A Lagrangian-based flame index for the transported probability density function method

We propose a new flame index for the transported probability density function(PDF) method. The flame index uses mixing flux projections of Lagrangian particles on mixture fraction and progress variable directions as the metrics to identify the combustion mode, with the Burke-Schumann solution as a reference. A priori validation of the flame index is conducted with a series of constructed turbulent partially premixed reactors. It indicates that the proposed flame index is able to identify the combustion mode based on the subgrid mixing information. The flame index is then applied the large eddy simulation/PDF datasets of turbulent partially premixed jet flames. Results show that the flame index separate different combustion modes and extinction correctly. The proposed flame index provides a promising tool to analyze and model the partially premixed flames adaptively.     

Comparison of Differing Formulations of the PCM Model by their Application to the Simulation of an Auto-igniting H 2/air Jet

Different combustion models such as PCM (Presumed Conditional Moments) or ADF-PCM (Approximated Diffusion Flames Presumed Conditional Moments) can be used for RANS simulations of non premixed or partially premixed turbulent flames. In this paper, the auto-ignition experiment performed by Mastorakos and co-workers at Cambridge University is used as a validation case for comparing these two approaches. Furthermore, the first order PCM model is introduced to analyze the effects of the progress variable segregation and an improved version of ADF-PCM is developed with a pdf of the scalar dissipation rate. Compared to ADF-PCM models, the first and second order PCM models predict very sharp temperature and progress variable increase after ignition for all simulated cases. The segregation factors of the progress variable reach important values during the ignition for ADF-PCM models whereas for PCM, high values are reached at the beginning of the ignition.     

Conditional Source-Term Estimation as a Method for Chemical Closure in Premixed Turbulent Reacting Flow

A Conditional Source-term Estimation (CSE) model is used to close the mean reaction rates for a turbulent premixed flame. A product-based reaction progress variable is introduced as the conditioning variable for the CSE method. Different presumed probability density function (PDF) models are studied and a modified version of a laminar flame-based PDF model is proposed. Improved predictions of the variable distribution are obtained. The conditional means of reactive scalars are evaluated with CSE and compared to the direct numerical simulation (DNS). The mean reaction rates in a turbulent premixed flame are evaluated with the CSE model and the presumed PDFs. Comparison of the CSE closure method to DNS shows promising results. This paper was presented at the 2nd ECCOMAS Thematic Conference on Computational Combustion.     

Heat Transfer Modeling in the Context of Large Eddy Simulation of Premixed Combustion with Tabulated Chemistry

Tabulated chemistry models like the Flamelet Generated Manifolds method are a good approach to include detailed information on the reaction kinetics in a turbulent flame at reasonable computational costs. However, so far, not all information on e.g. heat losses are contained in these models. As those often appear in typical technical applications with enclosed flames in combustion chambers, extensions to the standard FGM approach will be presented in this paper, allowing for the representation of non-adiabatic boundaries. The enthalpy as additional control variable for the table access is introduced, such that the chemistry database becomes three-dimensional with mixture fraction, reaction progress variable and enthalpy describing the thermo-chemical state. The model presented here is first validated with a two-dimensional enclosed Bunsen flame and then applied within the Large Eddy Simulations of a turbulent premixed swirl flame with a water-cooled bluff body and a turbulent stratified flame, where additional modeling for the flame structure using artificially thickened flames was included. The results are encouraging, as the temperature decrease towards the bluff body in the swirl flame and the cooling of the pilot flame exhaust gases in the stratified configuration can be observed in both experiments and simulation.     

Coupling tabulated chemistry with Large Eddy Simulation of turbulent reactive flows

A new modeling strategy is developed to introduce tabulated chemistry methods in the LES of turbulent premixed combustion. The objective is to recover the correct laminar flame propagation speed of the filtered flame front when the subgrid scale turbulence vanishes. The filtered flame structure is mapped by 1D filtered laminar premixed flames. Closure of the filtered progress variable and the energy balance equations are carefully addressed. The methodology is applied to 1D and 2D filtered laminar flames. These computations show the capability of the model to recover the laminar flame speed and the correct chemical structure when the flame wrinkling is completely resolved. The model is then extended to turbulent combustion regimes by introducing subgrid scale wrinkling effects on the flame front propagation. Finally, the LES of a 3D turbulent premixed flame is performed. To cite this article: R. Vicquelin et al., C. R. Mecanique 337 (2009).     

