A flamelet analysis of the burning velocity of premixed turbulent expanding flames

Direct numerical simulation is a very powerful tool to evaluate the validity of new models and theories for turbulent combustion. In this paper, direct numerical simulations of spherically expanding premixed turbulent flames in the corrugated flamelet regime are performed. The flamelet-generated manifold method is used to deal with detailed reaction kinetics. The numerical method is validated for both laminar and turbulent expanding flames. The computational results are analyzed by using an extended flame stretch theory. It is investigated whether this theory is able to describe the influence of flame stretch and curvature on the local burning velocity of the flame. If the full profiles of flame stretch and curvature through the flame front are included in the theory, the local mass burning rate is predicted accurately. The influence of several approximations, which are used in other existing theories, is studied. When flame stretch is assumed to be constant through the flame front or when curvature of the flame front is neglected, the theory fails to predict the local mass burning rate.     

湍流分层燃烧的直接数值模拟和小火焰模型研究

湍流分层燃烧广泛应用于工业燃烧装置,但是目前还比较缺乏适用于湍流分层燃烧的高精度数值模型。本文利用直接数值模拟数据库,对高Karlovitz数分层射流火焰的小火焰模型表现进行了先验性评估。考虑了两种小火焰模型,一种是基于自由传播层流预混火焰的小火焰模型M1,另一种是基于分层对冲小火焰的小火焰模型M2。研究发现M1和M2在c-Z空间的结果与直接数值模拟在定性上是一致的。在物理空间,M2对过程变量反应速率脉动值的预测结果要优于M1.     

Effects of compression and stretch on the determination of laminar flame speeds using propagating spherical flames

The effects of flow compression and flame stretch on the accurate determination of laminar flame speeds at normal and elevated pressures using propagating spherical flames at constant pressure or constant volume are studied theoretically and numerically. The results show that both the compression-induced flow motion and flame stretch have significant impacts on the accuracy of flame speed determination. For the constant pressure method, a new method to obtain a compression-corrected flame speed (CCFS) for nearly constant pressure spherical bomb experiments is presented. Likewise, for the constant volume method, a technique to obtain a stretch-corrected flame speed (SCFS) at elevated pressures and temperatures is developed. The validity of theoretical results for both constant pressure and constant volume methods is demonstrated by numerical simulations using detailed chemistry for hydrogen/air, methane/air, and propane/air mixtures. It is shown that the present CCFS and SCFS methods not only improve the accuracy of the flame speed measurements significantly but also extend the parameter range of experimental conditions. The results can be used directly in experimental measurements of laminar flame speeds.     

Modelling of turbulent scalar flux in turbulent premixed flames based on DNS databases

A transport equation for scalar flux in turbulent premixed flames was modelled on the basis of DNS databases. Fully developed turbulent premixed flames were obtained for three different density ratios of flames with a single-step irreversible reaction, while the turbulent intensity was comparable to the laminar burning velocity. These DNS databases showed that the countergradient diffusion was dominant in the flame region. Analyses of the Favre-averaged transport equation for turbulent scalar flux proved that the pressure related terms and the velocity–reaction rate correlation term played important roles on the countergradient diffusion, while the mean velocity gradient term, the mean progress variable gradient term and dissipation terms suppressed it. Based on these analyses, modelling of the combustion-related terms was discussed. The mean pressure gradient term and the fluctuating pressure term were modelled by scaling, and these models were in good agreement with DNS databases. The dissipation terms and the velocity–reaction rate correlation term were also modelled, and these models mimicked DNS well.     

Evaluation of models for flame stretch due to curvature in the thin reaction zones regime

Direct numerical simulation (DNS) was used to study modelling assumptions for the curvature-propagation component of flame stretch in the thin reaction zones regime of turbulent premixed combustion, a regime in which small eddies can penetrate the preheat zone but not the thinner fuel breakdown zone. Simulations of lean hydrogen–air and methane–air flames were conducted, and statistics of flame stretch due to curvature, henceforth referred to simply as stretch, were extracted from a species mass fraction iso-surface taken to represent the flame. The study focussed on investigating the modelling assumptions of Peters [J. Fluid Mech. 384 (1999) 107]. It was found that the mean stretch is dominated by stretch due to correlations of flame speed with curvature, and specifically the effects of tangential diffusion. The modelling suggestions of Peters were found to provide an improvement over the assumptions of a constant flame speed or a flame speed governed by the linear relationship with stretch at small and steady stretch. However for the conditions considered here, diffusive-thermal effects remain well into the thin reaction zones regime, and the suggestions of Peters generally over-predict the mean compressive stretch. An effective diffusivity for flame stretch was suggested and evaluated for the methane simulations. It was found that the effective diffusivity was comparable to the mass diffusivity for flames with a high ratio of flame time to eddy turnover time. The length scales contributing to stretch were investigated, and it was found that while most flame area has a radius of curvature greater than the laminar flame thickness, most stretch occurs in more tightly curved flame elements.     

