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A novel multiple mapping conditioning (MMC) mixing time scale model for turbulent premixed combustion has been developed. It combines time scales for the flamelet and distributed flame regimes with the aid of a blending function. The blending function serves two purposes. Firstly, it helps to identify zones where the premixed flame resides and where the time scale associated with the premixed flame shall be used. Secondly, it uses the Karlovitz number to identify the turbulent premixed combustion regime and to reduce the weighting of the premixed flame time scale if Karlovitz numbers are high and deviations from the flamelet regime are expected. A series of three-dimensional direct numerical simulations (DNS) of statistically one dimensional, freely propagating turbulent methane-air flames provides a wide range of turbulent combustion regimes for the mixing model validation. The new mixing time scale provides correct predictions of the flame speed of freely propagating turbulent flames which could not be matched by most recognized mixing models. The turbulent flame structure predicted by the new model is in good agreement with DNS for all combustion regimes from flamelet to the thickened reaction zone.

A coaxial burner with a hydrogen-supported pulverized coal flame, operated by the Central Research Institute of Electric Power Industry (CRIEPI, Japan), is investigated numerically. The flame is modeled using massively parallel large eddy simulation (LES). A flamelet/progress variable (FPV) approach is used for modeling the complex multiphase flow of the laboratory coal flame. A four-dimensional tabulation method based on non-premixed flamelets is introduced, which uses two mixture fractions for the hydrogen pilot and coal volatiles, respectively, as well as the absolute enthalpy and the reaction progress to parametrize the thermochemical space. Simulations are compared to the experiments in terms of the temperature, gas-phase velocities (with and without consideration of buoyancy), and gas compositions along the centerline and in the radial direction at different heights. The effect of the suction probe on the scalar field measurements is tested by simulating this probing, observing relative changes up to 50% in various quantities and locations. By consideration of these probe effects, the agreement between the experiment and simulation can be improved significantly; at the same time, the simulation also provides the unperturbed scalar fields, without probing effects. The new flamelet model gives a robust and cost-effective prediction of the investigated laboratory flame, provided that the probing effects are considered.

Machine learning techniques have been used for the closure of the conditional scalar dissipation rate in turbulent spray flames. Statistical data are extracted from carrier-phase direct numerical simulation (CP-DNS) results for the generation of artificial neural networks that are trained to predict the conditional scalar dissipation rate such that they could serve as a sub-grid model for large eddy simulations of spray combustion. A quantitative error assessment suggests that predictions of the conditionally averaged dissipation rate are in excellent agreement with CP-DNS data. Further comparison with commonly used models for the unconditionally filtered dissipation rate promises significant improvements if ANNs are used for closure. The artificial neural networks also help to identify the important features that affect the local dissipation rates. The results suggest that few - mostly droplet related - parameters suffice as input features for accurate ANNs. This is in contradiction to standard modeling techniques that are solely based on gas phase properties and highlights the need to revisit scalar dissipation rate modeling for spray flames if analytical expressions are to be used.

In the present study, we report the first large eddy simulation (LES) study of the Cambridge CCB2 coal flames, one of the target flames in the Workshop on Measurement and Simulation of Coal and Biomass Conversion, with an extended flamelet progress variable (FPV) model. The extended FPV model is based on two mixture fractions considering the volatiles and char off-gases. The normalized total enthalpy is used for the interphase heat transfer modelling. Turbulence-chemistry interaction is treated with an assumed probability density function approach. The results show that the present LES can generally capture the flow field and particle distribution, while there are considerable deviations in the OH prediction due to the boundary treatment of using a mixture of volatiles and carrier gas to replace the methane-containing mixtures in the primary and pilot flow. It indicates that for such gas-assisted coal flames, the pilot fuel stream needs to be rigorously considered in the flamelet tabulation that could be resolved by extending the two-mixture-fraction model into a three-mixture-fraction model. The instantaneous Lagrangian particles histories show that the increasing of coal load has a negligible effect on devolatilization, but delays the char conversion.

A sparse Lagrangian particle method (MMC) is coupled with large eddy simulations (LES) and applied to a series of ethanol spray flames that cover a wide range of jet Reynolds numbers and droplet loadings. Varying degrees of pre-evaporation of the liquid favour mixed combustion regimes and pose severe challenges to any combustion model. Three flames with gas-phase equivalence ratios of 1.75, 0.53 and 0.05 (with overall equivalence ratios of the fuel jet of 4.5, 1.4 and 1.8) are investigated and the simulations are overall in good agreement with the measurements. The dependencies of droplet velocities, evaporation rates and mean droplet diameters on flow and flame conditions are captured well, with a possible exception of a persistent underprediction of the average diameter at far downstream locations. This could be improved by modified inflow conditions where droplets are injected through a nozzle pipe far upstream of the nozzle exit plane. This ensures a correlation between the carrier phase and droplet velocities at the burner injection plane. The predictions of temperature are good to reasonable with some qualitative differences within the central jet for flames with high droplet loadings. Further analysis of the MMC model demonstrates that particle mixing preserves localness in composition space throughout the domain despite the presence of pre-evaporation and the related deviations from a pure non-premixed flame regime. MMC-LES predictions are very good for fully turbulent spray flames where evaporation is relatively fast and mixing is dominated by turbulence.