Assessing the Predictive Capabilities of Combustion LES as Applied to the Sydney Flame Series

Large Eddy Simulation (LES) and flamelet-based combustion models were applied to four bluff-body stabilized nonpremixed and partially premixed flames selected from the Sydney flame series, based on Masri’s bluff-body test rig (University of Sydney). Three related non-reacting flow cases were also investigated to assess the performance of the LES solver. Both un-swirled and swirled cases were studied exhibiting different flow features, such as recirculation, jet precessing and vortex breakdown. Due to various fuel compositions, flow rates and swirl numbers, the combustion characteristics of the flames varied greatly. On six meshes with different blocking structure and mesh sizes, good prediction of flow and scalar fields using LES/flamelet approaches and known fuel and oxidizer mass fluxes was achieved. The accuracy of predictions was strongly influenced by the combustion model used. All flames were calculated using at least two modeling strategies. Starting with calculations of isothermal flow cases, simple single flamelet based calculations were carried out for the corresponding reacting cases. The combustion models were then adjusted to fit the requirements of each flame. For all flame calculations good agreement of the main flow features with the measured data was achieved. For purely nonpremixed flames burning attached to the bluff-body’s outer edge, flamelet modeling including strain rate effects provided good results for the flow field and for most scalars. The prediction of a partially premixed swirl flame could only be achieved by applying a flamelet-based progress variable approach.     

Study of a Filtered Flamelet Formulation for Large Eddy Simulation of Premixed Turbulent Flames

Despite significant advances in the understanding and modelling of turbulent combustion, no general model has been proposed for simulating flames in industrial combustion devices. Recently, the increase in computational possibilities has raised the hope of directly solving the large turbulent scales using large eddy simulation (LES) and capturing the important time-dependant phenomena. However, the chemical reactions involved in combustion occur at very small scales and the modelling of turbulent combustion processes is still required within the LES framework. In the present paper, a recently presented model for the LES of turbulent premixed flames is presented, analysed and discussed. The flamelet hypothesis is used to derive a filtered source term for the filtered progress variable equation. The model ensures proper flame propagation. The effect of subgrid scale (SGS) turbulence on the flame is modelled through the flame-wrinkling factor. The present modelling of the source term is successfully tested against filtered direct numerical simulation (DNS) data of a V-shape flame. Further, a premixed turbulent flame, stabilised behind an expansion, is simulated. The predictions agree well with the available experimental data, showing the capabilities of the model for performing accurate simulations of unsteady premixed flames.     

Large Eddy Simulation of Stratified and Sheared Flames of a Premixed Turbulent Stratified Flame Burner Using a Flamelet Model with Heat Loss

This paper presents large eddy simulations (LES) of the Darmstadt turbulent stratified flame burner (TSF) at different operating conditions including detailed heat loss modeling. The target cases are a non-reacting and two reacting cases. Both reacting cases are characterized by stratification, while one flame additionally features shear. In the regime diagram for premixed combustion, the studied flames are found at the border separating the thin reaction zones regime and the broken reaction zones regime. A coupled level set/progress variable model is utilized to describe the combustion process. To account for heat loss, an enthalpy defect approach is adopted and reformulated to include differential diffusion effects. A novel power-law rescaling methodology is proposed to integrate the enthalpy defect approach into the level set/progress variable model which is extensively validated in two validation scenarios. It is demonstrated that the LES with the newly developed model captures the influence of heat loss well and that the incorporation of heat loss effects improves the predictions of the TSF-burner over adiabatic simulations, while reproducing the experimentally observed flame lift-off from the pilot nozzle.     

