Fuel-dilution effect on differential molecular diffusion in laminar hydrogen diffusion flames

Laminar flame calculations have been made for a Tsuji counterflow geometry to investigate salient features caused by the differential diffusion effect in nitrogen-diluted hydrogen diffusion flames. A strong dependence of the differential diffusion parameter z_H on fuel dilution is found, where z_H is the difference of the mixture fractions based on H and O elements. The strain rate, however, appears to have a relatively minor impact on z_H. A simplified transport equation for the z_H parameter has been derived to explain qualitatively the behaviours exhibited in the numerical solutions. Two source terms of z_H are identified in the transport equation; one is due to mixing among species of different diffusion coefficients and the other one is associated with chemical reactions of H₂. More importantly, the second source term is found to be dominant in reacting flows, and it increases with inert gas dilution. This feature causes the differential diffusion parameter to increase with the amount of fuel dilution. The z_H values at the stoichiometric position are shown to correlate well with the ratio, Y_H2O|_max/(Z_H,1?Z_H,2), which may be useful for quantifying the influence of chemical reactions on the differential diffusion effect. For flames at low strain rates, the scalar dissipation rate exhibits a local minimum near the stoichiometric position. This peculiar feature is found to be caused by the differential diffusion effect modulated by chemical reactions. The local minimum in the scalar dissipation rate disappears at high strain rates when the convective transport overwhelms the molecular diffusion.     

Experimental and numerical investigation of microscale hydrogen diffusion flames

Characteristics of microscale hydrogen diffusion flames produced from sub-millimeter diameter (d = 0.2 and 0.48 mm) tubes are investigated using non-intrusive UV Raman scattering coupled with LIPF technique. Simultaneous, temporally and spatially resolved point measurements of temperature, major species concentrations (O₂, N₂, H₂O, and H₂), and absolute hydroxyl radical concentration (OH) are made in the microflames for the first time. The probe volume is 0.02 × 0.04 × 0.04 mm³. In addition, photographs and 2-D OH imaging techniques are employed to illustrate the flame shapes and reaction zones. Several important features are identified from the detailed measurements of microflames. Qualitative 2-D OH imaging indicates that a spherical flame is formed with a radius of about 1 mm as the tube diameter is reduced to 0.2 mm. Raman/LIPF measurements show that the coupled effect of ambient air leakage and pre-heating enhanced thermal diffusion of H₂ leads to lean-burn conditions for the flame. The calculated characteristic features and properties indicate that the buoyancy effect is minor while the flames are in the convection–diffusion controlled regime because of low Peclet number. Also, the effect of Peclet number on the flame shape is minor as the flame is in the convection–diffusion controlled regime. Comparisons between the predicted and measured data indicate that the trends of temperature, major species, and OH distributions are properly modeled. However, the code does not properly predict the air entrainment and pre-heating enhanced thermal-diffusive effects. Therefore, thermal diffusion for light species and different combustion models might need to be considered in the simulation of microflame structure.     

Uncertainty propagation of chemical kinetics parameters and binary diffusion coefficients in predicting extinction limits of hydrogen/oxygen/nitrogen non-premixed flames

A comprehensive investigation of the uncertainties associated with the experimental and numerical evaluation of the extinction strain rate in hydrogen/oxygen/nitrogen non-premixed flames is presented in this work. The reported new experimental uncertainties of the extinction strain rate include several sources of uncertainties that typically affect the characterisation of velocity and boundary conditions of counterflow flames via particle image velocimetry. The uncertainties associated with the numerical determination of the extinction strain rate not only depend upon the selected chemical kinetics parameters but also on the binary diffusion coefficients. In order to identify the major sources of uncertainties in the chemical and diffusion models, a Monte Carlo based high-dimensional model representation analysis of the extinction curve was performed. Independent and simultaneous perturbations of relevant chemical kinetics and diffusion parameters have shown that the uncertainties associated with the binary diffusion coefficients are about a factor of 10 smaller than the uncertainty due to chemical kinetics parameters. Since the experimentally well known binary diffusion coefficient for hydrogen and nitrogen, , accounts for most of the propagated uncertainty of the diffusion model, it is shown here that only a reduction of the uncertainty of chemical kinetics parameters will have a significant impact in improving the accuracy of the extinction strain rate predictions.     

