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.     

Subgrid Scale Modeling in Large-Eddy Simulation of Turbulent Combustion Using Premixed Flamelet Chemistry

Large-eddy simulation (LES) of turbulent combustion with premixed flamelets is investigated in this paper. The approach solves the filtered Navier–Stokes equations supplemented with two transport equations, one for the mixture fraction and another for a progress variable. The LES premixed flamelet approach is tested for two flows: a premixed preheated Bunsen flame and a partially premixed diffusion flame (Sandia Flame D). In the first case, we compare the LES with a direct numerical simulation (DNS). Four non-trivial models for the chemical source term are considered for the Bunsen flame: the standard presumed beta-pdf model, and three new propositions (simpler than the beta-pdf model): the filtered flamelet model, the shift-filter model and the shift-inversion model. A priori and a posteriori tests are performed for these subgrid reaction models. In the present preheated Bunsen flame, the filtered flamelet model gives the best results in a priori tests. The LES tests for the Bunsen flame are limited to a case in which the filter width is only slightly larger than the flame thickness. According to the a posteriori tests the three models (beta-pdf, filtered flamelet and shift-inversion) show more or less the same results as the trivial model, in which subgrid reaction effects are ignored, while the shift-filter model leads to worse results. Since LES needs to resolve the large turbulent eddies, the LES filter width is bounded by a maximum. For the present Bunsen flame this means that the filter width should be of the order of the flame thickness or smaller. In this regime, the effects of subgrid reaction and subgrid flame wrinkling turn out to be quite modest. The LES-results of the second case (Sandia Flame D) are compared to experimental data. Satisfactory agreement is obtained for the main species. Comparison is made between different eddy-viscosity models for the subgrid turbulence, and the Smagorinsky eddy-viscosity is found to give worse results than eddy-viscosities that are not dominated by the mean shear. Paper presented on the Eccomas Thematic Conference Computational Combustion 2007, submitted for a special issue of Flow, Turbulence and Combustion.     

A Numerical Study Promoting Algebraic Models for the Lewis Number Effect in Atmospheric Turbulent Premixed Bunsen Flames

This numerical investigation carried out on turbulent lean premixed flames accounts for two algebraic – the Lindstedt–Vaos (LV) and the classic Bray–Moss–Libby (BML) – reaction rate models. Computed data from these two models is compared with the experimental data of Kobayashi et al. on 40 different methane, ethylene and propane Bunsen flames at 1 bar, where the mean flame cone angle is used for comparison. Both models gave reasonable qualitative trend for the whole set of data, in overall. In order to characterize quantitatively, firstly, corrections are made by tuning the model parameters fitting to the experimental methane–air (of Le = 1.0) flame data. In case of the LV model, results obtained by adjusting the pre-constant, i.e., reaction rate parameter, C_R, from its original value 2.6 to 4.0, has proven to be in good agreement with the experiments. Similarly, for the BML model, with the tuning of the exponent n, in the wrinkling length scale, L_y = C_l⋅ l_x(s_L/u′)ⁿ from value unity to 1.2, the outcome is in accordance with the measured data. The deviation between the measured and calculated data sharply rises from methane to propane, i.e., with increasing Lewis number. It is deduced from the trends that the effect of Lewis number (for ethylene–air mixtures of Le = 1.2 and propane–air mixtures of Le = 1.62) is missing in both the models. The Lewis number of the fuel–air mixture is related to the laminar flame instabilities. Second, in order to quantify for its influence, the Lewis number effect is induced into both the models. It is found that by setting global reaction rate inversely proportional to the Lewis number in both the cases leads to a much better numerical prediction to this set of experimental flame data. Thus, by imparting an important phenomenon (the Lewis number effect) into the reaction rates, the generality of the two models is enhanced. However, functionality of the two models differs in predicting flame brush thickness, giving scope for further analysis.     

