Low Lewis Number Research Articles

The lateral movement of the three-dimensional cellular flame at low Lewis numbers

Abstract The lateral movement of the three-dimensional (3-D) cellular flame at low Lewis numbers is numerically investigated. The equation used is the compressible Navier–Stokes equation including a one-step irreversible chemical reaction. We superimpose the hexagonal disturbance with the peculiar wave number on the stationary plane flame and calculate the evolution of the disturbed flame. When the Lewis number is unity, i.e., only the hydrodynamic effect has an influence on the flame instability, the stationary cellular flame is formed. When the Lewis number is lower than unity, i.e., the diffusive-thermal and hydrodynamic effects have an influence, the laterally moving cellular flame is formed. With a decrease in the Lewis number, the laterally moving velocity of the cell increases. The laterally moving velocity of the three-dimensional cellular flame is much larger than that of the two-dimensional (2-D) cellular flame. Because, the increment of local temperature at the convex flame front toward the unburned gas in the three-dimensional flame is great compared with that in the two-dimensional flame.

Effect of Lewis number on flame front fragmentation in narrow closed channels

This work is concerned with the numerical investigation of the influence of the ratio of thermal conductivity to diffusivity of a combustible gas mixture on the dynamics of adiabatic flame propagation in narrow closed planar channels under zero gravity. Reynolds numbers are less than 100. A low Mach number limit of the Navier-Stokes system for the A → B reaction was used. The appearance of a flame front bifurcation, resulting in flame inversion, was obtained numerically for low Lewis numbers. The combined effect of a specific hydrodynamic flow field in a closed channel and of the domination of diffusivity over thermal conductivity, similar to the mechanism of thermal-diffusive instability, was found to be the main driving force of the bifurcation. It was concluded that, both numerically and experimentally, the inverted flame front has the same general shape. However, this shape is unlikely to be attributed to the same physical mechanism of its formation over the entire range of regimes. Fragmentation of inverted flames into two segments is clearly observed for low Lewis numbers.

Existence conditions and drift velocities of adiabatic flame-balls in weak gravity fields

Combining activation energy asymptotics, suitable scalings and numerical methods, we study how flame-balls move under the action of the free convection that they themselves generate in the presence of a weak, uniform gravity field. Attention is focused on steady configurations (in a suitable reference frame), on an isolated flame-ball of size comparable to what is obtained in the absence of gravity, and on deficient reactants that are characterized by a low Lewis number. For the sake of simplicity, we consider an adiabatic combustion process, in the sense that the radiative exchanges are neglected. This work provides one with:(a) a description of the free-convection field around the flame-ball, along with an asymptotic estimate of the drift velocity;(b) a relationship between the flame-ball radius, strength of gravity and physico-chemical properties of the reactive premixture;(c) extinction conditions, caused by the net effect of heat extraction from the flame-ball to its surroundings by the free-convection field.Hints on generalizations currently under consideration are also given.

Overview of the NASA Microgravity Combustion Program

Recently, three major combustion experiments were carried out in the microgravity environment of the Space Shuttle on the Microgravity Science Laboratory-1 mission. These three efforts entailed a study of laminar soot processes in gaseous diffusion e ames, a study of the structure of e ame balls at low Lewis numbers, and a study of isolated droplet combustion. Descriptions of these three experiments and their preliminary results appear in the following three papers. The purpose of thispaperis to “ setthetable” forthese threepapers through a discussion of theimportanceof microgravity to the study offundamental combustion phenomena, a presentation of an overview of the current NASA microgravity combustion program, and a brief description (with references to morecomplete papers) of previous space-based microgravity combustion experiments carried out under the aegis of NASA.

Experimental Study of Flame Balls in Space: Preliminary Results from STS-83

Results from the Structure Of Flame Balls At Low Lewis-number (SOFBALL) spaceflight experiment conducted on the STS-83/MSL-1 Space Shuttle mission are reported. These are the first premixed gas combustion experiments to be performed in space. Two of the 15 scheduled tests were successfully completed on this shortened mission. Two different types of mixtures were burned, and both burned much longer than expected based on prior theoretical understanding. From these tests, two new insights were obtained, namely, on the buoyancy-induced drift speed and repulsion of adjacent flame balls due to their mutual interaction. Preliminary results from the STS-94/MSL-1 reflight are also presented and show a remarkable sensitivity of the flame balls to small accelerations resulting from Orbiter attitude control maneuvers. Comparison of experimental results to computational predictions reveals limitations in current models of H 2 -O 2 chemistry for very lean mixtures. It is shown how the results of these space experiments may provide an improved understanding of the interactions of the two most important phenomena in combusting materials, namely, chemical reaction and transport processes, in the unequivocally simplest possible configuration.