Conditional moment closure modelling of turbulent jet diffusion flames of helium-diluted hydrogen

First-order conditional moment closure (CMC) modelling of NO in non-premixed flames has met with limited success due to the need to consider turbulence influences on the conditional production rate of chemical species. This paper presents results obtained using a second-order approach where such effects are incorporated through solution of a transport equation for the conditional variance. In contrast to earlier work, second-order chemistry is implemented using a more robust numerical technique, with predictions obtained using a Reynolds stress turbulence model. First-order CMC and k–? turbulence model predictions are presented for comparison purposes. For the hydrogen flames examined, results demonstrate small differences between first- and second-order calculations of major species and temperature, although second-order corrections reduce NO and OH levels. Additionally, variations occur between results for these species derived using the two turbulence models due to differences in conditional variance predictions. This and the numerical solution method employed are responsible for deviations with earlier results. It is concluded that while the higher-order CMC model does not significantly improve NO predictions, agreement with OH data is superior. Physical space predictions are sufficiently accurate for assessing flame characteristics, with the Reynolds stress model providing superior results.     

Validation of a mixture-averaged thermal diffusion model for premixed lean hydrogen flames

The mixture-averaged thermal diffusion model originally proposed by Chapman and Cowling is validated using multiple flame configurations. Simulations using detailed hydrogen chemistry are done on one-, two-, and three-dimensional flames. The analysis spans flat and stretched, steady and unsteady, and laminar and turbulent flames. Quantitative and qualitative results using the thermal diffusion model compare very well with the more complex multicomponent diffusion model. Comparisons are made using flame speeds, surface areas, species profiles, and chemical source terms. Once validated, this model is applied to three-dimensional laminar and turbulent flames. For these cases, thermal diffusion causes an increase in the propagation speed of the flames as well as increased product chemical source terms in regions of high positive curvature. The results illustrate the necessity for including thermal diffusion, and the accuracy and computational efficiency of the mixture-averaged thermal diffusion model.     

Effect of pressure on structure and extinction of near-limit hydrogen counterflow diffusion flames

Results of measurements of critical conditions for extinction and of temperature profiles in counterflow diffusion flames are reported. The fuel was a hydrogen–nitrogen mixture with 14 mole percent hydrogen, and the oxidizer was air. Pressures ranged from 0.1 MPa to 1.5 MPa; measurements were made in a facility especially constructed for carrying out counterflow combustion experiments at high pressures. With increasing pressure, the strain rate at extinction first increases and then decreases, in qualitative agreement with predictions, but there are observable quantitative differences. Temperature profiles, obtained employing an R-type thermocouple at a fixed strain rate of 100/s, agree well with predictions, within experimental uncertainty. The results may help to improve knowledge of underlying chemical-kinetic and transport parameters at elevated pressures.     

Framework for simulating stationary spherical flames

Understanding and quantifying the effects of flame stretch rate on the laminar flame speed and flame structure plays an important role from interpreting experimentally-measured laminar burning velocities to characterizing the impact of turbulence on premixed flames. Unfortunately, accounting for these effects often requires an unsteady reacting flow solver and may be computationally expensive. In this work, we propose a mathematical framework to perform simulations of stationary spherical flames. The objective is to maintain the flame at a constant radius (and hence a constant stretch rate) by performing a coordinate change. The governing equations in the new flame-attached frame of reference resemble the original equations for freely-propagating spherical flames. The only difference is the presence of additional source terms whose purpose is to drive the numerical solution to a steady state. These source terms involve one free parameter: the flame stretch rate, which may either be computed in real time or imposed by the user. This parameter controls ultimately the steady state flame radius and the steady state flame speed. That is why, at a given stretch rate, the results of the stationary spherical flame simulations match those of a freely-expanding spherical flame. As an illustration, the dependence of the laminar flame speed on the stretch rate is leveraged to extract Markstein lengths for hydrogen/air mixtures at different equivalence ratios, as well as for hydrocarbon/air mixtures (CH₄ and C₇H₁₆). Numerical predictions are in good agreement with experimental measurements (within experimental uncertainties). Finally, the proposed methodology is implemented in the chemical kinetic software FlameMaster. The use of a dedicated steady-state solver with a non-uniform optimized mesh leads to significant reductions in the computational cost, highlighting that the proposed methodology is ideally suited for other chemical kinetic software such as Chemkin/Premix and Cantera.     

