Axis switching in turbulent buoyant diffusion flames

Dynamics of buoyant diffusion flames from rectangular, square, and round fuel sources were investigated using direct numerical simulation (DNS). Fully three-dimensional simulations were performed employing high-order numerical methods and boundary conditions to solve governing equations for variable-density flow and finite-rate Arrhenius chemistry. Significant differences among the different cases were revealed in the vortex dynamics, entrainment rate, small-scale mixing, and consequently flame structures. Mixing and entrainment enhancement in non-circular flames in comparison with circular ones was explained using the Biot–Savart instability theory, which relates vortex dynamics to the local azimuthal curvature. An extension of the theory elucidated why rectangular flames entrain more efficiently and spread wider than square ones, although both configurations have corners. It also provided an explanation for the aspect ratio effects in the near field. In the far field, nonlinear effects were dominant and the general transport equations for vorticity were analyzed in detail. The corner effects and aspect ratio effects were shown to be augmented by the intricate interactions among vortex dynamics, combustion, and buoyancy through the various terms in the equations. The presence of corners in non-circular flames led to concentrated regions of fine-scale mixing and intense reactions centered around the corners. Moreover, the rectangular flames exhibited a different dynamic behavior from even the square one, by creating discrepancies in entrainment, mixing, and combustion between the minor and major axis directions. Increasing the aspect ratio exacerbated such directional discrepancies, and ultimately led to axis switching. It was the first time that axis switching was observed by DNS in a rectangular flame of aspect ratio 3, which raised further questions in combustion prediction and control. Finally, a unified explanation for corner and aspect ratio effects was given on the basis of the Biot–Savart instability theory and the vorticity transport equations.     

The importance of thermal radiation transfer in laminar diffusion flames at normal and microgravity

The importance of radiation heat loss in laminar and turbulent diffusion flames at normal gravity has been relatively well recognized in recent years. There is currently lack of quantitative understanding on the importance of radiation heat loss in relatively small scale laminar diffusion flames at microgravity. The effects of radiation heat transfer and radiation absorption on the structure and soot formation characteristics of a coflow laminar ethylene/air diffusion flame at normal- and microgravity were numerically investigated. Numerical calculations were conducted using GRI-Mech 3.0 combustion chemistry without the NO_x mechanism and complex thermal and transport properties, an acetylene based soot formation model, and a statistical narrow-band correlated-k non-grey gas radiation model. Radiation heat transfer and radiation absorption in the microgravity flame were found to be much more important than their counterparts at normal gravity. It is important to calculate thermal radiation transfer accurately in diffusion flame modelling under microgravity conditions.     

Simulations of sooting turbulent jet flames using a hybrid flamelet/stochastic Eulerian field method

The stochastic Eulerian field method is applied to simulate 12 turbulent C₁?C₃ hydrocarbon jet diffusion flames covering a wide range of Reynolds numbers and fuel sooting propensities. The joint scalar probability density function (PDF) is a function of the mixture fraction, enthalpy defect, scalar dissipation rate and representative soot properties. Soot production is modelled by a semi-empirical acetylene/benzene-based soot model. Spectral gas and soot radiation is modelled using a wide-band correlated-k model. Emission turbulent radiation interactions (TRIs) are taken into account by means of the PDF method, whereas absorption TRIs are modelled using the optically thin fluctuation approximation. Model predictions are found to be in reasonable agreement with experimental data in terms of flame structure, soot quantities and radiative loss. Mean soot volume fractions are predicted within a factor of two of the experiments whereas radiant fractions and peaks of wall radiative fluxes are within 20%. The study also aims to assess approximate radiative models, namely the optically thin approximation (OTA) and grey medium approximation. These approximations affect significantly the radiative loss and should be avoided if accurate predictions of the radiative flux are desired. At atmospheric pressure, the relative errors that they produced on the peaks of temperature and soot volume fraction are within both experimental and model uncertainties. However, these discrepancies are found to increase with pressure, suggesting that spectral models describing properly the self-absorption should be considered at over-atmospheric pressure.     

