Filtered Reaction Rate Research Articles

Filtered reaction rate and interphase mass transfer models in reactive gas‐solid flows

AbstractThis work pursues the closure for the effective reaction rate based on fine‐grid two‐fluid model (TFM) simulations in reactive gas‐solid flows. It is found that the mesoscale mechanism in the solid‐catalyzed reaction is constrained by the kinetic regime (KR) and the external mass transfer‐controlled regimes (EMTR). Thus, a filtered reaction rate model ηsubgrid considered two different regimes is proposed. The mesoscale effectiveness factor proposed in previous work is adopted in KR. A filtered interphase mass transfer model QM, which is constructed by analogy to the interphase heat transfer model, is used in EMTR. ηsubgrid shows a good predictability in two regimes via a priori test. The fidelity of ηsubgrid is also assessed via a filtered TFM simulation. The results indicate that the simulations incorporating corrections for the drag force and reaction rate yield better agreement with the fine‐grid simulations for both mass fraction and reaction rate profiles.

A priori direct numerical simulation assessment of MILD combustion modelling in the context of large eddy simulation

A priori Direct Numerical Simulation (DNS) assessment of the closures for the filtered reaction rate and the Favre-filtered scalar dissipation rate (SDR) for large eddy simulations (LES) of homogenous and stratified mixture MILD combustion has been performed. It has been found that the probability density function of the reaction progress variable can be adequately predicted using the beta function for both homogenous and stratified mixture MILD combustion. It has also been found that a scalar dissipation rate closure characteristic of passive scalar mixing may not be suitable for homogenous and stratified mixture MILD combustion. The predictions of different filtered reaction rate closures have been assessed with respect to DNS data in this study. The Eddy Dissipation Concept (EDC), Eddy-Break Up (EBU) model, and SDR-based reaction rate closures for Reynolds Averaged Navier-Stokes simulations have been extended for MILD combustion in the context of LES. The SDR-based reaction rate closure captures the qualitative behaviour but overpredicts the filtered reaction rate for both homogenous and stratified mixture MILD combustion. The EBU-based reaction rate and flame surface density (FSD) closures did not capture the qualitative behaviour of the filtered reaction rate for both homogenous and stratified mixture MILD combustion. By contrast, the EDC model with bridging functions, which ensures asymptotic behaviour, shows the potential to provide reasonable predictions of the filtered reaction rate for a wide range of filter widths in the cases investigated here.

Probabilistic deep learning of turbulent premixed combustion

A probabilistic data-driven approach that models the filtered reaction rate in large-eddy simulation (LES) is investigated. We propose a novel framework that incorporates a conditional generative adversarial network and a Gaussian mixture model to take into account the statistical fluctuations that are present in LES of turbulent reacting flows due to non-resolved subgrid structures, which cannot be predicted by purely deterministic models and machine learning algorithms. The data from a direct numerical simulation of turbulent premixed combustion are spatially filtered using a wide range of filter widths and employed for the training. We extract physically relevant parameters from the database and reduce the input features to the network to the most influential ones based on the result of feature importance analysis. The trained model is then tested on unseen timesteps and untrained LES filter widths, where it is able to accurately predict the distribution of the filtered reaction rate.

Period-2 Thermoacoustics in a Swirl-Stabilised Partially Premixed Flame Computed Using Large Eddy Simulation

A partially premixed swirl-stabilised flame under thermoacoustically unstable conditions is studied using large eddy simulation with an unstrained flamelet model for the filtered reaction rate. The simulation results agree well with measured statistics of velocity, temperature and mixture fraction. Two thermoacoustic modes at approximately 300 and 590 Hz are excited for the case studied. The second mode pressure amplitude is comparable to that of the first mode. However, the second mode of heat release rate fluctuations is not as significant as for the pressure which results in a 2:1 frequency locking behaviour. The analysis offers insights into the physical mechanism involved in the excitation of the two modes and the 2:1 frequency locking behaviour. The index based on the Rayleigh Criterion in frequency domain is analysed to understand the coupling between the heat release rate and pressure fluctuations. It is observed that there is a nonlinear interaction between the two modes resulting in energy exchange across the two modes. The conventional Rayleigh Index has limitations in explaining the observed dynamics and therefore, a modified Rayleigh Index is defined to understand the effects of nonlinear mode interactions on thermoacoustic characteristics. A mode shape analysis using LES and acoustic-modelling reveals that the first mode may be a Helmholtz mode with internal damping that is excited by an acoustic source, and the second mode has the characteristic shape of a chamber mode.

