Scalar length scales and spatial averaging effects in turbulent piloted methane/air jet flames

The effects of spatial averaging in measurements of scalar variance and scalar dissipation in three piloted methane/air jet flames (Sandia flames C, D, and E) are investigated. Line imaging of Raman scattering, Rayleigh scattering, and laser-induced CO fluorescence is applied to obtain simultaneous single-shot measurements of temperature, the mass fractions of all major species, and mixture fraction, ξ, along 7-mm segments. Spatial filters are applied to ensembles of instantaneous profiles to quantify effects of spatial averaging on the Favre mean and variance of mixture fraction and scalar dissipation at several locations in the three flames. The radial contribution to scalar dissipation, χ_r = 2D_ξ (∂ξ/∂r)², is calculated from the filtered instantaneous profiles. The variance of mixture fraction tends to decrease linearly with increasing filter width, while the mean and variance of scalar dissipation are observed to follow an exponential dependence. In each case, the observed functional dependence is used to extrapolate to zero filter width, yielding estimates of the “fully resolved” profiles of measured quantities. Length scales for resolution of scalar variance and scalar dissipation are also extracted from the spatial filtering analysis and compared with length scales obtained from spatial autocorrelations. These results provide new insights on the small scale structure of turbulent jet flames and on the spatial resolution requirements for measurements of scalar variance and scalar dissipation.     

Nano organic carbon and soot in turbulent non-premixed ethylene flames

Spectral optical techniques are combined to characterise the distribution of large-molecule soot precursors, nanoparticles of organic carbon, and soot in two turbulent non-premixed ethylene flames with differing residence times. Laser-induced fluorescence, laser-induced incandescence and light scattering are used to define distributions across the particle size distribution. From the scattering and laser-induced emission measurements it appears that two classes of particles are formed. The first ones are preferentially formed in the fuel-rich region of the flame closer to the nozzle, have sizes of the order of few nanometers but are not fully solid particles, because the constituent molecules still maintain their individual identity exhibiting strong broadband fluorescence in the UV. The second class of particles constituted by solid particles, with sizes of the order of tens of nanometers are able to absorb a sufficient number of photons to be heated to incandescent temperatures. These larger particles are formed at larger residence times in the flame since they are the result of slow growth processes such as coagulation or carbonization. The flames are also modeled in order to produce mixture fraction maps. A new discovery is that nanoparticles of organic carbon concentration, unlike soot, does correlate well with mixture fraction, independent of position in the flame. This is likely to be a significant benefit to future modelling of soot inception processes in turbulent non-premixed flames.     

Analysis of the spatio-temporal scales of laminar premixed flames near equilibrium

The interplay between chemistry and transport is addressed by exploring the coupling between the spatial and temporal scales of one-dimensional laminar premixed combustion in reactive mixtures described by detailed chemical kinetics and multicomponent transport. System dynamics are investigated in the neighbourhood of the equilibrium state; in so doing, the time scales associated with modes of varying wavelength for the complete unsteady, spatially inhomogeneous system are obtained. The results reveal that short wavelength modes are dominated by diffusion-based time scales, and long wavelength modes are dominated by reaction-based time scales. The analysis further identifies critical wavelengths where the effects of reaction and diffusion are balanced, and it is seen that the critical wavelengths are well estimated by classical diffusion theory.     

Cell formation in non-premixed,axisymmetric jet flames near extinction

Systematic experiments with CO₂ diluted H₂–O₂ circular jet diffusion flames have been undertaken to study the formation of cellular flames, which occur for relatively low reactant Lewis numbers and near the extinction limit. The jet Reynolds number for all experiments was about 500, based on the centreline velocity, jet diameter and ambient fuel properties. The Lewis numbers, based on the initial mixture strength φ and ambient conditions of the investigated near-extinction mixtures, vary in the range 1.1–1.3 for oxygen and 0.25–0.29 for hydrogen (φ is defined here as the fuel-to-oxygen molar ratio normalized by the stoichiometric value). Various conditions near the extinction limit were investigated by fixing the fuel composition (H₂–CO₂ mixture), and systematically lowering the oxygen concentration in the co-flowing oxidizer stream past the point where cellular structures formed, until extinction occurred. The observed different instability states were correlated with the initial mixture strength and the proximity to the extinction limit.