Direct Numerical Simulations of Premixed Turbulent Flames with Reduced Chemistry: Validation and Flamelet Analysis

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 thin reaction zone regime and in the broken reaction zone regime are performed. The flamelet-generated manifold method is used in order to deal with detailed reaction kinetics. 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. It is found that if the full profiles of flame stretch and curvature through the flame front are included in the theory, the local mass burning rate is well predicted. The influence of several approximations, which are used in other existing theories, is studied. When flame stretch is assumed constant through the flame front or when curvature of the flame front is neglected, the theory fails to predict the local mass burning rate. The influence of using a reduced chemistry model is investigated by comparing flamelet simulations with reduced and detailed chemistry.     

Near-Equidiffusion Disturbed Premixed Flames with Wider Reaction Zones

Most of the asymptotic considerations of the interaction of premixed flames with a general flow, i.e. curved and stretched flames subjected to time dependent flow, are dedicated to high activation energy asymptotes. Therefore, in these considerations the reaction zone is thin and the temperature within the reaction zone is constant to the leading order of approximation. Here we consider an order unity activation energy for near-equidiffusion flames and show that the flame speed relations obtained are distinct from those obtained by high activation energy asymptotes. The flame is assumed to be thin in comparison with the flow scales but the reaction zone is no longer thin in comparison with the flame width. Although obtaining analytical solutions is problematic even for undisturbed flames with wide reaction zones, we found that the propagation speed of disturbed premixed flames with wide reaction zones is determined by analytical integrals involving the temperature profile of the undisturbed flame. We also found independent effects of curvature and stretch for the flames with wider reaction zones. This revised version was published online in July 2006 with corrections to the Cover Date.     

A Similarity Subgrid Model for Premixed Turbulent Combustion

The accuracy of large-eddy simulation (LES) of a turbulent premixed Bunsen flame is investigated in this paper. To distinguish between discretization and modeling errors, multiple LES, using different grid sizes h but the same filterwidth Δ, are compared with the direct numerical simulation (DNS). In addition, LES using various values of Δ but the same ratio Δ/h are compared. The chemistry in the LES and DNS is parametrized with the standard steady premixed flamelet for stochiometric methane-air combustion. The subgrid terms are closed with an eddy-viscosity or eddy-diffusivity approach, with an exception of the dominant subgrid term, which is the subgrid part of the chemical source term. The latter subgrid contribution is modeled by a similarity model based upon 2Δ, which is found to be superior to such a model based upon Δ. Using the 2Δ similarity model for the subgrid chemistry the LES produces good results, certainly in view of the fact that the LES is completely wrong if the subgrid chemistry model is omitted. The grid refinements of the LES show that the results for Δ = h do depend on the numerical scheme, much more than for h = Δ/2 and h = Δ/4. Nevertheless, modeling errors and discretization error may partially cancel each other; occasionally the Δ = h results were more accurate than the h ≤ Δ results. Finally, for this flame LES results obtained with the present similarity model are shown to be slightly better than those obtained with standard β-pdf closure for the subgrid chemistry.     

Turbulence Statistics and Scalar Transport in Highly-Sheared Premixed Flames

This paper describes recent progress in the analysis of the nature of turbulent premixed flames stabilised behind an axisymmetric baffle which are of fundamental interest in the development of new and cleaner combustion systems. The work includes the use of laser-based diagnostics for velocity and temperature measurements, which are extended to the analysis of turbulence statistics, including the energy spectrum and typical length scales in a reacting shear layer. The results provided experimental evidence of the extension of the flamelet regime beyond the Klimov--Williams criterion. Arguments based on the shape of the weighted-joint-probability distributions of axial velocity and temperature fluctuations show that the counter-gradient nature of heat flux is associated with the preferential deceleration of products of combustion in relation to the cold reactants.     

Flame Surface Density in Turbulent Premixed V-Flame with Buoyancy

A fractional step numerical model is established for turbulent premixed combustion with buoyancy. The flame front propagation is described by the level-set method. Simulated results without buoyancy have been previously validated with available experimental data on a premixed V-flame. A new formula is presented to fit the flame surface density with respect to the reaction progress variable in a turbulent premixed V-flame. By numerical simulations, dynamical behaviour of the flame under the interaction of turbulence, exothermicity and buoyancy are investigated.     