Evolution and scaling of the peak flame surface density in spherical turbulent premixed flames subjected to decaying isotropic turbulence

The peak flame surface density within the turbulent flame brush is central to turbulent premixed combustion models in the flamelet regime. This work investigates the evolution of the peak surface density in spherically expanding turbulent premixed flames with the help of direct numerical simulations at various values of the Reynolds and Karlovitz number. The flames propagate in decaying isotropic turbulence inside a closed vessel. The effects of turbulent transport, transport due to mean velocity gradient, and flame stretch on the peak surface density are identified and characterized with an analysis based on the transport equation for the flame surface density function. The three mechanisms are governed by distinct flow time scales; turbulent transport by the eddy turnover time, mean transport by a time scale related to the pressure rise in the closed chamber, and flame stretch by the Kolmogorov time scale. Appropriate scaling of the terms is proposed and shown to collapse the data despite variations in the dimensionless groups. Overall, the transport terms lead to a reduction in the peak value of the surface density, while flame stretch has the opposite effect. In the present configuration, a small imbalance between the two leads to an exponential decay of the peak surface density in time. The dimensionless decay rate is found to be consistent with the evolution of the wrinkling scale as defined in the Bray-Moss-Libby model.     

Premixed flames for arbitrary combinations of strain and curvature

Many modeling strategies for combustion rely on laminar flamelet concepts to determine structure and properties of multi-dimensional and turbulent flames. Using flamelet tabulation strategies, the user anticipates certain aspects of the combustion process prior to the simulation and selects a flamelet model which mimics local flame conditions in the more complex configuration. Flame stretch, which can be decomposed into contributions from strain and curvature, is one of the conditions influencing a flame’s properties, structure, and stability. The objective of this work is to study premixed flame structures in the strain-curvature space using a recently published composition space model (CSM) and three physical space models for canonical flame configurations (stagnation flame, spherical expanding flame and inwardly propagating flame). Flames with effective Lewis numbers both smaller and larger than unity are considered. For canonical laminar flames, the stretch components are inherently determined through boundary conditions and their specific flame configuration. Therefore, canonical flames can only represent a certain sub-set of stretch effects experienced by multi-dimensional and turbulent flames. On the contrary, the CSM allows arbitrary combinations of strain and curvature to be prescribed for premixed flames exceeding the conditions attainable with the canonical flame setups. Thereby, also influences of negative strain effects and large curvatures can be studied. A parameter variation with the CSM shows that flame structures still significantly change outside the region of the canonical flame configurations. Furthermore, limits in the strain-curvature space are discussed. The present paper highlights advantages of composition space modeling which is achieved by detaching the representation of the flame structure from a specific canonical flame configuration in physical space.     

Strain rates,flow patterns and flame surface densities in hydrodynamically unstable,weakly turbulent premixed flames

Recent numerical and experimental studies have unveiled a potentially marked difference between the laminar as well as turbulent propagation of premixed flames exhibiting Darrieus–Landau (DL) (or hydrodynamic) instabilities from flames for which instabilities are inhibited. In this study we utilize two-dimensional numerical simulations of slot burner flames as well as experimental Propane–Air Bunsen flames to analyse differences in turbulent propagation, strain rate and induced flow patterns of hydrodynamically stable and unstable flames. We also investigate the effects of hydrodynamic instability on quantities which are directly related to reaction rate closure models, such as flame surface density and stretch factor. A clear enhancement of turbulent flame speed can be observed for unstable flames, generally mitigated at higher turbulence intensity, which is attributed to a flame area increase induced by the characteristic cusp-like DL-induced corrugation, absent in stable flames, which occurs concurrently and in synergy with turbulent wrinkling. Unstable flames also exhibit, both numerically and experimentally, a different correlation between strain rate and flame curvature and are observed to give rise to a channeling of the induced flow in the fresh mixture. Conditionally averaged flame surface density is also observed to attain smaller values in unstable flames, as a result of the thicker turbulent flame brush, indicating that closure models should incorporate instability-related parameters in addition to turbulence-related parameters.     

