Investigation of conditional source-term estimation applied to a non-premixed turbulent flame

A turbulent combustion model, Conditional Source-term Estimation (CSE) is applied to a non-premixed turbulent jet methane flame. The conditional chemical source terms are determined on the basis of first order closure and the conditional averaged species concentrations are obtained by inverting an integral equation. The Tikhonov method is implemented for regularisation. Detailed chemistry is tabulated using the trajectory generated low-dimensional manifold method. Radiation due to the gaseous species is included. Reynolds Averaged Navier–Stokes calculations are performed using two different turbulence models. The objectives of the paper are (i) assessment of the impact of the main numerical parameters in CSE and (ii) comparison of the CSE numerical predictions with available experimental data and results from previous simulations for the selected flame. The number of CSE domains and the number of points in each CSE domain are shown to have a significant impact on the results if not selected appropriately. The present CSE calculations always converge to unique and stable predictions. The corrected k–ε model yields mixture fraction profiles in good agreement with the experimental data values for axial locations in the first half of the flame. Farther downstream, the RNG k–ε model performs better. Overall, the current predictions for the mixture fraction are in good agreement with the experimental data. The predicted temperatures using CSE and the k–ε turbulence model with a modified value of C_ε1 = 1.47 are found to be in very good agreement with the experimental data. Further, the current CSE results are of comparable quality with previous simulations using the flamelet model and conditional moment closure. Future work may include further investigation on optimal determination of the regularisation parameter and alternative regularisation techniques, soot modelling within the CSE formulation, and improved formulation of radiation.     

Inverse analysis and regularisation in conditional source-term estimation modelling

Conditional Source-term Estimation (CSE) obtains the conditional species mass fractions by inverting a Fredholm integral equation of the first kind. In the present work, a Bayesian framework is used to compare two different regularisation methods: zeroth-order temporal Tikhonov regulatisation and first-order spatial Tikhonov regularisation. The objectives of the current study are: (i) to elucidate the ill-posedness of the inverse problem; (ii) to understand the origin of the perturbations in the data and quantify their magnitude; (iii) to quantify the uncertainty in the solution using different priors; and (iv) to determine the regularisation method best suited to this problem. A singular value decomposition shows that the current inverse problem is ill-posed. Perturbations to the data may be caused by the use of a discrete mixture fraction grid for calculating the mixture fraction PDF. The magnitude of the perturbations is estimated using a box filter and the uncertainty in the solution is determined based on the width of the credible intervals. The width of the credible intervals is significantly reduced with the inclusion of a smoothing prior and the recovered solution is in better agreement with the exact solution. The credible intervals for temporal and spatial smoothing are shown to be similar. Credible intervals for temporal smoothing depend on the solution from the previous time step and a smooth solution is not guaranteed. For spatial smoothing, the credible intervals are not dependent upon a previous solution and better predict characteristics for higher mixture fraction values. These characteristics make spatial smoothing a promising alternative method for recovering a solution from the CSE inversion process.     

Zone conditional analysis of a freely propagating one-dimensional turbulent premixed flame

The zone conditional conservation equations are derived and validated against the DNS data of a freely propagating one-dimensional turbulent premixed flame. Conditional flow velocities are calculated by the conditional continuity and momentum equations, and a modeled transport equation for the Reynolds average reaction progress variable. An asymptotic formula for turbulent burning velocity is obtained with the effects of a finite Damköhler number accounted for as an additional factor. It is shown that flame generated turbulence is primarily due to correlations between fluctuating gas velocities and fluctuating unit normal vector on a flame surface. More investigation is required to validate general predictive capability of the derived conditional conservation equations and the relationships modeled for closure.     

Interaction of a Gaussian acoustic wave with a turbulent non-premixed flame

A Direct Numerical Simulation (DNS) of a turbulent non-premixed flame interacting with a Gaussian acoustic wave is carried out in this work. This numerical simulation takes into account detailed transport phenomena including the Soret effect as well as complete chemical kinetics on a very fine mesh. Turbulent non-premixed flame calculations are carried out both with and without an acoustic wave and results are recorded at the same time. By a simple difference it is then possible to obtain the influence of the acoustic wave/turbulent flame interaction. Using an extension of the non-linear Rayleigh criterion to a system with many species and elementary reactions, the obtained results can be further analysed. The initially planar acoustic wave develops strong perturbations along its transverse direction because of the interaction process, even at very early times. The amplitude of the pressure perturbation presents locally high positive as well as negative values, demonstrating the importance of focussing/defocussing effects and local amplification (resp. damping) phenomena. In the same way, the heat release rate is locally modified (either increased or decreased) during the interaction process. Finally, the presented Rayleigh criterion is used to identify regions where local amplification (respectively damping) takes place. Both amplification and damping zones coexist directly close to each other inside the reaction zone. The observed, resulting global effect is thus based on an average over highly varying local conditions within the flame front, leading to a smoothing effect. The complexity of the coupling procedure leading to this global wave amplification or damping is demonstrated by the present analysis.     

