An a priori study of different tabulation methods for turbulent pulverised coal combustion

In many practical pulverised coal combustion systems, different oxidiser streams exist, e.g. the primary- and secondary-air streams in the power plant boilers, which makes the modelling of these systems challenging. In this work, three tabulation methods for modelling pulverised coal combustion are evaluated through an a priori study. Pulverised coal flames stabilised in a three-dimensional turbulent counterflow, consisting of different oxidiser streams, are simulated with detailed chemistry first. Then, the thermo-chemical quantities calculated with different tabulation methods are compared to those from detailed chemistry solutions. The comparison shows that the conventional two-stream flamelet model with a fixed oxidiser temperature cannot predict the flame temperature correctly. The conventional two-stream flamelet model is then modified to set the oxidiser temperature equal to the fuel temperature, both of which are varied in the flamelets. By this means, the variations of oxidiser temperature can be considered. It is found that this modified tabulation method performs very well on prediction of the flame temperature. The third tabulation method is an extended three-stream flamelet model that was initially proposed for gaseous combustion. The results show that the reference gaseous temperature profile can be overall reproduced by the extended three-stream flamelet model. Interestingly, it is found that the predictions of major species mass fractions are not sensitive to the oxidiser temperature boundary conditions for the flamelet equations in the a priori analyses.     

SGS Reaction rate modelling for MILD combustion based on machine-learning combustion mode classification: Development and a priori study

A neural network (NN) aided model is proposed for the filtered reaction rate in moderate or intense low-oxygen dilution (MILD) combustion. The framework of the present model is based on the partially stirred reactor (PaSR) approach, and the fraction of the reactive structure appearing in the PaSR is predicted using different NN’s, to consider both premixed and non-premixed conditions while allowing the use of imbalanced training data between premixed and non-premixed combustion direct numerical simulation (DNS) data. The key ingredient in the present model is the use of local combustion mode prediction performed by using another NN, which is developed in a previous study. The trained model was then assessed by using two unknown combustion DNS cases, which yields much higher dilution level (more intense MILD condition) and higher Karlovitz number than the DNS cases used as training data. The model performance assessment has been carried out by means of the Pearson’s correlation coefficient and mean squared error. For both the present model and zeroth-order approximated reaction rate, the correlation coefficient with the target values shows relatively high values, suggesting that the trend of predicted field, by the present model and zeroth-order approximation, is well correlated with the actual reaction rate field. This suggests that the use of PaSR equation is promising if the fraction of the reactive structure is appropriately predicted, which is the objective in the present study. On the other hand, substantially lower mean squared error is observed for a range of filter sizes for the present model than that for the zeroth-order approximation. This suggests that the present filtered reaction rate model can account for the SGS contribution reasonably well.     

Large-scale parallel simulations of turbulent combustion using combined dimension reduction and tabulation of chemistry

Simulations of turbulent reacting flows with chemistry represented using detailed kinetic model involving a large number of species and reactions are computationally expensive. Here we present a combined dimension reduction and tabulation strategy for implementing chemistry in large scale parallel Large-Eddy Simulation (LES)/Probability Density Function (PDF) computations of turbulent reacting flows. In this approach, the dimension reduction is performed using the Rate Controlled Constrained-Equilibrium (RCCE) method, and tabulation of the reduced space is performed using the In Situ Adaptive Tabulation (ISAT) algorithm. In addition, we use x2f_mpi — a Fortran library for parallel vector-valued function evaluation (used with ISAT in this context) — to efficiently redistribute the chemistry workload among the participating cores in parallel LES/PDF computations to reduce the overall wall clock time of the simulation. We test three parallel strategies for redistributing the chemistry workload, namely (a) PLP, purely local processing; (b) URAN, the uniform random distribution of chemistry computations among all cores following an early stage of PLP; and (c) P-URAN, a Partitioned URAN strategy that redistributes the workload within partitions or subsets of the cores. To demonstrate the efficiency of this combined approach, we perform parallel LES/PDF computations (on 1024 cores) of the Sandia Flame D with chemistry represented using a 38-species C₁–C₄ skeletal mechanism. We show that relative to using ISAT alone with the 38-species full representation, the combined ISAT/RCCE approach with 10 represented species (i) predicts time-averaged mean and standard deviation statistics with a normalized root-mean-square difference of less than 3% (30 K) in temperature, less than 2% (0.02 kg/m³) in density, less than 2.5% in mass fraction of major species, and less than 8% in mass fraction of minor species of interest; and (ii) reduces the simulation wall clock time by over 40% with the P-URAN strategy.     