The parameter space for cellularity was found to increase with decreasing initial mixture strength. For a given initial mixture strength, several cellular states were found to co-exist near the extinction limit, and the preferred number of cells (the azimuthal wave number) was observed to decrease with decreasing oxygen concentration (Damköhler number). These trends are consistent with previous theoretical work and our own stability analysis that will be reported elsewhere.     

Time-resolved conditional flow field statistics in extinguishing turbulent opposed jet flames using simultaneous highspeed PIV/OH-PLIF

Time-resolved particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF), both at 5 kHz, were applied simultaneously on extinguishing turbulent opposed jet flames. This repetition rate allowed tracking of transient extinction events in turbulent combustion. The additional information acquired about time history enabled a study of the evolution of vortex-flame interactions leading to extinction from individual events. A newly introduced multidimensional conditioning technique to avoid spatial- and temporal-smearing of important flow field information was developed in order to compare individual extinction events in a meaningful, statistical manner. The conditional statistics show that vortices tend to align around the flame and generate regions of high strain in the region where the flame is about to extinguish.     

High-repetition rate measurements of temperature and thermal dissipation in a non-premixed turbulent jet flame

High-repetition rate laser Rayleigh scattering is used to study the temperature fluctuations, power spectra, gradients, and thermal dissipation rate characteristics of a non-premixed turbulent jet flame at a Reynolds number of 15,200. The radial temperature gradient is measured by a two-point technique, whereas the axial gradient is measured from the temperature time-series combined with Taylor’s hypothesis. The temperature power spectra along the jet centerline exhibit only a small inertial subrange, probably because of the low local Reynolds number (Re_δ ≈ 2000), although a larger inertial subrange is present in the spectra at off-centerline locations. Scaling the frequency by the estimated Batchelor frequency improves the collapse of the dissipation region of the spectra, but this collapse is not as good as is obtained in non-reacting jets. Probability density functions of the thermal dissipation are shown to deviate from lognormal in the low-dissipation portion of the distribution when only one component of the gradient is used. In contrast, nearly log-normal distributions are obtained along the centerline when both axial and radial components are included, even for locations where the axial gradient is not resolved. The thermal dissipation PDFs measured off the centerline deviate from log-normal owing to large-scale intermittency. At one-half the visible flame length, the radial profile of the mean thermal dissipation exhibits a peak off the centerline, whereas farther downstream the peak dissipation occurs on the centerline. The mean thermal dissipation on centerline is observed to increase linearly with downstream distance, reach a peak at the location of maximum mean centerline temperature, and then decrease for farther downstream locations. Many of these observed trends are not consistent with equivalent non-reacting turbulent jet measurements, and thus indicate the importance of understanding how heat release modifies the turbulence structure of jet flames.     

The effect of co-flow stream velocity on turbulent non-premixed jet flame stability

The stability behaviour of non-premixed jet flames in a co-flowing air stream was investigated experimentally. The experimental data obtained indicate that there exists a range of co-flow velocity where two distinctly different extinction limits can occur at the same co-flow velocity depending on whether the flame is lifted or attached at ignition. Results show that co-flow velocity has a much greater effect on the blowout limits of lifted flames than on the blowoff limits of attached flames. The blowout limit of lifted flames initially increase linearly with co-flow velocity independent of nozzle diameter until a peak value is reached, after which it decreases rapidly with increasing co-flow velocity. Such behaviour appears to be governed by two different mechanisms. A model for predicting lifted flame blowout limits has been developed. It is based on the ratio of the Kolmogorov time scale and the chemical time scale as a function of a jet similarity parameter. The model was used to predict the blowout limits for methane as well as the effect of diluents in either fuel or co-flow stream. Results show very good agreement with experimental data in the current investigation.     

Measurements of flame orientation and scalar dissipation in turbulent partially premixed methane flames

Three turbulent flames were studied using a new experimental facility developed at Sandia National Laboratories. Line imaging of Raman and Rayleigh scattering and CO laser-induced fluorescence (LIF) yielded information on all major species, temperature, mixture fraction, and a 1D surrogate measure of scalar dissipation. Simultaneously, crossed planar OH LIF imaging provided information on the instantaneous flame orientation, allowing estimation of the full 3D (flame-normal) scalar dissipation rate. The three flames studied were methane–air piloted jet flames (Sandia flames C, D, and E), which cover a range in Reynolds number from 13,400 to 33,600. The statistics of the instantaneous flame orientation are examined in the different flames, with the purpose of studying the prevailing kinematics of isoscalar contours. The 1D and 3D results for scalar dissipation rate are examined in detail, both in the form of conditional averages and in the form of probability density functions. The effect of overall strain and Reynolds number on flame suppression and eventual extinction is also investigated, by examining the doubly conditional statistics of temperature in the form of S-shaped curves. This latter analysis reveals that double conditioning of temperature on both mixture fraction and scalar dissipation does not collapse the data from these flames onto the same curve at low scalar dissipation rates, as might be expected from simple flamelet concepts.     

