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.     

Scalar dissipation rates in isothermal and reactive turbulent opposed-jets: 1-D-Raman/Rayleigh experiments supported by LES

Isothermal and reactive turbulent opposed flows are presented, which are appropriate to test the applicability and performance of models for turbulence, mixing, chemical reaction, and turbulence-chemistry interaction. Transient flow and scalar fields are measured using laser Doppler velocimetry and one-dimensionally resolved Raman/Rayleigh spectroscopy. Aside of statistical moments of temperature, mean species, and velocity components, scalar dissipation rate across the mixing and reaction layer is determined on a single-shot base. Using large eddy simulation in connection with a steady flamelet model, it is shown how numerical data can serve to estimate the influence of experimental noise upon a measured quantity, such as scalar dissipation. As a key result, it is shown that an increase in scalar rate of dissipation by chemical reactions is caused by a significant increase in the mixture fraction diffusivity, which outweighs the decrease in mixture fraction gradients. In mixture fraction space, local maxima of scalar dissipation rate are found on the rich side, which cannot be correctly reproduced by the steady flamelet model assuming equal species diffusivity. Furthermore, the impact of experimental noise on conditional probability density functions of scalar dissipation rate is shown (exemplary) to lead to erroneous conclusions from experimental data.     

Large eddy simulation of a turbulent nonpremixed piloted methane jet flame (Sandia Flame D)

Large eddy simulation (LES) is conducted of the Sandia Flame D [Proc. Combust. Inst. 27 (1998) 1087, Sandia National Laboratories (2004)], which is a turbulent piloted nonpremixed methane jet flame. The subgrid scale (SGS) closure is based on the scalar filtered mass density function (SFMDF) methodology [J. Fluid Mech. 401 (1999) 85]. The SFMDF is basically the mass weighted probability density function (PDF) of the SGS scalar quantities [Turbulent Flows (2000)]. For this flame (which exhibits little local extinction), a simple flamelet model is used to relate the instantaneous composition to the mixture fraction. The modelled SFMDF transport equation is solved by a hybrid finite-difference/Monte Carlo scheme. This is the first LES of a realistic turbulent flame using the transported PDF method as the SGS closure. The results via this method capture important features of the flame as observed experimentally.     

湍流扩散燃烧的数值研究-PDF方法和火焰面模型的性能比较

采用标量概率密度函数(PDF)方法、稳态和非稳态火焰面模型三种方法对一个值班湍流CH_4/O_2/N_2射流扩散火焰(Sandia Flame D)进行数值计算,以比较不同燃烧模型的性能。PDF方法通过计算反应标量的PDF输运方程来得到标量分布,而火焰面模型只求解单标量混合物分数的PDF方程,组分和温度分布通过火焰面方程的求解或者火焰面数据库的插值得到。计算结果和实验数据对比表明PDF方法计算结果最好但计算量相当大,稳态火焰面模型则反之。综合而言,非稳态火焰面模型的预测结果相对稳态模型有了非常大的改进,而计算量仍然容易接受,非常适合工程应用。     

湍流扩散火焰的非稳态火焰面模拟

采用稳态的和非稳态的火焰面模型同时对一个湍流甲烷射流扩散火焰进行了数值模拟,比较了两者对湍流平均火焰结构、活性自由基和污染物(氮氧化物)排放的模拟效果。速度场采用κ-ε模型计算,守恒标量混合物分数的分布通过其概率密度函数(PDF)输运方程的求解得到。稳态的火焰面结构由查询火焰面数据库得到,而非稳态的火焰面结构由火焰面方程和流场方程耦合求解来计算。采用详细的GRI—Mech 3.0机理描述甲烷的氧化和氮氧化物的形成。数值模拟结果和实验数据作了广泛的对比,验证了火焰面模型对湍流扩散燃烧的定量模拟能力。     

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.     

Laser imaging system for determination of three-dimensional scalar gradients in turbulent flames

An imaging system for the measurement of three-dimensional (3D) scalar gradients in turbulent hydrocarbon flames is described. Combined line imaging of Raman scattering, Rayleigh scattering, and CO laser-induced fluorescence (LIF) allows for simultaneous single-shot line measurements of major species, temperature, mixture fraction, and a one-dimensional surrogate of scalar dissipation rate in hydrocarbon flames, while simultaneous use of two crossed, planar LIF measurements of OH allows for determination of instantaneous flame orientation. In this manner the full 3D scalar dissipation can be estimated in some regions of a turbulent flame on a single-shot basis.     

