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.     

Turbulent scalar flux transport in head-on quenching of turbulent premixed flames: a direct numerical simulations approach to assess models for Reynolds averaged Navier Stokes simulations

The statistical behaviour and the modelling of turbulent scalar flux transport have been analysed using a direct numerical simulation (DNS) database of head-on quenching of statistically planar turbulent premixed flames by an isothermal wall. A range of different values of Damköhler, Karlovitz numbers and Lewis numbers has been considered for this analysis. The magnitudes of the turbulent transport and mean velocity gradient terms in the turbulent scalar flux transport equation remain small in comparison to the pressure gradient, molecular dissipation and reaction-velocity fluctuation correlation terms in the turbulent scalar flux transport equation when the flame is away from the wall but the magnitudes of all these terms diminish and assume comparable values during flame quenching before vanishing altogether. It has been found that the existing models for the turbulent transport, pressure gradient, molecular dissipation and reaction-velocity fluctuation correlation terms in the turbulent scalar flux transport equation do not adequately address the respective behaviours extracted from DNS data in the near-wall region during flame quenching. Existing models for transport equation-based closures of turbulent scalar flux have been modified in such a manner that these models provide satisfactory prediction both near to and away from the wall.     

Conditional dissipation of scalars in homogeneous turbulence: Closure for MMC modelling

While the mean and unconditional variance are to be predicted well by any reasonable turbulent combustion model, these are generally not sufficient for the accurate modelling of complex phenomena such as extinction/reignition. An additional criterion has been recently introduced: accurate modelling of the dissipation timescales associated with fluctuations of scalars about their conditional mean (conditional dissipation timescales). Analysis of Direct Numerical Simulation (DNS) results for a passive scalar shows that the conditional dissipation timescale is of the order of the integral timescale and smaller than the unconditional dissipation timescale. A model is proposed: the conditional dissipation timescale is proportional to the integral timescale. This model is used in Multiple Mapping Conditioning (MMC) modelling for a passive scalar case and a reactive scalar case, comparing to DNS results for both. The results show that this model improves the accuracy of MMC predictions so as to match the DNS results more closely using a relatively-coarse spatial resolution compared to other turbulent combustion models.     

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.     

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)     

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.     

PDF方法模拟钝体驻定的湍流扩散火焰

采用标量联合的概率密度函数方法,对钝体驻定的湍流射流扩散Sydney火焰HM1进行数值模拟,结合当地自适应建表方法加速化学反应计算,用修正的LRR-IP雷诺应力模型求解速度场.首次对3种不同规模的甲烷化学反应动力学机理进行研究,并与实验数据进行比较,结果表明,模型和反应机理很好地预测了速度场和标量场的变化及局部熄火现象,而考虑反应机理中的C2化学对火焰HM1的影响不大.     

Unsteady effects on flame extinction limits during gaseous and two-phase flame/vortex interactions

In highly fluctuating flows, it happens that high values of the strain-rate do not induce extinction of the flame front. Unsteady effects minimize the flame response to rapidly varying strain fields. In the present study, the effects of time-dependent flows on non-premixed flames are investigated during flame/vortex interactions. Gaseous flames and spray flames in the external sheath combustion regime are considered. To analyse the flame/vortex interaction process, the velocity field and the flame geometry are simultaneously determined using particle imaging velocimetry and laser-induced fluorescence of the CH radical. The influence of vortex flows on the extinction limits for different vortex parameters and for different gaseous and two-phase flames is examined. If the external perturbation is applied over an extended period of time, the extinction strain-rate is that corresponding to the steady-state flame, and this critical value mainly depends on the fuel and oxidizer compositions and the injection temperature. If the external perturbation is applied during a short period of time, extinction occurs at strain-rates above the steady-state extinction strain-rate. This deviation appears for flow fluctuation timescales below steady flame diffusion timescales. This behaviour is induced by diffusive processes, limiting the ability of the flame to respond to highly fluctuating flows. With respect to unsteady effects, the spray flames investigated in this article behave essentially like gaseous flames, because evaporation takes place in a thin layer before the flame front. Extinction limits are only slightly modified by the spray, controlling process being the competition between aerodynamic and diffusive timescales.     

