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.     

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.     

Capturing multi-regime combustion in turbulent flames with a virtual chemistry approach

Multiple flame regimes are encountered in industrial combustion chambers, where premixed, stratified and non-premixed flame regions may coexist. To obtain a predictive tool for pollutant formation predictions, chemical flame modeling must take into account the influence of such complex flame structure. The objective of this article is to apply and compare two reduced chemistry models on both laminar and turbulent multi-regime flame configurations in order to analyze their capabilities in predicting flame structure and CO formation. The challenged approaches are (i) a premixed flamelet-based tabulated chemistry method, whose thermochemical variables are parameterized by a mixture fraction and a progress variable, and (ii) a virtual chemical scheme which has been optimized to retrieve the properties of canonical premixed and non-premixed 1-D laminar flames. The methods are first applied to compute a series of laminar partially-premixed methane-air counterflow flames. Results are compared to detailed chemistry simulations. Both approaches reproduced the thermal flame structure but only the virtual chemistry captures the CO formation in all ranges of equivalence ratio from stoichiometry premixed flame to pure non-premixed flame. Finally, the two chemical models combined with the Thickened Flame model for LES are challenged on a piloted turbulent jet flame with inhomogeneous inlet, the Sydney inhomogeneous burner. Mean and RMS of temperature and CO mass fraction radial profiles are compared to available experimental data. Scatter data in mixture fraction space and Wasserstein metric of numerical and experimental data are also studied. The analyses confirm again that the virtual chemistry approach is able to account for the impact of multi-regime turbulent combustion on the CO formation.     

Effects of Lewis number,density ratio and gravity on burning velocity and conditional statistics in stagnating turbulent premixed flames

DNS is performed to analyse the effects of Lewis number (Le), density ratio and gravity in stagnating turbulent premixed flames. The results show good agreement with those of Lee and Huh (Combustion and Flame, Vol. 159, 2012, pp. 1576–1591) with respect to the turbulent burning velocity, S_T, in terms of turbulent diffusivity, flamelet thickness, mean curvature and displacement speed at the leading edge. In all four stagnating flames studied, a mean tangential strain rate resulting in a mean flamelet thickness smaller than the unstretched laminar flame thickness leads to an increase in S_T. A flame cusp of positive curvature involves a superadiabatic burned gas temperature due to diffusive–thermal instability for an Le less than unity. Wrinkling tends to be suppressed at a larger density ratio, not enhanced by hydrodynamic instability, in the stagnating flow configuration. Turbulence is produced, resulting in highly anisotropic turbulence with heavier unburned gas accelerating through a flame brush by Rayleigh–Taylor instability. Results are also provided on brush thickness, flame surface density and conditional velocities in burned and unburned gas and on flame surfaces to represent the internal brush structures for all four test flames.     

How fast can we burn, 2.0

We review the state of the art in measurements and simulations of the behavior of premixed laminar and turbulent flames, subject to differential diffusion, stretch and curvature. The first part of the paper reviews the behavior of premixed laminar flames subject to flow stretch, and how it affects the accuracy of measurements of unstrained laminar flame speeds in stretched and spherically propagating flames. We then examine how flow field stretch and differential diffusion interact with flame propagation, promoting or suppressing the onset of thermodiffusive instabilities. Secondly, we survey the methodology for and results of measurements of turbulent flame speeds in the light of theory, and identify issues of consistency in the definition of mean flame speeds, and their corresponding mean areas. Data for methane at a single operating condition are compared for a range of turbulent conditions, showing that fundamental issues that have yet to be resolved for Bunsen and spherically propagating flames. Finally, we consider how the laminar flame scale response of flames to flow perturbations interacting with differential diffusion leads to very different outcomes to the overall sensitivity of the burning rate to turbulence, according to numerical simulations (DNS). The paper concludes with opportunities for future measurements and model development, including the perennial recommendation for robust archival databases of experimental and DNS results for future testing of models.     

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.     