Non-premixed turbulent combustion modeling based on the filtered turbulent flamelet equation

In turbulent combustion simulations, the flow structure at the unresolved scale level needs to be reasonably modeled. Following the idea of turbulent flamelet equation for the non-premixed flame case, which was derived based on the filtered governing equations(L. Wang, Combust. Flame 175, 259(2017)), the scalar dissipation term for tabulation can be directly computed from the resolved flowing quantities, instead of solving species transport equations. Therefore, the challenging source term closure for the scalar dissipation or any assumed probability density functions can be avoided;meanwhile the chemical sources are closed by scaling relations. The general principles are discussed in the context of large eddy simulation with case validation. The new model predictions of the bluff-body flame show sufficiently improved results, compared with these from the classic progress-variable approach.     

Turbulence/flame/wall interactions in non-premixed inclined slot-jet flames impinging at a wall using direct numerical simulation

In the present work, three-dimensional turbulent non-premixed oblique slot-jet flames impinging at a wall were investigated using direct numerical simulation (DNS). Two cases are considered with the Damköhler number (Da) of case A being twice that of case B. A 17 species and 73-step mechanism for methane combustion was employed in the simulations. It was found that flame extinction in case B is more prominent compared to case A. Reignition in the lower branch of combustion for case A occurs when the scalar dissipation rate relaxes, while no reignition occurs in the lower branch for case B due to excessive scalar dissipation rate. A method was proposed to identify the flame quenching edges of turbulent non-premixed flames in wall-bounded flows based on the intersections of mixture fraction and OH mass fraction iso-surfaces. The flame/wall interactions were examined in terms of the quenching distance and the wall heat flux along the quenching edges. There is essentially no flame/wall interaction in case B due to the extinction caused by excessive turbulent mixing. In contrast, significant interactions between flames and the wall are observed in case A. The quenching distance is found to be negatively correlated with wall heat flux as previously reported in turbulent premixed flames. The influence of chemical reactions and wall on flow topologies was identified. The FS/U and FC/U topologies are found near flame edges, and the NNN/U topology appears when reignition occurs. The vortex-dominant topologies, FC/U and FS/S, play an increasingly important role as the jet turbulence develops.     

A DNS assessment of linear relations between filtered reaction rate,flame surface density,and scalar dissipation rate in a weakly turbulent premixed flame

Linear relations between (i) filtered reaction rate and filtered flame surface density (FSD) and (ii) filtered reaction rate and filtered scalar dissipation rate (SDR), which are widely used in Large Eddy Simulation (LES) research into premixed turbulent combustion, are examined by processing DNS data obtained from a statistically 1D planar flame under weakly turbulent conditions that are most favourable for the two approaches (flamelet combustion regime, single-step chemistry, equidiffusive mixture, adiabatic burner, and low Mach number). The analysis well supports the former approach provided that the filtered reaction rate is combined with filtered molecular transport term. In such a case, both the RANS and LES FSD approaches are based on local relations valid within weakly perturbed flamelets. Accordingly, simply recasting RANS expressions to a filtered form works well. On the contrary, while the FSD and SDR approaches appear to be basically similar at first glance, the analysis does not support the latter one, but shows that a ratio of the filtered reaction rate to the filtered SDR is strongly scattered within the studied flame brush, with its conditionally mean value varying significantly with Favre-filtered combustion progress variable. As argued in the paper, these limitations of the LES SDR approach stem from the fact that it is based on a relation valid after integration over weakly perturbed flamelets, but this relation does not hold locally within such flamelets. Consequently, when a sufficiently small filter is applied to instantaneous fields, the filter may contain only a part of the local flamelet, whereas the linear relation holds solely for the entire flamelet and may not hold within the filtered flamelet volume. Thus, the present study implies that straightforwardly recasting well-established RANS equations to a filtered form is a flawed approach if the equations are based on integral features of local burning.     

Modelling of lifted turbulent diffusion flames in a channel mixing layer by the flame hole dynamics

The partial quenching structure of turbulent diffusion flames in a turbulent mixing layer is investigated by the method of flame hole dynamics as an effort to develop a prediction model for the turbulent flame lift off. The essence of the flame hole dynamics is derivation of the random walk mapping, from the flame-edge theory, which governs expansion or contraction of the quenching holes initially created by the local quenching events. The numerical simulation for the flame hole dynamics is carried out in two stages. First, a direct numerical simulation is performed for a constant-density fuel–air channel mixing layer to obtain the background turbulent flow and mixing fields, from which a time series of two-dimensional scalar-dissipation-rate array is extracted. Subsequently, a Lagrangian simulation of the flame hole random walk mapping, projected to the scalar dissipation rate array, yields a temporally evolving turbulent extinction process and its statistics on partial quenching characteristics. In particular, the probability of encountering the reacting state, while conditioned with the instantaneous scalar dissipation rate, is examined to reveal that the conditional probability has a sharp transition across the crossover scalar dissipation rate, at which the flame edge changes its direction of propagation. This statistical characteristic implies that the flame edge propagation instead of the local quenching event is the main mechanism controlling the partial quenching events in turbulent flames. In addition, the conditional probability can be approximated by a heavyside function across the crossover scalar dissipation rate.     

