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.     

Large eddy simulation of turbulent premixed combustion using tabulated detailed chemistry and presumed probability density function

A method of chemistry tabulation combined with presumed probability density function (PDF) is applied to simulate piloted premixed jet burner flames with high Karlovitz number using large eddy simulation. Thermo-chemistry states are tabulated by the combination of auto-ignition and extended auto-ignition model. To evaluate the predictive capability of the proposed tabulation method to represent the thermo-chemistry states under the condition of different fresh gases temperature, a-priori study is conducted by performing idealised transient one-dimensional premixed flame simulations. Presumed PDF is used to involve the interaction of turbulence and flame with beta PDF to model the reaction progress variable distribution. Two presumed PDF models, Dirichlet distribution and independent beta distribution, respectively, are applied for representing the interaction between two mixture fractions that are associated with three inlet streams. Comparisons of statistical results show that two presumed PDF models for the two mixture fractions are both capable of predicting temperature and major species profiles, however, they are shown to have a significant effect on the predictions for intermediate species. An analysis of the thermo-chemical state-space representation of the sub-grid scale (SGS) combustion model is performed by comparing correlations between the carbon monoxide mass fraction and temperature. The SGS combustion model based on the proposed chemistry tabulation can reasonably capture the peak value and change trend of intermediate species. Aspects regarding model extensions to adequately predict the peak location of intermediate species are discussed.     

Complex chemistry simulations of spark ignition in turbulent sprays

Three-dimensional DNS of two-phase flows with the point-source approximation and with complex chemistry for n-heptane has been used to extract physical information on the structure of igniting kernels following localised heat deposition in turbulent monodisperse sprays. Consistent with experiment, small sparks fail to ignite and sprays ignite later than premixed gaseous mixtures. Reaction rates are intense in spherical zones near droplets and much lower in the interdroplet spacing, resulting in a highly wrinkled flame surface. The propagation of these reaction zones was observed. The flame shows a locally non-premixed character, with reactions proceeding at a wide range of mixture fractions, which increases as evaporation progresses. The distribution of various chemical species is presented. The results constitute a database for model validation and physical analysis.     

A LES/PDF simulator on block-structured meshes

A block-structured mesh large-eddy simulation (LES)/probability density function (PDF) simulator is developed within the OpenFOAM framework for computational modelling of complex turbulent reacting flows. The LES/PDF solver is a hybrid solution methodology consisting of (i) a finite-volume (FV) method for solving the filtered mass and momentum equations (LES solver), and (ii) a Lagrangian particle-based Monte Carlo algorithm (PDF solver) for solving the modelled transport equation of the filtered joint PDF of compositions. Both the LES and the PDF methods are developed and combined to form a hybrid LES/PDF simulator entirely within the OpenFOAM framework. The in situ adaptive tabulation method [S.B. Pope, Computationally efficient implementation of combustion chemistry using in situ adaptive tabulation, Combust. Theory Model. 1 (1997), pp. 41–63; L. Lu, S.R. Lantz, Z. Ren, and B.S. Pope, Computationally efficient implementation of combustion chemistry in parallel PDF calculations, J. Comput. Phys. 228 (2009), pp. 5490–5525] is incorporated into the new LES/PDF solver for efficient computations of combustion chemistry with detailed reaction kinetics. The method is designed to utilise a block-structured mesh and can readily be extended to unstructured grids. The three-stage velocity interpolation method of Zhang and Haworth [A general mass consistency algorithm for hybrid particle/finite-volume PDF methods, J. Comput. Phys. 194 (2004), pp. 156–193] is adapted to interpolate the LES velocity field onto particle locations accurately and to enforce the consistency between LES and PDF fields at the numerical solution level. The hybrid algorithm is fully parallelised using the conventional domain decomposition approach. A detailed examination of the effects of each stage and the overall performance of the velocity interpolation algorithm is performed. Accurate coupling of the LES and PDF solvers is demonstrated using the one-way coupling methodology. Then the fully two-way coupled LES/PDF solver is successfully applied to simulate the Sandia Flame-D, and a turbulent non-swirling premixed flame and a turbulent swirling stratified flame from the Cambridge turbulent stratified flame series [M.S. Sweeney, S. Hochgreb, M.J. Dunn, and R.S. Barlow, The structure of turbulent stratified and premixed methane/air flames I: Non-swirling flows, Combust. Flame 159 (2012), pp. 2896–2911; M.S. Sweeney, S. Hochgreb, M.J. Dunn, and R.S. Barlow, The structure of turbulent stratified and premixed methane/air flames II: Swirling flows, Combust. Flame 159 (2012), pp. 2912–2929]. It is found that the LES/PDF method is very robust and the results are in good agreement with the experimental data for both flames.     

