A numerical study of reignition induced by a diffusion flame

We present a numerical study of the reignition of a cold reactant mixture by the interaction with a nearby diffusion flame. This reignition mechanism may be an important process in turbulent non-premixed flames at high rates of strain where quenched sections of the stoichiometric surface are folded by the turbulent flow and come in close proximity with other burning flame sections. We consider an idealized one-dimensional setup containing the fundamental ingredients that are expected to contribute to this reignition mode. One- and two-step irreversible chemical mechanisms with heat release levels typical of practical hydrocarbon fuels are considered. It is observed that a slow moving reignition kernel originates on the high-temperature region of the burning flame in the one-step chemistry case owing to small leakage of oxidizer from the cold-mixture side. This kernel gradually moves, increasing the local temperature above that provided by diffusion and eventually leads to thermal runaway with the formation of a deflagration wave. The reignition time depends on the chemistry details, the Damköhler number, but in any case it cannot exceed the mixing time. This implies that the flame-induced reignition time is essentially bounded from above by mixing. Unless one of the free streams is hotter, in which case auto-ignition (as opposed to reignition) may proceed first, the reignition time is chemistry dependent. In the case of two-step chemistry, the reignition pathway is different initially owing to leakage of the radical species, but it approaches that of the one-step chemistry case shortly thereafter. It is observed that the only difference between the two cases is in the initial phase of the evolution of the reignition kernel. This phase appears to be very sensitive to the chemistry details, a general aspect of ignition. A parametric study is carried out to elucidate the effect of each non-dimensional quantity on the reignition time for the one-step chemistry case.     

Diffusive-thermal instabilities of diffusion flames: onset of cells and oscillations

A comprehensive stability analysis of planar diffusion flames is presented within the context of a constant-density model. The analysis provides a complete characterization of the possible patterns that are likely to be observed as a result of differential and preferential diffusion when a planar flame becomes unstable. A whole range of physical parameters is considered, including the Lewis numbers associated with the fuel and the oxidizer, the initial mixture fraction, and the flow conditions. The two main forms of instability are cellular flames, obtained primarily in fuel-lean systems when the Lewis numbers are generally less than one, and planar pulsations, obtained in fuel-rich systems when the Lewis numbers are generally larger than one. The cellular instability is predominantly characterized by stationary cells of characteristic dimension comparable to the diffusion length, but smaller cells that scale on the reaction zone thickness are also possible near extinction conditions. The pulsating instability is characterized by planar oscillations normal to the flame sheet with a well-defined frequency comparable to the reciprocal of the diffusion time; high-frequency modes are also possible just prior to extinction. The analysis also alludes to other possible patterns, such as oscillating cellular structures, which result from competing modes of instability of comparable and/or disparate scales. The expected pattern depends of course on the underlying physical parameters. Consequently, stability boundaries have been identified for the onset of one or another form of the instability. The conditions for the onset of cellular and pulsating flames, as well as the predicted cell size and the frequency of oscillations, compare well with the experimental record.     

The effect of preferential diffusion on soot formation in a laminar ethylene/air diffusion flame

The influence of preferential diffusion on soot formation in a laminar ethylene/air diffusion flame was investigated by numerical simulation using three different transport property calculation methods. One simulation included preferential diffusion and the other two neglected preferential diffusion. The results show that the neglect of preferential diffusion or the use of unity Lewis number for all species results in a significant underprediction of soot volume fraction. The peak soot volume fraction is reduced from 8.0 to 2.0 ppm for the studied flame when preferential diffusion is neglected in the simulation. Detailed examination of numerical results reveals that the underprediction of soot volume fraction in the simulation neglecting preferential diffusion is due to the slower diffusion of some species from main reaction zone to PAH and soot formation layer. The slower diffusion of these species causes lower PAH formation rate and thus results in lower soot inception rate and smaller particle surface area. The smaller surface area further leads to smaller surface growth rate. In addition, the neglect of preferential diffusion also leads to higher OH concentration in the flame, which causes the higher specific soot oxidation rate. The lower inception rate, smaller surface growth rate and higher specific oxidation rate results in the lower soot volume fraction when preferential diffusion is neglected. The finding of the paper implies the importance of preferential diffusion for the modeling of not only laminar but maybe also some turbulent flames.     

