Finite Rate Chemistry Effects in Turbulent Reacting Flows

The classical “fast chemistry” analysis by Damköhler remains a common basis for calculation methods aimed at turbulent reacting flows. Perturbation approaches can be used to introduce finite rate chemistry effects, particularly where a distinct chemical time-scale separation is present, though more comprehensive techniques, e.g. based on a transported joint probability density function (JPDF), are typically required. Potential difficulties with the JPDF technique include issues related to the intrinsic structure of turbulent flames, particularly at low Reynolds numbers, and models for molecular mixing. The ability to predict the formation of NO is particularly interesting in this context given the strong sensitivity to chemical kinetic and non-adiabatic effects. The current work initially provides an assessment of uncertainties in the formation chemistry of NO in the context of new quantitative measurements, obtained in non-premixed laminar methane/air counterflow flames using ps-LIF, and subsequently explores how these translate to turbulent flames. A consistent systematically reduced (16 independent, 4 dependent and 28 steady state scalars) reaction mechanism is applied to model the turbulent flames of Barlow and co-workers (8200 ≤Re≤ 44000). The highest Re number flame additionally permits an investigation into the ability of the transported JPDF technique to deal with emissions of nitric oxide in flames close to global extinction. The work shows that the technique has the potential to reproduce NO levels and conditional PDFs under conditions with significant local extinction/re-ignition to within the uncertainties associated with the principal elementary reaction steps.     

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.     

Effects of Body Forces on Turbulent Kinetic Energy Transport in Premixed Flames

Flow, Turbulence and Combustion - The effects of buoyancy on turbulent premixed flames are expected to be strong due to the large changes in density between the unburned and fully burned gases. The...     

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.     

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.     

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.     

Heat Release Imaging in Turbulent Premixed Ethylene-Air Flames Near Blow-off

The focus of this work is to visualise the regions of CH₂O and heat release (HR) of an unconfined turbulent premixed bluff body stabilised ethylene-air flame at conditions approaching lean blow-off using simultaneous imaging of OH- and CH₂O-PLIF. The HR regions are estimated from the product of the OH and CH₂O profiles. At conditions near blow-off, wide regions of CH₂O are observed inside the recirculation zone (RZ). The presence of CH₂O and HR inside the RZ is observed to follow fragmentation of the downstream flame parts near the top of the RZ. The presence of wide regions void of both OH and CH₂O inside the RZ at conditions very close to blow-off indicates the possible entrainment of un-reacted gases into the RZ. The behaviour of the lean ethylene-air flame with Lewis number (Le) greater than 1 is compared to that of a lean methane-air flame with Le of approximately 1. For both fuels, qualitatively similar observations of flame fragmentation downstream followed by build-up of CH₂O and HR inside the RZ are observed at conditions near lean blow-off. Also, a similar trend of flame front curvature conditioned on HR was observed for both the ethylene-air and methane-air flames, where the magnitude of HR was observed to increase with the absolute value of curvature.     

Noise Correction and Length Scale Estimation for Scalar Dissipation Rate Measurements in Turbulent Partially Premixed Flames

A recently developed conditional sampling-based method for correcting noise effects in scalar dissipation rate measurements and for estimating the extent of resolution of the dissipation rate is employed to analyze the data obtained in turbulent partially premixed (Sandia) flames. The method uses conditional sampling to select instantaneous fully resolved local scalar fields, which are analyzed to determine the measurement noise and to correct the Favre mean, conditional, and conditionally filtered dissipation rates. The potentially under-resolved local scalar fields, also selected using conditional sampling, are corrected for noise and are analyzed to examine the extent of resolution. The error function is used as a model for the potentially under-resolved local scalar to evaluate the scalar dissipation length scales and the percentage of the dissipation resolved. The results show that the Favre mean dissipation rate, the mean dissipation rate conditional on the mixture fraction, and dissipation rate filtered conditionally on the mixture fraction generally are well resolved in the flames. Analyses of the dissipation rates filtered conditionally on the mixture fraction and temperature show that the length scale increases with temperature, due to lower dissipation rate and higher diffusivity. The dissipation rate is well resolved for temperatures above 1,300 K but is less resolved at lower temperatures, although the probability of very low temperature events is low. To fully resolve these rare events the sample spacing needs to be reduced by approximately one half. The present study further demonstrates the effectiveness of the new noise correction and length scale estimation method.     