A quadrature-based LES/transported probability density function approach for modeling supersonic combustion

The joint-scalar probability density function (PDF) approach provides a comprehensive framework for large eddy simulation (LES) based combustion modeling. However, currently available stochastic approaches for solving the high-dimensional PDF transport equation can be error prone and numerically unstable in highly compressible shock-containing flows. In this work, a novel Eulerian approach called the direct quadrature method of moments (DQMOM) is developed for evolving the PDF-based supersonic combustion model. The DQMOM technique uses a set of scalar transport equations with specific source terms to recover the PDF. The new technique is coupled to a compressible LES solver through the energy equation. The DQMOM approach is then used to simulate two practical flow configurations: a supersonic reacting jet and a cavity-stabilized supersonic combustor. Comparisons with experimental data demonstrate the predictive accuracy of the method.     

Effects of subgrid scale and combustion modelling on flame structure of a turbulent premixed flame within LES and tabulated chemistry framework

The effects of combustion and SubGrid Scale (SGS) modelling on the overall flame characteristics of a turbulent premixed flame are investigated. This is achieved in terms of mean flow statistics, variances and flame surfaces. In particular, the chemical flame structure is analysed and compared. The Artificially Thickened Flame (ATF) approach coupled with the Flamelet Generated Manifolds (FGMs) and Filtered TAbulated Chemistry for LES (F-TACLES) approaches are used for this investigation. A Germano like procedure for dynamical calculation of SGS wrinkling is used which ensures the conservation of the total flame surface for both models. It turns out that using the dynamic SGS wrinkling model improves the results. Although the results of both combustion models in terms of statistics, mean and variances show very good agreement, the resolved flame surfaces hide different dynamic behaviour.     

Large eddy simulations of turbulent flames using the filtered density function model

Large eddy simulations (LES) of the Sandia/Sydney swirl burners (SM1 and SMA1) and the Sandia/Darmstadt piloted jet diffusion flame (Flame D) are performed. These flames are part of the database of turbulent reacting flows widely considered as benchmark test cases for validating turbulent-combustion models. In the simulations presented in this paper, the subgrid scale (SGS) closure model adopted for turbulence-chemistry interactions is based on the transport filtered density function (FDF) model. In the FDF model, the transport equation for the joint probability density function (PDF) of scalars is solved. The main advantage of this model is that the filtered reaction rates can be exactly computed. However, the density field, computed directly from the FDF solver and needed in the hydrodynamic equations, is noisy and causes numerical instability. Two numerical approaches that yield a smooth density field are examined. The two methods are based on transport equations for specific sensible enthalpy (h_s) and RT, where R is the gas constant and T is the temperature. Consistency of the two methods is assessed in a bluff-body configuration using Reynolds averaged Navier-Stokes (RANS) methodology in conjunction with the transported PDF method. It is observed that the h_s method is superior to the RT method. Both methods are used in LES of the SM1 burner. In the near-field region, the h_s method produces better predictions of temperature. However, in the far-field region, both methods show deviation from data. Simulations of the SMA1 burner and Flame D are also presented using the h_s method. Some deficiencies are seen in the predictions of the SMA1 burner that may be related to the simple chemical kinetics model and mixing model used in the simulations. Simulations of Flame D show good agreement with data. These results indicate that, while further improvements to the methodology are needed, the LES/FDF method has the potential to accurately predict complex turbulent flames.     

Effect of non-zero relative velocity on the flame speed of two-phase laminar flames

A numerical study of one-dimensional n-heptane/air spray flames is presented. The objective is to evaluate the flame propagation speed in the case where droplets evaporate inside the reaction zone with possibly non-zero relative velocity. A Direct Numerical Simulation approach for the gaseous phase is coupled to a discrete particle Lagrangian formalism for the dispersed phase. A global two-step n-heptane/air chemical mechanism is used. The effects of initial droplet diameter, overall equivalence ratio, liquid loading and relative velocity between gaseous and liquid phases on the laminar spray flame speed and structure are studied. For lean premixed cases, it is found that the laminar flame speed decreases with increasing initial droplet diameter and relative velocity. On the contrary, rich premixed cases show a range of diameters for which the flame speed is enhanced compared to the corresponding purely gaseous flame. Finally, spray flames controlled by evaporation always have lower flame speeds. To highlight the controlling parameters of spray flame speed, approximate analytical expressions are proposed, which give the correct trends of the spray flame propagation speed behavior for both lean and rich mixtures.     

