Prediction of local extinction and re-ignition effects in non-premixed turbulent combustion using a flamelet/progress variable approach

The flamelet/progress variable approach (FPVA) has been proposed by Pierce and Moin as a model for turbulent non-premixed combustion in large-eddy simulation. The filtered chemical source term in this model appears in unclosed form, and is modeled by a presumed probability density function (PDF) for the joint PDF of the mixture fraction Z and a flamelet parameter λ. While the marginal PDF of Z can be reasonably approximated by a beta distribution, a model for the conditional PDF of the flamelet parameter needs to be developed. Further, the ability of FPVA to predict extinction and re-ignition has also not been assessed. In this paper, we address these aspects of the model using the DNS database of Sripakagorn et al. It is first shown that the steady flamelet assumption in the context of FPVA leads to good predictions even for high levels of local extinction. Three different models for the conditional PDF of the flamelet parameter are tested in an a priori sense. Results obtained using a delta function to model the conditional PDF of λ lead to an overprediction of the mean temperature, even with only moderate extinction levels. It is shown that if the conditional PDF of λ is modeled by a beta distribution conditioned on Z, then FPVA can predict extinction and re-ignition effects, and good agreement between the model and DNS data for the mean temperature is observed.     

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.     

Direct numerical simulation of a statistically stationary,turbulent reacting flow

An inhomogeneous, non-premixed, stationary, turbulent, reacting model flow that is accessible to direct numerical simulation (DNS) is described for investigating the effects of mixing on reaction and for testing mixing models. The mixture-fraction-progress-variable approach of Bilger is used, with a model, finite-rate, reversible, single-step thermochemistry, yielding non-trivial stationary solutions corresponding to stable reaction and also allowing local extinction to occur. There is a uniform mean gradient in the mixture fraction, which gives rise to stationarity as well as a flame brush. A range of reaction zone thicknesses and Damkohler numbers are examined, yielding a broad spectrum of behaviour, including thick and thin flames, local extinction and near equilibrium. Based on direct numerical simulations, results from the conditional moment closure (CMC) and the quasi-equilibrium distributed reaction (QEDR) model are evaluated. Large intermittency in the scalar dissipation leads to local extinction in the DNS. In regions of the flow where local extinction is not present, CMC and QEDR based on the local scalar dissipation give good agreement with the DNS.M This article features multimedia enhancements available from the supplemental page in the online journal.     

DNS assessment of relation between mean reaction and scalar dissipation rates in the flamelet regime of premixed turbulent combustion

The linear relation between the mean rate of product creation and the mean scalar dissipation rate, derived in the seminal paper by K.N.C. Bray [‘The interaction between turbulence and combustion’, Proceedings of the Combustion Institute, Vol. 17 (1979), pp. 223–233], is the cornerstone for models of premixed turbulent combustion that deal with the dissipation rate in order to close the reaction rate. In the present work, this linear relation is straightforwardly validated by analysing data computed earlier in the 3D Direct Numerical Simulation (DNS) of three statistically stationary, 1D, planar turbulent flames associated with the flamelet regime of premixed combustion. Although the linear relation does not hold at the leading and trailing edges of the mean flame brush, such a result is expected within the framework of Bray's theory. However, the present DNS yields substantially larger (smaller) values of an input parameter c_m (or K₂ = 1/(2c_m ? 1)), involved by the studied linear relation, when compared to the commonly used value of c_m = 0.7 (or K₂ = 2.5). To gain further insight into the issue and into the eventual dependence of c_m on mixture composition, the DNS data are combined with the results of numerical simulations of stationary, 1D, planar laminar methane–air flames with complex chemistry, with the results being reported in terms of differently defined combustion progress variables c, i.e. the normalised temperature, density, or mole fraction of CH₄, O₂, CO₂ or H₂O. Such a study indicates the dependence of c_m both on the definition of c and on the equivalence ratio. Nevertheless, K₂ and c_m can be estimated by processing the results of simulations of counterpart laminar premixed flames. Similar conclusions were also drawn by skipping the DNS data, but invoking a presumed beta probability density function in order to evaluate c_m for the differently defined c's and various equivalence ratios.     

Conditional moment closure and transient flamelet modelling for detailed structure and NO x formation characteristics of turbulent nonpremixed jet and recirculating flames

This study has been mainly motivated to assess computationally and theoretically the conditional moment closure (CMC) model and the transient flamelet model for the simulation of turbulent nonpremixed flames. These two turbulent combustion models are implemented into the unstructured grid finite volume method that efficiently handles physically and geometrically complex turbulent reacting flows. Moreover, the parallel algorithm has been implemented to improve computational efficiency as well as to reduce the memory load of the CMC procedure. Example cases include two turbulent CO/H₂/N₂ jet flames having different flow timescales and the turbulent nonpremixed H₂/CO flame stabilized on an axisymmetric bluff-body burner. The Lagrangian flamelet model and the simplified CMC formulation are applied to the strongly parabolic jet flame calculation. On the other hand, the Eulerian particle flamelet model and full conservative CMC formulation are employed for the bluff-body flame with flow recirculation. Based on the numerical results, a detailed discussion is given for the comparative performances of the two combustion models in terms of the flame structure and NO _x formation characteristics.     

