Analysis of kinetic mechanism performance in conditional moment closure modelling of turbulent,non-premixed methane flames

This paper presents results obtained from the application of a first-order conditional moment closure approach to the modelling of two methane flames of differing geometries. Predictions are based upon a second-moment turbulence and scalar-flux closure, and supplemented with full and reduced chemical kinetic mechanisms, ranging from a simple 12-step to a complex 1207-step mechanism. Alongside analysis of the full kinetic schemes' performance, is an appraisal of the behaviour of their derivatives obtained using mechanism-reduction techniques. The study was undertaken to analyse the practicality of incorporating kinetic models of varying complexity into calculations of turbulent non-premixed flames, and to make comparison of their performance. Despite extensive studies of the predictive ability of such schemes under laminar flame conditions, systematic evaluations have not been performed for turbulent reacting flows. This paper reflects upon the impact that selection of chemical kinetics has upon subsequent calculations and concludes that, although application of reduced schemes is more than adequate to reproduce experimental data, selection of the parent mechanism is of paramount importance to the prediction of minor species. Although widely used schemes are well documented and validated, their performances vary considerably. Thus, careful consideration must be made to their application and origins during the evaluation of combustion models.     

Simulations of turbulent lifted jet flames with two-dimensional conditional moment closure

Simulations of H₂ air lifted jet flames are presented, obtained in terms of two-dimensional, first-order conditional moment closure (CMC). The unsteady CMC equation with detailed chemistry is solved without the need for operator splitting, while the accompanying flow field is determined using commercial CFD software employing a k − ε turbulence model. Computed lift-off heights and Favre-averaged species mole fractions are found to be very close to values obtained experimentally for a wide range of jet velocities and fuel–air mixtures. Simulations for which the initial condition is an attached flame and the jet velocity gradually increased do not result in lift-off, a result fully consistent with experimental observation and capturing the hysteresis behaviour of lifted flames. The stabilisation mechanism is explored by quantifying the balance of terms comprising the CMC in the lift-off region. In line with experimental data, it is found that the scalar dissipation rate at the stabilisation height is well below the extinction value, and that axial transport and molecular diffusion play a major role. The radial components of spatial convection and diffusion are always small, fully justifying the alternative approach of employing a cross-stream averaged CMC.     

Chemistry computation without a sub-grid PDF model in LES of turbulent non-premixed flames showing moderate local extinction

The use of the Eulerian Stochastic Fields (ESF) method to model the sub-grid turbulence-chemistry interaction (TCI) in the LES context can be computationally expensive if detailed chemistry mechanisms are involved. This work aims to assess whether it is possible to neglect the modelling of the TCI on sufficiently refined meshes while using finite rate chemistry, provided that at least 80 % of the turbulent kinetic energy scales are resolved. Turbulent non-premixed methane-air flames showing a moderate degree of local extinction are selected as benchmark. Results obtained for the Sandia flame E with and without transporting the ESF on three different meshes are discussed. Sensible deviations are visible on the fuel-rich side from section x/D = 30, by reducing the grid refinement. The influence of three finite rate chemistry solvers is further investigated on flame D, without the sub-grid scale chemistry model. All simulations are in good agreement with the experimental data and show a weak dependence on the chemistry involved. A trade-off assessment between computational time and accuracy is provided, in order to extend the validation to a more severe extinction regime.     

Lagrangian conditional moment closure model with flame group interaction for lifted turbulent spray jet flames