Large Eddy Simulations of a piloted lean premix jet flame using finite-rate chemistry

A Large Eddy Simulation (LES) model capable of accurately representing finite-rate chemistry effects in turbulent premixed combustion is presented. The LES computations use finite-rate chemistry and implicit LES combustion modelling to simulate an experimentally well-documented lean-premixed jet flame stabilized by a stoichiometric pilot. The validity of the implicit LES assumption is discussed and criteria are expressed in terms of subgrid scale Damköhler and Karlovitz numbers. Simulation results are compared to experimental data for velocity, temperature and species mass fractions of CH₄, CO and OH. The simulation results highlight the validity and capability of the present approach for the flame and in general the combustion regime examined. A sensitivity analysis to the choice of the finite-rate chemistry mechanism is reported, this analysis indicates that the one and two-step global reaction mechanisms evaluated fail to capture the reaction layer with sufficient accuracy, while a 20-species skeletal mechanism reproduces the experimental observations accurately including the key finite-rate chemistry indicators CO and OH. The LES results are shown to be grid insensitive and that the grid resolution within the bounds examined is far less important compared to the sensitivity of the finite-rate chemistry representation. The results are analyzed in terms of the flame dynamics and it is shown that intense small scale mixing (high Karlovitz number) between the pilot and the jet is an important mechanism for the stabilization of the flame.     

Prediction of local extinction and re-ignition effects in non-premixed turbulent combustion using a flamelet/progress variable approach

The flamelet/progress variable approach (FPVA) has been proposed by Pierce and Moin as a model for turbulent non-premixed combustion in large-eddy simulation. The filtered chemical source term in this model appears in unclosed form, and is modeled by a presumed probability density function (PDF) for the joint PDF of the mixture fraction Z and a flamelet parameter λ. While the marginal PDF of Z can be reasonably approximated by a beta distribution, a model for the conditional PDF of the flamelet parameter needs to be developed. Further, the ability of FPVA to predict extinction and re-ignition has also not been assessed. In this paper, we address these aspects of the model using the DNS database of Sripakagorn et al. It is first shown that the steady flamelet assumption in the context of FPVA leads to good predictions even for high levels of local extinction. Three different models for the conditional PDF of the flamelet parameter are tested in an a priori sense. Results obtained using a delta function to model the conditional PDF of λ lead to an overprediction of the mean temperature, even with only moderate extinction levels. It is shown that if the conditional PDF of λ is modeled by a beta distribution conditioned on Z, then FPVA can predict extinction and re-ignition effects, and good agreement between the model and DNS data for the mean temperature is observed.     

Simulation of transient turbulent methane jet ignition and combustion under engine-relevant conditions using conditional source-term estimation with detailed chemistry

The ignition and combustion processes of transient turbulent methane jets under high-pressure and moderate temperature conditions were simulated using a computationally efficient combustion model. Closure for the mean chemical source-terms was obtained with Conditional Source-term Estimation (CSE) using first conditional moment closure in conjunction with a detailed chemical kinetic mechanism, which was reduced to a Trajectory-Generated Low-Dimensional Manifold (TGLDM). The accuracy of the manifold was first validated against the direct integral method by comparing the predicted reactive scalar profiles in three methane–air reaction systems: a laminar premixed flame, a laminar flamelet and a perfectly stirred reactor. Detailed CFD simulations incorporating the CSE-TGLDM model were able to provide reasonably good predictions of the experimental ignition delay and initial ignition kernel locations of the methane jets reported in the literature with relatively low computational cost. Nitrogen oxides formed in the methane jet flame were found to be underpredicted by the model by as much as a factor of 2. The discrepancy may be attributable to the inability of the simulation to account for the effects of the rarefaction wave in the shock-tube experiments.     