Flame Bifurcations and Flammable Regions of Radiative Counterflow Premixed Flames with General Lewis Numbers

Flame bifurcations, extinction, and flammable regions of radiative counterflow premixed flames and the planar propagating flames are investigated numerically with general Lewis numbers. New insights and phenomena are presented by examining the interaction of radiation heat loss, Lewis number effect, and stretch. At a low Lewis number, the results show that for equivalence ratio lower than the standard flammability limit, radiation extinction limit and stretch extinction limit exist, respectively, at low and high stretch rates. For a higher equivalence ratio, this flame isola opens up and yields two stable flame branches, a normal flame branch, and a weak flame branch. A G-shaped curve showing the limits and flammable regions of these two flame regimes is obtained. The results show that the inferior limit of counterflow flame is lower than the standard limit. At unity Lewis number, the results show that, for equivalence ratio lower than the standard limit, there is also a flame isola with two distinct extinction limits at low and high stretch rates. For equivalence ratio larger than the standard limit, a new flame branch with flame standing far from the stagnation plane emerges on the low stretch rate side of the flame isola. This flame is related to the standard limit with the decrease of fuel concentration and merges with the flame isola when the fuel concentration is larger than a critical value. The extinction curve is also a G-shaped curve and the inferior limit is lower than the standard limit. At Lewis number larger than a critical value, for equivalence ratio near the standard limit, there is only the weakly stretched flame branch with a single stretch extinction limit. With an increase of fuel concentration, a weak flame isola emerges. As the fuel concentration further increases, this weak flame isola merges with the weakly stretched flame branch yielding three kinds of flame regimes. The resulting extinction curve is a K-shaped curve and the inferior limit is equal to the standard limit. The present results show that flame bifurcations and the existence of weak flames are physically intrinsic phenomena of radiative counterflow premixed flames. It is found that the normal flame and the weak flame can jump to each other at their limits. The obtained G and K-shaped curves show a clear relation between the counterflow flame and the planar propagating flame. The occurrence of G–K transition with the increase of Lewis number also gives a good explanation to the physics of the experimental results.

Non-isothermal gas absorption with reversible chemical reaction

A fundamental description of non-isothermal mass transfer accompanied by a single reversible chemical reaction has been presented. The description is based on the Higbie penetration theory. Arrhenius type dependence of solubility, reaction rates and diffusivities on temperature has been assumed. Special emphasis has been paid to bimolecular irreversible reactions where depletion of the liquid phase reactant occurs. In addition, the mass transfer behavior in the infinite enhancement regime has also been presented. It has been shown that the Shah criterion fails under conditions where depletion of the liquid phase reactant occurs. In the infinite enhancement regime, the non-isothermal enhancement factor is dependent on the ratio of the diffusivities of the reactants, the ratio of the initial stoichiometric reactant concentrations and the activation energies of solubility and reactant diffusivity. These characteristics of the infinite non-isothermal enhancement factor have been reported earlier by Asai et al. (1985, A.I.Ch.E. J.31, 1304–1312). Additionally, it has been shown that, for bimolecular irreversible reactions, the use of correlations for interfacial temperature rise that assume all heat to be released at the interface is not valid for systems with low Lewis numbers but also not for systems where depletion of the liquid phase reactant occurs. Further, the model has been used to study the effect of reversibility on bimolecular reactions. The effect of temperature dependence of the solubility of the gaseous component and diffusivities of the various species on the overall enhancement has been presented. Since the non-isothermal enhancement factor of bimolecular reversible reactions is dependent on various parameters, it is not possible to determine its value by analytical or via approximate techniques. One is forced to use numerical methods for this purpose instead.

Interaction between two premixed laminar V-shaped flame fronts at low Lewis number

In studies of flamelets in premixed turbulent combustion, the interaction between laminar flames is of great importance. To study this, measurements have been made of the interaction between two premixed laminar V-shaped flames (“W” configuration) for a Lewis number less than 1. When the Lewis number differs greatly from unity, differential diffusion effects dominate and lead to considerable complexity. Flow visualization is used in association with laser Doppler velocimetry. Temperatures are measured with a thermocouple and species are sampled through a probe. The results show repulsion between the two oblique flame fronts separated by fresh mixture. This induces a divergent flow in the whole interaction zone and an overall shifting of the two V-shaped flames. The influence of the Lewis number is first noticeable on the unburned gases between the two flames since it induces preferential diffusion of hydrogen in the transverse direction. This leads to an increase of temperature inside the two V-shaped flames. As a consequence, it also prevents the intersection and coalescence of the two inner fronts as they propagate towards each other.

Effects of Radiation Heat Loss on the Flammable Region of Counterflow Premixed Flames at a Large Lewis Number.

The extinction limits and flammable regions of a nonadiabatic counterflow premixed flame at a large Lewis number are investigated numerically. It is found that interaction between the radiative heat loss and the Lewis number effect results in four kinds of flame bifurcations. Furthermore, the results show that there exist four different kinds of flame regimes : normal flames, radiation-stretch-induced weak flames, radiation-Lewis number effect-induced weak flames and unified weak flames at typical equivalence ratios. An increase in the radiation intensity reduces the extinction limit of a normal flame but extends the flammable region of weak flames to large stretch rates. A general graph showing the extinction limits and the flammable regions is obtained. It is found that the G-shaped curve obtained at a low Lewis number is reduced to a K-shaped curve at a large Lewis number. This G-K transition presents a good explanation for the experimental results obtained in microgravity experiments.