A new Lagrangian conditional moment closure (CMC) model is developed for multiple Lagrangian groups of sequentially evaporating fuel in turbulent spray combustion. Flame group interaction is taken into account as premixed combustion by the eddy breakup (EBU) model in terms of the probability of finding flame groups in the burned and the unburned state. Evaporation source terms are included in the two phase conditional transport equations, although they turn out to have negligible influence on the mean temperature field during combustion. The Lagrangian CMC model is implemented in OpenFOAM [1 H.G. Weller, G. Tabor, H. Jasak, and C. Fureby, A tensorial approach to computational continuum mechanics using object-oriented techniques, Comput. Phys. 12 (1998), pp. 620–631.[Crossref] [Google Scholar]] and validated for test cases in the Engine Combustion Network (ECN) [2 Engine Combustion Network. (2011). Available at http://www.sandia.gov/ecn. [Google Scholar],3 L.M. Pickett, C.L. Genzale, G. Bruneaux, L. Malbec, L. Hermant, C. Christian, and J. Schramm, Comparison of diesel spray combustion in different high-temperature, high-pressure facilities, SAE technical paper 2010-01-2106 (2010). [Google Scholar]]. Similar ignition delays and lift-off lengths are predicted by the incompletely stirred reactor (ISR) and the Eulerian CMC models due to relatively uniform conditional flame structure in the domain. The improved Lagrangian CMC model shows no abrupt reaction or oscillatory behaviour with an appropriate model constant K and gives results in better agreement with measurements lying between the predictions by ISR and Lagrangian CMC without flame group interaction.     

Conditional moment closure modelling of turbulent methanol jet flames

Conditional moment closure (CMC) predictions for a turbulent piloted jet diffusion flame of methanol in air at velocities of 66.2 and 90.3 m s^?1 are presented. Predictions are compared with the experimental joint Raman-Rayleigh-LIF results of Masri et al and laminar flamelet calculations. Three comprehensive chemical mechanisms (SKELETAL, GRI-Mech and SUBGRI) are used to represent the chemistry of the methanol flame. The SKELETAL mechanism shows the best agreement among the various mechanisms employed. It is found that the SUBGRI mechanism reduces computational cost in terms of memory and CPU time without compromising results where the focus is on the main reactive chemistry.

The k-ε-g turbulence model underpredicts the rate of mixing and the predicted flames are somewhat longer than that reported by experiment. In general, the CMC predictions for conditional mean temperature and species mass fractions are very good and show qualitative agreement with experiment. At downstream locations, the overall trends of predicted temperature and species concentration levels are similar to the upstream ones with the latter showing better agreement with the conditional measured levels. CMC predictions show the same order of agreement at higher velocities.

It is believed that the discrepancies on the fuel-rich side may be due to lack of consideration of the conditional fluctuations. The absence of a radially dependent CMC formulation, excluding differential diffusion effects and the inadequacy of the chemical mechanism may also account, partly, for the degree of discrepancy in the predictions.     

Spatial scales of extinction and dissipation in the near field of non-premixed turbulent jet flames

Simultaneous high-resolution Rayleigh scattering imaging and planar laser-induced fluorescence (PLIF) of OH are combined to measure the dissipative scales associated with thermal mixing and the structure and scales of extinguished regions of the reaction zone. Measurements are performed throughout the near field (x/d = 5, 10, 15, 20) of two turbulent, non-premixed methane/hydrogen/nitrogen jet flames with Re = 15,200 and 22,800 (flames DLR-A and DLR-B of the TNF workshop). Locally extinguished regions are identified by discontinuities in the OH layers, and the extinction hole sizes are measured. For each flame, the probability density function of the hole sizes is very similar throughout the entire near field, with the most likely hole size being 1.9 mm in DLR-A and 1.1 mm in DLR-B. Extinction events are equally probable at all measurement locations in DLR-A. In the DLR-B flame, there is a progression from frequent extinction close to the nozzle to more continuous reaction zones further downstream. The approximate instantaneous location of the stoichiometric contour is determined using the OH-PLIF images, enabling statistical analysis of dissipative scales conditioned on rich and lean conditions. The widths of the thin, elongated structures that dominate the thermal dissipation field are measured. Statistics of this microscale are qualitatively similar in both flames, with the higher Reynolds number producing smaller scales throughout the flow field. For dissipation layers in rich regions, the layer widths increase significantly with increasing temperature, while on the lean side the layer widths decrease with increasing temperature.     