Computationally-efficient and accurate particle PDF simulations of turbulent combustion using coupled pre-partitioned adaptive chemistry and tabulation

LES/PDF methods are known to provide accurate results for challenging turbulent combustion configurations with strong turbulence-chemistry interactions. These methods are generally applicable as they do not make any assumptions on the topology of the underlying flame structure. However, this added generality comes at an increased computational cost. To mitigate this added cost, the majority of the LES/PDF computations performed to date utilize reduced mechanisms. We recently presented a coupled pre-partitioned adaptive chemistry (PPAC) and tabulation (ISAT) methodology (Newale et al., Comb. Th. Mod., 2019), which retains the fidelity of the detailed mechanism, while keeping the computational cost affordable. This methodology was tested in a partially-stirred reactor configuration. In this work, we describe the developments required for a holistic integration of PPAC-ISAT with a LES/PDF framework. We examine the performance of this coupled methodology in two LES/PDF configurations of Sandia flame D. A smaller simulation domain is initially utilized to characterize the efficiency and accuracy of standalone PPAC and coupled PPAC-ISAT in detail. Then, the performance of PPAC-ISAT is examined in a full-scale LES/PDF simulation. We show that the coupled PPAC-ISAT LES/PDF captures the resolved mean and RMS profiles of temperature and major species mass fractions to within 2% and OH to within 5%, with a reduction in the average simulation wall clock time per time step of 39% over an ISAT implementation using the detailed mechanism.     

An a priori assessment of the Partially Stirred Reactor (PaSR) model for MILD combustion

Moderate or Intense Low-oxygen Dilution (MILD) combustion has drawn increasing attention as it allows to avoid the thermo-chemical conditions prone to the formation of pollutant species while ensuring high energy efficiency and fuel flexibility. MILD combustion is characterized by a strong competition between turbulent mixing and chemical kinetics so that turbulence-chemistry interactions are naturally strengthened and unsteady phenomena such as local extinction and re-ignition may occur. The underlying physical mechanisms are not fully understood yet and the validation of combustion models featuring enhanced predictive capabilities is required. Within this context, high-fidelity data from Direct Numerical Simulation (DNS) represent a great opportunity for the assessment and the validation of combustion closure formulations. In this study, the performance of the Partially Stirred Reactor (PaSR) combustion model in MILD conditions is a priori assessed on Direct Numerical Simulations (DNS) of turbulent combustion of MILD mixtures in a cubical domain. Modeled quantities of interest, such as heat release rate and reaction rates of major and minor species, are compared to the corresponding filtered quantities extracted from the DNS. Different submodels for the key model parameters, i.e., the chemical time scale τ_c and the mixing time scale τ_mix, are considered and their influence on the results is evaluated. The results show that the mixing time scale is the leading scale in the investigated cases. The best agreement with the DNS data regarding the prediction of heat release rate and chemical source terms is achieved by the PaSR model that employs a local dynamic approach for the estimation of the mixing time scale. An overestimation of the OH species source terms occurs in limited zones of the computational domain, characterized by low heat release rates.     

Modeling subfilter soot-turbulence interactions in Large Eddy Simulation: An a priori study

A new LES model for subfilter soot-turbulence interactions is developed based on an a priori analysis using large-scale DNS data of temporally evolving non premixed n-heptane jet flames at a jet Reynolds number of 15,000. In this work, soot formation is modeled in LES by solving explicit transport equations for soot moments, and the unclosed filtered soot moment source terms are closed by a presumed PDF approach. Due to the strong intermittency of soot fields, a previous modeling approach assumes the presumed PDF to be bimodal accounting for sooting and non-sooting subfilter regions but neglects any sub-structure of the soot distribution. In this work, the modeling framework is improved by a new presumed PDF model that explicitly accounts for the sub-structure of the sooting mode, which is modeled by a log-normal distribution. The previous and new models are assessed by means of their prediction of the filtered source terms and the filtered intermittency, and the log-normal distribution is found to significantly reduce modeling errors, in particular, for the coagulation source term. Introducing a log-normal distribution for the PDF of the sooting mode involves a large amount of additional model parameters, such as the width of the distribution and correlation coefficients among different soot moments, so model assumptions to reduce the number of model parameters are discussed by means of the DNS data. The conclusions are found to be robust with respect to a variation in the global Damköhler number in the DNS datasets. The final model formulation only requires solving two additional transport equations in LES compared to previous models, while significantly improved model predictions are obtained for the coagulation source term which is import for predicting the number of soot particles.     