A sparse-Lagrangian particle implementation of the multiple mapping conditioning / large-eddy simulation (MMC-LES) model for two-phase flows is developed with the aid of carrier-phase direct numerical simulation (CP-DNS) of a droplet-laden temporally evolving reacting double shear layer. In sparse-Lagrangian MMC for spray combustion, the liquid fuel droplets are represented by a first set of Lagrangian particles, while the reacting gas phase is described by a second set of (stochastic) particles. The two phases exchange heat and mass and a one-to-one coupling technique of liquid and gas particles with particle pair selection conditional on mixture fraction and/or temperature is introduced. The simulations show that unconditional mean and rms of mixture fraction are accurately reproduced by MMC and are largely independent of the particle coupling. Temperature, however, is significantly underpredicted when using the Eulerian mixture fraction for particle selection as is conventional for particle-particle selection in MMC. This is due to a lack of correlation between temperature and mixture fraction caused by excessive cooling of selected fluid elements due to evaporation and subsequent local flame extinction and reignition. Conditioning on temperature leads to mild improvements but does not prevent a decorrelation of the temperatures “seen” by the droplets. Alternatively, a minimization based on stochastic particle temperature is suggested. This leads to good agreement between our MMC-LES model and the CP-DNS. The comparison between the CP-DNS data and MMC-LES also confirms that the anisotropic mixing time scale derived for gaseous flows ensures an accurate degree of micro-mixing also for two-phase flows and provides very good predictions of conditional fluctuations of reacting scalars around the conditional means.

This paper is a continuation of our work done in Part I, in which the a priori and budget analyses were conducted, Wen et al. (2019). In this work, we focus on addressing specific and recurring issues in flamelet modeling for pulverized coal combustion, including strong heat losses, multi-mode combustion and reaction progress variable definition. First, extended flamelet formulations are developed that can take into account strong heat loss effects in pulverized coal combustion systems. Then, to characterize multi-mode combustion in pulverized coal flames, a coupled premixed and non-premixed flamelet model is developed using the combustion mode index. Finally, the effects of reaction progress variable definition on the flamelet predictions are quantified. A state-of-the-art direct numerical simulation database is employed to challenge the newly developed flamelet models. The tabulated thermo-chemical quantities are compared with the reference direct numerical simulation results through a priori analyses. Comparisons show that the newly developed flamelet models which take into account strong heat loss effects can predict the gas temperature and species mass fractions correctly. The adiabatic flamelet models over-predict the corresponding thermo-chemical quantities in regions where the interphase heat transfer is significant. Coupled with a linear extrapolation method, the prediction of the gas temperature with the adiabatic flamelet models can be improved. The performance of the multi-mode flamelet model depends on whether the local combustion mode can be correctly identified. The conventional combustion mode index based on the gradients of fuel and oxidizer species mass fractions cannot correctly identify the combustion mode in the entire combustion field.

Gas-assisted pulverized coal combustion in the laboratory-scale Cambridge Coal Burner configuration CCB1 is studied using a large eddy simulation (LES) coupled with a multistream flamelet/progress ...

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A two-phase multiple mapping conditioning/large eddy simulation (MMC-LES) model for turbulent flames with solid fuel pyrolysis is derived, numerically implemented and tested. A hybrid approach is used that consists of an Eulerian LES, a stochastic filtered density function method with MMC closure and an inertial Lagrangian fuel particle scheme. A simultaneous interphase heat and mass transfer model with conserved scalar Spalding transfer numbers and localness in mixture fraction space models the pyrolysis of solid fuel particles and volatile gas mixing in the unresolved diffusive layer around each fuel particle. The MMC-LES model is applied to a laboratory-scale, turbulent, pyrolysing coal flame and the predictions are found to be in good overall agreement with the experimental data and comparable to previously reported LES and carrier-phase direct numerical simulations. This paper focuses on the sensitivity of the predictions to numerical parameters and variations in the models for pyrolysis rate and volatile gas composition. Both single first order reaction rate and competing rate pyrolysis models are used and the volatile composition is modelled as both pure methane and a detailed gaseous mixture. The sensitivity of these variations on the predictions of temperature and reactive species mass fractions is marked. Additionally the sensitivity to the presence of envelope flames around individual coal particles is explored and while there are some minor local variations, the steady-state statistics do not vary much.

This work develops flamelet tabulation methods for solid fuel combustion with and without fuel-bound nitrogen based on computations in particle-laden counterflow flames. The proposed flamelet tabulation methods for NO prediction are evaluated for two different coal types. The results show that extracting the NO mass fraction from the flamelet library directly results in significant discrepancies in the studied fuel nitrogen-free flame, while reasonable predictions can be obtained by using the same method in the fuel-bound nitrogen flames for both coal types. In contrast, solving a transport equation for the NO mass fraction tends to improve the NO prediction. The NO concentration is well predicted by splitting the NO source term into a formation part and a rescaled consumption part. The best NO prediction is obtained by extracting the formation part and the rescaled consumption part with a modified reaction progress variable.

A series of turbulent, piloted dimethyl ether (DME)/air jet flames (Sandia DME flames D–G’), with Reynolds numbers ranging from 29,300 to 73,250, has been simulated using a sparse-Lagrangian multiple mapping conditioning (MMC) approach coupled to a large eddy simulation (LES) flow field solver. Mixing between the Monte-Carlo particles is modelled by a generalised form of MMC combined with a sparse distribution of particles leading to significant computational savings compared to what is required for conventional mixing models. This is achieved by pairwise mixing of particles that are selected dependent on their distance in an extended space comprised of a reference variable, given by the LES mixture fraction, and spatial location. The MMC-LES method successfully predicts the flame structure and composition field for the full flame series. Numerical results are compared against conditional statistics and spatially resolved experimental data acquired with Raman/Rayleigh scattering and laser-induced fluorescence measurements. They show good agreement even for flame DME-G’ where large turbulence-chemistry interactions lead to significant local extinction and large deviations from a flamelet structure. The influence of the mixing time on the predicted flame structure is investigated, and the systematic validation of the time scale models with the aid of measurements of the entire flame series has corroborated the findings of earlier DNS and single flame studies: a modified time scale model is needed to provide accurate predictions of conditional fluctuations and thus of possible deviations from a flamelet-like combustion regime.