Investigation of the ignition processes of a multi-injection flame in a Diesel engine environment using the flamelet model

In this work, the first flamelet analysis is conducted of a highly resolved DNS of a multi-injection flame with both auto-ignition and ignition induced by flame-flame interaction. A novel method is proposed to identify the different combustion modes of ignition processes using generalized flamelet equations. The state-of-the-art DNS database generated by Rieth et al. (US National Combustion Meeting, 2019) for a multi-injection flame in a Diesel engine environment is investigated. Three-dimensional flamelets are extracted from the DNS at different time instants with a focus on auto-ignition and interaction-ignition processes. The influences of mixture field interactions and the scalar dissipation rate on the ignition process are investigated by varying the species composition boundary conditions of the transient flamelet equations. Budget analyses of the generalized flamelet equations show that the transport along the mixture fraction iso-surface is insignificant during the auto-ignition process, but becomes important when interaction-ignition occurs, which is further confirmed through a flamelet regime classification method.     

Critical temperature and reactant mass flux for radiative extinction of ethylene microgravity spherical diffusion flames at 1 bar

In microgravity combustion, where buoyancy is not present to accelerate the flow field and strain the flame, radiative extinction is of fundamental importance, and has implications for spacecraft fire safety. In this work, the critical point for radiative extinction is identified for normal and inverse ethylene spherical diffusion flames via atmospheric pressure experiments conducted aboard the International Space Station, as well as with a transient numerical model. The fuel is ethylene with nitrogen diluent, and the oxidizer is an oxygen/nitrogen mixture. The burner is a porous stainless-steel sphere. All experiments are conducted at constant reactant flow rate. For normal flames, the ambient oxygen mole fraction was varied from 0.2 to 0.38, burner supply fuel mole fraction from 0.13 to 1, total mass flow rate, ṁ_total, from 0.6 to 12.2 mg/s, and adiabatic flame temperature, T_ad, from 2000 to 2800 K. For inverse flames, the ambient fuel mole fraction was varied from 0.08 to 0.12, burner supply oxygen mole fraction from 0.4 to 0.85, ṁ_total from 2.3 to 11.3 mg/s, and T_ad from 2080 to 2590 K. Despite this broad range of conditions, all flames extinguish at a critical extinction temperature of 1130 K, and a fuel-based mass flux of 0.2 g/m²-s for normal flames, and an oxygen-based mass flux of 0.68 g/m²-s for inverse flames. With this information, a simple equation is developed to estimate the flame size (i.e., location of peak temperature) at extinction for any atmospheric-pressure ethylene spherical diffusion flame given only the reactant mass flow rate. Flame growth, which ultimately leads to radiative extinction if the critical extinction point is reached, is attributed to the natural development of the diffusion-limited system as it approaches steady state and the reduction in the transport properties as the flame temperature drops due to increasing flame radiation with time (radiation-induced growth.)     

Unsteady flamelet/progress variable approach for non-premixed turbulent lifted flames

The unsteady flamelet/progress variable approach has been developed for the prediction of a lifted flame to capture the extinction and re-ignition physics. In this work inclusion of the time variant behavior in the flamelet generation embedded in the large eddy simulation technique, allows better understanding of partially premixed flame dynamics. In the process sufficient simulations to generate unsteady laminar flamelets are performed, which are a function of time. These flamelets are used for the generation of the look-up table and the flamelet library is produced. This library is used for the calculation of temperature and other species in the computational domain as the solution progresses. The library constitutes filtered quantities of all the scalars as a function of mean mixture fraction, mixture fraction variance and mean progress variable. Mixture fraction and progress variable distributions are assumed to be β-PDF and δ-PDF respectively. The technique used here is known as the unsteady flamelet progress variable (UFPV) approach. One of the well known lifted flames is considered for the present modeling which shows flame lift-off. The results are compared with the experimental data for the mixture fraction and temperature. Lift off height is predicted from the numerical calculations and compared with the experimentally given value. Comparisons show a reasonably good agreement and the UFPV combustion model appears to be a promising technique for the prediction of lifted and partially premixed flames.     

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.     