An a priori evaluation of a principal component and artificial neural network based combustion model in diesel engine conditions

A principal component analysis (PCA) and artificial neural network (ANN) based chemistry tabulation approach is presented. ANNs are used to map the thermochemical state onto a low-dimensional manifold consisting of five control variables that have been identified using PCA. Three canonical configurations are considered to train the PCA-ANN model: a series of homogeneous reactors, a nonpremixed flamelet, and a two-dimensional lifted flame. The performance of the model in predicting the thermochemical manifold of a spatially-developing turbulent jet flame in diesel engine thermochemical conditions is a priori evaluated using direct numerical simulation (DNS) data. The PCA-ANN approach is compared with a conventional tabulation approach (tabulation using ad hoc defined control variables and linear interpolation). The PCA-ANN model provides higher accuracy and requires several orders of magnitude less memory. These observations indicate that the PCA-ANN model is superior for chemistry tabulation, especially for modelling complex chemistries that present multiple combustion modes as observed in diesel combustion. The performance of the PCA-ANN model is then compared to the optimal estimator, i.e. the conditional mean from the DNS. The results indicate that the PCA-ANN model gives high prediction accuracy, comparable to the optimal estimator, especially for major species and the thermophysical properties. Higher errors are observed for the minor species and reaction rate predictions when compared to the optimal estimator. It is shown that the prediction of minor species and reaction rates can be improved by using training data that exhibits a variation of parameters as observed in the turbulent flame. The output of the ANN is analysed to assess mass conservation. It is observed that the ANN incurs a mean absolute error of 0.05% in mass conservation. Furthermore, it is demonstrated that this error can be reduced by modifying the cost function of the ANN to penalise for deviation from mass conservation.     

2D mixture fraction measurements in a high pressure and high temperature combustion system using NO tracer-LIF

Mixture fraction measurements in a jet-in-cross flow configuration at high pressures (15 bar) and temperatures (above 1000 K) were performed using planar laser induced fluorescence of nitric oxide (NO-PLIF) as trace species. The goal was the evaluation of this tracer LIF technique for the characterization of the mixing of fuel and hot exhaust gas in the mixing channel. The fuel (natural gas (NG) or H₂/N₂/NG mixture) along with the tracer were injected into the crossflow of the exhaust gas and PLIF measurements were performed in different planes. In order to relate the measured NO-LIF signal to fuel concentration and mixture fraction, effects of pressure, temperature and species concentration were taken into account. Numerical calculations and spectroscopic simulations that mimic the experimental conditions were performed to identify excitation schemes that give optimum correlations between the NO-LIF signal and the mixture fraction. The measured NO-PLIF images were transformed into mixture fraction plots using the computed correlations. The paper reports on the experimental challenges encountered during the measurements and the steps taken to overcome those difficulties. Examples of mixture fraction distributions are presented and discussed. The paper concludes with a detailed analysis on the accuracy of the measured mixture fraction values.     

Modelling of turbulent lifted jet flames using flamelets: a priori assessment and a posteriori validation

This study focuses on the modelling of turbulent lifted jet flames using flamelets and a presumed Probability Density Function (PDF) approach with interest in both flame lift-off height and flame brush structure. First, flamelet models used to capture contributions from premixed and non-premixed modes of the partially premixed combustion in the lifted jet flame are assessed using a Direct Numerical Simulation (DNS) data for a turbulent lifted hydrogen jet flame. The joint PDFs of mixture fraction Z and progress variable c, including their statistical correlation, are obtained using a copula method, which is also validated using the DNS data. The statistically independent PDFs are found to be generally inadequate to represent the joint PDFs from the DNS data. The effects of Z–c correlation and the contribution from the non-premixed combustion mode on the flame lift-off height are studied systematically by including one effect at a time in the simulations used for a posteriori validation. A simple model including the effects of chemical kinetics and scalar dissipation rate is suggested and used for non-premixed combustion contributions. The results clearly show that both Z–c correlation and non-premixed combustion effects are required in the premixed flamelets approach to get good agreement with the measured flame lift-off heights as a function of jet velocity. The flame brush structure reported in earlier experimental studies is also captured reasonably well for various axial positions. It seems that flame stabilisation is influenced by both premixed and non-premixed combustion modes, and their mutual influences.     