Modelling of turbulent scalar flux in turbulent premixed flames based on DNS databases

A transport equation for scalar flux in turbulent premixed flames was modelled on the basis of DNS databases. Fully developed turbulent premixed flames were obtained for three different density ratios of flames with a single-step irreversible reaction, while the turbulent intensity was comparable to the laminar burning velocity. These DNS databases showed that the countergradient diffusion was dominant in the flame region. Analyses of the Favre-averaged transport equation for turbulent scalar flux proved that the pressure related terms and the velocity–reaction rate correlation term played important roles on the countergradient diffusion, while the mean velocity gradient term, the mean progress variable gradient term and dissipation terms suppressed it. Based on these analyses, modelling of the combustion-related terms was discussed. The mean pressure gradient term and the fluctuating pressure term were modelled by scaling, and these models were in good agreement with DNS databases. The dissipation terms and the velocity–reaction rate correlation term were also modelled, and these models mimicked DNS well.     

Polydisperse spray diffusion flames in oscillating flow

The phenomenon of droplet clustering or grouping found when a spray of droplets is moving in an oscillating host flow field is investigated for the case of a polydisperse spray that fuels a laminar co-flow diffusion flame. A mathematical solution is developed for the liquid phase based on use of small Stokes numbers for size sections into which the polydisperse spray size distribution is divided. Droplet clustering in the oscillatory flow field is accounted for by constructing a special model for the sectional vaporization Damkohler numbers in accordance with droplet size. Combining this with a formal solution for a gas phase Schvab-Zel'dovich variable yields the means whereby flame dynamics can be described. Results calculated from this solution demonstrate that preferential droplet size behaviour (with smaller droplets tending to cluster to a greater extent and reduce the vaporization Damkohler number more than larger ones) can have a major impact on the flame dynamics through local droplet enrichment with attendant consequences on the production of fuel vapour. The dynamics of the sort of flame (over- or under-ventilated) and the occurrence of flame pinching leading to multiple flame sheets are altered under these circumstances. However, potential control of the actual initial spray polydispersity may reduce the intensity of such effects.     

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.     

Counterflow diffusion flames: effects of thermal expansion and non-unity Lewis numbers

In this work we re-examine the counterflow diffusion flame problem focusing in particular on the flame–flow interactions due to thermal expansion and its influence on various flame properties such as flame location, flame temperature, reactant leakage and extinction conditions. The analysis follows two different procedures: an asymptotic approximation for large activation energy chemical reactions, and a direct numerical approach. The asymptotic treatment follows the general theory of Cheatham and Matalon, which consists of a free-boundary problem with jump conditions across the surface representing the reaction sheet, and is well suited for variable-density flows and for mixtures with non-unity and distinct Lewis numbers for the fuel and oxidiser. Due to density variations, the species and energy transport equations are coupled to the Navier–Stokes equations and the problem does not possess an analytical solution. We thus propose and implement a methodology for solving the free-boundary problem numerically. Results based on the asymptotic approximation are then verified against those obtained from the ‘exact’ numerical integration of the governing equations, comparing predictions of the various flame properties.     

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.     

Compressible turbulent flame speeds of highly turbulent standing flames

In this paper we present the first measurement of turbulent burning velocities of a highly turbulent compressible standing flame induced by shock-driven turbulence in a Turbulent Shock Tube. High-speed schlieren, chemiluminescence, PIV, and dynamic pressure measurements are made to quantify flame–turbulence interaction for high levels of turbulence at elevated temperatures and pressure. Distributions of turbulent velocities, vorticity and turbulent strain are provided for regions ahead and behind the standing flame. The turbulent flame speed is directly measured for the high-Mach standing turbulent flame. From measurements of the flame turbulent speed and turbulent Mach number, transition into a non-linear compressibility regime at turbulent Mach numbers above 0.4 is confirmed, and a possible mechanism for flame generated turbulence and deflagration-to-detonation transition is established.     

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.     