Computations of turbulent lean premixed combustion using conditional moment closure

Conditional Moment Closure (CMC) is a suitable method for predicting scalars such as carbon monoxide with slow chemical time scales in turbulent combustion. Although this method has been successfully applied to non-premixed combustion, its application to lean premixed combustion is rare. In this study the CMC method is used to compute piloted lean premixed combustion in a distributed combustion regime. The conditional scalar dissipation rate of the conditioning scalar, the progress variable, is closed using an algebraic model and turbulence is modelled using the standard k–? model. The conditional mean reaction rate is closed using a first order CMC closure with the GRI-3.0 chemical mechanism to represent the chemical kinetics of methane oxidation. The PDF of the progress variable is obtained using a presumed shape with the Beta function. The computed results are compared with the experimental measurements and earlier computations using the transported PDF approach. The results show reasonable agreement with the experimental measurements and are consistent with the transported PDF computations. When the compounded effects of shear-turbulence and flame are strong, second order closures may be required for the CMC.     

Lagrangian investigation of local extinction,re-ignition and auto-ignition in turbulent flames

Lagrangian PDF investigations are performed of the Sandia piloted flame E and the Cabra H₂/N₂ lifted flame to help develop a deeper understanding of local extinction, re-ignition and auto-ignition in these flames, and of the PDF models' abilities to represent these phenomena. Lagrangian particle time series are extracted from the PDF model calculations and are analyzed. In the analysis of the results for flame E, the particle trajectories are divided into two groups: continuous burning and local extinction. For each group, the trajectories are further sub-divided based on the particles' origin: the fuel stream, the oxidizer stream, the pilot stream, and the intermediate region. The PDF calculations are performed using each of three commonly used models of molecular mixing, namely the EMST, IEM and modified Curl mixing models. The calculations with different mixing models reproduce the local extinction and re-ignition processes observed in flame E reasonably well. The particle behavior produced by the IEM and modified Curl models is different from that produced by the EMST model, i.e., the temperature drops prior to (and sometimes during) re-ignition. Two different re-ignition mechanisms are identified for flame E: auto-ignition and mixing-reaction. In the Cabra H₂/N₂ lifted flame, the particle trajectories are divided into different categories based on the particles' origin: the fuel stream, the oxidizer stream, and the intermediate region. The calculations reproduce the whole auto-ignition process reasonably well for the Cabra flame. Four stages of combustion in the Cabra flame are identified in the calculations by the different mixing models, i.e., pure mixing, auto-ignition, mixing-ignition, and fully burnt, although the individual particle behavior by the IEM and modified Curl models is different from that by the EMST model. The relative importance of mixing and reaction during re-ignition and auto-ignition are quantified for the IEM model.     

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.     

Stability characteristics and flowfields of turbulent non-premixed swirling flames

A simple, yet representative, burner geometry is used for the investigation of highly swirling turbulent unconfined, non-premixed, flames of natural gas. The burner configuration comprises a ceramic faced bluff-body with a central fuel jet. The bluff-body is surrounded by an annulus that delivers a swirling primary flow of air. The entire burner assembly is housed in a wind tunnel providing a secondary co-flowing stream of air. This hybrid bluff-body/swirl burner configuration stabilizes complex turbulent flames not unlike those found in practical combustors, yet is amenable to modelling because of its well-defined boundary conditions. Full stability characteristics including blow-off limits and comprehensive maps of flame shapes are presented for swirling flames of three different fuel mixtures: compressed natural gas (CNG), CNG–air (1:2 by volume) and CNG–H₂ (1:1 by volume).

It is found that with increased fuel flow, flame blow-off mode may change with swirl number, S_g. At low swirl, the flame remains stable at the base but blows off in the neck region further downstream. At higher swirl numbers, the flames peel off completely from the burner's base. Swirling CNG–air flames are distinct in that they only undergo base blow-off. In the low range of swirl number, increasing S_g causes limited improvement in the blow-off limits of the flames investigated and (for a few cases) can even lead to some deterioration over a small intermediate range of S_g. It is only above a certain threshold of swirl that significant improvements in blow-off limits appear. Six flames are selected for further detailed flowfield and composition measurements and these differ in the combination of swirl number, primary axial velocity through the annulus, U_s, and bulk fuel jet velocity, U_j. Only velocity field measurements are presented in this paper. A number of flow features are resolved in these flames, which resemble those already associated with non-reacting swirling flows of equivalent swirl obtained with the present burner configuration. Additionally, asymmetric flowfields inherent to some flames are revealed where the fluidic centreline of the flow (defined in the two-dimensional (U–W velocity pair) velocity field by the ?ω? = 0 tangential velocity contour), meanders strongly on either side of the geometric centreline downstream by about one bluff-body diameter. Flow structures revealed by the velocity data are correlated to flame shapes to yield a better understanding of how the velocity field influences the flames physical characteristics.     