Species and temperature predictions in a semi-industrial MILD furnace using a non-adiabatic conditional source-term estimation formulation

A Reynolds-Averaged Navier–Stokes (RANS) simulation of the semi-industrial International Flame Research Foundation (IFRF) furnace is performed using a non-adiabatic Conditional Source-term Estimation (CSE) formulation. This represents the first time that a CSE formulation, which accounts for the effect of radiation on the conditional reaction rates, has been applied to a large scale semi-industrial furnace. The objective of the current study is to assess the capabilities of CSE to accurately reproduce the velocity field, temperature, species concentration and nitrogen oxides (NO_x) emission for the IFRF furnace. The flow field is solved using the standard k–ε turbulence model and detailed chemistry is included. NO_x emissions are calculated using two different methods. Predicted velocity profiles are in good agreement with the experimental data. The predicted peak temperature occurs closer to the centreline, as compared to the experimental observations, suggesting that the mixing between the fuel jet and vitiated air jet may be overestimated. Good agreement between the species concentrations, including NO_x, and the experimental data is observed near the burner exit. Farther downstream, the centreline oxygen concentration is found to be underpredicted. Predicted NO_x concentrations are in good agreement with experimental data when calculated using the method of Peters and Weber. The current study indicates that RANS-CSE can accurately predict the main characteristics seen in a semi-industrial IFRF furnace.     

High-repetition rate measurements of temperature and thermal dissipation in a non-premixed turbulent jet flame

High-repetition rate laser Rayleigh scattering is used to study the temperature fluctuations, power spectra, gradients, and thermal dissipation rate characteristics of a non-premixed turbulent jet flame at a Reynolds number of 15,200. The radial temperature gradient is measured by a two-point technique, whereas the axial gradient is measured from the temperature time-series combined with Taylor’s hypothesis. The temperature power spectra along the jet centerline exhibit only a small inertial subrange, probably because of the low local Reynolds number (Re_δ ≈ 2000), although a larger inertial subrange is present in the spectra at off-centerline locations. Scaling the frequency by the estimated Batchelor frequency improves the collapse of the dissipation region of the spectra, but this collapse is not as good as is obtained in non-reacting jets. Probability density functions of the thermal dissipation are shown to deviate from lognormal in the low-dissipation portion of the distribution when only one component of the gradient is used. In contrast, nearly log-normal distributions are obtained along the centerline when both axial and radial components are included, even for locations where the axial gradient is not resolved. The thermal dissipation PDFs measured off the centerline deviate from log-normal owing to large-scale intermittency. At one-half the visible flame length, the radial profile of the mean thermal dissipation exhibits a peak off the centerline, whereas farther downstream the peak dissipation occurs on the centerline. The mean thermal dissipation on centerline is observed to increase linearly with downstream distance, reach a peak at the location of maximum mean centerline temperature, and then decrease for farther downstream locations. Many of these observed trends are not consistent with equivalent non-reacting turbulent jet measurements, and thus indicate the importance of understanding how heat release modifies the turbulence structure of jet flames.     

Effects of confinement on premixed turbulent swirling flame using large Eddy simulation

This paper utilises large eddy simulation (LES) to study swirling reacting flows by comparison with experimental observations. The purpose is to provide further insights in engineering designs, as well as to improve modelling. A reduced-scale swirl burner has been developed for the experiments. Comparison of particle image velocimetry (PIV) measurements with LES results using finite rate chemistry shows that LES captures all the salient features of an unconfined flame including velocity and temperature distributions. However, when the flame is confined within a cylindrical combustor, the simulated flame shape is initially not consistent with experimental observation. Investigations show that the discrepancy is caused by the often practised assumption of adiabatic wall temperature. With the use of an assumed wall temperature distribution guided by laboratory observation, results of LES are consistent with experiments. Although the latter LES approach requires more computational resources, the improvement is found to be justified.     

Transported probability density function modeling of a bluff body stabilized turbulent flame

A transported probability density function (PDF) approach closed at the joint scalar level is used to model the bluff body stabilized turbulent diffusion flame (HM1) investigated experimentally by Masri and co-workers (Re = 15,800). The current effort extends previous work through the introduction of comprehensive thermochemistry computed via a systematically reduced C/H/N/O mechanism featuring 300 reactions, 20 solved, and 28 steady-state species. Molecular mixing is modelled using the modified Curl’s model. The current computations have been performed via a hybrid Monte Carlo/Finite Volume algorithm. The joint scalar PDF equations are solved using moving particles in a Lagrangian framework, and the velocity field is closed at the second moment level. The redistribution terms are modelled using the Generalized Langevin Model of Haworth and Pope. The principal aim was to investigate the thermochemical effects, and thus a steady-state calculation procedure is adopted. The computations are shown to reproduce experimental mean and rms values of velocities, temperature, mixture, and species mass fractions. In particular, mass fractions of CO and NO are well predicted. Conditional PDFs are also well reproduced although uncertainties in boundary conditions influence results close to the bluff body.     