Numerical simulation of catalytic combustion of methane using washcoat model and external model: a comparison study

This paper presents a comparison study of numerical simulation of catalytic combustion of methane on Pt catalyst using two different physical models. The external surface model and the washcoat model were employed. The simulations were conducted in a two-dimensional monolith reactor with detail surface kinetics. The agreement of simulation results of the washcoat model with the measured data is good. However, in contrast to experimental data, the external surface method will produce a lower result of conversion of CH₄ at low temperature due to the neglecting of the larger inner surface of the washcoat. Moreover, the effects of specific surface area and pore size of washcoat on reaction rate were discussed. It can be concluded that the washcoat model would provide a more realistic result and can enrich the contents of numerical simulation of catalytic reaction.     

An experimental study of coal particle group combustion in conventional and oxy-fuel atmospheres using multi-parameter optical diagnostics

The present work reports an experimental study of particle group combustion of pulverized bituminous coal in laminar flow conditions using advanced multi-parameter optical diagnostics. Simultaneously conducted high-speed scanning OH-LIF, diffuse backlight-illumination (DBI), and Mie scattering measurements enable analyses of three-dimensional volatile flame structures and soot formation in conventional (i.e., N${}_2$/O${}_2$) and oxy-fuel (i.e., CO${}_2$/O${}_2$) atmospheres with increasing O${}_2$ enrichment. Particle-flame interaction is assessed by calculating instantaneous particle number density (PND), whose uncertainties are estimated by generating synthetic particles in DBI image simulations. Time-resolved particle sequences allow the evaluation of the particle velocity, which indicates a PND dependency and interactions between particles and volatile flames. 3D flame structure reconstruction and soot formation detection are first demonstrated in single-shot visualizations and then extended to analyze effects of O${}_2$ concentration, PND, and inert gas composition statistically. The increasing O${}_2$ concentration significantly reduces local flame extinction and suppresses soot formation in N${}_2$ and CO${}_2$ atmospheres. Volatile flames reveal higher intensities and lower lift-off heights as O${}_2$ concentration increases. In contrast to that, an increased PND leads to earlier flame extinction and stronger soot formation due to the local gas temperature reduction and oxygen depletion. The lift-off height reduces with increasing PND, which is explained by the complex interaction between particle dynamics, heat transfer, and volatile reactions. Slightly stronger soot formation and delayed ignition are observed in CO${}_2$ atmospheres, whereas CO${}_2$ replacement reveals insignificant influences on the flame extinction behavior. Finally, non-flammability is quantified for particle group combustion at varying PNDs in different atmospheres.     

An analytical study of droplet combustion under microgravity: Quasi-steady transient approach

An analytical model based on an assumption of combined quasi-steady and transient behavior of the process is presented to exemplify the unsteady, sphero-symmetric single droplet combustion under microgravity. The model used in the present study includes an alternative approach of describing the droplet combustion as a process where the diffusion of fuel vapor residing inside the region between the droplet surface and the flame interface experiences quasi-steadiness while the diffusion of oxidizer inside the region between the flame interface and the ambient surrounding experiences unsteadiness. The modeling approach especially focuses on predicting; the variations of droplet and flame diameters with burning time, the effect of vaporization enthalpy on burning behavior, the average burning rates and the effect of change in ambient oxygen concentration on flame structure. The modeling results are compared with a wide range of experimental data available in the literature. It is shown that this simplified quasi-steady transient approach towards droplet combustion yields behavior similar to the classical droplet theory.     

Interaction of a Hopf bifurcation and a symmetry-breaking bifurcation: Stochastic potential and spatial correlations

The multivariate master equation for a general reaction-diffusion system is solved perturbatively in the stationary state, in a range of parameters in which a symmetry-breaking bifurcation and a Hopf bifurcation occur simultaneously. Thestochastic potential U is, in general, not analytic. However, in the vicinity of the bifurcation point and under precise conditions on the kinetic constants, it is possible to define a fourth-order expansion ofU around the bifurcating fixed point. Under these conditions, the domains of existence of different attractors, including spatiotemporal structures as well as the spatial correlations of the fluctuations around these attractors, are determined analytically. The role of fluctuations in the existence and stability of the various patterns is pointed out.     