An apparatus-independent extinction strain rate in counterflow flames

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

Spontaneous transition of turbulent flames to detonations in unconfined media

A deflagration-to-detonation transition (DDT) can occur in environments ranging from experimental and industrial systems to astrophysical thermonuclear (type Ia) supernovae explosions. Substantial progress has been made in explaining the nature of DDT in confined systems with walls, internal obstacles, or preexisting shocks. It remains unclear, however, whether DDT can occur in unconfined media. Here we use direct numerical simulations (DNS) to show that for high enough turbulent intensities unconfined, subsonic, premixed, turbulent flames are inherently unstable to DDT. The associated mechanism, based on the nonsteady evolution of flames faster than the Chapman-Jouguet deflagrations, is qualitatively different from the traditionally suggested spontaneous reaction-wave model. Critical turbulent flame speeds, predicted by this mechanism for the onset of DDT, are in agreement with DNS results.     

A LES-CMC formulation for premixed flames including differential diffusion

A finite volume large eddy simulation–conditional moment closure (LES-CMC) numerical framework for premixed combustion developed in a previous studyhas been extended to account for differential diffusion. The non-unity Lewis number CMC transport equation has an additional convective term in sample space proportional to the conditional diffusion of the progress variable, that in turn accounts for diffusion normal to the flame front and curvature-induced effects. Planar laminar simulations are first performed using a spatially homogeneous non-unity Lewis number CMC formulation and validated against physical-space fully resolved reference solutions. The same CMC formulation is subsequently used to numerically investigate the effects of curvature for laminar flames having different effective Lewis numbers: a lean methane–air flame with Le_eff = 0.99 and a lean hydrogen–air flame with Le_eff = 0.33. Results suggest that curvature does not affect the conditional heat release if the effective Lewis number tends to unity, so that curvature-induced transport may be neglected. Finally, the effect of turbulence on the flame structure is qualitatively analysed using LES-CMC simulations with and without differential diffusion for a turbulent premixed bluff body methane–air flame exhibiting local extinction behaviour. Overall, both the unity and the non-unity computations predict the characteristic M-shaped flame observed experimentally, although some minor differences are identified. The findings suggest that for the high Karlovitz number (from 1 to 10) flame considered, turbulent mixing within the flame weakens the differential transport contribution by reducing the conditional scalar dissipation rate and accordingly the conditional diffusion of the progress variable.     

Direct numerical simulations of rich premixed turbulent n-dodecane/air flames at diesel engine conditions

Rich premixed turbulent n-dodecane/air flames at diesel engine conditions are analyzed using direct numerical simulations. The conditions correspond to a parametric variation of the Engine Combustion Network Spray A (pressure 60 atm; oxidizer oxygen level and temperature 21% and 900 K, respectively; fuel temperature 363 K). Three simulations with equivalence ratios of 3, 5, and 7 are performed with a Karlovitz number (Ka, based on flame time) of order 100 to match the estimated Ka of the rich premixed combustion region in Spray A. At these conditions, the reference laminar flames exhibit a complex structure which involves both low-temperature chemistry (LTC) and high-temperature chemistry over a wide range of length scales. In the presence of turbulence, the flame structure is strongly affected in physical space and the reaction zone exhibits a very complex structure in which broken, distributed, and thin regions co-exist, especially for the leanest case. However, the contribution of the LTC pathway is only weakly affected by turbulence. In progress variable space, the mean flame structure, including the chemical source terms, is found to match remarkably well that of the corresponding unity Lewis number laminar flame, particularly for the $?=$ 3 and 5 cases. This behavior is attributed to the strong turbulent mixing occurring throughout the flames/reaction zones, which suppresses differential diffusion effects. Nevertheless, large conditional fluctuations around the mean chemical source terms are identified. These are found to correlate very well with radical species mass fractions such as OH. In addition, a similar functional dependence is obtained from counterflow laminar flames. As such, it appears from these results that laminar flame models have a potential to be used to represent the thermochemical state of rich premixed turbulent flames under diesel engine conditions.     

Stabilization, propagation and instability of tribrachial triple flames

A tribrachial (or triple) flame is one kind of edge flame that can be encountered in nonpremixed mixing layers, consisting of a lean and a rich premixed flame wing together with a trailing diffusion flame all extending from a single point. The flame could play an important role on the characteristics of various flame behaviors including lifted flames in jets, flame propagation in two-dimensional mixing layers, and autoignition fronts. The structure of tribrachial flame suggests that the edge is located along the stoichiometric contour in a mixing layer due to the coexistence of all three different types of flames. Since the edge has a premixed nature, it has unique propagation characteristics. In this review, the propagation speed of tribrachial flames will be discussed for flames propagating in mixing layers, including the effects of concentration gradient, velocity gradient, and burnt gas expansion. Based on the tribrachial edge structure observed experimentally in laminar lifted flames in jets, the flame stabilization characteristics including liftoff height, reattachment, and blowout behaviors and their buoyancy-induced instability will be explained. Various effects on liftoff heights in both free and coflow jets including jet velocity, the Schmidt number of fuel, nozzle diameter, partial premixing of air to fuel, and inert dilution to fuel are discussed. Implications of edge flames in the modeling of turbulent nonpremixed flames and the stabilization of turbulent lifted flames in jets are covered.     