Studies of the flow and turbulence fields in a turbulent pulsed jet flame using LES/PDF

A turbulent piloted jet flame subject to a rapid velocity pulse in its fuel jet inflow is proposed as a new benchmark case for the study of turbulent combustion models. In this work, we perform modelling studies of this turbulent pulsed jet flame and focus on the predictions of its flow and turbulence fields. An advanced modelling strategy combining the large eddy simulation (LES) and the probability density function (PDF) methods is employed to model the turbulent pulsed jet flame. Characteristics of the velocity measurements are analysed to produce a time-dependent inflow condition that can be fed into the simulations. The effect of the uncertainty in the inflow turbulence intensity is investigated and is found to be very small. A method of specifying the inflow turbulence boundary condition for the simulations of the pulsed jet flame is assessed. The strategies for validating LES of statistically transient flames are discussed, and a new framework is developed consisting of different averaging strategies and a bootstrap method for constructing confidence intervals. Parametric studies are performed to examine the sensitivity of the predictions of the flow and turbulence fields to model and numerical parameters. A direct comparison of the predicted and measured time series of the axial velocity demonstrates a satisfactory prediction of the flow and turbulence fields of the pulsed jet flame by the employed modelling methods.     

Modelling of the subgrid scale wrinkling factor for large eddy simulation of turbulent premixed combustion

We propose a model for assessing the unresolved wrinkling factor in the large eddy simulation of turbulent premixed combustion. It relies essentially on a power-law dependence of the wrinkling factor on the filter size and an original expression for the ‘active’ corrugating strain rate. The latter is written as the turbulent strain multiplied by an efficiency function that accounts for viscous effects and the kinematic constraint of Peters. This yields functional expressions for the fractal dimension and the inner cut-off length scale, the latter being (i) filter-size independent and (ii) consistent with the Damköhler asymptotic behaviours at both large and small Karlovitz numbers. A new expression for the wrinkling factor that incorporates finite Reynolds number effects is further proposed. Finally, the model is successfully assessed on an experimental filtered database.     

Direct numerical simulations of rich premixed turbulent n-dodecane/air flames at diesel engine conditions

Rich premixed turbulent n-dodecane/air flames at diesel engine conditions are analyzed using direct numerical simulations. The conditions correspond to a parametric variation of the Engine Combustion Network Spray A (pressure 60 atm; oxidizer oxygen level and temperature 21% and 900 K, respectively; fuel temperature 363 K). Three simulations with equivalence ratios of 3, 5, and 7 are performed with a Karlovitz number (Ka, based on flame time) of order 100 to match the estimated Ka of the rich premixed combustion region in Spray A. At these conditions, the reference laminar flames exhibit a complex structure which involves both low-temperature chemistry (LTC) and high-temperature chemistry over a wide range of length scales. In the presence of turbulence, the flame structure is strongly affected in physical space and the reaction zone exhibits a very complex structure in which broken, distributed, and thin regions co-exist, especially for the leanest case. However, the contribution of the LTC pathway is only weakly affected by turbulence. In progress variable space, the mean flame structure, including the chemical source terms, is found to match remarkably well that of the corresponding unity Lewis number laminar flame, particularly for the $?=$ 3 and 5 cases. This behavior is attributed to the strong turbulent mixing occurring throughout the flames/reaction zones, which suppresses differential diffusion effects. Nevertheless, large conditional fluctuations around the mean chemical source terms are identified. These are found to correlate very well with radical species mass fractions such as OH. In addition, a similar functional dependence is obtained from counterflow laminar flames. As such, it appears from these results that laminar flame models have a potential to be used to represent the thermochemical state of rich premixed turbulent flames under diesel engine conditions.     

A multi-zone chemistry mapping approach for direct numerical simulation of auto-ignition and flame propagation in a constant volume enclosure