Hybrid Transported-Tabulated Strategy to Downsize Detailed Chemistry for Numerical Simulation of Premixed Flames

A strategy to introduce hydrocarbon combustion detailed chemistry into three-dimensional numerical simulation of flames is reported. Significant progress has been made recently in terms of accuracy and robustness in both chemical kinetics and flow computations. However, the highest resolution reached in simulation of practical burner does not yet ensure that the response of intermediate radical species is fully captured. In the method discussed, the full set of species and elementary reaction rates of the detailed mechanism are retained, but only species featuring non-zero concentration in fresh and burnt gases are transported with the flow. Intermediate chemical species, developing within thin flame layers, are expressed resorting to their self-similar properties observed in a series of canonical combustion problems, projected into an optimized progress variable defined from all transported species. The method is tested with success in various adiabatic and non-adiabatic laminar steady- and unsteady-strained premixed flames.     

Large Eddy Simulation of Turbulent Premixed Swirling Flames Using Dynamic Thickened Flame with Tabulated Detailed Chemistry

A sub-grid scale (SGS) combustion model by combining dynamic thickened flame (DTF) with flamelet generated manifolds (FGM) tabulation approach (i.e. DTF-FGM) is developed for investigating turbulent premixed combustion. In contrast to the thickened flame model, the dynamic thickening factor of the DTF model is determined from the flame sensor, which is obtained from the normalized gradient of the reaction progress variable from the one-dimensional freely propagating premixed flame simulations. Therewith the DTF model can ensure that the thickening of the flame is limited to the regions where it is numerically necessary. To describe the thermo-chemistry states, large eddy simulation (LES) transport equations for two characteristic scalars (the mixture fraction and the reaction progress variable) and relevant sub-grid variances in the DTF-FGM model are presented. As to the evaluation of different SGS combustion models, another model by utilizing the combination of presumed probability density function (PPDF) and FGM (i.e. PPDF-FGM) is also described. LES of two cases with or without swirl in premixed regime of the Cambridge swirl burner flames are performed to evaluate the developed SGS combustion model. The predicted results are compared with the experimental data in terms of the influence of different LES grids, model sensitivities to the thickening factor, the wrinkling factor, and the PPDF of characteristic scalars, the evaluation of different modelling approaches for the sub-grid variances of characteristic scalars, and the predictive capability of different SGS combustion models. It is shown that the LES results with the DTF-FGM model are in reasonable agreement with the experimental data, and better than the results with the PPDF-FGM approach due to its ability to predict better in regions where flame is not resolved.     

A Two-Dimensional Tabulated Flamelet Combustion Model for Furnace Applications

A new tabulated chemistry approach for representing turbulent combustion in industrial furnaces is presented. This model is based on the tabulation of two dimensional diffusion flamelets to account for ternary mixtures between fuel, oxidant and burned gases which are integrated over probability density functions. To avoid excessive CPU time for the table generation, the calculation of the two dimensional flamelets is performed using the method proposed in the ADF-PCM (Approximated Diffusion Flame - Presumed Conditional Moment) approach: only the equation for the progress variable is solved, instead of the equations for all species. The progress variable reaction rate is given by a table of homogeneous reactors using the DHR model (Diluted Homogeneous Reactor) proposed by Locci et al. These approximated diffusion flames are first compared to exact diffusion flames computed using the flamelet equations and the chemistry for all species. The resulting model, called A2DF (Approximate 2 Dimensional Flamelet) is then applied to the RANS (Reynolds Averaged Navier-Stokes) simulations of Sandia Flames D and F, showing a good agreement with experimental measurements. Finally, this model is applied to the flameless and conventional combustion cases of the burner of Verissimo et al., showing a correct agreement for temperature and species predictions.     

LES/PDF Modeling of Turbulent Premixed Flames with Locally Enhanced Mixing by Reaction