Carrier-phase direct numerical simulations (CP-DNS) are performed for turbulent spray combustion. The CP-DNS database is used to evaluate scaling laws for modelling characteristic mixing quantities, such as the mixture fraction conditional scalar dissipation, Nf, and its probability density function (PDF or Pf) in inter-droplet space. Three different methods to process the input parameters for the scaling laws are evaluated. If conditionally averaged quantities are used as input, the models can better capture (1) the scalar dissipation’s exponential increase for larger mixture fraction values and (2) the overall shape of the mixture fraction distribution featuring a distinct secondary peak at stoichiometry that results from increased droplet evaporation in regions where the flame is located. It is also found that the scaling laws provide acceptable estimates independent of droplet equivalence ratio, droplet pre-evaporation rate, spray combustion regime, droplet Stokes number, droplet size and large turbulence scale. This study provides a more physical perspective to the understanding of the mixing in spray combustion. The scaling laws for turbulent micro-mixing may have better predictive capability than the existing sub-models for single phase combustion used in flamelet and conditional moment closure (CMC) approaches that provide sub-grid closures for turbulence-chemistry interactions in LES or RANS.

This paper presents a comparison of experimental and numerical results for a series of turbulent reacting jets where silica nanoparticles are formed and grow due to surface growth and agglomeration. We use large-eddy simulation coupled with a multiple mapping conditioning approach for the solution of the transport equation for the joint probability density function of scalar composition and particulate size distribution. The model considers inception based on finite-rate chemistry, volumetric surface growth and agglomeration. The sub-models adopted for these particulate processes are the standard ones used by the community. Validation follows the “paradigm shift” approach where elastic light scattering signals (that depend on particulate number and size), OH- and SiO-LIF signals are computed from the simulation results and compared with “raw signals” from laser diagnostics. The sensitivity towards variable boundary conditions such as co-flow temperature, Reynolds number and precursor doping of the jet is investigated. Agreement between simulation and experiments is very good for a reference case which is used to calibrate the signals. While keeping the model parameters constant, the sensitivity of the particulate size distribution on co-flow temperature is predicted satisfactorily upstream although quantitative differences with the data exist downstream for the lowest coflow temperature case that is considered. When the precursor concentration is varied, the model predicts the correct direction of the change in signal but notable qualitative and quantitative differences with the data are observed. In particular, the measured signals show a highly non-linear variation while the predictions exhibit a square dependence on precursor doping at best. So, while the results for the reference case appear to be very good, shortcomings in the standard submodels are revealed through variation of the boundary conditions. This demonstrates the importance of testing complex nanoparticle synthesis models on a flame series to ensure that the physical trends are correctly accounted for., Deutsche Forschungsgemeinschaft, Australian Research Council, 2016 Universities Australia - Germany Joint Research Co-operation Scheme, Projekt DEAL

A comprehensive Euler–Lagrange framework for pulverized coal combustion using detailed multi-step heterogeneous kinetics is presented. The heterogeneous kinetics employ the POLIMI model that involves 37 species (22 solid species and 15 gas species) and 49 reactions to describe detailed pyrolysis as well as char oxidation, gasification, and annealing for a wide range of coals. The porous structure of the coal particles is considered, and the heterogeneous reactions are assumed to occur throughout the entire particle in a volume-based approach. The ordinary differential equations of the heterogeneous kinetics are integrated on each Lagrangian coal particle and predict the conversion of the raw coal components to light volatile hydrocarbons, heavy tar species, and char off-gases. Hence, the composition of the solid fuel components and the released gas changes dynamically in space and time, providing high-fidelity predictions of solid fuel combustion. The chemical conversion of the released species in the gas phase is described by a homogeneous kinetic mechanism with 76 species and 973 reactions that was reduced from the comprehensive CRECK-G-1407 kinetic mechanism. The new modeling framework is employed within carrier-phase direct numerical simulations (CP-DNS) of pulverized coal combustion in a three-dimensional turbulent mixing layer. This configuration includes the additional physics of turbulence and particle group combustion by mixing solid fuel particles suspended in a primary oxidizer stream with the products from lean volatile combustion in a secondary stream. The CP-DNS results are analyzed with and without the available set of 14 char conversion reactions, and a low degree of char conversion indicated by an increased rate of CO production is captured for particles with temperatures higher than 1800 K. The CP-DNS results from the detailed POLIMI approach feature a distinct bimodal shape of the volatile release curve and multi-regime combustion. The POLIMI data are used to evaluate the predictive capability of simpler pyrolysis models. The original competing two-step model (C2SM) by Kobayashi is investigated and shown to predict heavily delayed ignition. A new competing two-step devolatilization approach is proposed as an alternative model reduction suitable for fitting bimodal volatile release rates, such as that predicted by POLIMI. The CP-DNS using the alternative pyrolysis model faithfully captures the onset of ignition and multi-regime flame branches. Differences arise in the local tar species compositions in the gas phase as a result of the time-varying (POLIMI) and fixed (new C2SM) volatile compositions for the respective models. The flame structure is further analyzed by chemical explosive mode analysis (CEMA), and the occurrence of premixed and non-premixed flames zones is confirmed, whereas a simpler flame index analysis fails to correctly indicate the multi-regime nature of the flame. This recognition of multi-regime combustion serves as a guidance for selecting suitable conditioning variables for flamelet and other combustion submodels in large eddy simulation.