The rate of expansion of spherical flames

In this paper we investigate the acceleration of the expansion of premixed spherical flames and evolution of the cellular patterns on their surfaces. An asymptotic model is used for the simulations and a spectral numerical algorithm is employed to study flames over large time intervals. Numerous numerical experiments indicate that for large enough time the acceleration of a two-dimensional expanding flame slows down but the expansion rate is still able to reach values significantly exceeding the burning rate of an exactly circular flame. The importance of the effect of forcing was also confirmed and the validity of simulations of sectors of circular flame fronts was studied in order to justify prospective use of the Fourier spectral model for three-dimensional spherical flames.     

Cellular instabilities of expanding hydrogen/propane spherical flames at elevated pressures: theory and experiment

An experimental and theoretical investigation of the onset of cellular instabilities on spherically expanding flames in mixtures of hydrogen and propane in air at elevated pressures was conducted. Critical conditions for the onset of instability were measured and mapped out over a range of pressures and mixture compositions. An asymptotic theory of hydrodynamic and diffusional-thermal cell development on flames in mixtures comprised of two scarce fuels burning in air was also formulated. Predicted values of Peclet number, defined as the flame radius at the onset of instability normalized by the flame thickness, were shown to compare favorably with the experimentally measured values.     

On the existence of steady-state gaseous microgravity spherical diffusion flames in the presence of radiation heat loss

Whether steady-state gaseous microgravity spherical diffusion exist in the presence of radiation heat loss is an important fundamental question and has important implications for spacecraft fire safety. In this work, experiments aboard the International Space Station and a transient numerical model are used to investigate the existence of steady-state microgravity spherical diffusion flames. Gaseous spherical diffusion flames stabilized on a porous spherical burner are employed in normal (i.e., fuel flowing into an ambient oxidizer) and inverse (i.e., oxidizer flowing into an ambient fuel) flame configurations. The fuel is ethylene and the oxidizer oxygen, both diluted with nitrogen. The flow rate of the reactant gas from the burner is held constant. It is found that steady-state gaseous microgravity spherical diffusion flames can exist in the presence of radiation heat loss, provided that the steady-state flame size is less than the flame size for radiative extinction, and the flame develops fast enough that radiation heat loss does not drop the flame temperature below the critical temperature for radiative extinction (1130 K). A simple model is provided that allows for the identification of initial conditions that can lead to steady-state spherical diffusion flames. In the spherical, infinite domain configuration, the characteristic time for the diffusion-controlled system to effectively reach steady-state is found to be on the order of 100,000 s. Despite a narrow range of attainable conditions, flames that exhibit steady-state behavior are observed aboard the ISS for up to 870 s, even with the constraint of a finite boundary. Steady-state flames are simulated using the numerical model for over 100,000 s.     

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.     

Spherical gas-fueled cool diffusion flames

An improved understanding of cool diffusion flames could lead to improved engines. These flames are investigated here using a spherical porous burner with gaseous fuels in the microgravity environment of the International Space Station. Normal and inverse flames burning ethane, propane, and n-butane were explored with various fuel and oxygen concentrations, pressures, and flow rates. The diagnostics included an intensified video camera, radiometers, and thermocouples. Spherical cool diffusion flames burning gases were observed for the first time. However, these cool flames were not readily produced and were only obtained for normal n-butane flames at 2 bar with an ambient oxygen mole fraction of 0.39. The hot flames that spawned the cool flames were 2.6 times as large. An analytical model is presented that combines previous models for steady droplet burning and the partial-burning regime for cool diffusion flames. The results identify the importance of burner temperature on the behavior of these cool flames. They also indicate that the observed cool flames reside in rich regions near a mixture fraction of 0.53.     

The fast-time instability of diffusion flames

A diffusion flame burns with varying intensity if the pressure is varied, and the nonlinear steady-state response is typically S-shaped; that is, multiple solutions exist for some range of pressure. The physically relevant branch can only be determined by unsteady analyses, and in this paper we discuss the stability of a large class of diffusion flames when the activation energy characterizing the reaction rate is large. Specifically, we examine the evolution from the stationary solution on a time scale so short that changes are confined to the thin flame sheet where all the reaction occurs. In this region time derivatives are added to the steady state equations, which otherwise describe a balance between diffusion and chemical reaction. The stability problem is then reduced to the determination of the spectrum of Schrödinger's equation, defined on the infinite interval, with a potential that is not of one sign on this interval. In this way certain conclusions about extinction are drawn and certain past misconceptions are clarified.     