Large-eddy simulations (LES) combined with the transported probability density function (PDF) method are carried out for two turbulent piloted premixed methane-air jet flames (flame F1 and flame F3) to assess the capability of LES/PDF for turbulent premixed combustion. The conventionally used model for the sub-filter scale mixing time-scale (or the mixing frequency) fails to capture the premixed flames correctly. This failure is expected to be caused by the lack of the sub-filter scale premixed flame propagation property in the sub-filter scale mixing process when the local flame front is under-resolved. It leads to slower turbulent premixed flame propagation and wider flame front. A new model for specifying the sub-filter scale mixing frequency is developed to account for the effect of sub-filter scale chemical reaction on mixing, based on past development of models for the sub-filter scale scalar dissipation rate in premixed combustion. The new model is assessed in the two turbulent premixed jet flames F1 and F3. Parametric studies are performed to examine the new model and its sensitivity when combined with the different mixing models. Significantly improved performance of the new mixing frequency model is observed to capture the premixed flame propagation reasonably, when compared with the conventional model. The sensitivity of the flame predictions is found be relatively weak to the different mixing models in conjunction with the new mixing frequency model.     

Towards an Extension of TFC Model of Premixed Turbulent Combustion

In order to determine the mean rate of product creation within the framework of the Turbulent Flame Closure (TFC) model of premixed combustion, the model is combined with a simple closure of turbulent scalar flux developed recently by the present authors based on the flamelet concept of turbulent burning. The model combination is assessed by numerically simulating statistically planar, one-dimensional, developing premixed flames that propagate in frozen turbulence. The mean rate of product creation yielded by the combined model decreases too slowly at the trailing edges of the studied flames, with the effect being more pronounced at longer flame-development times and larger ratios of rms turbulent velocity u′ to laminar flame speed S _L . To resolve the problem, the above closure of turbulent scalar flux is modified and the combination of the modified closure and TFC model yields reasonable behaviour of the studied rate. In particular, simulations indicate an increase in the mean combustion progress variable associated with the maximum rate by u′/S _L , in line with available DNS data. Finally, the modified closure of turbulent scalar flux is validated by computing conditioned velocities and turbulent scalar fluxes in six impinging-jet flames. The use of the TFC model for simulating such flames is advocated.     

Effects of Lewis Number on Scalar Variance Transport in Premixed Flames

The influences of differential diffusion rates of heat and mass on the transport of the variances of Favre fluctuations of reaction progress variable and non-dimensional temperature have been studied using three-dimensional simplified chemistry based Direct Numerical Simulation (DNS) data of statistically planar turbulent premixed flames with global Lewis number ranging from Le?= 0.34 to 1.2. The Lewis number effects on the statistical behaviours of the various terms of the transport equations of variances of Favre fluctuations of reaction progress variable and non-dimensional temperature have been analysed in the context of Reynolds Averaged Navier Stokes (RANS) simulations. It has been found that the turbulent fluxes of the progress variable and temperature variances exhibit counter-gradient transport for the flames with Lewis number significantly smaller than unity whereas the extent of this counter-gradient transport is found to decrease with increasing Lewis number. The Lewis number is also shown to have significant influences on the magnitudes of the chemical reaction and scalar dissipation rate contributions to the scalar variance transport. The modelling of the unclosed terms in the scalar variance equations for the non-unity Lewis number flames have been discussed in detail. The performances of the existing models for the unclosed terms are assessed based on a-priori analysis of DNS data. Based on the present analysis, new models for the unclosed terms of the active scalar variance transport equations are proposed, whenever necessary, which are shown to satisfactorily capture the behaviours of unclosed terms for all the flames considered in this study.     

Comparison of Combustion Models and Assessment of Their Applicability to the Simulation of Premixed Turbulent Combustion in IC-Engines

In order to simulate the turbulent combustion process occurring in spark-ignition (IC) engines, it is necessary to provide suitable and numerically economical models, the latter being particularly important in the application to industrial problems. Moreover, these models must deliver sufficiently accurate results for the unsteady operation of spark combustion engines, concerning variable geometries, temperatures, pressures and charge development in different configurations. In this work different turbulent combustion models for premixed hydrocarbon combustion are compared with respect to their ability to accurately predict the propagation of turbulent perfectly premixed flames. As a first configuration a cylinder of constant volume was studied. Transient calculations were used to simulate the propagation of the turbulent flame and to evaluate the resulting turbulent burning velocity. These calculations were performed for a perfect mixture of air and hydrocarbons at stoichiometric mixture and different initial conditions concerning pressure, temperature and turbulence intensity. As a second configuration a stationary turbulent bunsen-type flame with methane fuel was used to validate the turbulent combustion model of [Lindstedt and Vaos, Combust. Flame 116 (1999) 461] at different pressures. Calculated results were then compared to experimental data of [Kobayashi, Tamura, Maruta and Niioka. In: Proceedings of the 26th Symposium on Combustion, 1996, p. 389] and show excellent agreement for the turbulent burning velocity at several pressure levels using only a single set of model parameters.     