A carrier-phase direct numerical simulation (CP-DNS) of pulverized coal combustion in a mixing layer is performed, considering three NOx formation mechanisms (fuel-NOx, thermal-NOx and prompt-NOx). Detailed analyses, including reaction path analysis, chemical timescale analysis, and a priori and budget analyses are conducted to investigate the NOx production mechanisms and the performance of the flamelet model. Considering the high computational cost of CP-DNS, this work focuses on the early phase governed by devolatilization, where char reactions are less important. The reaction path analyses show that the principal thermal-NO reaction contributes to the net consumption of NO in fuel-bound nitrogen pulverized coal flames, which is essentially different from fuel-nitrogen-free flames. The chemical timescale analyses show that the production rates of NOx species are faster than those of major species, which confirms the suitability of the flamelet tables. The a priori analyses show that the gas temperature and major/intermediate species can be predicted well by the flamelet model, while the NOx species show significant discrepancies in certain regions. Finally, the budget analyses explain why the flamelet model performs differently for major/intermediate and NOx species.

A novel multiple mapping conditioning (MMC) approach has been developed for the modelling of turbulent premixed flames including mixture inhomogeneities due to mixture stratification or mixing with the cold surroundings. MMC requires conditioning of a mixing operator on characteristic quantities (reference variables) to ensure localness of mixing in composition space. Previous MMC used the LES-filtered reaction progress variable as reference field. Here, the reference variable space is extended by adding the LES-filtered mixture fraction effectively leading to a double conditioning of the mixing operator. The model is used to predict a turbulent stratified flame and is validated by comparison with experimental data. The introduction of the second reference variable also requires modification of the mixing time scale. Two different mixing time scale models are compared in this work. A novel anisotropic model for stratified combustion leads to somewhat higher levels of fluctuations for the passive scalar when compared with the original model but differences remain small within the flame front. The results show that both models predict flame position and flame structure with good accuracy., Deutsche Forschungsgemeinschaft, Australia-Germany Joint Research Cooperation Scheme, Projekt DEAL

Spray evaporation in spatially decaying turbulence is simulated using carrier-phase direct numerical simulations (CP-DNS). The CP-DNS cover a much wider parameter range than earlier fully resolved DNS of regular droplet arrays that were used to calibrate scaling laws for sub-grid closures of the distribution of mixture fraction and its conditionally averaged scalar dissipation. The scaling laws include the effects of sub-grid interactions between droplet evaporation and turbulence, and here they are assessed by direct comparison with the statistics from the CP-DNS. Two issues can be observed: Firstly, care must be taken when interpreting the CP-DNS statistics as the lack of resolution of the point particle surface could impact on the values in DNS cells that are located within the (unresolved) quasi-laminar wake. Secondly, the scaling laws present similar agreement with CP-DNS data as had been observed before for the fully resolved DNS. The scaling law for the scalar dissipation approximates the DNS statistics well, independent of the droplet number density, Stokes number and turbulence intensity. The estimated mixture fraction distribution (the PDF) is good for the mixture fraction values larger than a suitable average value but deteriorates for smaller mixture fractions due to inherent model limitations. The data corroborate that the scaling laws for turbulent micro-mixing can potentially serve as sub-grid closures for mixture fraction based combustion models such as flamelet and conditional moment closure approaches in large eddy simulations and may provide better approximations than existing expressions derived from single-phase non-premixed combustion.

A stochastic sparse particle approach is coupled with an artificial thickening flame (ATF) model for large eddy simulations (LES) to predict a series of turbulent premixed-stratified flames with and without shear and stratification. The thickened reaction progress variable serves as reference variable for the multiple mapping conditioning (MMC) mixing model which emulates turbulent mixing of the stochastic particles. The key feature of MMC is to enforce localness in this reference space when particle pairs are mixed and prevents unphysical mixing of burnt and unburnt fluid across the flame front. We apply MMC-ATF to three flames of a series of turbulent stratified flames and validate the method by comparison with experimental data. The new measurements feature increased accuracy in comparison to previously published data of the same flames due to a better signal-to-noise ratio and a setup which is less prone to beam steering. All flame locations are well predicted by the LES-ATF approach and an analysis of the MMC particle statistics demonstrates that MMC preserves the flamelet-like behaviour in regions where the experiments show low scatter around the flamelet solution. Predicted (local) deviations from the flamelet-solution are comparable to deviations observed in the measurements and variations in the flame structure due to differences in stratification and shear are reasonably well captured by the method.

This paper presents results from a joint experimental and numerical study of silica particulate synthesis for a turbulent reacting jet configuration where a cold jet doped with silane issues into a hot vitiated coflow. The experimental investigation involves simultaneous measurements of elastic light scattering and planar laser-induced fluorescence signals and these are used for validation of a novel computational approach, called PBE-MMC-LES, for the solution of the joint scalar probability density function of the gas phase species and the discretised particulate size distribution. Model validation follows the “paradigm shift” approach which is based on the computation of “predicted signals” which are compared directly with the experimentally-acquired signals. The results demonstrate that PBE-MMC-LES can model particulate inception, surface growth and agglomeration at reasonable computational cost. The agreement between the measured and computed signals is good in the light of the modelling complexities associated with particle flame synthesis, but predictions are rather sensitive to the uncertainties in precursor chemistry leading to nucleation and growth.