Nonlinear hydrodynamic and thermoacoustic oscillations of a bluff-body stabilised turbulent premixed flame

Turbulent premixed flames often experience thermoacoustic instabilities when the combustion heat release rate is in phase with acoustic pressure fluctuations. Linear methods often assume a priori that oscillations are periodic and occur at a dominant frequency with a fixed amplitude. Such assumptions are not made when using nonlinear analysis. When an oscillation is fully saturated, nonlinear analysis can serve as a useful avenue to reveal flame behaviour far more elaborate than period-one limit cycles, including quasi-periodicity and chaos in hydrodynamically or thermoacoustically self-excited system. In this paper, the behaviour of a bluff-body stabilised turbulent premixed propane/air flame in a model jet-engine afterburner configuration is investigated using computational fluid dynamics. For the frequencies of interest in this investigation, an unsteady Reynolds-averaged Navier–Stokes approach is found to be appropriate. Combustion is represented using a modified laminar flamelet approach with an algebraic closure for the flame surface density. The results are validated by comparison with existing experimental data and with large eddy simulation, and the observed self-excited oscillations in pressure and heat release are studied using methods derived from dynamical systems theory. A systematic analysis is carried out by increasing the equivalence ratio of the reactant stream supplied to the premixed flame. A strong variation in the global flame structure is observed. The flame exhibits a self-excited hydrodynamic oscillation at low equivalence ratios, becomes steady as the equivalence ratio is increased to intermediate values, and again exhibits a self-excited thermoacoustic oscillation at higher equivalence ratios. Rich nonlinear behaviour is observed and the investigation demonstrates that turbulent premixed flames can exhibit complex dynamical behaviour including quasiperiodicity, limit cycles and period-two limit cycles due to the interactions of various physical mechanisms. This has implications in selecting the operating conditions for such flames and for devising proper control strategies for the avoidance of thermoacoustic instability.     

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.     

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.     

Turbulent flame speed and morphology of pure ammonia flames and blends with methane or hydrogen

Ammonia appears a promising hydrogen-energy carrier as well as a carbon-free fuel. However, there remain limited studies for ammonia combustion especially under turbulent conditions. To that end, using the spherically expanding flame configuration, the turbulent flame speeds of stoichiometric ammonia/air, ammonia/methane and ammonia/hydrogen were examined. The composition of blends studied are currently being investigated for gas turbine application and are evaluated at various turbulent intensities, covering different kinds of turbulent combustion regimes. Mie-scattering tomography was employed facilitating flame structure analysis. Results show that the flame propagation speed of ammonia/air increases exponentially with increasing hydrogen amount. It is less pronounced with increasing methane addition, analogous to the behavior displayed in the laminar regime. The turbulent to laminar flame speed ratio increases with turbulence intensity. However, smallest gains were observed at highest hydrogen content, presumably due to differences in the combustion regime, with the mixture located within the corrugated flamelet zone, with all other mixtures positioned within the thin reaction zone. A good correlation of the turbulent velocity based on the Karlovitz and Damköhler numbers is observable with the present dataset, as well as previous experimental measurements available in literature, suggesting that ammonia-based fuels may potentially be described following the usual turbulent combustion models. Flame morphology and stretch sensitivity analysis were conducted, revealing that flame curvature remains relatively similar for pure ammonia and ammonia-based mixtures. The wrinkling ratio is found to increase with both increasing ammonia fraction and turbulent intensity, in good agreement with measured increases in turbulent flame speed. On the other hand, in most cases, the flame stretch effect does not change significantly with increasing turbulence, whilst following a similar trend to that of the laminar Markstein length.     

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.     

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.     

Thermal and chemical effects of differential diffusion in turbulent non-premixed H2 flames

As a renewable fuel, hydrogen (H₂) may play an increasingly important role in the development and control of piston and gas turbine engines to achieve zero carbon emissions. Predictive modeling of H₂-fueled combustion processes requires a clear understanding of differential diffusion (DD) due to the high diffusivity of H₂. On the assumption that turbulent mixing is a far more dominant process than molecular mixing, DD effects are typically neglected in turbulent combustion simulations to reduce modeling complications. While this assumption is reasonable for hydrocarbon fuels, it is less valid for H₂ combustion, where DD is significant. In this work, two three-dimensional direct numerical simulations of temporally evolving turbulent H₂ jet flames with and without considering DD are performed and compared with laminar flamelet solutions to assess DD effects under turbulent conditions. The emphasis is placed on assessing the suitability of classical mixture fraction Z and Bilger mixture fraction Z_Bilger as conditioning variables for non-premixed turbulent combustion modeling through analyzing DD effects on flame structure, chemical reactions, and tangential diffusion (TD). Furthermore, the persistence of DD effects under turbulent conditions and the suitability of a conventional DD parameter are investigated by comparing the turbulent flames to laminar flamelet solutions. It is found that conditioning the thermochemical state on Z_Bilger helps to capture DD effects and mitigate the relative contribution of TD, which gives Z_Bilger advantages over Z when employing flamelet modeling. Due to close coupling between DD and local chemical reactions, DD can affect the turbulent/laminar flames in the form of thermal effects due to the change in flame temperature, chemical effects due to the change in chemical reactions, and transport effects due to multiple species with varying diffusivities that could result in the difference between Z and Z_Bilger. While the transport effects are suppressed, significant chemical and thermal effects of DD still persist under turbulent conditions, which indicates that the DD parameter is probably unsuitable for comprehensively characterizing and assessing DD effects on the structure of turbulent non-premixed flames.     