Scale similarity based models and their application to subgrid scale scalar flux modelling in the context of turbulent premixed flames

The performance of a variety of scale similarity (SS) type models for closure of sub-grid scalar flux in the context of Large Eddy Simulations (LES) of premixed turbulent combustion has been assessed. In addition to the well-known SS models, a more recent development by Anderson and Domaradzki (2012) is included in the analysis and also further model extensions and improvements are discussed. The work is based on a priori analysis of two Direct Numerical Simulation (DNS) databases of freely propagating turbulent premixed flames with a range of different Lewis and turbulent Reynolds numbers. Depending on the balance between the effects of flame normal acceleration due to heat release and the effects of turbulent velocity fluctuations, as well as the filter size, the subgrid-scalar flux exhibits both local gradient and counter-gradient transport which presents a considerable modelling challenge. The assessment is based on a correlation analysis and on the magnitude of the model expressions conditional on the Favre averaged reaction progress variable in comparison to the value obtained from DNS. Despite the fact that most of the models have been developed in the context of momentum transport in non-reactive flows they show either comparable or better performance in comparison to more conventional models used for reactive scalar flux closure. It is found that some models are sensitive to the test filter width and recommendations are provided in this regard. Further it is observed that the use of a Favre test filter substantially increases the correlation strength in direction of mean flame propagation where effects of heat release are most pronounced.     

Leading-Edge Reaction Zones in Lifted-Jet Gas and Spray Flames

An investigation of the leading edge characteristics in lifted turbulent methane-air (gaseous) and ethanol-air (spray) diffusion flames is presented. Both combustion systems consist of a central nonpremixed fuel jet surrounded by low-speed air co-flow. Non-intrusive laser-based diagnostic techniques have been applied to each system to provide information regarding the behavior of the combustion structures and turbulent flow field in the regions of flame stabilization. Simultaneous sequential CH-PLIF/particle image velocimetry and CH-PLIF/Rayleigh scattering measurements are presented for the lifted gaseous flame. The CH-PLIF data for the lifted gas flame reveals the role that ``leading-edge' combustion plays as the stabilization mechanism in gaseous diffusion flames. This phenomenon, characterized by a fuel-lean premixed flame branch protruding radially outward at the flame base, permits partially premixed flame propagation against the incoming flow field. In contrast, the leading edge of the ethanol spray flame, examined using single-shot OH-PLIF imaging and smoke-based flow visualization, does not exhibit the same variety of leading-edge combustion structure, but instead develops a dual reaction zone structure as the liftoff height increases. This dual structure is a result of the partial evaporation (hence partial premixing) of the polydisperse spray and the enhanced rate of air entrainment with increased liftoff height (due to co-flow). The flame stabilizes in a region of the spray, near the edge, occupied by small fuel droplets and characterized by intense mixing due to the presence of turbulent structures. This revised version was published online in July 2006 with corrections to the Cover Date.     

Analysis of Algebraic Closures of the Mean Scalar Dissipation Rate of the Progress Variable Applied to Stagnating Turbulent Flames

In the turbulent premixed reactive flows considered in this study, i.e. large Damköhler and Reynolds numbers, the flamelet regime of turbulent combustion applies and the scalar dissipation rate and mean reaction rate are inter related. In this situation various algebraic models for the mean chemical rate that are obtained from an equilibrium of the dominant terms of the transport equation for the scalar dissipation rate, are evaluated through their application to flames stabilized in a turbulent stagnating flow. An asymptotic analysis is first performed and results obtained through the resulting one-dimensional calculation are compared with the experimental data of Li et al. (Proc Combust Inst 25:1207–1214, 1994). Eventually, three-dimensional CFD calculations including suited algebraic closures to represent the turbulent transport terms are carried out. Results are satisfactorily compared to the experimental data of Cho et al. (Proc Combust Inst 22:739–745, 1988). As a first outcome, the analysis confirms the interest and the relevance of the corresponding algebraic closures to deal with turbulent premixed combustion in such conditions. In the search of a satisfactory representation of such premixed impinging flames, the computational results also clearly emphasize the strong intertwinment that exits between the mean reaction rate, i.e. scalar dissipation rate or micro-mixing taking place at the smallest scale of the reactive flowfield, and the Reynolds fluxes modelling, i.e. turbulent macro-mixing.     

