and 4. The results are presented in Section 5. In Section 6, the mixture-fraction field and associated scalar dissipat ion rates for spray ignition are discussed. Finally, some brief conclusions are drawn in Section 7