A numerical study of reignition induced by a diffusion flame

We present a numerical study of the reignition of a cold reactant mixture by the interaction with a nearby diffusion flame. This reignition mechanism may be an important process in turbulent non-premixed flames at high rates of strain where quenched sections of the stoichiometric surface are folded by the turbulent flow and come in close proximity with other burning flame sections. We consider an idealized one-dimensional setup containing the fundamental ingredients that are expected to contribute to this reignition mode. One- and two-step irreversible chemical mechanisms with heat release levels typical of practical hydrocarbon fuels are considered. It is observed that a slow moving reignition kernel originates on the high-temperature region of the burning flame in the one-step chemistry case owing to small leakage of oxidizer from the cold-mixture side. This kernel gradually moves, increasing the local temperature above that provided by diffusion and eventually leads to thermal runaway with the formation of a deflagration wave. The reignition time depends on the chemistry details, the Damköhler number, but in any case it cannot exceed the mixing time. This implies that the flame-induced reignition time is essentially bounded from above by mixing. Unless one of the free streams is hotter, in which case auto-ignition (as opposed to reignition) may proceed first, the reignition time is chemistry dependent. In the case of two-step chemistry, the reignition pathway is different initially owing to leakage of the radical species, but it approaches that of the one-step chemistry case shortly thereafter. It is observed that the only difference between the two cases is in the initial phase of the evolution of the reignition kernel. This phase appears to be very sensitive to the chemistry details, a general aspect of ignition. A parametric study is carried out to elucidate the effect of each non-dimensional quantity on the reignition time for the one-step chemistry case.     

Kinetics and extinction of non-premixed cool and warm flames of dimethyl ether at elevated pressure

The growing demand of clean and efficient propulsion and energy systems has sparked an interest in understanding low-temperature combustion at high pressure. Cool flame transition and extinction limits as well as oxygen concentration dependence at elevated pressures provide insights of the low-temperature and high-pressure fuel reactivity. A new experimental high-pressure counterflow burner platform was designed and developed to achieve the studies of high-pressure cool flames. Dimethyl ether (DME) was chosen to study its non-premixed cool flame in high-pressure counterflow burner at pressure up to 5 atm, perhaps for the first time. This paper investigates the effects of pressure on cool flame structure, extinction and transition limits, and oxygen concentration dependence as well as ozone assisted warm flames of DME in experiments and numerical simulations. The results show that the reignition transition from cool flame to hot flame occurs either with the decrease of the strain rate at a given fuel concentration and pressure or with the increase of fuel mole fraction or pressure at a given strain rate. Furthermore, it is shown that the higher pressure shifts the cool flame to higher strain rates and results in higher cool flame extinction strain rates. However, the existing kinetic model of DME fails in predicting the cool flame extinction limit at elevated pressures. Besides, the cool flame extinction limits are proportional to nth power of the oxygen concentration, [O₂]ⁿ, and the increase of pressure leads to stronger extinction limit dependence (larger n) on oxygen concentration. The present experiment and detailed kinetic analysis show clearly that increasing pressure promotes the low-temperature chemistry including the oxygen addition reactions. In addition, stable warm flame was first experimentally observed by using DME at elevated pressure with ozone sensitization.     

湍流扩散火焰局部熄火和再燃现象的PDF模拟

对一个值班湍流CH4／O2／N2射流扩散火焰(Sandia Flame D)进行了数值模拟研究．所采用的数学物理模型包括双尺度的k—ε湍流模型，标量联合的概率密度函数(PDF)输运方程方法，甲烷氧化的ARM简化化学反应机理(包含16种组分，12步总包反应)和欧几里德最小生成树(EMST)小尺度混合模型．将计算结果和实验数据进行了比较，不仅对于平均量，对于标量的散点分布和条件概率密度分布也是如此．计算结果表明文中采用的模型不仅能够预测宏观的火焰结构，而且预测了湍流燃烧中复杂的局部熄火和再燃过程．     

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.     

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.     

Paradigms in turbulent combustion research

The development of the basic conceptual viewpoints, or paradigms, for turbulent combustion in gases over the last 50 years is reviewed. Significant progress has been made. Recent successes in the prediction of pollutant species and extinction/re-ignition phenomena in non-premixed flames are seen as the result of close interaction between experimentalists, theoreticians, and modellers. Premixed turbulent flames seem to be dependent on a much wider range of factors, and predictive capabilities are not so advanced. Implications for large eddy simulation (LES) and partially premixed combustion are outlined.     