Analytical predictions of shapes of laminar diffusion flames in microgravity and earth gravity

Flame shape is an important observed characteristic of flames that can be used to scale flame properties such as heat release rates and radiation. Flame shape is affected by fuel type, oxygen levels in the oxidiser, inverse burning and gravity. The objective of this study is to understand the effect of high oxygen concentrations, inverse burning, and gravity on the predictions of flame shapes. Flame shapes are obtained from recent analytical models and compared with experimental data for a number of inverse and normal ethane flame configurations with varying oxygen concentrations in the oxidiser and under earth gravity and microgravity conditions. The Roper flame shape model was extended to predict the complete flame shapes of laminar gas jet normal and inverse diffusion flames on round burners. The Spalding model was extended to inverse diffusion flames. The results show that the extended Roper model results in reasonable predictions for all microgravity and earth gravity flames except for enhanced oxygen normal diffusion flames under earth gravity conditions. The results also show trends towards cooler flames in microgravity that are in line with past experimental observations. Some key characteristics of the predicted flame shapes and parameters needed to describe the flame shape using the extended Roper model are discussed.     

Computational and experimental study of JP-8, a surrogate, and its components in counterflow diffusion flames

Non-sooting counterflow diffusion flames have been studied both computationally and experimentally, using either JP-8, or a six-component JP-8 surrogate mixture, or its individual components. The computational study employs a counterflow diffusion flame model, the solution of which is coupled with arc length continuation to examine a wide variety of inlet conditions and to calculate extinction limits. The surrogate model includes a semi-detailed kinetic mechanism composed of 221 gaseous species participating in 5032 reactions. Experimentally, counterflow diffusion flames are established, in which multicomponent fuel vaporization is achieved through the use of an ultrasonic nebulizer that introduces small fuel droplets into a heated nitrogen stream, fostering complete vaporization without fractional distillation. Temperature profiles and extinction limits are measured in all flames and compared with predictions using the semi-detailed mechanism. These measurements show good agreement with predictions in single-component n-dodecane, methylcyclohexane, and iso-octane flames. Good agreement also exists between predicted and measured variables in flames of the surrogate, and the agreement is even better between the experimental JP-8 flames and the surrogate predictions.     

Use of laser-induced spark for studying ignition stability and unburned hydrogen escaping from laminar diluted hydrogen diffusion jet flames

Ignition and unburned hydrogen escaping from hydrogen jet diffusion flames diluted with nitrogen up to 70% were experimentally studied. The successful ignition locations were about 2/3 of the flame length above the jet exit for undiluted flames and moved much closer to the exit for diluted flames. For higher levels of dilution or higher flow rates, there existed a region within which a diluted hydrogen diffusion flame can be ignited and burns with a stable liftoff height. This is contrary to previous findings that pure and diluted hydrogen jet diffusion cannot achieve a stable lifted flame configuration. With liftoff, the flame is noisy and short with significant amount of unburned hydrogen escaping into the product gases. If ignition is initiated below this region, the flame propagates upstream quickly and attaches to the burner rim. Results from measurements of unburned hydrogen in the combustion products showed that the amount of unburned hydrogen increased as the nitrogen dilution level was increased. Thus, hydrogen diffusion flame diluted with nitrogen cannot burn completely.     

Non-diffusive ignition of a gaseous reactive mixture following time-resolved,spatially distributed energy deposition

Systematic asymptotic methods are applied to the compressible conservation and state equations for a reactive gas, including transport terms, to develop a rational thermomechanical formulation for the ignition of a chemical reaction following time-resolved, spatially distributed thermal energy addition from an external source into a finite volume of gas. A multi-parameter asymptotic analysis is developed for a wide range of energy deposition levels relative to the initial internal energy in the volume when the heating timescale is short compared to the characteristic acoustic timescale of the volume. Below a quantitatively defined threshold for energy addition, a nearly constant volume heating process occurs, with a small but finite internal gas expansion Mach number. Very little added thermal energy is converted to kinetic energy. The gas expelled from the boundary of the hot, high-pressure spot is the source of mechanical disturbances (acoustic and shock waves) that propagate away into the neighbouring unheated gas. When the energy addition reaches the threshold value, the heating process is fully compressible with a substantial internal gas expansion Mach number, the source of blast waves propagating into the unheated environmental gas. This case corresponds to an extremely large non-dimensional hot-spot temperature and pressure. If the former is sufficiently large, a high activation energy chemical reaction is initiated on the short heating timescale. This phenomenon is in contrast to that for more modest levels of energy addition, where a thermal explosion occurs only after the familiar extended ignition delay period for a classical high activation reaction. Transport effects, modulated by an asymptotically small Knudsen number, are shown to be negligible unless a local gradient in temperature, concentration or velocity is exceptionally large.     