The effect of co-flow stream velocity on turbulent non-premixed jet flame stability

The stability behaviour of non-premixed jet flames in a co-flowing air stream was investigated experimentally. The experimental data obtained indicate that there exists a range of co-flow velocity where two distinctly different extinction limits can occur at the same co-flow velocity depending on whether the flame is lifted or attached at ignition. Results show that co-flow velocity has a much greater effect on the blowout limits of lifted flames than on the blowoff limits of attached flames. The blowout limit of lifted flames initially increase linearly with co-flow velocity independent of nozzle diameter until a peak value is reached, after which it decreases rapidly with increasing co-flow velocity. Such behaviour appears to be governed by two different mechanisms. A model for predicting lifted flame blowout limits has been developed. It is based on the ratio of the Kolmogorov time scale and the chemical time scale as a function of a jet similarity parameter. The model was used to predict the blowout limits for methane as well as the effect of diluents in either fuel or co-flow stream. Results show very good agreement with experimental data in the current investigation.     

Large eddy simulation of turbulent combustion systems

This paper reviews recent and ongoing work on numerical models for turbulent combustion systems based on a classical LES approach. The work is confined to single-phase reacting flows. First, important physico-chemical features of combustion-LES are discussed along with several aspects of overall LES models. Subsequently, some numerical issues, in particular questions associated with the reliability of LES results, are outlined. The details of chemistry, its reduction, and tabulation are not addressed here. Second, two illustrative applications dealing with non-premixed and premixed flame configurations are presented. The results show that combustion-LES is able to provide predictions very close to measured data for configurations where the flow is governed by large turbulent structures. To meet the future demands, new key challenges in specific modelling areas are suggested, and opportunities for advancements in combustion-LES techniques are highlighted. From a predictive point of view, the main target must be to provide a reliable method to aid combustion safety studies and the design of combustion systems of practical importance.     

Analysis of kinetic mechanism performance in conditional moment closure modelling of turbulent,non-premixed methane flames

This paper presents results obtained from the application of a first-order conditional moment closure approach to the modelling of two methane flames of differing geometries. Predictions are based upon a second-moment turbulence and scalar-flux closure, and supplemented with full and reduced chemical kinetic mechanisms, ranging from a simple 12-step to a complex 1207-step mechanism. Alongside analysis of the full kinetic schemes' performance, is an appraisal of the behaviour of their derivatives obtained using mechanism-reduction techniques. The study was undertaken to analyse the practicality of incorporating kinetic models of varying complexity into calculations of turbulent non-premixed flames, and to make comparison of their performance. Despite extensive studies of the predictive ability of such schemes under laminar flame conditions, systematic evaluations have not been performed for turbulent reacting flows. This paper reflects upon the impact that selection of chemical kinetics has upon subsequent calculations and concludes that, although application of reduced schemes is more than adequate to reproduce experimental data, selection of the parent mechanism is of paramount importance to the prediction of minor species. Although widely used schemes are well documented and validated, their performances vary considerably. Thus, careful consideration must be made to their application and origins during the evaluation of combustion models.     

LES modelling of turbulent non-premixed jet flames with correlated dynamic adaptive chemistry

Large eddy simulations (LES) for turbulent flames with detailed kinetic mechanisms have received growing interest. However, a direct implementation of detailed kinetic mechanisms in LES modelling of turbulent combustion remains a challenge due to the requirement of huge computational resources. An on-the-fly mechanism reduction method named correlated dynamic adaptive chemistry (CoDAC) is proposed to overcome this issue. A LES was conducted for Sandia Flame-D, with the reaction mechanism of GRI-Mech 3.0 consisting of 53 species and 325 reactions. The reduction threshold used in LES was obtained a priori by using auto-ignition model and partially stirred reactor (PaSR) with pairwise mixing model. LES results with CoDAC are in good agreement with experimental data and those without reduction. The conditional mean of the number of selected species indicates that a large size of locally reduced mechanism is required in the reaction zone where CH₄ is destructed. A computational time analysis shows that the PaSR model predicts better than the auto-ignition model on the wall time reduction with CoDAC in LES.     