Flame-Flow Interaction in Premixed Turbulent Flames During Transient Head-On Quenching

This paper reports on experimental investigations of turbulent flame-wall interaction (FWI) during transient head-on quenching (HOQ) of premixed flames. The entire process, including flame-wall approach and flame quenching, was analyzed using high repetition rate particle image velocimetry (PIV) and simultaneous flame front tracking based on laser-induced fluorescence (LIF) of the OH molecule. The influence of convection upon flame structures and flow fields was analyzed qualitatively and quantitatively for the fuels methane (CH₄) and ethylene (C₂H₄) at ? = 1. For this transient FWI, flames were initialized by laser spark ignition 5 mm above the burner nozzle. Subsequently, flames propagated against a steel wall, located 32 mm above the burner nozzle, where they were eventually quenched in the HOQ regime due to enthalpy losses. Twenty ignition events were recorded and analyzed for each fuel. Quenching distances were 179 μm for CH₄ and 159 μm for C₂H₄, which lead by nondimensionalization with flame thickness to Peclet numbers of 3.1 and 5.5, respectively. Flame wrinkling and fresh gas velocity fluctuations proved flame and flow laminarization during wall approach. Velocity fluctuations cause flame wrinkling, which is higher for CH₄ than C₂H₄ despite lower velocity fluctuations. Lewis number effects explained this phenomenon. Results from flame propagation showed that convection dominates propagation far from the wall and differences in flame propagation are related to the different laminar flame speeds of the fuels. Close to the wall flames of both fuels propagate similarly, but experimental results clearly indicate a decrease in intrinsic flame speed. In general, the experimental results are in good agreement with other experimental studies and several numerical studies, which are mainly based on direct numerical simulations.     

Resolution Requirements in Stochastic Field Simulation of Turbulent Premixed Flames

The spatial resolution requirements of the Stochastic Fields probability density function approach are investigated in the context of turbulent premixed combustion simulation. The Stochastic Fields approach is an attractive way to implement a transported Probability Density Function modelling framework into Large Eddy Simulations of turbulent combustion. In premixed combustion LES, the numerical grid should resolve flame-like structures that arise from solution of the Stochastic Fields equation. Through analysis of Stochastic Fields simulations of a freely-propagating planar turbulent premixed flame, it is shown that the flame-like structures in the Stochastic Fields simulations can be orders of magnitude narrower than the LES filter length scale. The under-resolution is worst for low Karlovitz number combustion, where the thickness of the Stochastic Fields flame structures is on the order of the laminar flame thickness. The effect of resolution on LES predictions is then assessed by performing LES of a laboratory Bunsen flame and comparing the effect of refining the grid spacing and filter length scale independently. The usual practice of setting the LES filter length scale equal to grid spacing leads to severe under-resolution and numerical thickening of the flame, and to substantial error in the turbulent flame speed. The numerical resolution required for accurate solution of the Stochastic Fields equations is prohibitive for many practical applications involving high-pressure premixed combustion. This motivates development of a Thickened Stochastic Fields approach (Picciani et al. Flow Turbul. Combust. X, YYY (2018) in order to ensure the numerical accuracy of Stochastic Fields simulations.     

Subgrid Modeling of Turbulent Premixed Flames in the Flamelet Regime

Large eddy simulation (LES) models for flamelet combustion are analyzed by simulating premixed flames in turbulent stagnation zones. ALES approach based on subgrid implementation of the linear eddy model(LEM) is compared with a more conventional approach based on the estimation of the turbulent burning rate. The effects of subgrid turbulence are modeled within the subgrid domain in the LEM-LES approach and the advection (transport between LES cells) of scalars is modeled using a volume-of-fluid (VOF) Lagrangian front tracking scheme. The ability of the VOF scheme to track the flame as a thin front on the LES grid is demonstrated. The combined LEM-LES methodology is shown to be well suited for modeling premixed flamelet combustion. The geometric characteristics of the flame surfaces, their effects on resolved fluid motion and flame-turbulence interactions are well predicted by the LEM-LES approach. It is established here that local laminar propagation of the flamelets needs to be resolved in addition to the accurate estimation of the turbulent reaction rate. Some key differences between LEM-LES and the conventional approach(es) are also discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

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 Study of Strain Rate Effects for Turbulent Premixed Flames with Application to LES of a Gas Turbine Combustor Model

Large-scale strain rate field, a resolved quantity which is easily computable in large-eddy simulations (LES), could have profound effects on the premixed flame properties by altering the turbulent flame speed and inducing local extinction. The role of the resolved strain rate has been investigated in a posterior LES study of GE lean premixed dry low-NOx emissions LM6000 gas turbine combustor model. A novel approach which is based on the coupling of the linear-eddy model with a one-dimensional counterflow solver has been applied to obtain the parameterizations of the resolved premixed flame properties in terms of the reactive progress variable, the local strain rate measure, and local Reynolds and Karlovitz numbers. The strain rate effects have been analyzed by comparing LES statistics for several models of the turbulent flame speed, i.e, with and without accounting for the local strain rate effects, with available experimental data. The sensitivity of the simulation results to the inflow velocity conditions as well as the grid resolution have been also studied. Overall, the results obtained demonstrate that the effects of the resolved strain rate are not dominant for the considered premixed flame configuration and the unstrained turbulent flame speed model is found to perform as well as the one that allows for the strain rate effects.     

