Large Eddy Simulation of Premixed Turbulent Flames Using the Probability Density Function Approach

In the present study a Large Eddy Simulation and Filtered Density Function model is applied to three premixed piloted turbulent methane flames at different Reynolds Numbers using the Eulerian stochastic fields approach. The model is able to reproduce the flame structure and flow characteristics with a low number of fields (between 4 and 16 fields). The results show a good agreement with experimental data with the same closures employed in non-premixed combustion without any adjustment for combustion regime. The effect of heat release on the flow field is captured correctly. A wide range of sensitivity studies is carried out, including the number of fields, the chemical mechanism, differential diffusion effects and micro-mixing closures. The present work shows that premixed combustion (at least in the conditions under study) can be modelled using LES-PDF methods.. Finally, the ability of the model to predict flame quenching is studied. The model can accurate capture the conditions at which combustion is not sustainable and large pockets of extinction appear.     

Scalar Dissipation Rate Transport in the Context of Large Eddy Simulations for Turbulent Premixed Flames with Non-Unity Lewis Number

The effects of global Lewis number Le on the statistical behaviour of the unclosed terms in the transport equation of the Favre-filtered scalar dissipation rate (SDR) Ñ _c have been analysed using a Direct Numerical Simulation (DNS) database of freely propagating statistically planer turbulent premixed flames with Le ranging from 0.34 to 1.2. The DNS data has been explicitly filtered to analyse the statistical behaviour of the unclosed terms in the SDR transport equation arising from turbulent transport T ₁, density variation due to heat release T ₂, scalar-turbulence interaction T ₃, reaction rate gradient T ₄, molecular dissipation (?D ₂) and diffusivity gradients f(D) in the context of Large Eddy Simulations (LES). It Le has significant effects on the magnitudes of T ₁, T ₂, T ₃, T ₄, (?D ₂) and f(D). Moreover, both qualitative and quantitative behaviours of the unclosed terms T ₁, T ₂, T ₃, T ₄, (?D ₂) and f(D) are found to be significantly affected by the LES filter width Δ, which have been explained based on a detailed scaling analysis. Both scaling analysis and DNS data suggest that T ₂, T ₃, T ₄, (?D ₂) and f(D) remain leading order contributors to the SDR \(\tilde {{N}}_{c} \) transport for LES. The scaling estimates of leading order contributors to the SDR \(\tilde {{N}}_{c} \) transport has been utilised to discuss the possibility of extending an existing SDR model for Reynolds Averaged Navier Stokes (RANS) simulation for SDR \(\tilde {{N}}_{c} \) closure in the context of LES of turbulent premixed combustion.     

Flame Curvature Distribution in High Pressure Turbulent Bunsen Premixed Flames

The flame curvature statistics of turbulent premixed Bunsen flames have been analysed in this paper using a Direct Numerical Simulation (DNS) database of turbulent Bunsen flames at ambient and elevated pressures. In order to be able to perform a large parametric study in terms of pressure, heat release parameter, turbulence conditions and nozzle diameter, a single step Arrhenius type irreversible chemistry has been used for the purpose of computational economy, where thermo-chemical parameters are adjusted to match the behavior of stoichiometric methane-air flames. This analysis focuses on the characterization of the local flame geometry in response to turbulence and hydro-dynamic instability. The shape of the flame front is found to be consistent with existing experimental data. Although the Darrieus Landau instability promotes cusp formation, a qualitatively similar flame morphology can be observed for hydro-dynamically stable flames. A criterion has been suggested for the curvature PDF to become negatively skewed.     

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.     

Joint PDF Closure of Turbulent Premixed Flames

In this paper, a novel model for turbulent premixed combustion in the corrugated flamelet regime is presented, which is based on transporting a joint probability density function (PDF) of velocity, turbulence frequency and a scalar vector. Due to the high dimensionality of the corresponding sample space, the PDF equation is solved with a Monte-Carlo method, where individual fluid elements are represented by computational particles. Unlike in most other PDF methods, the source term not only describes reaction rates, but accounts for “ignition” of reactive unburnt fluid elements due to propagating embedded quasi laminar flames within a turbulent flame brush. Unperturbed embedded flame structures and a constant laminar flame speed (as expected in the corrugated flamelet regime) are assumed. The probability for an individual particle to “ignite” during a time step is calculated based on an estimate of the mean flame surface density (FSD), latter gets transported by the PDF method. Whereas this model concept has recently been published [21], here, a new model to account for local production and dissipation of the FSD is proposed. The following particle properties are introduced: a flag indicating whether a particle represents the unburnt mixture; a flame residence time, which allows to resolve the embedded quasi laminar flame structure; and a flag indicating whether the flame residence time lies within a specified range. Latter is used to transport the FSD, but to account for flame stretching, curvature effects, collapse and cusp formation, a mixing model for the residence time is employed. The same mixing model also accounts for molecular mixing of the products with a co-flow. To validate the proposed PDF model, simulation results of three piloted methane-air Bunsen flames are compared with experimental data and very good agreement is observed.     

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.     

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.     

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.     

Topology and Brush Thickness of Turbulent Premixed V-shaped Flames

Topology and brush thickness of turbulent premixed V-shaped flames were investigated using Mie scattering and Particle Image Velocimetry techniques. Mean bulk flow velocities of 4.0, 6.2, and 8.3 m/s along with two fuel-air equivalence ratios of 0.6 and 0.7 were tested in the experiments. Using a novel experimental turbulence generating apparatus, three turbulence intensities of approximately 2 %, 6 %, and 17 % were tested in the experiments. The results show that topology of the flame front is significantly altered by changing the turbulence intensity. Specifically, at relatively small turbulence intensities, the flame fronts feature wrinkles which are symmetric with respect to the vertical axis. At moderate values of turbulence intensities, the flame fronts form cusps. The formation of cusps is more pronounced at large mean bulk flow velocities. The results associated with relatively large turbulence intensity show that flame surfaces feature: mushroom-shaped structures, freely propagating sub-flames, pocket formation, localized extinction, and horn-shaped structures. Analysis of the results show that the flame brush thickness follows a linear correlation with the root-mean-square of the flame front position. The correlation is in agreement with the results of past experimental investigations associated with moderately turbulent premixed V-shaped flames, and holds for the range of turbulence conditions tested. This suggests that the underlying mechanism associated with the dynamics of moderately turbulent premixed V-shaped flames proposed in past studies can potentially be valid for the the wide range of turbulence conditions examined in the present investigation.     

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.