LES of the Sydney swirl flame series: A study of vortex breakdown in isothermal and reacting flows

This work examines the flow and mixing in selected non-premixed cases of the Sydney Swirl Flame series by Large Eddy Simulation. A mixture fraction approach with a steady flamelet model, based on a detailed chemical mechanism, is applied to determine the chemical state in the flame. The isothermal case N29S054 is simulated to provide insights into the flow field, the resolution requirements for the simulation, and to allow for various measures of validation and verification. For the reactive case, the high-speed hydrogen/methane flame SMH1 is chosen for its similarity to the non-swirling Sydney flames and its good stability. In experiments carried out previously at Sydney University, vortex breakdown has been observed and in the isothermal case, this is clearly predicted by the LES. However, no vortex breakdown is observed in the simulations of flame SMH1, which necessitates further studies on this and similar flames to investigate this phenomenon. Studies of the low-velocity flames SM1 and SM2 show that reactive vortex breakdown can be predicted successfully. This difficulty in the prediction of vortex breakdown is another indication that the Sydney Swirl Flame series, especially at high velocities of the central jet, is an interesting and challenging test-case for the development of combustion LES.     

CMC simulations of lifted turbulent jet flame in a vitiated coflow

Lifted turbulent jet diffusion flame is simulated using Conditional Moment Closure (CMC). Specifically, the burner configuration of Cabra et al. [R. Cabra, T. Myhrvold, J.Y. Chen, R.W. Dibble, A.N. Karpetis, R.S. Barlow, Proc. Combust. Inst. 29 (2002) 1881–1887] is chosen to investigate H₂/N₂ jet flame supported by a vitiated coflow of products of lean H₂/air combustion. A 2D, axisymmetric flow-model fully coupled with the scalar fields, is employed. A detailed chemical kinetic scheme is included, and first order CMC is applied. Simulations are carried out for different jet velocities and coflow temperatures (T_c). The predicted liftoff generally agrees with experimental data, as well as joint-PDF results. Profiles of mean scalar fluxes in the mixture fraction space, for T_c=1025 and 1080 K reveal that (1) Inside the flame zone, the chemical term balances the molecular diffusion term, and hence the structure is of a diffusion flamelet for both cases. (2) In the pre-flame zone, the structure depends on the coflow temperature: for the 1025 K case, the chemical term being small, the advective term balances the axial turbulent diffusion term. However, for the 1080 K case, the chemical term is large and balances the advective term, the axial turbulent diffusion term being small. It is concluded that, lift-off is controlled (a) by turbulent premixed flame propagation for low coflow temperature while (b) by autoignition for high coflow temperature.     

Identification and analysis of instability in non-premixed swirling flames using LES

Large eddy simulations (LES) of turbulent non-premixed swirling flames based on the Sydney swirl burner experiments under different flame characteristics are used to uncover the underlying instability modes responsible for the centre jet precession and large scale recirculation zone. The selected flame series known as SMH flames have a fuel mixture of methane-hydrogen (50:50 by volume). The LES solves the governing equations on a structured Cartesian grid using a finite volume method, with turbulence and combustion modelling based on the localised dynamic Smagorinsky model and the steady laminar flamelet model respectively. The LES results are validated against experimental measurements and overall the LES yields good qualitative and quantitative agreement with the experimental observations. Analysis showed that the LES predicted two types of instability modes near fuel jet region and bluff body stabilised recirculation zone region. The mode I instability defined as cyclic precession of a centre jet is identified using the time periodicity of the centre jet in flames SMH1 and SMH2 and the mode II instability defined as cyclic expansion and collapse of the recirculation zone is identified using the time periodicity of the recirculation zone in flame SMH3. Finally frequency spectra obtained from the LES are found to be in good agreement with the experimentally observed precession frequencies.     

Application of Conditional Source-term Estimation to two turbulent non-premixed methanol flames

Conditional Source-term Estimation (CSE) is a turbulent combustion model that uses conditional averages to close the chemical source term. Previous CSE studies have shown that the model is able to predict the flame characteristics successfully; however, these studies have only focused on simple hydrocarbon fuels mostly composed of methane. The objective of the present paper is to evaluate the capabilities of CSE applied to turbulent non-premixed methanol flames, which has never been done previously. The current study investigates two different types of methanol flames: piloted and bluff-body flames. For the piloted flame, the standard k–ε model is used for turbulence modelling, while the Shear Stress Transport (SST) k–ω model is applied to the bluff-body case. Different values of empirical constants within the turbulence models were tested, and it was found that C_ε1 = 1.7 for the piloted flame and γ₂ = 0.66 for the bluff-body flame provided the best agreement with experimental measurements for the mixing field. Detailed chemistry is included in tabulated form using the Trajectory Generated Low-Dimensional Manifold (TGLDM) method. The predictions including both the Favre-averaged and conditional mass fraction of reactive species and temperature are compared with available experimental data and previous numerical results. Overall, the CSE predictions of conditional and unconditional quantities are in good agreement with the experimental data except for hydrogen. Sources of discrepancies are identified such as the chemical kinetics and neglect of differential diffusion. Large eddy simulations may also help to improve the velocity and mixing field predictions.