Analysis of a spray diffusion flame and its extinction in a shear layer

A new semi-analytical solution for a laminar spray diffusion flame in the shear layer between fuel and oxidant streams is developed. The Stokes number is identified as a small spray droplet-related parameter to be used in a perturbation analysis of the liquid phase governing equations. Appropriate specification of an additional parameter ensures that similarity is achieved so that the concentration field of the liquid in the spray can be readily found. The coupled gas-phase equations are treated using the usual inverse of the large Zeldovitch number for the asymptotic analysis. Numerical results demonstrate how the distribution of the liquid phase in the developing shear layer between two unidirectional gas streams flowing over one another with (the possibility of) dissimilar velocities in their respective free-streams influences the flame shape, location, fuel vapour and temperature fields. An extinction analysis enables a parametric mapping of conditions for extinguishment of the spray diffusion flames to be drawn.     

On the global structure and asymptotic stability of low-stretch diffusion flame: Forced convection

The present work analyzes cylindrical diffusion flames (Tsuji burner) under low stretch condition, considering fuel injection also from the backward region of the burner. To highlight the fundamental aspects of this flame, some assumptions are imposed, like constant thermodynamic and transport coefficients, unitary Lewis number and no radiative heat loss. It is also considered potential flow model and incompressible Navier–Stokes model. Despite the simplicity of the former model, results from both models show good agreement. Also, an asymptotic analysis describing the problem far from the burner is able to capture the most important mechanisms controlling the flame, then the flame shape is determined and the dependence of the characteristic length scales on Peclet number (based on the burner properties), free stream velocity and stoichiometry is revealed. The results show that the flame width is proportional to the mass stoichiometric coefficient and reciprocal to the Peclet number the 1/4 power and free stream velocity the 3/4 power, and that the flame height is proportional to the square of the mass stoichiometric coefficient and to the square root of the ratio of Peclet number to free stream velocity. In addition, an asymptotic stability analysis reveals low-stretch flame extinction to be caused by reduction in fuel and oxidizer concentrations, which provides the range of the stoichiometric coefficient for stable regime, and at the same time the range of heat released.     

Stability and diffusion properties of self-interstitial atoms in tungsten:a first-principles investigation

Employing a first-principles method based on the density function theory,we systematically investigate the structures,stability and diffusion of self-interstitial atoms(SIAs) in tungsten(W).The <111> dumbbell is shown to be the most stable SIA defect configuration with the formation energy of ~9.43 eV.The on-site rotation modes can be described by a quite soft floating mechanism and a down-hill "drift" diffusion process from <110> dumbbell to <111> dumbbell and from <001> dumbbell to <110> dumbbell,respectively.Among different SIA configurations jumping to near neighboring site,the <111> dumbbell is more preferable to migrate directly to first-nearest-neighboring site with a much lower energy barrier of 0.004 eV.These results provide a useful reference for W as a candidate plasma facing material in fusion Tokamak.     

Measurements of Silica Aggregate Particle Growth Using Light Scattering and Thermophoretic Sampling in a Coflow Diffusion Flame

The evolution of silica aggregate particles in a coflow diffusion flame has been studied experimentally using light scattering and thermophoretic sampling techniques. An attempt has been made to calculate the aggregate number density and volume fraction using the measurements of scattering cross section from 90° light scattering with combination of measuring the particle size and morphology from the localized sampling and a TEM image analysis. Aggregate or particle number densities and volume fractions were calculated using Rayleigh–Debye–Gans and Mie theory for fractal aggregates and spherical particles, respectively. Using this technique, the effects of H₂ flow rates on the evolution of silica aggregate particles have been studied in a coflow diffusion flame burner. As the flow rate of H₂ increases, the primary particle diameters of silica aggregates have been first decreased, but, further increase of H₂ flow rate causes the diameter of primary particles to increase and for sufficiently larger flow rates, the fractal aggregates finally become spherical particles. For the cases of high flame temperatures, the particle sizes become larger and the number densities decrease by coagulation as the particles move up within the flame. For cases of low flame temperatures, the primary particle diameters of aggregates vary a little following the centerline of burner and for the case of the lowest flame temperature in the present experiments, the sizes of primary particles even decrease as particles move upward.     