A three mixture fraction flamelet model for multi-stream laminar pulverized coal combustion

A three mixture fraction flamelet model is proposed for multi-stream laminar pulverized coal combustion. The technique of coordinate transformation is utilized to map the flamelet solutions from a unit pyramid space into a unit cubic space to improve the stability of the simulation. The validity of the three mixture fraction flamelet model was assessed on different configurations, including a laminar counterflow pulverized coal/methane flame and a laminar piloted pulverized coal jet flame. The flamelet predictions were compared to the reference results of the detailed chemistry solutions. For the counterflow flame, it was found that the flame temperature and major species mass fractions are correctly predicted by the three mixture fraction flamelet model. However, discrepancies are observed for combustion-mode-sensitive species such as CO and H₂ in the premixed combustion region. The thermo-chemical quantities in the char surface reaction zone cannot be correctly predicted if the mixing between the char off-gas stream and other streams is neglected. For the piloted jet flame, it was shown that the stable thermo-chemical variables can be correctly predicted at the upper and middle stream locations. However, at the downstream location, discrepancies can be observed in certain regions. Overall, the validity of the three mixture fraction flamelet model for multi-stream pulverized coal combustion is confirmed and its performance in turbulent pulverized coal combustion will be tested in future work.     

A Eulerian PDF scheme for LES of nonpremixed turbulent combustion with second-order accurate mixture fraction

Monte Carlo simulations of joint probability density function (PDF) approaches have been developed in the past largely with Reynolds averaged Navier Stokes (RANS) applications. Current interests are in the extension of PDF approaches to large eddy simulation (LES). As LES resolves accurately the large scales of turbulence in time, the Monte Carlo simulation and the flow field need to be tightly coupled. A tight coupling can be achieved if the consistency between the scalar field solution obtained via finite-volume (FV) methods and that from the stochastic solution of the PDF is ensured. For nonpremixed turbulent flames with two distinct streams, the local reactive mixture is described by the mixture fraction. A Eulerian Monte Carlo method is developed to achieve a second-order accuracy in the instantaneous filtered mixture fraction that is consistent with the corresponding FV. The performances of the proposed scheme are extensively evaluated using a one-dimensional model. Then, the scheme is applied to two cases with LES. The first one is a non-reacting mixing flow of two different fluids. The second case is the Sandia piloted turbulent flame D with a steady state flamelet model. Both results confirm the consistency of the proposed method to the level of filtered mixture fraction.     

Large Eddy Simulation of a turbulent lifted flame using multi-modal manifold-based models: Feasibility and interpretability

A general model for multi-modal turbulent combustion is achievable with two-dimensional manifold equations that use the mixture fraction and a generalized progress variable as coordinates. Information about the underlying mode of combustion is encoded in three scalar dissipation rates that appear as parameters in the two-dimensional equations. In this work, Large Eddy Simulation (LES) of a multi-modal turbulent lifted hydrogen jet flame in a vitiated coflow is performed using this new turbulent combustion model, leveraging both convolution-on-the-fly and In-Situ Adaptive Tabulation for computational tractability. The simulation predicts a lifted flame consistent with observations from past experiments. The feasibility of such a model implemented in LES is examined, and the cost per timestep is found to be comparable to conventional one-dimensional manifold-based models describing one asymptotic mode of combustion. Additionally, the model provides clear interpretability, allowing for combustion mode analysis to be performed with ease by evaluating the scalar dissipation rates and generalized progress variable source term. This analysis is used to show that the flame is stabilized by autoignition and has a trailing nonpremixed flame. Furthermore, transport of progress variable from the most reactive mixture fraction towards richer mixtures at the centerline is found to be important.     

Comparison of a spectral model for premixed turbulent flame propagation to DNS and experiments

A recently developed spectral model for premixed turbulent combustion in the flamelet regime (based on the EDQNM turbulence theory) has been compared with both direct numerical simulations (DNS) and experimental data. The 128³ DNS is performed at a Reynolds number of 223 based on the integral length scale. Good agreement is observed for both single- and two-point quantities (i.e. ratio of the turbulent to laminar burning velocities, scalar autocorrelation, dissipation and scalar-velocity cross correlation spectra) for the two different values of u′/s _L0 considered. The model also predicts the rapid transient behaviour of the flame at early times. An experimental set-up is then described for generating a lean methane-air flame and measuring two-point spatial correlations along the midpoint of the flame brush (i.e. along the C¯=0.5 contour). The experimental measurements in the flamelet regime take the form of a discontinuous or ‘telegraph’ signal. The EDQNM model, in contrast, describes an ‘ensemble’ of flames, and thus is based solely on continuous variables. A theoretical relationship between the correlation obtained from the EDQNM model and the equivalent correlation for a discontinuous (experimental) flame is derived. The relationship is used to enable a meaningful comparison between experimentally observed and model correlations. In general, the agreement is good for the three different cases considered in this study, with most of the error occurring at the lowest Reynolds number (Re _L =22). Furthermore, it is shown that considerably more error would result if no attempt is made to convert the ensemble representation in the model to an equivalent single-flame or ‘telegraph’ signal.     