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.     

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.     

Assessment of subgrid-scale stress statistics in non-premixed turbulent wall-jet flames

We investigate the heat-release effects on the characteristics of the subgrid-scale (SGS) stress tensor and SGS dissipation of kinetic energy and enstrophy. Direct numerical simulation data of a non-premixed reacting turbulent wall-jet flow with and without substantial heat release is employed for the analysis. This study comprises, among others, an analysis of the eigenvalues of the resolved strain rate and SGS stress tensors, to identify the heat-release effects on their topology. An assessment of the alignment between the eigenvectors corresponding to the largest eigenvalues of these two tensors is also given to provide further information for modelling of the SGS stress tensor. To find out the heat-release effects on the dynamics of the turbulent kinetic energy and enstrophy dissipation, probability density functions (PDFs) and mean values are analysed. The mean SGS shear stress and turbulent kinetic energy both slightly increase in the buffer layer and substantially decrease further away from the wall, due to the heat-release effects. Contrary to the kinetic energy, heat release decreases the mean SGS dissipation of enstrophy in the near-wall region. Moreover, differences in the shapes of the PDFs between the isothermal and exothermic cases indicate changes in the intermittency level of both SGS dissipations. Heat release also increases the SGS stress anisotropy in the near-wall region. Although, the structure of the mean resolved strain-rate tensor only marginally differs between the isothermal and exothermic cases in the near-wall region, substantial differences are observed in the jet area, where compressibility effects are important and heat-release effects are found to promote compression states. The differences in the relative alignment between the SGS stress and resolved strain-rate tensors in the isothermal and exothermic cases are discussed in connection with the differences in the SGS dissipation of kinetic energy.     

Second-order conditional moment closure modeling of a turbulent CH4/H2/N2 jet diffusion flame

The second-order CMC model for a detailed chemical mechanism is used to model a turbulent CH₄/H₂/N₂ jet diffusion flame. Second-order corrections are made to the three rate limiting steps of methane–air combustion, while first-order closure is employed for all the other steps. Elementary reaction steps have a wide range of timescales with only a few of them slow enough to interact with turbulent mixing. Those steps with relatively large timescales require higher-order correction to represent the effect of fluctuating scalar dissipation rates. Results show improved prediction of conditional mean temperature and mass fractions of OH and NO. Major species are not much influenced by second-order corrections except near the nozzle exit. A parametric study is performed to evaluate the effects of the variance parameter in log-normal scalar dissipation PDF and the constants for the dissipation term in conditional variance and covariance equations.     

Modeling curvature effects in turbulent autoigniting non-premixed flames using tabulated chemistry

Turbulent flames are intrinsically curved. In the presence of preferential diffusion, curvature effects either enhance or suppress molecular diffusion, depending on the diffusivity of the species and the direction of the flame curvature. When a tabulated chemistry type of modeling is employed, curvature-preferential diffusion interactions have to be taken into consideration in the construction of manifolds. In this study, we employ multistage stage flamelet generated manifolds (MuSt-FGM) method to model autoigniting non-premixed turbulent flames with preferential diffusion effects included. The conditions for the modeled flame are in MILD combustion regime. To model the above-mentioned curvature-preferential diffusion interactions, a new mixture fraction which has a non-unity Lewis number is defined and used as a new control variable in the manifold generation. 1D curved flames are simulated to create the necessary flamelets. The resulting MuSt-FGM tables are used in the simulation of 1D laminar flames, and then also applied to turbulent flames using 2D direct numerical simulations (DNS). It was observed that when the curvature effects are included in the manifold, the MuSt-FGM results agree well with the detailed chemistry results; whereas the results become unsatisfactory when the curvature effects are ignored.