Effects of gas and soot radiation on soot formation in counterflow ethylene diffusion flames

Numerical study of soot formation in counterflow ethylene diffusion flames at atmospheric pressure was conducted using detailed chemistry and complex thermal and transport properties. Soot kinetics was modelled using a semi-empirical two-equation model. Radiation heat transfer was calculated using the discrete-ordinates method coupled with an accurate band model. The calculated soot volume fractions are in reasonably good agreement with the experimental results in the literature. The individual effects of gas and soot radiation on soot formation were also investigated.     

Multiple mapping conditioning of turbulent jet diffusion flames

The multiple mapping conditioning (MMC) approach is applied to two non-piloted CH₄/H₂/N₂ turbulent jet diffusion flames with Reynolds numbers of Re = 15,200 and 22,800. The work presented here examines primarily the suitability of MMC to simulate CH₄/H₂ flames with varying Re numbers. The equations are solved in a prescribed Gaussian reference space with only one stochastic reference variable emulating the fluctuations of mixture fraction. The mixture fraction is considered as the only major species on which the remaining minor species are conditioned. Fluctuations around the conditional means are ignored. It is shown that the statistics of the mapped reference field are an accurate model for the statistics of the physical field for both flames. A transformation of the Gaussian reference space introduced in previous work on MMC is used to express the MMC model in the same form as CMC. The most important advantage of this transformation is that the conditionally averaged scalar dissipation term is in a closed form. The corresponding temperature and reactive species predictions are generally in good agreement with experimental data. The application to real laboratory flames and the assessment of the new conditional scalar dissipation model for the closure of the singly conditioned CMC equation is the major novelty of this paper. The results are therefore primarily examined with respect to changes of the conditionally averaged quantities in mixture fraction space.     

Structure and dynamic response of radiative diffusion flames

Nitrogen-diluted hydrogen burning in air is modeled numerically using a constant density and one-step reaction model in a plane two-dimensional counterflow configuration. An optically thin assumption is used to investigate the effects of radiation on the dynamics, structure, and extinction of diffusion flames. While there exist dual steady-state extinction limits for the 1D radiative flame response, it is found that as the 1D radiative extinction point is approached the 1D low-stretch diffusion flame exhibits oscillatory response, even with sub-unity Lewis number fuel. These radiation-induced limit cycle oscillations are found to have increasing amplitude and decreasing frequency as the stretch rate is reduced. Flame oscillation eventually leads to permanent extinction at the stretch rate which is larger than the steady-state radiative extinction value. Along the 1D radiative response curve, the transition from 1D flame to 2D structure and the differences in the resulting 2D flame patterns are also examined using a variety of initial profiles, with special emphasis on the comparison of using the initial profiles with and without a flame edge. Similar to the previous studies on the high-stretch adiabatic edge flames using the same configuration, the high-stretch radiative flames are found to resist 1D blow-off quenching through various 2D structures, including propagating front and steady cellular flames for initial profiles with and without flame edges. For all initial profiles studied, the low-stretch radiative flames are also found to exhibit different 2D flame phenomena near the 1D radiative extinction limit, such as transient cellular structures, steady cellular structures, and pulsating ignition fronts. Although the results demonstrate the presence of low-stretch and high-stretch 2D bifurcation branches close to the corresponding 1D extinction limits irrespective of the initial profile used, particular 2D flame structures in certain stretch rate range are initial profile dependent. The existence of two-dimensional flame structures beyond the 1D steady-state radiative extinction limit suggests that the flammable range is expanded as compared to that predicted by the 1D model. Hence, multi-dimensional flame patterns need to be accounted for when determining the flammability limits for a given system.     