An efficient approach of unsteady flamelet modeling of a cross-flow-jet combustion system using LES

Steady flamelet models have been widely used in turbulent combustion simulations because of their simplicity, efficiency, yet physics-based nature. They are, however, unable to handle slow chemical and physical processes such as pollutant formation. Unsteady flamelet models have been shown to be able to provide accurate predictions especially for pollutants, but their implementations are usually not as straightforward as for the steady models, and additional assumptions are involved. One relatively straightforward approach of implementing the unsteady flamelet model is to tabulate the time history of unsteady flamelet solutions. This often leads to flamelet libraries of large sizes because of increased dimensions for the new physics. The purpose of this paper is to introduce a new and efficient approach of tabulating unsteady flamelet solutions in the LES of complex systems, here demonstrated in simulations of a cross-flow-jet combustion system. This approach employs Taylor series expansions to represent the time history of unsteady flamelet solutions. Compared with other approaches, the new approach retains the efficiency and simplicity benefits of steady flamelet models but possesses the accuracy of unsteady flamelet models. Various issues associated with the formulation and implementation of this approach are discussed, which include the selection of the base solution, the order of accuracy of the expansion, and the treatment of simultaneous wall heat losses and heat transfer through thermal radiation. This approach is validated in large eddy simulations of a cross-flow-jet combustion system. Good agreement with experiments is obtained for both temperature and NO concentration, as well as for major species.     

A study of the characteristics of the combustion of a Ti +0.5C granular mixture in an inert gas flow

The characteristics of the combustion of a Ti +0.5C granular mixture in a quartz tube under conditions of blowing with argon are studied. The gas flow (cocurrent filtration) is provided by a fixed pressure drop (<1 atm) across the feedstock bed. The dynamics of gas evolution during the combustion the Ti + 0.5C granular mixture, both in the presence and absence of blowing is investigated. The blowing is demonstrated to influence the chemical and phase composition of the condensed synthesis products. It is shown that blowing the Ti + 0.5C granular mixture with a cocurrent argon flow of increases the burning rate.     

The role of a split injection strategy in the mixture formation and combustion of diesel spray: A large-eddy simulation

The role of a split injection in the mixture formation and combustion characteristics of a diesel spray in an engine-like condition is investigated. We use large-eddy simulations with finite rate chemistry in order to identify the main controlling mechanism that can potentially improve the mixture quality and reduces the combustion emissions. It is shown that the primary effect of the split injection is the reduction of the mass of the fuel-rich region where soot precursors can form.Furthermore, we investigate the interaction between different injections and explain the effects of the first injection on the mixing and combustion of the second injection. Results show that the penetration of the second injection is faster than that of the first injection. More importantly, it is shown that the ignition delay time of the second injection is much shorter than that of the first injection. This is due to the residual effects of the ignition of the first injection which increases the local temperature and maintains a certain level of combustion some intermediates or radical which in turn boosts the ignition of the second injection.     

Quasiperiodicity in chemistry: An experimental path in the neighbourhood of a codimension-two bifurcation

A bifurcation sequence from a periodic to a quasiperiodic regime leading ultimately to a steady state, is reported in an experimental study of the Belousov-Zhabotinsky reaction. This sequence is understood in the frame of the interaction of two instabilities, namely a “hysteresis” and a Hopf bifurcation.     

Rotational viscosity of a liquid crystal mixture: a fully atomistic molecular dynamics study

Fully atomistic molecular dynamics (MD) simulations at 293, 303 and 313~K have been performed for the four-component liquid crystal mixture, E7, using the software package Material Studio. Order parameters and orientational time correlation functions (TCFs) were calculated from MD trajectories. The rotational viscosity coefficients (RVCs) of the mixture were calculated using the Nemtsov--Zakharov and Fialkowski methods based on statistical-mechanical approaches. Temperature dependences of RVC and density were discussed in detail. Reasonable agreement between the simulated and experimental values was found.     

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.     

The quantitative analysis of a two-medium mixture using holographic interferometry: the determination of the size corresponding to circular- and rectangular-column voids in a two-medium mixture

The purpose of this paper is to extend the holographic technique to the optical measurement of a two-medium mixture. Assume there exists a void in medium A and the void contains medium B, an experimental technique and the corresponding theories are proposed in this paper, in order to quantitatively determine the size of void in the two-medium mixture. Then the amount of medium B can be determined. An empty glass container was simulated as a void in the mixture. Two different types of glass containers were used and the corresponding theories were derived. The test results show that the errors were in a reasonable range and support the application of holography in the quantitative optical measurement of a two-medium mixture.