A direct numerical simulation (DNS) coupling with multi-zone chemistry mapping (MZCM) is presented to simulate flame propagation and auto-ignition in premixed fuel/air mixtures. In the MZCM approach, the physical domain is mapped into a low-dimensional phase domain with a few thermodynamic variables as the independent variables. The approach is based on the fractional step method, in which the flow and transport are solved in the flow time steps whereas the integration of the chemical reaction rates and heat release rate is performed in much finer time steps to accommodate the small time scales in the chemical reactions. It is shown that for premixed mixtures, two independent variables can be sufficient to construct the phase space to achieve a satisfactory mapping. The two variables can be the temperature of the mixture and the specific element mass ratio of H atom for fuels containing hydrogen atoms. An aliasing error in the MZCM is investigated. It is shown that if the element mass ratio is based on the element involved in the most diffusive molecules, the aliasing error of the model can approach zero when the grid in the phase space is refined. The results of DNS coupled with MZCM (DNS-MZCM) are compared with full DNS that integrates the chemical reaction rates and heat release rate directly in physical space. Application of the MZCM to different mixtures of fuel and air is presented to demonstrate the performance of the method for combustion processes with different complexity in the chemical kinetics, transport and flame–turbulence interaction. Good agreement between the results from DNS and DNS-MZCM is obtained for different fuel/air mixtures, including H₂/air, CO/H₂/air and methane/air, while the computational time is reduced by nearly 70%. It is shown that the MZCM model can properly address important phenomena such as differential diffusion, local extinction and re-ignition in premixed combustion.     

Effects of combined dimension reduction and tabulation on the simulations of a turbulent premixed flame using a large-eddy simulation/probability density function method

A turbulent lean-premixed propane–air flame stabilised by a triangular cylinder as a flame-holder is simulated to assess the accuracy and computational efficiency of combined dimension reduction and tabulation of chemistry. The computational condition matches the Volvo rig experiments. For the reactive simulation, the Lagrangian Large-Eddy Simulation/Probability Density Function (LES/PDF) formulation is used. A novel two-way coupling approach between LES and PDF is applied to obtain resolved density to reduce its statistical fluctuations. Composition mixing is evaluated by the modified Interaction-by-Exchange with the Mean (IEM) model. A baseline case uses In Situ Adaptive Tabulation (ISAT) to calculate chemical reactions efficiently. Its results demonstrate good agreement with the experimental measurements in turbulence statistics, temperature, and minor species mass fractions. For dimension reduction, 11 and 16 represented species are chosen and a variant of Rate Controlled Constrained Equilibrium (RCCE) is applied in conjunction with ISAT to each case. All the quantities in the comparison are indistinguishable from the baseline results using ISAT only. The combined use of RCCE/ISAT reduces the computational time for chemical reaction by more than 50%. However, for the current turbulent premixed flame, chemical reaction takes only a minor portion of the overall computational cost, in contrast to non-premixed flame simulations using LES/PDF, presumably due to the restricted manifold of purely premixed flame in the composition space. Instead, composition mixing is the major contributor to cost reduction since the mean-drift term, which is computationally expensive, is computed for the reduced representation. Overall, a reduction of more than 15% in the computational cost is obtained.     

A Eulerian PDF scheme for LES of nonpremixed turbulent combustion with second-order accurate mixture fraction

Monte Carlo simulations of joint probability density function (PDF) approaches have been developed in the past largely with Reynolds averaged Navier Stokes (RANS) applications. Current interests are in the extension of PDF approaches to large eddy simulation (LES). As LES resolves accurately the large scales of turbulence in time, the Monte Carlo simulation and the flow field need to be tightly coupled. A tight coupling can be achieved if the consistency between the scalar field solution obtained via finite-volume (FV) methods and that from the stochastic solution of the PDF is ensured. For nonpremixed turbulent flames with two distinct streams, the local reactive mixture is described by the mixture fraction. A Eulerian Monte Carlo method is developed to achieve a second-order accuracy in the instantaneous filtered mixture fraction that is consistent with the corresponding FV. The performances of the proposed scheme are extensively evaluated using a one-dimensional model. Then, the scheme is applied to two cases with LES. The first one is a non-reacting mixing flow of two different fluids. The second case is the Sandia piloted turbulent flame D with a steady state flamelet model. Both results confirm the consistency of the proposed method to the level of filtered mixture fraction.     

Transported PDF simulation of turbulent CH4/H2 flames under MILD conditions with particle-level sensitivity analysis