Self-fragmentation of nonadiabatic cellular flames

A simple thermal-diffusive model for premixed flames with radiative heat losses is studied numerically. In accordance with previous analytical predictions, it is shown that cellular flames occurring in low Lewis number premixtures can propagate with heat-loss rates greater than the maximum that extinguishes the planar flame. At sufficiently high heat losses, the flame interface breaks up into separate caplike propagating flamelets while a significant portion of the fuel remains unconsumed. A further increase in heat losses leads to a total suppression of the flame.

セル状火炎の燃焼速度に及ぼす拡散・熱的不安定の影響

The effect of the diffusive-thermal instability on the burning velocity of cellular flames is numerically studied. The burning velocity of cellular flames is large compared with that of plane flames and increases as the Lewis number becomes lower. When the Lewis number is unity, rise of the burning velocity is equal to that of the area of a flame surface. On the other hand, when the Lewis number is lower than unity, the former is larger than the latter. The local burning velocity increases/decreases at the convex/concave flame surface toward the unburned gas for low Lewis numbers. The increase of the local burning velocity at the convex surpasses the decrease at the concave. Thus, the ratio of the burning velocity to the surface area increases as intensity of the diffusive-thermal instability becomes greater.

Fingering instability in nonadiabatic low-Lewis-number flames.

Employing the formal similarity between the dispersion relations for the hydrodynamic (Darrieus-Landau) and the diffusive instabilities at the quenching threshold, a phenomenological model for the nonlinear evolution of the near-limit premixed flame is proposed. Numerical simulations of the model show that at sufficiently high Zeldovich and low Lewis numbers the cellular flame resulting from the diffusive instability exhibits a tendency towards self-fragmentation resembling that known to occur in near-limit low-Lewis-number systems. (c) 1995 The American Physical Society

Near-limit flame structures at low Lewis number

The characteristics of premixed gas flames in mixtures with low Lewis numbers near flammability limits were studied experimentally using a low-gravity environment to reduce buoyant convection. The behavior of such flames was found to be dominated by diffusive-thermal instabilities. For sufficiently reactive mixtures, cellular structures resulting from these instabilities were observed and found to spawn new cells in regular patterns. For less reactive mixtures, cells formed shortly after ignition but did not spawn new cells; instead these cells evolved into a flame structure composed of stationary, apparently stable spherical flamelets. Experimental observations are found to be in qualitative agreement with elementary analytical models based on the interaction of heat release due to chemical reaction, differential diffusion of thermal energy and mass, flame front curvature, and volumetric heat losses due to gas and/or soot radiation.

Condensation Effects in a Fibrous Insulation Slab

This paper analyzes the moisture accumulation and the increase in the effective thermal conductivity of a fibrous insulation slab due to moisture migration. The problem is modeled as a transient, multiphase flow, with variable properties, in a porous slab with impermeable, adiabatic horizontal boundaries and permeable vertical boundaries, A detailed investigation of the interaction between condensation rate, temperature, liquid content, and vapor density fields is presented. The influences of different humidity levels at the boundaries of the insulation slab are investigated in detail and the importance of the Peclet and Lewis numbers on the condensation process is demonstrated. The analysis shows that condensation, and the resulting augmentation of heat transfer, is a serious problem at large Peclet numbers (Pe > 1). Furthermore, the increase in the Nusselt number for fibrous insulation due to condensation is found to be minimized by designing an insulation slab which has a low Lewis number.

Theoretical Analysis of Catalytic Combustion in a Monolith Reactor

A theoretical model of catalytic combustion is developed which allows calculation of temperature and reactant/product distribution in a tubular duct with catalytic walls. Under adiabatic conditions, as prevail in the central ducts of a catalytic monolith combustor, and in the absence of heat conduction along the reactor walls, the model provides an analytic solution. It exhibits the existence of multiple steady states and, for gas mixtures with low Lewis number, temperature excursions in excess of the adiabatic reaction temperature, Gas-phase reactions are shown to increase the fuel consumption in a given length of catalytic duct but leave unchanged the relations between the temperature and species distributions. The model is applied to a series of experimental results obtained with different fuels in tubular reactors. Satisfactory agreement is found between theoretical and experimental data when account is taken of the effects of heat loss from the reactor to the environment.

Effect of lewis number on the transient behavior of catalytic gas—solid systems

The influence of Lewis number, ρ Ĉ p D e /ϵλ e , on the transient behavior of exothermic irreversible first-order catalytic reaction inside a spherical porous pellet is analyzed taking into account external heat and mass transport as well as initial conditions corresponding to a pellet at uniform temperature and devoid of reactant. The destabilizing effect of low Lewis number and the existence of a limit cycle are confirmed and a qualitative interpretation is put forward. In regions of multiple stationary states, the Lewis number modifies substantially the domains of attraction of the stable solutions. Moreover, for certain values of this group and over the whole range of realistic initial conditions, the system remains entirely within the domain of attraction of just one of the steady states.