Detailed investigation of soot formation from jet fuel in a diffusion flame with comprehensive and hybrid chemical mechanisms

A numerical and experimental study is performed to investigate soot formation from jet fuel in a laminar coflow diffusion flame. The combustion chemistry of the fuel is simulated using (1) the MURI jet fuel surrogate (Dooley et al. 2012) with a modestly reduced Ranzi mechanism (Ranzi et al. 2012), and (2) the recently proposed HyChem model (Xu et al. 2018) combined with the KAUST PAH mechanism 2 (Wang et al. 2013). The two reaction mechanisms are coupled with a sectional soot model to simulate a coflow diffusion flame of methane doped with the MURI jet fuel surrogate. The combined laser extinction and two-angle elastic light scattering method is used to perform non-intrusive in situ measurements of soot volume fraction, primary particle diameter and number density. The good agreement including soot particle size and number density between the experimental data and the simulation results computed with the reduced Ranzi mechanism demonstrate the robustness of the soot model to changes in fuel composition, as the model parameters are unchanged with a previous numerical study of soot formation of n-propylbenzene/n-dodecane mixtures (Zhang and Thomson, 2018). The computation with the combined HyChem/KAUST mechanism predicts similar results as the computation with the detailed chemistry of the reduced Ranzi mechanism for fuel breakdown, thus the basic premise of the HyChem model that the fuel decomposition process can be greatly simplified with the lumped reaction steps is supported. The results also show that by adding a PAH growth scheme to the HyChem model, the approach can be used to predict soot formation from jet fuel combustion in a laminar coflow diffusion flame. Finally, the dependency of the soot prediction on PAH chemistry is discussed and it is suggested that more experimental data is needed to validate the PAH mechanism and improve the predictive accuracy of the model.     

Modelling of the effect of DC and AC electric fields on the stability of a lifted diffusion methane/air flame

The application of an external electric field is known to improve flame stability significantly. Until now, few studies have proposed modelling approaches for combustion in the presence of an externally applied voltage. In these numerical studies, the negative ions are overlooked, and only the displacement of positive ions and electrons under the effect of a direct electric field was examined. In the present paper, a simplified mathematical model including negative ions is proposed based on a kinetic mechanism featuring 39 ionic reactions and 5 charged species. This mechanism is first evaluated by comparison of a monodimensional premixed flame with the available experimental data. Then it is used to analyse the stabilisation mechanism of a diffusion lifted flame in the presence of direct or alternating electric fields. It was concluded that the role of negative ions is crucial, and they are not to be neglected. Moreover, the simulations have shown that the magnitude of the flame stabilisation improvement depends, mainly, on the intensity and polarity of the applied voltage. If the applied voltage is alternating, its frequency is also found to influence the extent of the flame stabilisation improvement.     

Effects of controlling Cu spacer inter-diffusion by diffusion barriers on the magnetic and electrical stability of GMR spin-valve devices

An ultra-thin Co or CoFe diffusion barrier inserted at the NiFe/Cu interfaces was revealed to effectively control the electrical and magnetic stability of NiFe/Cu/NiFe-based giant magnetoresistance (GMR) spin-valve spintronics devices (SVSDs) operating at high current density. It was found that the activation energy, E_a, related to the electromigration (EM)-induced inter-diffusion process for the patterned NiFe(3)/Cu(2)/NiFe(3 nm) magnetic multi-layered devices (MMLD) was remarkably increased from 0.52±0.2 eV to 1.17±0.16 eV after the insertion of an ultra-thin Co diffusion barrier at the NiFe/Cu interfaces. The dramatically reduced “current shunting paths” from the Cu spacer to the NiFe thin films and the development of “self-healing process” resulted from the effectively restrained Cu inter-diffusion (intermixing with Ni atoms) due to the diffusion barriers were found to be primarily responsible for the improvement of electrical and magnetic stability. The further investigation on the effects of controlling Cu spacer inter-diffusion by diffusion barriers on the EM and thermomigration (TM)-induced magnetic degradation was carried out for the NiFe/(Co or Co₉₀Fe₁₀)/Cu/(Co or Co₉₀Fe₁₀)/NiFe/FeMn top exchange-biased GMR (EBGMR) SVSDs electrically stressed under the applied DC current density of J=2.5×10⁷ A/cm² (I=16.5∼17.25 mA). It was clearly confirmed that the Co and the CoFe diffusion barriers effectively control the Cu spacer inter-diffusion resulting in a smaller reduction in both GMR ratio and exchange bias field of the EBGMR SVSDs. Furthermore, it was obviously observed that the effects of CoFe diffusion barrier on controlling the Cu spacer inter-diffusion are more significant than that of Co. The effectively reduced Mn atomic inter-diffusion at the NiFe/FeMn interface and the well-maintained interfacial spin-dependent scattering resulted from the control of EM and TM-induced Cu spacer inter-diffusion were the main physical reasons for the significant improvement of magnetic and electrical degradation of top EBGMR SVSDs.     