A hybrid Euler/Lagrange approach is introduced for the simulation of turbulent stratified flames. Large eddy simulations (LES) are used for the simulation of the flow field while artificial thickening of the flame provides sufficient resolution for the computation of the evolution of the filtered reaction progress variable. This model is complemented by a sparse Lagrangian particle method that provides instantaneous and local solutions of the species composition and can account for deviations from the flamelet-structure due to turbulence. The combined approach provides a model applicable to different premixed flame regimes including the corrugated and thickened flame regimes. The particle mixing model is based on a multiple mapping conditioning (MMC) approach that conditions mixing on a reference field (the reaction progress variable). Thus, the model ensures localness of mixing in composition space and prevents unphysical mixing of unburnt fluid with burnt fluid across the flame front. The MMC-LES results show good agreement with experimental data, and flamelet-like structures as well as deviations thereof can be predicted. The results are rather insensitive towards the MMC specific modelling parameters but the modelling of the mixing time scale needs to be adapted to achieve consistency between the flame propagation speed predicted by the artificially thickened flame model and the flame dynamics predicted by MMC.

Computational models for combustion must account for complex and inherently interconnected physical processes including dispersion, mixing, chemical reactions, particulate nucleation and growth and, critically, the interactions of these with turbulence. The development of affordable and accurate models that are widely applicable is a work in progress. Stochastic multiple mapping conditioning (MMC) is a fast-emerging approach that has been successfully applied to non-premixed, premixed and partially premixed flames as well to the modelling of liquid and solid particulate synthesis. The method solves the conventional PDF transport equation but incorporates an additional constraint in that the mixing is localised in a reference space. This paper describes the numerical implementation of stochastic MMC in an OpenFOAM compatible code called mmcFoam. The model concepts and equations along with alternative submodels, code structure and numerical schemes are explained. A focus is placed on validation of the computational methods in particular demonstrating numerical convergence and mass consistency of the hybrid Eulerian/Lagrangian schemes. Four validation cases are selected including a combustion direct numerical simulation (DNS) case, two combustion experimental jet flame cases and a non-combusting particulate synthesis case. The results show that the total mass and mass distribution of Eulerian and Lagrangian schemes are consistent and confirm that the solutions numerically converge with increasing number of stochastic computational particles and sections for describing particulate size distribution.

A multiple mapping conditioning/large eddy simulation model (MMC–LES) is formulated for turbulent spray flames. Heat and mass transfer between the gaseous and liquid phases is modelled using a conserved scalar form of the Spalding transfer number approach along with an evaporative mixing model that is local in mixture fraction space. The model and the numerical implementation are tested in a non-reacting and two reacting experimental acetone spray cases. Model predictions are generally in good agreement with the velocity, liquid volume flow rate and mean temperature data and are shown to have a low sensitivity to the sparse stochastic particle resolution. The consistency of the heat and mass transfer coupling between the hybrid Eulerian–Lagrangian–Lagrangian schemes is demonstrated by comparison of mixture fraction fields solved on both the LES and the stochastic particles. A comprehensive appendix contains a derivation of the phase-weighted form of the MMC–LES governing equations along with a derivation and single-droplet test of the conserved scalar heat and mass transfer formulation.

An efficient ensemble learning approach is used for modeling the filtered density function (FDF) of mixture fraction in turbulent evaporating sprays. This is achieved by implementing the state-of-the-art eXtreme Gradient Boosting (XGBoost) and Light Gradient Boosting Machine (LightGBM) algorithms. The results show that ensemble learning models achieve a very high accuracy that is comparable to a deep neural network. Computational requirements are, however, much reduced and of the order of those needed for the computation of a conventional β -FDF. Ensemble learning thus provides a suitable alternative to model FDF statistics and corresponding software for training and a C++ model library are provided.

The combustion of droplets in turbulent convective flows is simulated using direct numerical simulations (DNS). The liquid–vapour interface between kerosene droplets and the surrounding air is fully resolved with realistic boundary conditions for mass conservation, heat conduction and species diffusion. The study focuses on the characterisation of the mixing process between the evaporating fuel and the surrounding gas in regions that are dominated by small turbulent scales. For inertial droplets, these regions are characterised by Kolmogorov time scales and the mean relative velocity between droplets and the surrounding gas phase. Scaling laws for quantities of interest that require sub-grid modelling for LES, such as mixture fraction, its conditional scalar dissipation and probability density functions (PDF), are presented and assessed by comparisons with the DNS data. The scaling laws provide satisfactory estimates and are validated for different inflow Reynolds numbers, turbulence intensities and integral length scales, droplet diameters, inter-droplet distances, droplet combustion regimes and various instants of the transient evaporation process. Suitable modelling parameters are extracted from the DNS and functional dependencies of the parameters are suggested. This study demonstrates that the scaling laws are suitable to serve as sub-grid scale models for mixture fraction based approaches such as flamelet, conditional moment closure (CMC) or multiple mapping conditioning (MMC) methods.

Direct numerical simulations (DNS) of a three-dimensional turbulent mixing layer are performed, where coal particles seeded in an air stream mix with hot lean combustion products in a second stream. This case mimicks conditions of a pulverized coal flame stabilized by hot products such as found in industrial furnaces. Particles are heated up by the hot gases and devolatilize, followed by volatile combustion in the gas phase. The carrier-phase DNS resolves all relevant scales of the fluid phase except the boundary layers around individual particles. The simulation results are assessed in terms of instantaneous contour plots of relevant quantities, spatially averaged statistics, scatter plots and (pseudo-)flamelets. The analysis provides insight into the mechanisms of solid particle ignition and burning stabilized by hot combustion products, as well as the flame structure and combustion mode. It is shown that ignition initially occurs at very lean conditions when particles are entrained in the hot gases. Subsequently volatile combustion proceeds in non-premixed as well as premixed combustion modes, characterized by means of the flame index, with an overall higher heat release in non-premixed zones. At late times two flames can be clearly distinguished, an upper flame burning into the air carrying the particles and a lower flame burning into the lean products. The latter flame shows a pure non-premixed behavior, while the former illustrates a complex flame structure with both premixed and non-premixed modes, as well as flame quenching. The DNS database and initial analysis lay the foundation for future systematic studies in similar configurations and support the development of models suitable for the combustion of solid fuel particles.