Influence of advective heat flux on extinction scalar dissipation rate and velocity in negative edge flames

A counterflow flame geometry, which has previously been experimentally shown to produce stable negative edge flames, was studied using numerical simulations. In this geometry, the flame edge is formed off the counterflow centreline owing to a local increase in scalar dissipation rate. Hot products from the stable nonpremixed flame on the centreline flow through the edge at velocities of ～ 1–5 m/s. The size of the counterflow burner and the gas flowrates are varied in the simulations to alter the flame strength and velocity at the flame edge. The advection of products through the edge is shown to extend the flame extinction to higher scalar dissipation rates than required for centreline extinction. For high velocities, the scalar dissipation rate required for flame extinction can be related to the centreline extinction value by considering only the effect of energy addition to the flame edge via advection. However, for lower edge flame velocities, the effects of increased thermal and species diffusion through the edge must also be included. Since the advection at the edge is a product of both the local velocity and temperature gradient, a single correlation between the scalar dissipation rate and the negative edge flame velocity does not exist.     

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.     

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.     

Stationary combustion regimes and extinction limits of one-dimensional stretched premixed flames in a gap between two heat conducting plates

Stationary combustion regimes, their linear stability and extinction limits of stretched premixed flames in a narrow gap between two heat conducting plates are studied by means of numerical simulations in the framework of one-dimensional thermal-diffusion model with overall one-step reaction. Various stationary combustion modes including normal flame (NF), near-stagnation plane flame (NSF), weak flame (WF) and distant flame (DF) are detected and found to be analogous to the same-named regimes of conventional counterflow flames. For the flames stabilized in the vicinity of stagnation plane at moderate and large stretch rates (which are NF, NSF and WF) the effect of channel walls is basically reduced to additional heat loss. For distant flame characterized by large flame separation distance and small stretch rates intensive interphase heat transfer and heat recirculation are typical. It is shown that in mixture content / stretch rate plane the extinction limit curve has ε-shape, while for conventional counterflow flames it is known to be C-shaped. This result is quite in line with recent experimental findings and is explained by extension of extinction limits at small stretch rates at the expense of heat recirculation. Analysis of the numerical results makes possible to reveal prime mechanisms of flame quenching on different branches of ε-shaped extinction limit curve. Namely, two upper limits are caused by stretch and heat loss. These limits are direct analogs of the upper and lower limits on conventional C-shaped curve. Two other limits are related with weakening of heat recirculation and heat dissipation to the burner. Thus, the present study provides a satisfactory explanation for the recent experimental observations of stretched flames in narrow channel.     

Problems of predicting turbulent burning rates

Different approaches to the modelling of turbulent combustion first are reviewed briefly. A unified, stretched flamelet approach then is presented. With Reynolds stress modelling and a generalized probability density function (PDF) of strain rate, it enables a source term, in the form of a probability of burning function, P_b, to be expressed as a function of Markstein numbers and the Karlovitz stretch factor. When P_b is combined with some turbulent flame fractal considerations, an expression is obtained for the turbulent burning velocity. When it is combined with the profile of the unstretched laminar flame volumetric heat release rate plotted against the reaction progress variable and the PDF of the latter, an expression is obtained for the mean volumetric turbulent heat release rate. Through these relationships experimental values of turbulent burning velocity might be used to evaluate P_b and hence the CFD source term, the mean volumetric heat release rate.

Different theoretical expressions for the turbulent burning velocity, including the present one, are compared with experimental measurements. The differences between these are discussed and this is followed by a review of CFD applications of these flamelet concepts to premixed and non-premixed combustion. The various assumptions made in the course of the analyses are scrutinized in the light of recent direct numerical simulations of turbulent flames and the applications to the flames of laser diagnostics. Remaining problem areas include a sufficiently general combination of strain rate and flame curvature PDFs to give a single PDF of flame stretch rate, the nature of flame quenching under positive and negative stretch rates, flame responses to changing stretch rates and the effects of flame instabilities.