Joint RANS/LES Approach to Premixed Flame Modelling in the Context of the TFC Combustion Model

We present an original timesaving joint RANS/LES approach to simulate turbulent premixed combustion. It is intended mainly for industrial applications where LES may not be practical. It is based on successive RANS/LES numerical modelling, where turbulent characteristics determined from RANS simulations are used in LES equations for estimation of the subgrid chemical source and viscosity. This approach has been developed using our TFC premixed combustion model, which is based on a generalization of the Kolmogorov’s ideas. We assume existence of small-scale statistically equilibrium structures not only of turbulence but also of the reaction zones. At the same time, non-equilibrium large-scale structures of reaction sheets and turbulent eddies are described statistically by model combustion and turbulence equations in RANS simulations or follow directly without modelling in LES. Assumption of small-scale equilibrium gives an opportunity to express the mean combustion rate (controlled by small-scale coupling of turbulence and chemistry) in the RANS and LES sub-problems in terms of integral or subgrid parameters of turbulence and the chemical time, i.e. the definition of the reaction rate is similar to that of the mean dissipation rate in turbulence models where it is expressed in terms of integral or subgrid turbulent parameters. Our approach therefore renders compatible the combustion and turbulent parts of the RANS and LES sub-problems and yields reasonable agreement between the RANS and averaged LES results. Combining RANS simulations of averaged fields with LES method (and especially coupled and acoustic codes) for simulation of corresponding nonstationary process (and unsteady combustion regimes) is a promising strategy for industrial applications. In this work we present results of simulations carried out employing the joint RANS/LES approach for three examples: High velocity premixed combustion in a channel, combustion in the shear flow behind an obstacle and the impinging flame (a premixed flame attached to an obstacle).     

Flame Structure and Propagation in Turbulent Flame-Droplet Interaction: A Direct Numerical Simulation Analysis

Three-dimensional Direct Numerical Simulations (DNS) in canonical configuration have been employed to study the combustion of mono-disperse droplet-mist under turbulent flow conditions. A parametric study has been performed for a range of values of droplet equivalence ratio ?_d, droplet diameter a_d and root-mean-square value of turbulent velocity u^′. The fuel is supplied entirely in liquid phase such that the evaporation of the droplets gives rise to gaseous fuel which then facilitates flame propagation into the droplet-mist. The combustion process in gaseous phase takes place predominantly in fuel-lean mode even for ?_d>1. The probability of finding fuel-lean mixture increases with increasing initial droplet diameter because of slower evaporation of larger droplets. The chemical reaction is found to take place under both premixed and non-premixed modes of combustion: the premixed mode ocurring mainly under fuel-lean conditions and the non-premixed mode under stoichiometric or fuel-rich conditions. The prevalence of premixed combustion was seen to decrease with increasing droplet size. Furthermore, droplet-fuelled turbulent flames have been found to be thicker than the corresponding turbulent stoichiometric premixed flames and this thickening increases with increasing droplet diameter. The flame thickening in droplet cases has been explained in terms of normal strain rate induced by fluid motion and due to flame normal propagation arising from different components of displacement speed. The statistical behaviours of the effective normal strain rate and flame stretching have been analysed in detail and detailed physical explanations have been provided for the observed behaviour. It has been found that the droplet cases show higher probability of finding positive effective normal strain rate (i.e. combined contribution of fluid motion and flame propagation), and negative values of stretch rate than in the stoichiometric premixed flame under similar flow conditions, which are responsible for higher flame thickness and smaller flame area generation in droplet cases.