The present study addresses the grid dependence of evaporation rates in the context of Euler-Lagrange simulations and presents error estimates as a function of characteristic parameters. The common approach of using local cell values as ambient conditions for the evaporation model and returning heat and mass to the gas phase via source terms, which is known as the particle-source-in-cell (PSI-cell) model, is not grid independent and leads to large deviations in the evaporation rates if the cell size is of the order of the droplet diameter. This problem has become increasingly important in recent years as increased computing power now allow direct numerical simulations of the carrier gas and large-eddy simulations with much smaller cell sizes to be used, making the point-source approximation increasingly inadequate. It is therefore necessary to estimate the error that is introduced by the PSI-cell model to be able to perform simulations with a given (and a priori known) error level. Focusing on a single droplet in an infinite environment, expressions are derived for the deviation of the evaporation rate and time compared to a reference solution for both quiescent and convective environments and including the effects of heat transfer. It is found that the error of the steady-state evaporation rate is a function of the ratio of cell size to droplet diameter and the cell Peclet number. The error of the evaporation time additionally depends on the initial ratio of liquid to gaseous mass in the computational cell and on the reference mass transfer number, whose influence can be combined in a modified mass ratio. The presented expressions are simple to use and valid across a wide range of gas and droplet properties that are typical for spray combustion applications and provide guidelines for the correct choice of the cell size in Euler-Lagrange simulations of dilute sprays.

An Eulerian large-eddy simulation (LES) is coupled with a sparse-Lagrangian particle method to solve the population balance equation for aersol nucleation and growth in turbulent flows. We use the LES for the solution of the filtered velocity and mixing fields while the particle method provides one-point statistics of the gaseous species and the condensed phase such that the non-linear aerosol nucleation and growth terms appear naturally in closed form. A sparse particle implementation requires additional localisation in a reference space, and this localisation is realised here by employing the generalised multiple mapping conditioning (MMC) mixing model. The complete model, called MMC-LES, is validated by comparison with experimental data from nucleation studies in a turbulent, hot, nitrogen jet laden with dibutyl-phthalate (DBP) that condenses during mixing with a coflow of cold air. Acceptable agreement is found between the MMC-LES predictions and the experimental data. The average DBP droplet sizes are well predicted, and predictions of the total droplet number and the dependencies of droplet statistics on precursor concentrations are satisfactory. A comparison of the sparse particle method with results from conventional (dense) Monte Carlo-LES simulations demonstrates the capabilities of MMC-LES to predict aerosol nucleation and growth at relatively low computational cost. An additional quantitative analysis of the interactions between the turbulence and the non-linear nucleation source and growth terms shows that sub-grid effects must not be neglected and interactions between turbulence and nucleation can modify averaged nucleation rates by more than 250%.

A sparse particle implementation of the multiple mapping conditioning / large eddy simulation (MMC-LES) model is assessed against direct numerical simulations (DNS) of non-premixed syngas combustion in the double shear layer configuration of Hawkes et al. (2007). The considered configuration features strong extinction and reignition and therefore poses a stringent test of the model’s capabilities to capture finite-rate chemistry effects. The investigation focuses on the modelling of the Lagrangian mixing time scale, τL, which emulates the dissipation of conditional subfilter scalar fluctuations. An a posteriori strategy is used to separate LES errors from potential shortcomings in modelling of τL. The DNS data are filtered on the LES grid to compute all LES-filtered quantities that are needed for the modelling of τL while the (unfiltered) DNS velocity and mixture fraction fields are used for particle transport and mixing model localization, respectively. The results show that the previously derived and most commonly used model for τL (Cleary & Klimenko, 2011) is capable of accurately capturing the temporal evolution of the mean quantities in the flame and that, by virtue of the controlled localisation of the generalised MMC mixing model in a reference mixture fraction space, statistical predictions are quite insensitive to variations in the spatial distance between particles. However, the model yields significant under-predictions of the conditional variances of the reactive scalars, both for the reference case and an additional case with a reduced reaction zone thickness. It is shown that for these particular flames the conditional variance under-predictions cannot be completely remedied by tuning the input parameter fm which determines the amount of mixing localisation in reference mixture fraction space. Instead, this shortcoming is attributed to the model for τL. Alternative model closures are suggested which are based on a consistent anisotropic or isotropic perspective on subfilter scalar mixing in sparse particle schemes. The anisotropic closure is demonstrated to significantly improve the model predictions, in particular for the conditional scalar variances. Additionally the predictions show less sensitivity to variations in fm providing good potential for improved robustness of sparse particle methods for MMC-LES. A series of tests involving a three order of magnitude increase in particle number is conducted to demonstrate numerical convergence. During those tests the two primary model parameters, fm and rm which control the mixing distance between particles in both mixture fraction space and physical space, are held constant so that those mixing distances are independent of the number of particles used and, at the same time, the sparse character of the mixing model is preserved.