The effect of timescale variation in multiple mapping conditioning mixing of PDF calculations for Sandia Flame series D–F

A stochastic implementation of the multiple mapping conditioning (MMC) model has been used for the modelling of turbulence–chemistry interactions in a series of turbulent jet diffusion flames with varying degrees of local extinction (Sandia Flames D–F). The mapping function approximates the cumulative probability distribution of mixture fraction and the corresponding variance can be controlled by a standard implementation of the scalar mixing timescale. The conditional fluctuations are controlled by a minor dissipation timescale, τ_min. The results show a clear dependence of the conditional fluctuations on the choice of the minor timescale, and the appropriate value for turbulent jet flames is similar to values determined in related direct numerical simulation (DNS) studies of homogeneous turbulent reacting flows. The predictions of means and variances of temperature and species mass fractions are very good for all flames, indicating an appropriate modelling of the conditional variances. Further sensitivity studies with respect to particle number density demonstrate a relative insensitivity of the results to the particle number in the numerical solution procedure. Good results can be obtained with as few as 10 particles per cell, allowing for a computationally inexpensive implementation of a Monte Carlo/probability density function (PDF) method.     

Investigation of lengthscales, scalar dissipation, and flame orientation in a piloted diffusion flame by LES

This work investigates the structure of a diffusion flame in terms of lengthscales, scalar dissipation, and flame orientation by using large eddy simulation. This has been performed for a turbulent, non-premixed, piloted methane/air jet flame (Flame D) at a Reynolds-number of 22,400. A steady flamelet model, which was represented by artificial neural networks, yields species mass fractions, density, and viscosity as a function of the mixture fraction. This will be shown to suffice to simulate such flames. To allow to examine scalar dissipation, a grid of 1.97 × 10⁶ nodes was applied that resolves more than 75% of the turbulent kinetic energy. The accuracy of the results is assessed by varying the grid-resolution and by comparison to experimental data by Barlow, Frank, Karpetis, Schneider (Sandia, Darmstadt), and others. The numerical procedure solves the filtered, incompressible transport equations for mass, momentum, and mixture fraction. For subgrid closure, an eddy viscosity/diffusivity approach is applied, relying on the dynamic Germano model. Artificial turbulent inflow velocities were generated to feature proper one- and two-point statistics. The results obtained for both the one- and two-point statistics were found in good agreement to the experimental data. The PDF of the flame orientation shows the tilting of the flame fronts towards the centerline. Finally, the steady flamelet approach was found to be sufficient for this type of flame unless slowly reacting species are of interest.     

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.     

LES of oxy-fuel jet flames using the Eulerian Stochastic Fields method with differential diffusion

The Eulerian Stochastic Fields (ESF) Monte Carlo method to solve the transported PDF (TPDF) equation is extended to account for differential diffusion effects by incorporating species individual molecular diffusivities. The method has been applied in Large Eddy simulation (LES) to non-piloted oxy-fuel jet flames at different Reynolds numbers experimentally investigated by Sevault et al. [1]. Due to the high H₂ content in the fuel stream and CO₂ in the oxidizer these flames pose new challenges to combustion modeling as the flame structures are different compared to CH₄/air flames. The simulations show very good agreement with the experiments in terms of mixture fraction conditional mean values for temperature and mayor species on the fuel lean side and the reaction zone, deviations on the fuel rich side are discussed. The trend and location of localized extinction is reproduced well in the simulations, as well as differential diffusion effects in the near field. Additionally, it is shown that a neglect of differential diffusion in the combustion model leads to a lifted flame.     

Turbulent piloted partially-premixed flames with varying levels of O2/N2: stability limits and PDF calculations

This paper reports measured stability limits and PDF calculations of piloted, turbulent flames of compressed natural gas (CNG) partially-premixed with either pure oxygen, or with varying levels of O₂/N₂. Stability limits are presented for flames of CNG fuel premixed with up to 20% oxygen as well as CNG–O₂–N₂ fuel where the O₂ content is varied from 8 to 22% by volume. Calculations are presented for (i) Sydney flame B [Masri et al. 1988] which uses pure CNG as well as flames B15 to B25 where the CNG is partially-premixed with 15–25% oxygen by volume, respectively and (ii) Sandia methane–air (1:3 by volume) flame E [Barlow et al. 2005] as well as new flames E15 and E25 that are partially-premixed with ‘reconstituted air’ where the O₂ content in nitrogen is 15 and 25% by volume, respectively. The calculations solve a transported PDF of composition using a particle-based Monte Carlo method and employ the EMST mixing model as well as detailed chemical kinetics. The addition of oxygen to the fuel increases stability, shortens the flames, broadens the reaction zone, and shifts the stoichiometric mixture fraction towards the inner side of the jet. It is found that for pure CNG flames where the reaction zone is narrow (～0.1 in mixture fraction space), the PDF calculations fail to reproduce the correct level of local extinction on approach to blow-off. A broadening in the reaction zone up to about 0.25 in mixture fraction space is needed for the PDF/EMST approach to be able to capture these finite-rate chemistry effects. It is also found that for the same level of partial premixing, increasing the O₂/N₂ ratio increases the maximum levels of CO and NO but shifts the peak to richer mixture fractions. Over the range of oxygenation investigated here, stability limits have shown to improve almost linearly with increasing oxygen levels in the fuel and with increasing the contribution of release rate from the pilot.     