A Comparison of Strategies for Direct Numerical Simulation of Turbulence Chemistry Interaction in Generic Planar Turbulent Premixed Flames

Three different methods to introduce turbulence in the computational domain of Direct Numerical Simulations (DNS) of statistically planar turbulent premixed flame configurations have been reviewed and their advantages and disadvantages in terms of run time, natural flame development, control of turbulence parameters and convergence of statistics extracted from the simulations have been discussed in detail. It has been found that there is no method, which is clearly superior to the other two alternative methods. An analysis has been performed to explain why Lundgren’s physical space linear forcing results in an integral length scale which is, independent of the Reynolds number, a constant fraction of the domain size. Furthermore, an evolution equation for the integral length scale has been derived, and a scaling analysis of its terms has been performed to explain the evolution of the integral length scale in the context of Lundgren’s physical space linear forcing. Finally, a modification to Lundgren’s forcing approach has been suggested which ensures that the integral length scale settles to a predetermined value so that DNS of statistically planar turbulent premixed flames with physical space forcing can be conducted for prescribed values of Damköhler and Karlovitz numbers.     

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.     

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.     

Statistical Analysis of Scalar Dissipation Rate Transport in Turbulent Partially Premixed Flames: A Direct Numerical Simulation Study

Statistically planar turbulent premixed and partially premixed flames for different initial turbulence intensities are simulated for global equivalence ratios ??>?=?0.7 and ??>?=?1.0 using three-dimensional Direct Numerical Simulations (DNS) with simplified chemistry. For the simulations of partially premixed flames, a random distribution of equivalence ratio following a bimodal distribution of equivalence ratio is introduced in the unburned reactants ahead of the flame. The simulation parameters in all of the cases were chosen such that the combustion situation belongs to the thin reaction zones regime. The DNS data has been used to analyse the behaviour of the dissipation rate transports of both active and passive scalars (i.e. the fuel mass fraction Y _F and the mixture fraction ξ) in the context of Reynolds Averaged Navier–Stokes (RANS) simulations. The behaviours of the unclosed terms of the Favre averaged scalar dissipation rates of fuel mass fraction and mixture fraction (i.e. \(\widetilde {\varepsilon }_Y =\overline {\rho D\nabla Y_F^{\prime \prime } \cdot \nabla Y_F^{\prime \prime } } /\overline{\rho }\) and \(\widetilde {\varepsilon }_\xi =\overline {\rho D\nabla \xi ^{\prime \prime }\cdot \nabla \xi ^{\prime \prime }} /\overline {\rho })\) transport equations have been analysed in detail. In the case of the \(\widetilde {\varepsilon }_Y \) transport, it has been observed that the turbulent transport term of scalar dissipation rate remains small throughout the flame brush whereas the terms due to density variation, scalar–turbulence interaction, reaction rate and molecular dissipation remain the leading order contributors. The term arising due to density variation remains positive throughout the flame brush and the combined contribution of the reaction and molecular dissipation to the \(\widetilde {\varepsilon }_Y \) transport remains negative throughout the flame brush in all cases. However, the behaviour of scalar–turbulence interaction term of the \(\widetilde {\varepsilon }_Y \) transport equation is significantly affected by the relative strengths of turbulent straining and the straining due to chemical heat release. In the case of the \(\widetilde {\varepsilon }_\xi \) transport, the turbulent transport term remains small throughout the flame brush and the density variation term is found to be negligible in all cases, whilst the reaction rate term is exactly zero. The scalar–turbulence interaction term and molecular dissipation term remain the leading order contributors to the \(\widetilde {\varepsilon }_\xi \) transport throughout the flame brush in all cases that have been analysed in the present study. Performances of existing models for the unclosed terms of the transport equations of \(\widetilde {\varepsilon }_Y \) and \(\widetilde {\varepsilon }_\xi \) are assessed with respect to the corresponding quantities obtained from DNS data. Based on this exercise either suitable models have been identified or new models have been proposed for the accurate closure of the unclosed terms of both \(\widetilde {\varepsilon }_Y \) and \(\widetilde {\varepsilon }_\xi \) transport equations in the context of Reynolds Averaged Navier–Stokes (RANS) simulations.