LES modelling of turbulent non-premixed jet flames with correlated dynamic adaptive chemistry

Large eddy simulations (LES) for turbulent flames with detailed kinetic mechanisms have received growing interest. However, a direct implementation of detailed kinetic mechanisms in LES modelling of turbulent combustion remains a challenge due to the requirement of huge computational resources. An on-the-fly mechanism reduction method named correlated dynamic adaptive chemistry (CoDAC) is proposed to overcome this issue. A LES was conducted for Sandia Flame-D, with the reaction mechanism of GRI-Mech 3.0 consisting of 53 species and 325 reactions. The reduction threshold used in LES was obtained a priori by using auto-ignition model and partially stirred reactor (PaSR) with pairwise mixing model. LES results with CoDAC are in good agreement with experimental data and those without reduction. The conditional mean of the number of selected species indicates that a large size of locally reduced mechanism is required in the reaction zone where CH₄ is destructed. A computational time analysis shows that the PaSR model predicts better than the auto-ignition model on the wall time reduction with CoDAC in LES.     

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.     

An apparatus-independent extinction strain rate in counterflow flames

Resistance to extinction by stretch is a key property of any flame, and recent work has shown that this property controls the overall structure of several important types of turbulent flames. Multiple definitions of the critical strain rate at extinction (ESR) have been presented in the literature. However, even if the same definition is used, different experiments report different extinction strain rates for flames burning the same fuel-air mixture at very similar temperatures using similarly constructed opposed-flow instruments. Here we show that at extinction, all these flames are essentially identical, so one would expect that each would be assigned the same value of a parameter representing its intrinsic resistance-to-stretch-induced-extinction, regardless of the specifics of the experimental apparatus. A similar situation arises in laminar flame speed measurements since different apparatuses could result in different strain rate distributions. In that instance, the community has agreed to report the unstretched laminar flame speed, and methods have been developed to translate the experimental (stretched) flame speed into a universal unstretched laminar flame speed. We propose an analogous method for translating experimental measurements for stretch-induced extinction into an unambiguous and apparatus-independent quantity (ESR_∞) by extrapolating to infinite opposing burner separation distance. The uniqueness of the flame at extinction is shown numerically and supported experimentally for twin premixed, single premixed, and diffusion flames at Lewis numbers greater than and less than one. A method for deriving ESR_∞ from finite-boundary experimental studies is proposed and demonstrated for methane and propane experimental diffusion and premixed single flame data. The two values agree within the range of ESR differences typically observed between experimental measurements and simulation results for the traditional ESR definition.     

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.     

Conditional analysis of temperature and strain rate effects on dissipation structure in turbulent non-premixed jet flames

This work presents results from simultaneous high-resolution temperature and velocity measurements in a series of turbulent non-premixed jet flames. The filtered Rayleigh scattering (FRS)-based temperature measurements demonstrate sufficient signal-to-noise (SNR) and spatial resolution to estimate the smallest scalar length scales and accurately determine dissipation rate fields. A comprehensive set of conditional statistics are used to characterize the small-scale structure, including the dependence of dissipation layer widths on Reynolds number, temperature, and dissipation magnitude. In general, the dissipation layer thickness decrease with increasing Reynolds number and increase with increasing temperature. However, dissipation layer widths show two distinct behaviors with respect to dissipation magnitude. For small dissipation values, increases in magnitude results in broadening of the dissipation layer, while for larger magnitude values of dissipation, the layer widths are thinned, highlighting the complexity of small-scale turbulent mixing. Additionally, measured ratios of the dissipation layer width to the Batchelor length scale are consistent across all Reynolds numbers and agree with previous studies in non-reacting flows. The unique aspect about the current set of measurements is the ability to examine the interaction of dissipation structure with turbulent flow parameters for the first time in turbulent non-premixed flames. Particularly, the strain rate/dissipation relationship is examined and compared to previous studies in non-reacting flows. It is found that the dissipation layers tend to align normal to the principal compressive strain axis and this tendency increases with increasing Reynolds number. For the lowest Reynolds number case, no dependence of the dissipation layer width nor dissipation rate magnitude on strain rate is found. However, for higher Reynolds numbers, a strong dependence of the dissipation layer width and dissipation rate magnitude on the principal compressive strain rate is observed. These results indicate the direct role of the compressive strain rate field on small-scale mixing structure in reacting flows.     