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.     

Investigation of Modeling for Non-Premixed Turbulent Combustion

A method for predicting filtered chemical species concentrations and filtered reaction rates in Large-Eddy Simulations of non-premixed, non-isothermal, turbulent reacting flows has been demonstrated to be quite accurate for higher Damköhler numbers. This subgrid-scale model is based on flamelet theory and uses presumed forms for both the dissipation rate and subgrid-scale probability density function of a conserved scalar. Inputs to the model are the chemistry rates, the Favre-filtered scalar, and its subgrid-scale variance and filtered dissipation rate. In this paper, models for the filtered dissipation rate and subgrid-scale variance are evaluated by filtering data from 5123-point Direct Numerical Simulations of a single-step, isothermal reaction developing in the isotropic, incompressible, decaying turbulence field of Comte-Bellot and Corrsin. Both the subgrid-scale variance and the filtered dissipation rate models (the sub-models) are found to be reasonably accurate. The effect of the errors introduced by the sub-models on the overall model is found to be small, and the overall model is shown to accurately predict the spatial average of the filtered species concentrations over a wide range of times.     

A Priori Evaluation of the Laminar Flamelet Decomposition Model for Turbulent Premixed Flames using DNS Data

Laminar flamelet decomposition (LFD) is a dynamic approach for modelling sub-filter scale turbulence-chemistry interactions in Large-Eddy Simulations using a stretched flamelet library. In this work, the performance of the LFD model – that was previously used only in non-premixed combustion—is investigated a priori for premixed combustion using positively-strained flamelets in the reactant-to-product configuration. For this purpose, a DNS database of methane-air premixed flames is utilized. The flames are propagating in a rectangular box under homogeneous isotropic turbulence conditions over a wide range of Karlovitz numbers. The results show that the LFD model can correctly account for the sub-filter scale turbulence-chemistry interactions to predict the filtered reaction rates and the filtered scalar field, provided that turbulent and laminar mixing are well predicted. The deviations from the DNS results are attributed to the shortcomings of the strained flamelet library and the non-flamelet effects. Finally, the LFD results are compared with a different sub-filter scale model using the same strained flamlelet library, and the relative performances of the two models are discussed.—

     

A Priori Testing of Flamelet Generated Manifolds for Turbulent Partially Premixed Methane/Air Flames

To reduce high computational cost associated with simulations of reacting flows chemistry tabulation methods like the Flamelet Generated Manifold (FGM) method are commonly used. However, H₂, CO and OH predictions in RANS and LES simulations using the FGM (or a similar) method usually show a substantial deviation from measurements. The goal of this study is to assess the accuracy of low-dimensional FGM databases for the prediction of these species in turbulent, partially-premixed reacting flows. It will be examined to what extent turbulent, partially-premixed jet flames can be described by FGM databases based on premixed or counterflow diffusion flamelets and to what extent the chosen molecular transport model for the flamelet influences the accuracy of species mass fraction predictions in CFD-simulations. For LES and RANS applications a model that accounts for subgrid fluctuations has to be added introducing additional errors in numerical results. A priori analysis of FGM databases enables the exclusion of numerical errors (scheme accuracy, convergence) that occur in CFD simulations as well as the exclusion of errors originating from subgrid modeling assumptions in LES and RANS. Four different FGM databases are compared for H₂O, H₂, CO, CO₂ and OH predictions in Sandia Flames C to F. Species mass fractions will be compared to measurements directly and conditioned on mixture fraction. Special attention is paid to the representation of experimentally observed differential diffusion effects by FGM databases.     