A LES-CMC formulation for premixed flames including differential diffusion

A finite volume large eddy simulation–conditional moment closure (LES-CMC) numerical framework for premixed combustion developed in a previous studyhas been extended to account for differential diffusion. The non-unity Lewis number CMC transport equation has an additional convective term in sample space proportional to the conditional diffusion of the progress variable, that in turn accounts for diffusion normal to the flame front and curvature-induced effects. Planar laminar simulations are first performed using a spatially homogeneous non-unity Lewis number CMC formulation and validated against physical-space fully resolved reference solutions. The same CMC formulation is subsequently used to numerically investigate the effects of curvature for laminar flames having different effective Lewis numbers: a lean methane–air flame with Le_eff = 0.99 and a lean hydrogen–air flame with Le_eff = 0.33. Results suggest that curvature does not affect the conditional heat release if the effective Lewis number tends to unity, so that curvature-induced transport may be neglected. Finally, the effect of turbulence on the flame structure is qualitatively analysed using LES-CMC simulations with and without differential diffusion for a turbulent premixed bluff body methane–air flame exhibiting local extinction behaviour. Overall, both the unity and the non-unity computations predict the characteristic M-shaped flame observed experimentally, although some minor differences are identified. The findings suggest that for the high Karlovitz number (from 1 to 10) flame considered, turbulent mixing within the flame weakens the differential transport contribution by reducing the conditional scalar dissipation rate and accordingly the conditional diffusion of the progress variable.     

A comparison of computational and experimental lift-off heights of coflow laminar diffusion flames

As a sensitive marker of changes in flame structure, the number densities of excited-state CH (denoted CH^*), and excited-state OH (denoted OH^*) are imaged in coflow laminar diffusion flames. Measurements are made both in normal gravity and on the NASA KC-135 reduced-gravity aircraft. The spatial distribution of these radicals provides information about flame structure and lift-off heights that can be directly compared with computational predictions. Measurements and computations are compared over a range of buoyancy and fuel dilution levels. Results indicate that the lift-off heights and flame shapes predicted by the computations are in excellent agreement with measurement for both normal gravity (1g) and reduced gravity flames at low dilution levels. As the fuel mixture is increasingly diluted, however, the 1g lift-off heights become underpredicted. This trend continues until the computations predict stable flames at highly dilute fuel mixtures beyond the 1g experimental blow-off limit. To better understand this behavior, an analysis was performed, which indicates that the lift-off height is sensitive to the laminar flame speed of the corresponding premixed mixture at the flame edge. By varying the rates of two key “flame speed” controlling reactions, we were able to modify the predicted lift-off heights so as to be in closer agreement with the experiments. The results indicate that reaction sets that work well in low dilution systems may need to be modified to accommodate high dilution flames.     

Computational study of lean premixed turbulent flames using RANSPDF and LESPDF methods

A computational study is performed on a series of four piloted, lean, premixed turbulent jet flames. These flames use the Sydney Piloted Premixed Jet Burner (PPJB), and with jet velocities of 50, 100, 150 and 200 m/s are denoted PM150, PM1100, PM1150 and PM1200, respectively. Calculations are performed using the RANSPDF and LESPDF methodologies, with different treatments of molecular diffusion, with detailed chemistry and flamelet-based chemistry modelling, and using different imposed boundary conditions. The sensitivities of the calculations to these different aspects of the modelling are compared and discussed. Comparisons are made to experimental data and to previously-performed calculations. It is found that, given suitable boundary conditions and treatment of molecular diffusion, excellent agreement between the calculations and experimental measurements of the mean and variance fields can be achieved for PM150 and PM1100. The application of a recently developed implementation of molecular diffusion results in a large improvement in the computed variance fields in the LESPDF calculations. The inclusion of differential diffusion in the LESPDF calculations provides insight on the behaviour in the near-field region of the jet, but its effects are found to be confined to this region and to the species CO, OH and H₂. A major discrepancy observed in many previous calculations of these flames is an overprediction of reaction progress in PM1150 and PM1200, and this discrepancy is also observed in the LESPDF calculations; however, a parametric study of the LESPDF mixing model reveals that, with a sufficiently large mixing frequency, calculations of these two flames are capable of yielding improved reaction progress in good qualitative agreement with the mean and RMS scalar measurements up to an x/D of 30. Lastly, the merits of each computational methodology are discussed in light of their computational costs.     