Simultaneous PIV/PTV/OH PLIF imaging: Conditional flow field statistics in partially premixed turbulent opposed jet flames

A combination of particle imaging velocimetry (PIV), particle tracking velocimetry (PTV) and planar laser-induced fluorescence (PLIF) was employed to measure conditional flow field statistics in partially premixed turbulent opposed jet flames. These flames were observed to be very sensitive to excessive seeding of particles. Since flames close to extinction were studied, very low seeding densities were required to prevent impact on the extinction behavior of the flame, and conventional PIV algorithms would have resulted in poor spatial resolution. An improved PIV algorithm was developed, in connection with a PTV procedure used in high-temperature regions of low seed density, and revealed high in-plane resolution up to 300 μm. The PIV/PTV algorithm slightly under-resolved the Kolmogorov scales for the present cases, whereas Batchelor scales were fully resolved in-plane by the simultaneous OH PLIF. In the data processing, transient OH contours obtained from single-shots were used to define flame-fixed coordinates. Conditional velocities, out-of-plane vorticity, 2D dilatation, and both axial and radial strain were processed from the data. The conditional statistics show that vorticity is preferably generated close to the reaction zone, particularly at off-centerline positions. Hence, flow-chemistry interactions could be identified directly in the region of the reaction zone. This finding was also supported by qualitative high speed Mie scattering/chemiluminescence imaging that permitted temporally resolved visualization of the formation of eddies just upstream of the luminous flame areas.     

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.     

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.     

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 stabilization mechanism and structure of turbulent hydrocarbon lifted flames

The structure and stabilization mechanism of turbulent lifted non-premixed hydrocarbon flames have been investigated using combined laser imaging techniques. The techniques include Rayleigh scattering, laser induced predissociation fluorescence of OH, LIF of PAH, LIF of CH₂O, and planar imaging velocimetry. The geometrical structure of multi-reaction zones and flow field at the stabilization region have been simultaneously measured in 16 hydrocarbon flames. The data reveal the existence of triple flame structure at the stabilization region of turbulent lifted flames. Increasing the jet velocity leads to an increase of the lift-off height and to a broadening of the lift-off region. Further analysis of the stabilization criterion at the lift-off height based on the premixed nature of triple-flame propagation and flow field data has been presented and discussed.     

Comparisons of Lagrangian and Eulerian PDF methods in simulations of non-premixed turbulent jet flames with moderate-to-strong turbulence-chemistry interactions

Transported probability density function (PDF) methods have been applied widely and effectively for modelling turbulent reacting flows. In most applications of PDF methods to date, Lagrangian particle Monte Carlo algorithms have been used to solve a modelled PDF transport equation. However, Lagrangian particle PDF methods are computationally intensive and are not readily integrated into conventional Eulerian computational fluid dynamics (CFD) codes. Eulerian field PDF methods have been proposed as an alternative. Here a systematic comparison is performed among three methods for solving the same underlying modelled composition PDF transport equation: a consistent hybrid Lagrangian particle/Eulerian mesh (LPEM) method, a stochastic Eulerian field (SEF) method and a deterministic Eulerian field method with a direct-quadrature-method-of-moments closure (a multi-environment PDF-MEPDF method). The comparisons have been made in simulations of a series of three non-premixed, piloted methane–air turbulent jet flames that exhibit progressively increasing levels of local extinction and turbulence-chemistry interactions: Sandia/TUD flames D, E and F. The three PDF methods have been implemented using the same underlying CFD solver, and results obtained using the three methods have been compared using (to the extent possible) equivalent physical models and numerical parameters. Reasonably converged mean and rms scalar profiles are obtained using 40 particles per cell for the LPEM method or 40 Eulerian fields for the SEF method. Results from these stochastic methods are compared with results obtained using two- and three-environment MEPDF methods. The relative advantages and disadvantages of each method in terms of accuracy and computational requirements are explored and identified. In general, the results obtained from the two stochastic methods (LPEM and SEF) are very similar, and are in closer agreement with experimental measurements than those obtained using the MEPDF method, while MEPDF is the most computationally efficient of the three methods. These and other findings are discussed in detail.