One-Dimensional Modeling of Turbulent Premixed Jet Flames - Comparison to DNS

The one-dimensional turbulence (ODT) model, formulated in an Eulerian reference frame, is applied to a temporally-evolving premixed turbulent hydrogen plane-jet flame and results are compared with direct numerical simulation (DNS) data. This is the first published study to perform direct comparisons of ODT to DNS for premixed flames. The ODT model solves the full set of conservation equations for mass, momentum, energy, and species on a one-dimensional domain corresponding to the transverse jet direction. The effects of turbulent mixing are modeled via a stochastic process, while the full range of diffusive-reactive length and time scales are resolved directly on the one-dimensional domain. A detailed chemical mechanism for hydrogen combustion consisting of 9 species and 21 reactions and a mixture-averaged transport model are used (consistent with the DNS). Cases with two different Damköhler numbers are considered and comparisons between the ODT and DNS data are shown with respect to flow dynamics and thermochemistry. The ODT compared favorably with the DNS in terms of the overall entrainment as judged by the streamwise velocity profile and in terms of local flamelet structure as judged by progress-variable conditional reaction and scalar dissipation rates. While the ODT agreed qualitatively with the overall flame evolution, the net fuel consumption rate was somewhat over-predicted for a brief early period and under-predicted later on, leading to an overly long flame burnout time. It was demonstrated that adjusting a parameter controlling the selection of large eddies improved the prediction of the peak fuel consumption rate and overall reaction progress but worsened the prediction of jet entrainment. An analysis of the 1D nature of ODT is presented that suggests the FSD in ODT needs to be much higher than the FSD in the DNS in order to achieve the same overall burning rate, suggesting that the FSD is under-predicted by a significant fraction. While the success of the ODT in reproducing many of the salient features of nonpremixed flames has been demonstrated, the current study suggests that improvements are needed when applied to premixed flames. It is also important to note that the DNS required approximately 40×10⁶ CPU hours while the ODT required approximately 10³ CPU hours.     

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.     

Subgrid continuum modeling of particle motion in a turbulent flow

An Eulerian continuum approach to modeling the motion of dispersed particles within the framework of the large-eddy simulation method is developed. The approach is based on a kinetic equation for the filtered probability density function for the particle velocity in a turbulent flow. Models for the subgrid turbulent stresses of the dispersed phase are presented.     

Modelling Turbulent Premixed Combustion Using the Level Set Approach for Reynolds Averaged Models

A model for premixed turbulent combustion is investigated using a RANS-approach. The evolution of the flame front is described in terms of the G-equation. The numerical instabilities of the G-field are resolved using a reinitialisation procedure. For the G-points near the flame surface an algorithm proposed by Russo and Smereka [1] and modificated by Düsing [2] is presented. For all other points the standard Sussman algorithm is employed. Fluid properties are conditioned on the flame front position using a burnt-unburnt probability function across the flame front. Computations are performed using the code FASTEST-3D [3] which is a flow solver for a non-orthogonal, block-structured grid. The computational examples include two test cases, the first containing the propagation of two circular merging flames and the second one containing the simulation of the ORACLES-burner [4].     

Transient Behavior of Turbulent Scalar Transport in Premixed Flames

Transition from gradient to countergradient scalar transport in a statistically planar, one-dimensional, developing, premixed turbulent flame is studied both theoretically and numerically. A simple criterion of the transition referred to is derived from the balance equation for the combustion progress variable, with the criterion highlighting an important role played by flame development. A balance equation for the difference in velocities $\bar{u}_b$ and $\bar{u}_u$ conditioned on burned and unburned mixture, respectively, is numerically integrated. Both analytical and computed results show that; (1) The flux $\overline{\rho u'' c''}$ is gradient during an early stage of flame development followed by transition to countergradient scalar transport at certain instant t _tr . (2) The transition time is increased when turbulence length scale L is increased or when the laminar flame speed S _L and/or the density ratio are decreased. (3) The transition time normalized using the turbulence time scale is increased by u??. Moreover, the numerical simulations have shown that the transition time is increased by u?? if a ratio of u??/S _L is not large. This dependence of t _tr on u?? is substantially affected by (i) the mean pressure gradient induced within the flame due to heat release and (ii) by the damping effect of combustion on the growth rate of mean flame brush thickness. The reasonable qualitative agreement between the computed trends and available experimental and DNS data, as well as the agreement between the computed trends and the present theoretical results, lends further support to the conditioned balance equation used in the present work.     

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.