Transported probability density function (TPDF) simulation with sensitivity analysis has been conducted for turbulent non-premixed CH₄/H₂ flames of the jet-into-hot-coflow (JHC) burner, which is a typical model to emulate moderate or intense low oxygen dilution combustion (MILD). Specifically, two cases with different levels of oxygen in the coflow stream, namely HM1 and HM3, are simulated to reveal the differences between MILD and hot-temperature combustion. The TPDF simulation well predicts the temperature and species distributions including those of OH, CO and NO for both cases with a 25-species mechanism. The reduced reaction activity in HM1 as reflected in the peak OH concentration is well correlated to the reduced oxygen in the coflow stream. The particle-level local sensitivities with respect to mixing and chemical reaction further show dramatic differences in the flame characteristics. HM1 is less sensitive to mixing and reaction parameters than HM3 due to the suppressed combustion process. Specifically, for HM1 the sensitivities to mixing and chemical reactions have comparable magnitude, indicating that the combustion progress is controlled by both mixing and reaction in MILD combustion. For HM3, there is however a change in the combustion mode: during the flame initialization, the combustion progress is more sensitive to chemical reactions, indicating that finite-rate chemistry is the controlling process during the autoignition process for flame stabilization; at further downstream where the flame has established, the combustion progress is controlled by mixing, which is characteristic of nonpremixed flames. An examination of the particles with the largest sensitivities reveals the difference in the controlling mixtures for flame stabilization, namely, the stoichiometric mixtures are important for HM1, whereas, fuel-lean mixtures are controlling for HM3. The study demonstrates the potential of TPDF simulations with sensitivity analysis to investigate the effects of finite-rate chemistry on the flame characteristics and emissions, and reveal the controlling physio-chemical processes in MILD combustion.     

A spray flamelet/progress variable approach combined with a transported joint PDF model for turbulent spray flames

A spray flamelet/progress variable approach is developed for use in spray combustion with partly pre-vaporised liquid fuel, where a laminar spray flamelet library accounts for evaporation within the laminar flame structures. For this purpose, the standard spray flamelet formulation for pure evaporating liquid fuel and oxidiser is extended by a chemical reaction progress variable in both the turbulent spray flame model and the laminar spray flame structures, in order to account for the effect of pre-vaporised liquid fuel for instance through use of a pilot flame. This new approach is combined with a transported joint probability density function (PDF) method for the simulation of a turbulent piloted ethanol/air spray flame, and the extension requires the formulation of a joint three-variate PDF depending on the gas phase mixture fraction, the chemical reaction progress variable, and gas enthalpy. The molecular mixing is modelled with the extended interaction-by-exchange-with-the-mean (IEM) model, where source terms account for spray evaporation and heat exchange due to evaporation as well as the chemical reaction rate for the chemical reaction progress variable. This is the first formulation using a spray flamelet model considering both evaporation and partly pre-vaporised liquid fuel within the laminar spray flamelets. Results with this new formulation show good agreement with the experimental data provided by A.R. Masri, Sydney, Australia. The analysis of the Lagrangian statistics of the gas temperature and the OH mass fraction indicates that partially premixed combustion prevails near the nozzle exit of the spray, whereas further downstream, the non-premixed flame is promoted towards the inner rich-side of the spray jet since the pilot flame heats up the premixed inner spray zone. In summary, the simulation with the new formulation considering the reaction progress variable shows good performance, greatly improving the standard formulation, and it provides new insight into the local structure of this complex spray flame.     

Effect of fuel mixture fraction and velocity perturbations on the flame transfer function of swirl stabilized flames

A novel methodology is developed to decompose the classic Flame Transfer Function (FTF) used in the thermo-acoustic stability analysis of lean premix combustors into contributions of different types. The approach is applied, in the context of Large Eddy Simulation (LES), to partially-premixed and fully-premixed flames, which are stabilized via a central recirculation zone as a result of the vortex breakdown phenomenon. The first type of decomposition is into contributions driven by fuel mixture fraction and dynamic velocity fluctuations. Each of these two contributions is further split into the components of turbulent flame speed and flame surface area. The flame surface area component, driven by the pure dynamic velocity fluctuation, which is shown to be a dominant contribution to the overall FTF, is also additionally decomposed over the coherent flow structures using proper orthogonal decomposition. Using a simplified model for the dynamic response of premixed flames, it is shown that the distribution of the FTF, as obtained from LES, is closely related to the characteristics of the velocity field frequency response to the inlet perturbation. Initially, the proposed method is tested and validated with a well characterized laboratory burner geometry. Subsequently, the method is applied to an industrial gas turbine burner.     

A flamelet analysis of the burning velocity of premixed turbulent expanding flames

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 corrugated flamelet regime are performed. The flamelet-generated manifold method is used to deal with detailed reaction kinetics. The numerical method is validated for both laminar and turbulent expanding flames. 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. If the full profiles of flame stretch and curvature through the flame front are included in the theory, the local mass burning rate is predicted accurately. The influence of several approximations, which are used in other existing theories, is studied. When flame stretch is assumed to be constant through the flame front or when curvature of the flame front is neglected, the theory fails to predict the local mass burning rate.