LES-CMC simulations of a turbulent bluff-body flame

The large Eddy simulations (LES)-conditional moment closure (CMC) method with detailed chemistry is applied to a bluff-body stabilized flame. Computations of the velocity and mixture fraction fields show good agreement with the experiments. Temperature and major species are well-predicted throughout the flame with the exception of the flow regions in the outer shear layer close to the nozzle where the pure mixing between hot recirculating products and fresh oxidizer cannot be captured. LES-CMC generally improves on results obtained with RANS-CMC and on LES that uses one representative flamelet to model the dependence of reactive species on mixture fraction. Simulated CO mass fractions are generally in good agreement with the experimental data although a 10% overprediction can be found at downstream positions. NO predictions show a distinct improvement over the flamelet approach, however, simulations overpredict NO mass fractions at all downstream locations due to an overprediction of temperature close to the nozzle. The potential of LES-CMC to predict unsteady finite rate effects is demonstrated by the prediction of endothermic—or “flame cooling”—regions close to the neck of the recirculation zone that favours ethylene production via the methane fuel decomposition channel.     

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.     

Modelling effects of subgrid-scale mixture fraction variance in LES of a piloted diffusion flame

A posteriori analysis of the statistics of two large-eddy simulation (LES) solutions describing a piloted methane–air (Sandia D) flame is performed on a series of grids with progressively increased resolution reaching about 10.5 million cells. Chemical compositions, density and temperature fields are modelled with a steady flamelet approach and parametrised by the mixture fraction. The difference between the LES solutions arises from a different numerical treatment of the subgrid scale (SGS) mixture fraction variance – an important quantity of interest in non-premixed combustion modelling. In the first case (model I), the variance transport equation is solved directly, while in the second (model II), an equation for the square of the mixture fraction is solved, and the variance is computed from its definition. The comparison of the LES solutions is based on the convergence properties of their statistics with respect to the turbulence resolution length scale. The dependence of the LES statistics is analysed for velocity and the mixture fraction fields, and tested for convergence. For the most part, the statistics converge for the finest grids, but the variance of the mixture fraction shows some residual grid dependence in the high-gradient regions of the jet near field. The SGS variance given by model I exhibits realisability everywhere, whereas in regions of the flame model II is non-realisable, predicting negative variances. Furthermore, the LES statistics of model I exhibit superior convergence behaviour.     

An elementary model for the validation of flamelet approximations in non-premixed turbulent combustion

The fundamental soundness of three flamelet models for non-premixed turbulent combustion is examined on the basis of their performance in an idealized model problem that merges ideas from the laminar asymptotic theory for non-premixed flames and rigorous homogenization theory for the diffusion of a passive scalar. The overall flame configuration is stabilized by a mean gradient in the passive scalar: large Damköhler number asymptotics results are available for the laminar case to quantify the finite-rate effects that cause the flame to depart from its equilibrium state; the same results can also be used to incorporate higher-order corrections in the approximation of the reactive variables in terms of the passive scalar. The use of such flamelet approximations has been extended well beyond the laminar regime as they lie at the core of practical strategies to simulate non-premixed flames in the turbulent regime: the flamelet representation avoids the problem of turbulence closure for the reactive variables by replacing it by the presumably much simpler closure problem for a passive scalar. It is precisely the validity of this substitution outside the laminar regime that is addressed here in the idealized context of a class of small-scale periodic flows for which extensive rigorous results are available for the passive scalar statistics. Results for this simplified problem are reported here for significant wide ranges of Peclet and Damköhler numbers. Asymptotic convergence is observed in terms of the Damköhler number, with a convergence rate that is found to match the laminar predictions and appears relatively insensitive to the Peclet number. The passive scalar dissipation plays a key role in achieving higher-order corrections for the finite-rate case: replacing its pointwise value by an averaged value is convenient practically and can be rigorously motivated for the class of flows studied here, but while it does achieve an overall improvement over the lower-order equilibrium model, the simplification compromises the higher asymptotic convergence observed with the original finite-rate flamelet model with exact local dissipation.(Some figures in this article are in colour only in the electronic version; see www.iop.org)