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.     

Modelling compression ignition engines by incorporation of the flamelet generated manifolds combustion closure

Tabulated chemistry models allow to include detailed chemistry effects at low cost in numerical simulations of reactive flows. Characteristics of the reactive fluid flows are described by a reduced set of parameters that are representative of the flame structure at small scales so-called flamelets. For a specific turbulent combustion configuration, flamelet combustion closure, with proper formulation of the flame structure can be applied. In this study, flamelet generated manifolds (FGM) combustion closure with progress variable approach were incorporated with OpenFOAM® source code to model combustion within compression ignition engines. For IC engine applications, multi-dimensional flamelet look-up tables for counter flow diffusive flame configuration were generated. Source terms of non-premixed combustion configuration in flamelet domain were tabulated based on pressure, temperature of unburned mixture, mixture fraction, and progress variable. A new frozen flamelet method was introduced to link one dimensional reaction diffusion space to multi-dimensional Computational Fluid Dynamics (CFD) physical space to fulfill correct modelling of thermal state of the engine at expansion stroke when charge composition was changed after combustion and reaction rates were subsided. Predictability of the developed numerical framework were evaluated for Sandia Spray A (constant volume vessel), Spray B (light duty optical Diesel engine), and a heavy duty Diesel engine experiments under Reynolds averaged Navier Stokes turbulence formulation. Results showed that application of multi-dimensional FGM combustion closure can comprehensively predict key parameters such as: ignition delay, in-cylinder pressure, apparent heat release rate, flame lift-off , and flame structure in Diesel engines.     

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.     

Transient interactions between a premixed double flame and a vortex

The interaction between a laminar flame and a vortex is an important study for understanding the fundamentals of turbulent combustion. In the past, however, flame-vortex interactions have been investigated only for high-temperature flames. In this study, the impact of a vortex on a premixed double flame, which consists of a coupled cool flame and a hot flame, is examined experimentally and computationally using dimethyl ether/oxygen/ozone mixtures. The double flame is first shown to occur near the extinction limit of the hot flame. The differences between steady-state cool flames, double flames, and hot flames are explored in a one-dimensional counterflow configuration. The transient interactions between double flames and impinging vortices are then investigated experimentally using a micro-jet and numerically in two-dimensional transient modeling. It is seen that the vortex can extinguish the near-limit hot flame locally, resulting in a lone cool flame. At higher vortex intensities, the cool flame may also be extinguished after the extinction of the hot flame. It is found that there can be three different transient flame structures coexisting at the same time: an extinguished flame hole, a cool flame, and a double flame. Moreover, flame curvature is shown to play an important role in determining whether the vortex weakens or strengthens the cool flame and double flame.     

Experimental measurements of geometric properties of turbulent stratified flames

Combustion under stratified conditions is common in many systems. However, relatively little is known about the structure and dynamics of turbulent stratified flames. Two-dimensional imaging diagnostics are applied to premixed and stratified V-flames at a mean equivalence ratio of 0.77, and low turbulent intensity, within the corrugated flame range. The present results show that stratification affects the mean turbulent flame speed, structure and geometric properties. Stratification increases the flame surface density above the premixed flame levels in all cases, with a maximum reached at intermediate levels of stratification. The flame surface density (FSD) of stratified flames is higher than that of premixed flames at the same mean equivalence ratio. Under the present conditions, the FSD peaks at a stratification ratio around 3.0. The FSD curves for stratified flames are further skewed towards the product side. The distribution of flame curvature in stratified flames is broader and more symmetric relative to premixed flames, indicating an additional mechanism of curvature generation, which is not necessarily due to cusping. These experiments indicate that flame stratification affects the intrinsic behaviour of turbulent flames and suggest that models may need to be revised in the light of the current evidence.