Energy,force and field strength in a system of two charged conducting balls

A calculation has been performed for the interaction force and the field strength in a system consisting of two charged conducting balls in three cases: 1) the balls are maintained at the preset potentials; 2) the balls are insulated and have fixed charges; 3) one of the balls has the preset potential, and the second one has the preset charge. Experimental measurements of forces in the first and third cases were performed and fair agreement with calculations was confirmed. A calculation method has been suggested, and the electric field strength on the nearest poles of the balls has been calculated for the three mentioned cases. A good agreement with the other authors' calculation results has been demonstrated.     

Determination of Soot Particle Size in a Premixed Flame: a Static and Dynamic Light Scattering Study

In this contribution we report upon our static and dynamic light scattering experiments to characterize soot particles in flames. We studied sooting laminar premixed flame with acetylene as fuel mixed with air as oxidizer. The air equivalence ratio of the combustion was larger than one. We used a Kaskan type burner with circular geometry and a stabilizing flow of nitrogen around the flame. We focused on the determination of the size of the soot particles in the center of the flame as a function of height above burner. In addition we investigated the influence of the mixing ratio of the gases on the size of the particles. Our results show that static light scattering is better suited than dynamic light scattering for a fast and reliable characterization of soot particles in flames. The latter needs detailed a priori information about the flame to allow the unique determination of sizes from the diffusion measurements. The soot particles grow monotonously with height above burner and with decreasing air equivalence ratio. The aggregates have a fractal dimension lower than two.     

Particle Sampling and Real Time Size Distribution Measurement in H2/O2/TEOS Diffusion Flame

Growth characteristics of silica particles have been studied experimentally using in situ particle sampling technique from H₂/O₂/Tetraethylorthosilicate (TEOS) diffusion flame with carefully devised sampling probe. The particle morphology and the size comparisons are made between the particles sampled by the local thermophoretic method from the inside of the flame and by the electrostatic collector sampling method after the dilution sampling probe. The Transmission Electron Microscope (TEM) image processed data of these two sampling techniques are compared with Scanning Mobility Particle Sizer (SMPS) measurement. TEM image analysis of two sampling methods showed a good agreement with SMPS measurement. The effects of flame conditions and TEOS flow rates on silica particle size distributions are also investigated using the new particle dilution sampling probe. It is found that the particle size distribution characteristics and morphology are mostly governed by the coagulation process and sintering process in the flame. As the flame temperature increases, the effect of coalescence or sintering becomes an important particle growth mechanism which reduces the coagulation process. However, if the flame temperature is not high enough to sinter the aggregated particles then the coagulation process is a dominant particle growth mechanism. In a certain flame condition a secondary particle formation is observed which results in a bimodal particle size distribution.     

Uniqueness,reciprocity theorem,and plane waves in thermoelastic diffusion with a fractional order derivative

In this work, a theory of thermoelasticity with diffusion is taken into consideration by using the methodology of fractional calculus. The governing equations for particle motion in a homogeneous anisotropic fractional order generalized thermoelastic diffusive medium are presented. Uniqueness and reciprocity theorems are proved. The plane wave propagation in the homogeneous transversely isotropic thermoelastic diffusive medium with fractional order derivative is studied. For the two-dimensional problem, there exist a quasi-longitudinal wave, a quasi-transverse wave, a quasi-mass diffusion wave, and a quasi-thermal wave. From the obtained results, the different characteristics of waves, like phase velocity, attenuation coefficient, specific loss, and penetration depth, are computed numerically and presented graphically. Some special cases are also discussed.