Modelling of turbulent lifted jet flames using flamelets: a priori assessment and a posteriori validation

This study focuses on the modelling of turbulent lifted jet flames using flamelets and a presumed Probability Density Function (PDF) approach with interest in both flame lift-off height and flame brush structure. First, flamelet models used to capture contributions from premixed and non-premixed modes of the partially premixed combustion in the lifted jet flame are assessed using a Direct Numerical Simulation (DNS) data for a turbulent lifted hydrogen jet flame. The joint PDFs of mixture fraction Z and progress variable c, including their statistical correlation, are obtained using a copula method, which is also validated using the DNS data. The statistically independent PDFs are found to be generally inadequate to represent the joint PDFs from the DNS data. The effects of Z–c correlation and the contribution from the non-premixed combustion mode on the flame lift-off height are studied systematically by including one effect at a time in the simulations used for a posteriori validation. A simple model including the effects of chemical kinetics and scalar dissipation rate is suggested and used for non-premixed combustion contributions. The results clearly show that both Z–c correlation and non-premixed combustion effects are required in the premixed flamelets approach to get good agreement with the measured flame lift-off heights as a function of jet velocity. The flame brush structure reported in earlier experimental studies is also captured reasonably well for various axial positions. It seems that flame stabilisation is influenced by both premixed and non-premixed combustion modes, and their mutual influences.     

Detailed analysis of early-stage NOx formation in turbulent pulverized coal combustion with fuel-bound nitrogen

A carrier-phase direct numerical simulation (CP-DNS) of pulverized coal combustion in a mixing layer is performed, considering three NO_x formation mechanisms (fuel-NO_x, thermal-NO_x and prompt-NO_x). Detailed analyses, including reaction path analysis, chemical timescale analysis, and a priori and budget analyses are conducted to investigate the NO_x production mechanisms and the performance of the flamelet model. Considering the high computational cost of CP-DNS, this work focuses on the early phase governed by devolatilization, where char reactions are less important. The reaction path analyses show that the principal thermal-NO reaction contributes to the net consumption of NO in fuel-bound nitrogen pulverized coal flames, which is essentially different from fuel-nitrogen-free flames. The chemical timescale analyses show that the production rates of NO_x species are faster than those of major species, which confirms the suitability of the flamelet tables. The a priori analyses show that the gas temperature and major/intermediate species can be predicted well by the flamelet model, while the NO_x species show significant discrepancies in certain regions. Finally, the budget analyses explain why the flamelet model performs differently for major/intermediate and NO_x species.     

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.     

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.     

Experimental evaluation of flame observables for simplified scalar dissipation rate measurements in laminar diffusion flamelets

We present a comparative evaluation of the potential of several flame observables to yield a simplified measurement of the scalar dissipation rate (χ). The realization of the importance of this quantity for the structure of diffusion flamelets has led to brilliant experimental efforts targeted to its measurement, with a particular emphasis on χ_stoich, i.e., its value at the stoichiometric surface, which has been shown to control extinction. Such measurements require a significant amount of experimental resources, since they necessitate the simultaneous acquisition of multi-scalar data. The possibility of a simplified measurement stems from the realization that the related gradient of the mixture fraction scales as the inverse of an appropriately defined thickness of the mixing layer. In this paper, we investigate experimentally the utilization of several flame observables for the measurement of this thickness. In a flat, nitrogen diluted, counterflow, methane/oxygen diffusion flame, the scalar dissipation rate was first measured directly using line Raman imaging of major species and a N₂-molecule based definition of the mixture fraction. Additionally, LIF measurements of the hydroxyl radical (OH) and formaldehyde (HCHO) as well as Raman measurements of carbon monoxide (CO) were performed across the flamelet. The precision of χ_stoich estimates based on the thickness of the layers of these three observables as well as the layers corresponding to [HCHO] × [OH] and [CO] × [OH] “overlap” zones was evaluated in terms of following the theoretically expected inverse-square-root dependence on strain rate. Also, the absolute thickness of these layers was recorded, since it may restrict the application of simplified techniques in turbulent flow fields.