In this work, a comprehensive study of flamelet tabulation methods for pulverized coal combustion in a turbulent mixing layer is conducted. At first, a priori analyses are conducted to evaluate the suitability of the premixed and non-premixed flamelet models for the studied pulverized coal flame with multiple combustion modes. Then, to clarify why a certain flamelet model does work or not work in certain regions, a more in-depth investigation of the premixed and non-premixed flamelet models is conducted through a budget analysis. The results show that the first and second derivatives in physical space can be well reproduced by the tabulated manifolds in trajectory variable space for both the premixed and non-premixed flamelet models, between which the non-premixed flamelet model performs slightly better. For the time derivative, large discrepancies can be observed, although the predicted variation trend overall follows the reference results. Through the analysis of the individual budget terms in the trajectory variable space, the individual trajectory variable’s contributions to the convection and diffusion of thermo-chemical variables are quantified. Through the analysis of the individual budget terms for the sensible enthalpy and the CO mass fraction governing equations, the influences of the space transformation on the individual transport process (e.g., convection, diffusion, etc.) are clarified. Overall, the findings obtained from the budget analyses are consistent with those obtained from the a priori analyses.

In this paper a study of the sparse-Lagrangian multiple mapping conditioning (MMC) model for the synthesis of silica nanoparticles is presented. This is the first attempt using the model to simulate the formation of kinetically limited solid state species. A simplified differential diffusion model, involving a modified mixing timescale, is used to account for the much lower diffusion of the solid species. The model is validated against DNS of a counterflowing double shear layer of silane and hot combustion products. The reduced reaction mechanism involves silane decomposition and clustering leading to silica. The model is implemented in the context of large eddy simulations (LES). The MMC model allows a sparse distribution of stochastic particles for computing the reactive scalar field, including silica number density, by enforcing the property of localness in mixture fraction space onto the mixing model. Gas phase mixture fraction and fast reactive species are predicted with acceptable accuracy. The prediction of silica number density is qualitatively correct although the magnitude is underpredicted somewhat and the rms is greatly underpredicted. The effects of differential diffusion are clearly visible in the modelling and the simplified model correctly predicts the trend of increasing silica formation when differential diffusion is included.

Droplet evaporation and subsequent mixing of the fuel vapor with the turbulent surrounding hot oxidizer has been simulated using direct numerical simulations (DNS). The kerosene droplets are fully resolved with realistic boundary conditions at the liquid–vapor interface to ensure the correct heat and mass transfer between the two phases. The study focuses on combustible mixture preparation in the inter-droplet space at scales larger than the quasi-laminar near droplet zone. The data are analysed with respect to key quantities for mixture fraction based combustion models such as mixture fraction distribution and its dissipation. The DNS is compared with scaling relationships for the wake and for length scales of Kolmogorov size where the wake seizes to be the dominant flow structure. The scaling relationships agree reasonably well with DNS data and they may serve as sub-grid scale closures for combustion models such as conditional moment closure or flamelets. Their respective regions of validity are quantified for the different cases of turbulence intensity that are investigated here.

A resolved laminar flow simulation approach is used to investigate the effect of enhanced oxygen levels on single coal particle ignition, comparing the numerical results against experimental data for well-defined conditions (Molina and Shaddix, 2007). Devolatilization is described by a generic boundary condition at the particle surface that accounts for both convective and diffusive phenomena during pyrolysis. The heating rate history of the particle is obtained by solving for intra-particle heat transfer and heat exchange between the particle and its surroundings. The time evolution of volatile release is captured by using the particle mean temperature to calculate the devolatilization rate from a single kinetic rate law with CPD-fitted parameters. The assumed volatile composition includes both light gases and larger hydrocarbons to represent tars. A skeletal kinetic mechanism for pyrolysis and oxidation of hydrocarbon and oxygenated fuels containing 52 species and 452 reactions is used to accurately describe homogeneous chemistry. Particle heat-up, pyrolysis, ignition and envelope flame stabilization are characterized in four gas atmospheres differing in oxygen content and the use of either N2 or CO2 as balance gas. In agreement with the experimental evidence, enhanced oxygen levels shorten ignition delay time τ ign and result in a higher intensity of the combustion process according to temperature and radical production peaks for all studied mixtures. For the studied oxy-mixtures the presence of CO2 in substitution of N2 delays ignition. The observed behavior is coherent with the different thermo-physical properties of the gas mixtures. The sensitivity of predicted ignition delay to a set of uncertainties is also discussed. It is found that while the absolute values of predicted ignition delay time are functions of potential particle preheating, particle Reynolds number and the chosen criterion to extract ignition delay, the relative trends among the gas mixtures remain in line with the experimental evidence.

Large-eddy simulations have been coupled with a conservative formulation of the conditional moment closure (CMC) approach for the computation of a turbulent, partially-premixed dimethyl-ether jet flame. Two different numerical setups and 3 different detailed chemical mechanisms were investigated. The results are compared with measurements of velocity, temperature, and major and intermediate species. The general agreement between simulations and experiments is very good, and differences between the different mechanisms are limited to the predicted concentrations of intermediates only. Larger differences can be observed if the CMC grid size is reduced. This is due to reduced averaging effects on the conditionally averaged dissipation rates that allow to better capture high dissipation events that lead to larger deviations from a fully burning solution. A high CMC resolution provides excellent agreement with experiments throughout the flame and the results demonstrate CMC’s capability to accurately predict turbulence-chemistry interactions in partially-premixed flames involving complex chemistry.