Reaction zone structures and mixing characteristics of partially premixed swirling CH4/air flames in a gas turbine model combustor

The mixing, reaction progress, and flame front structures of partially premixed flames have been investigated in a gas turbine model combustor using different laser techniques comprising laser Doppler velocimetry for the characterization of the flow field, Raman scattering for simultaneous multi-species and temperature measurements, and planar laser-induced fluorescence of CH for the visualization of the reaction zones. Swirling CH₄/air flames with Re numbers between 7500 and 60,000 have been studied to identify the influence of the turbulent flow field on the thermochemical state of the flames and the structures of the CH layers. Turbulence intensities and length scales, as well as the classification of these flames in regime diagrams of turbulent combustion, are addressed. The results indicate that the flames exhibit more characteristics of a diffusion flame (with connected flame zones) than of a uniformly premixed flame.     

A physical relationship between consumption and displacement speed for premixed flames with finite thickness

The characterization of premixed flames by a flame speed has been a subject that has occupied much interest in the literature in many systematic studies on combustion phenomena. Consumption and displacement speeds are two such flame speeds that are understood to describe the flame dynamics under the effect of flame curvature, flow non-uniformities, Lewis number and turbulence effects along with heat transfer with flame holders and cold walls. As such, much work has been done in the past where either one of these two speeds has been employed along with a linear sensitivity coefficient (Markstein length) for describing different sensitivities to stretch effects. However, despite recent attempts using the asymptotic theory, the relationship between these two quantities has only been clarified in a limited manner for flames of finite thickness. In this study, we use flame stretch theory that takes into account changes of stretch, curvature, heat transfer and Lewis number effects throughout the pre-heat zone and its integral effect on the flame reaction zone. A sound mathematical and physical basis is provided for understanding the two speeds that is valid for weak as well as strong stretch effects. Understanding from theory is further demonstrated by analysing several example 1D stretched flames along with a 2D bluff body flame near extinction.     

Minimum ignition energy and propagation dynamics of laminar premixed cool flames

Laminar premixed cool flames, induced by the coupling of low-temperature chemistry and convective-diffusive transport process, have recently attracted extensive interest in combustion and engine research. In this work, numerical simulations have been conducted using a recently developed open-source reacting flow platform reactingFOAM-SCT, to investigate the minimum ignition energy (MIE) and propagation dynamics of premixed cool flames in a 1D spherical coordinate. Results have shown that when ignition energy is below the MIE of regular hot flames, a class of cool flames could be initiated, which allow much wider flammability limits, both lean and rich, compared to hot flames. Furthermore, the overall cool flame propagation dynamics exhibit intrinsic similarity to those of hot flames, in that, they begin with an ignition kernel propagation regime, followed by two transition regimes, and eventually reach a normal flame propagation regime. However, a spherical expanding cool flame responds completely differently to stretch. Specifically, a regular outwardly propagating hot spherical flame accelerates with increasing stretch rate when the mixture Le < 1 and decelerates when Le > 1. However, it is found that a cool flame always tends to decelerate with increasing stretch rate regardless of mixture composition, exhibiting unique flame aerodynamic characteristic. This research discovers novel features of premixed cool flame initiation and propagation dynamics and sheds light on flame transition, spark-ignition system design, and advanced engine combustion control.     

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.     

An assessment of large eddy simulations of premixed flames propagating past repeated obstacles

This paper presents an assessment of Large Eddy Simulations (LES) in calculating the structure of turbulent premixed flames propagating past solid obstacles. One objective of the present study is to evaluate the LES simulations and identify the drawbacks in accounting the chemical reaction rate. Another objective is to analyse the flame structure and to calculate flame speed, generated overpressure at different time intervals following ignition of a stoichiometric propane/air mixture. The combustion chamber has built-in repeated solid obstructions to enhance the turbulence level and hence increase the flame propagating speed. Various numerical tests have also been carried out to determine the regimes of combustion at different stages of the flame propagation. These have been identified from the calculated results for the flow and flame characteristic parameters. It is found that the flame lies within the ‘thin reaction zone’ regime which supports the use of the laminar flamelet approach for modelling turbulent premixed flames. A submodel to calculate the model coefficient in the algebraic flame surface density model is implemented and examined. It is found that the LES predictions are slightly improved owing to the calculation of model coefficient by using submodel. Results are presented and discussed in this paper are for the flame structure, position, speed, generated pressure and the regimes of combustion during all stages of flame propagation from ignition to venting. The calculated results are validated against available experimental data.