Experimental measurements of geometric properties of turbulent stratified flames

Combustion under stratified conditions is common in many systems. However, relatively little is known about the structure and dynamics of turbulent stratified flames. Two-dimensional imaging diagnostics are applied to premixed and stratified V-flames at a mean equivalence ratio of 0.77, and low turbulent intensity, within the corrugated flame range. The present results show that stratification affects the mean turbulent flame speed, structure and geometric properties. Stratification increases the flame surface density above the premixed flame levels in all cases, with a maximum reached at intermediate levels of stratification. The flame surface density (FSD) of stratified flames is higher than that of premixed flames at the same mean equivalence ratio. Under the present conditions, the FSD peaks at a stratification ratio around 3.0. The FSD curves for stratified flames are further skewed towards the product side. The distribution of flame curvature in stratified flames is broader and more symmetric relative to premixed flames, indicating an additional mechanism of curvature generation, which is not necessarily due to cusping. These experiments indicate that flame stratification affects the intrinsic behaviour of turbulent flames and suggest that models may need to be revised in the light of the current evidence.     

A numerical study of auto-ignition in turbulent lifted flames issuing into a vitiated co-flow

This paper presents a numerical study of auto-ignition in simple jets of a hydrogen–nitrogen mixture issuing into a vitiated co-flowing stream. The stabilization region of these flames is complex and, depending on the flow conditions, may undergo a transition from auto-ignition to premixed flame propagation. The objective of this paper is to develop numerical indicators for identifying such behavior, first in well-known simple test cases and then in the lifted turbulent flames. The calculations employ a composition probability density function (PDF) approach coupled to the commercial CFD code, FLUENT. The in-situ-adaptive tabulation (ISAT) method is used to implement detailed chemical kinetics. A simple k–ε turbulence model is used for turbulence along with a low Reynolds number model close to the solid walls of the fuel pipe.

The first indicator is based on an analysis of the species transport with respect to the budget of convection, diffusion and chemical reaction terms. This is a powerful tool for investigating aspects of turbulent combustion that would otherwise be prohibitive or impossible to examine experimentally. Reaction balanced by convection with minimal axial diffusion is taken as an indicator of auto-ignition while a diffusive–reactive balance, preceded by a convective–diffusive balanced pre-heat zone, is representative of a premixed flame. The second indicator is the relative location of the onset of creation of certain radical species such as HO₂ ahead of the flame zone. The buildup of HO₂ prior to the creation of H, O and OH is taken as another indicator of autoignition.

The paper first confirms the relevance of these indicators with respect to two simple test cases representing clear auto-ignition and premixed flame propagation. Three turbulent lifted flames are then investigated and the presence of auto-ignition is identified. These numerical tools are essential in providing valuable insights into the stabilization behaviour of these flames, and the demarcation between processes of auto-ignition and premixed flame propagation.     

Simulations of normal and inverse laminar diffusion flames under oxygen enhancement and gravity variation

Steady-state global chemistry calculations for 20 different flames were carried out using an axisymmetric Computational Fluid Dynamics (CFD) code. Computational results for 16 flames were compared with flame images obtained at the NASA Glenn Research Center. The experimental flame data for these 16 flames were taken from Sunderland et al. [4 Sunderland, P. B., Krishnan, S. S and Gore, J. P. 2004. Effects of oxygen enhancement and gravity on normal and inverse laminar jet diffusion flames. Combust. Flame, 136: 254–256. [Crossref], [Web of Science ®] , [Google Scholar]] which included normal and inverse diffusion flames of ethane with varying oxidiser compositions (21, 30, 50, 100% O₂ mole fraction in N₂) stabilised on a 5.5 mm diameter burner. The test conditions of this reference resulted in highly convective inverse diffusion flames (Froude numbers of the order of 10) and buoyant normal diffusion flames (Froude numbers ～0.1). Additionally, six flames were simulated to study the effect of oxygen enhancement on normal diffusion flames. The enhancement in oxygen resulted in increased flame temperatures and the presence of gravity led to increased gas velocities. The effect of gravity-variation and oxygen enhancement on flame shape and size of normal diffusion flames was far more pronounced than for inverse diffusion flames. For normal-diffusion flames, their flame-lengths decreased (1 to 2 times) and flames-widths increased (2 to 3 times) when going from earth-gravity to microgravity, and flame height decreased by five times when going from air to a pure oxygen environment.