In this work, effects of air and oxy-fuel atmospheres on flamelet modeling of NO x and SO x formation in two-dimensional laminar counterflow pulverized coal flames are investigated. The release and combustion of volatile-N, char-N and volatile-S are incorporated in the flamelet model, and a newly developed reaction mechanism for oxy-fuel combustion (129 species and 911 elementary reactions) is employed to describe the chemistry. Two different methods for prediction of pollutant species are evaluated using the flamelet model, in which the pollutant mass fractions are obtained by either extracting the flamelet library directly (“M1”) or solving the corresponding transport equations with the reaction source terms being taken from the flamelet library (“M2”). To evaluate the performance of proposed flamelet models, the flamelet predictions are compared to the reference results of the detailed chemistry solutions, in which the transport equations for the species mass fractions and total enthalpy are directly solved. At first, the atmosphere effects on the NO x and SO x formation are analyzed based on the detailed chemistry solutions, then the effects of atmosphere on flamelet modeling of pollutant formation are evaluated. The results show that M1 overall performs better than M2 at predicting the NO x and SO x species in both air and oxy-fuel atmospheres. The major pollutant species of NO and SO 2 are over-predicted by M2 in certain regions for both atmospheres, and the reason for the incorrect prediction is explored by attributing to the interpolation error of the reaction source terms in the middle branch of the S-Shaped curve.

Deep artificial neural networks (ANNs) are used for modeling sub-grid scale mixing quantities such as the filtered density function (FDF) of the mixture fraction and the conditional scalar dissipation rate. A deep ANN with four hidden layers is trained with carrier-phase direct numerical simulations (CP-DNS) of turbulent spray combustion. A priori validation corroborates that ANN predictions of the mixture fraction FDF and the conditional scalar dissipation rate are in very good agreement with CP-DNS data. ANN modeled solutions show much better performance with a mean error of around 1%, which is one order of magnitude smaller than that of standard modeling approaches such as the β-FDF and its modified version. The predicted conditional scalar dissipation rate agrees very well with CP-DNS data over the entire mixture fraction space, whereas conventional models derived for pure gas phase combustion fail to describe ⟨N|ξ = η⟩ in regions with higher mixture fraction and low probability. In the second part of this paper, uncertainties associated with ANN predictions are analyzed. It is shown that a suitable selection of training sets can reduce the size of the necessary test database by ∼50% without compromising the accuracy. Feature importance analysis is used to analyze the importance of different combustion model parameters. While the droplet evaporating rate, the droplet number density, and the mixture fraction remain the dominant features, the influence of turbulence related parameters only becomes important if turbulence levels are sufficiently high.

A steady flamelet/progress variable (FPV) approach for pulverized coal flames is employed to simulate coal particle burning in a turbulent shear and mixing layer. The configuration consists of a carrier-gas stream of air laden with coal particles that mixes with an oxidizer stream of hot products from lean combustion. Carrier-phase DNS (CP-DNS) are performed, where the turbulent flow field is fully resolved, whereas the coal is represented by Lagrangian point particles. CP-DNS with direct chemistry integration is performed first and provides state-of-the-art validation data for FPV modeling. In a second step the control variables for FPV are extracted from the CP-DNS and used to test if the tabulated manifold can correctly describe the reacting flow (a priorianalysis). Finally a fully coupled a posteriori FPV simulation is performed, where only the FPV control variables are transported, and the chemical state is retrieved from the table and fed back to the flow solver. The a priori results show that the FPV approach is suitable for modeling the complex reacting multiphase flow considered here. The a posteriori data is similarly in good agreement with the reference CP-DNS, although stronger deviations than a priori can be observed. These discrepancies mainly appear in the upper flame (of the present DNS), where premixing and highly unsteady extinction and re-ignition effects play a role, which are difficult to capture by steady non-premixed FPV modeling. However, the present FPV model accurately captures the lower, more stable flame that burns in non-premixed mode.

Fully-resolved simulations of the heating, ignition, volatile flame combustion and char conversion of single coal particles in convective gas environments are conducted and compared to experimental data (Molina and Shaddix, 2007). This work extends a previous computational study (Tufano et al., 2016) by adding a significant level of model fidelity and generality, in particular with regard to the particle interior description and heterogeneous kinetics. The model considers the elemental analysis of the given coal and interpolates its properties by linear superposition of a set of reference coals. The improved model description alleviates previously made assumptions of single-step pyrolysis, fixed volatile composition and simplified particle interior properties, and it allows for the consideration of char conversion. The results show that the burning behavior is affected by the oxygen concentration, i.e. for enhanced oxygen levels ignition occurs in a single step, whereas decreasing the oxygen content leads to a two-stage ignition process. Char conversion becomes dominant once the volatiles have been depleted, but also causes noticeable deviations of temperature, released mass, and overall particle conversion during devolatilization already, indicating an overlap of the two stages of coal conversion which are usually considered to be consecutive. The complex pyrolysis model leads to non-monotonous profiles of the combustion quantities which introduce a minor dependency of the ignition delay time τ ign on its definition. Regardless of the chosen extraction method, the simulations capture the measured values of τ ign very well.

A piloted pulverized coal jet flame was simulated by Large Eddy Simulation (LES). For the sub-grid scale (SGS) effects of the turbulence velocity and the scalar fluctuation of the gas flow on the coal particles, the velocity-scalar joint filtered density function (VSJFDF) model was used. Other models such as the governing equations for particles and coal combustion sub-models were also presented. Simulation results with the VSJFDF model, non-VSJFDF model and those by Franchetti et al. [7] were compared with the experimental data, including the mean and RMS (root mean square) velocity, temperature and species concentrations. The results showed that VSJFDF can distinctly improve the predictions, both in quantity and quality. The location where coal particles start burning could be roughly predicted along the centerline of the flame by VSJFDF model.