Characteristics of microjet methane diffusion flames

Characteristics of microjet methane diffusion flames stabilized on top of the vertically oriented, stainless-steel tubes with an inner diameter ranging from 186 to 778 μ m are investigated experimentally, theoretically and numerically. Of particular interest are the flame shape, flame length and quenching limit, as they may be related to the minimum size and power of the devices in which such flames would be used for future micro-power generation. Experimental measurements of the flame shape, flame length and quenching velocity are compared with theoretical predictions as well as detailed numerical simulations. Comparisons of the theoretical predictions with measured results show that only Roper's model can satisfactorily predict the flame height and quenching velocity of microjet methane flames. Detailed numerical simulations, using skeletal chemical kinetic mechanism, of the flames stabilized at the tip of d = 186, 324 and 529 μ m tubes are performed to investigate the flame structures and the effects of burner materials on the standoff distance near extinction limit. The computed flame shape and flame length for the d = 186 μm flame are in excellent agreement with experimental results. Numerical predictions of the flame structures strongly suggest that the flame burns in a diffusion mode near the extinction limit. The calculated OH mass fraction isopleths indicate that different tube materials have a minor effect on the standoff distance, but influence the quenching gap between the flame and the tube.     

Blowout limits of inclined nonpremixed turbulent jet flames

The blowout behavior of inclined nonpremixed turbulent jet flames is investigated by varying the jet inclined angle in the range of -90° to 90° The critical jet velocity at blow-out limit is quantified experimentally for various nozzle diameters, different fuels and inclined angles. Numerical simulations are performed to emphasize the flow field difference for the positive and negative inclined angles. Physical modeling is conducted to incorporate the effect of the inclined angle on blow-out behavior. Major findings include: (1) The negatively inclined jet flames show more intense yellow luminosity with larger sooting zones than the positively inclined jet flames; (2) The blowout limit decreases appreciably with the jet inclined angle for the negatively inclined flames, while for the positively inclined jet flames, this decrease is relatively small; (3) Physical analysis of the flow development of inclined jets is conducted, indicating the centerline velocity along the jet trajectory decreases faster for the flame with smaller inclined angle. And the decrease rate is relatively larger for the negatively inclined jet flames; (4) Based on the analysis of the flow development as well as the characteristic velocity with the inclined angle variation, a model based on the Damköhler number (Da) accounting for the effect of jet inclined angle is developed to characterize the blowout limits of inclined jet flames. The proposed model successfully correlates the experimental data. The present findings provide new data and a basic scaling law for the blowout limit of nonpremixed inclined turbulent jet flames, revealing the effect of the relative angle between the jet momentum and buoyancy.     

Numerical studies of flames in wide tubes: stability limits of curved stationary flames

Flame dynamics in wide tubes with ideally adiabatical and slip walls is studied by means of direct numerical simulations of the complete set of hydrodynamical equations including thermal conduction, fuel diffusion, viscosity, and chemical kinetics. Stability limits of curved stationary flames in wide tubes and the hydrodynamic instability of these flames (the secondary Darrieus-Landau instability) are investigated. The stability limits found in the present numerical simulations are in a very good agreement with the previous theoretical predictions. It is obtained that close to the stability limits the secondary Darrieus-Landau instability results in an extra cusp at the flame front. It is shown that the curved flames subject to the secondary Darrieus-Landau instability propagate with velocity considerably larger than the velocity of the stationary flames.     

Homoclinic bifurcations in radiating diffusion flames

We analyse the dynamics of a model describing a planar diffusion flame with radiative heat losses incorporating a single step kinetic using timestepping techniques for Lewis number equal to one. We construct the full bifurcation diagram with respect to the Damköhler number including the branches of oscillating solutions. Based on this analysis we found, for the first time, homoclinic bifurcations that mark the abrupt disappearance of the nonlinear oscillations near extinction as reported in experiments.     

Period doubling cascade in diffusion flames

Here it is shown that chaotic oscillations can appear after a series of period doublings in radiating diffusion flames when the activation temperature is high enough. It is also shown that period doubling cascades appear typically in very small regions and that they may not be observable if one starts with small perturbations of a steady flame.