Towards a generalised artificial neural network for sub-grid filtered density function closure in turbulent combustion

An artificial neural network (ANN) is trained on moderate or intense low-oxygen dilution (MILD) combustion to predict the sub-grid filtered density function (FDF) in large eddy simulation (LES). For wide usability, a new quantity ψ is calculated by scaling the filtered mixture fraction using the stoichiometric value and a logarithmic function, which is used as an input feature of the ANN. Self-testing on MILD combustion is first conducted for validation and determining the best layout of ANN. An ANN with 4 hidden layers and the activation function of rectified linear unit (ReLU) has the highest accuracy. This ANN is subsequently tested on five different premixed combustion cases. Overall predictions of the progress variable FDF are satisfactory, and the filtered chemical source term modelled by the FDFs is in good agreement with the DNS data for each case. However, an underprediction of the filtered reaction rate occurs for the hydrogen–air flames, and the ANN accuracy is lower than that of a presumed β-FDF approach. DNS data of one premixed flame are then added to the training datasets, and newly trained ANNs are tested on remaining premixed flame cases. When the testing cases are similar to the added training dataset, improved predictions of marginal FDFs are observed, and the modelled progress variable source terms show good comparisons with the corresponding DNS data. Compared to the presumed β-FDF method, the new ANN shows an improved accuracy and serves as a viable alternative for FDF-based combustion modelling in the LES of turbulent flames.

BLASTNet: A call for community-involved big data in combustion machine learning

Many state-of-the-art machine learning (ML) fields rely on large datasets and massive deep learning models (with O(109) trainable parameters) to predict target variables accurately without overfitting. Within combustion, a wealth of data exists in the form of high-fidelity simulation data and detailed measurements that have been accumulating since the past decade. Yet, this data remains distributed and can be difficult to access. In this work, we present a realistic and feasible framework which combines (i) community involvement, (ii) public data repositories, and (iii) lossy compression algorithms for enabling broad access to high-fidelity data via a network-of-datasets approach. This Bearable Large Accessible Scientific Training Network-of-Datasets (BLASTNet) is consolidated on a community-hosted web-platform (at https://blastnet.github.io/), and is targeted towards improving accessibility to diverse scientific data for deep learning algorithms. For datasets that exceed the storage limitations in public ML repositories, we propose employing lossy compression algorithms on high-fidelity data, at the cost of introducing controllable amounts of error to the data. This framework leverages the well-known robustness of modern deep learning methods to noisy data, which we demonstrate is also applicable in combustion by training deep learning models on lossy direct numerical simulation (DNS) data in two completely different ML problems — one in combustion regime classification and the other in filtered reaction rate regression. Our results show that combustion DNS data can be compressed by at least 10-fold without affecting deep learning models, and that the resulting lossy errors can even improve their training. We thus call on the research community to help contribute to opening a bearable pathway towards accessible big data in combustion.

Modelling filtered reaction rate in turbulent premixed flames using feature importance analysis, gene expression programming and tiny artificial neural networks

Two different machine learning (ML) approaches, Symbolic regression, more precisely Gene Expression Programming (GEP) and Tiny Artificial Neural Networks (TANN), have been used for deducing a model for the filtered reaction rate in the context of Large Eddy Simulation (LES) of premixed combustion. The models have been trained on data generated from a large range of filter widths and for different turbulence intensities, using a simple chemistry Direct Numerical Simulation (DNS) database of statistically planar turbulent premixed flames. Feature importance analysis has been applied to identify the important input variables for modelling filtered reaction rate in order to enable an efficient optimization process as well as moderate inference times. The resulting models show excellent correlation and good quantitative agreement with the filtered reaction rates extracted from explicitly filtered DNS data. The genetic optimization results in a mathematical expression that can be easily implemented, analysed and documented. Also, the TANN has a small number of trainable parameters that can be shared with the research community. The present results demonstrate that ML algorithms can be successfully used for modelling turbulent premixed flames in the context of Large Eddy Simulation. Both approaches can fulfil the requirements of transparency and have inference times that are acceptable in comparison to algebraic models.

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.

Development of a turbulence dissipation based reaction rate model for progress variable in turbulent premixed flames

This study presents an algebraic combustion closure for Large eddy simulation (LES) exhibiting attributes of simplicity and simultaneous accuracy under realistic combustion conditions. The model makes use of the interlink between the reaction and dissipation rates in premixed turbulent combustion but relaxes the thin flame assumption by considering finite-rate chemistry effects in the small-scale turbulence structure. The core idea of the approach is to approximate the reaction progress in the unresolved spectrum of wave lengths and to use it within a filtered reaction rate expression. The model is implemented in OpenFOAM 4.0 and is tested on a turbulent, premixed flame behind a bluff-body, applying an LES approach for turbulence modelling. The cross comparison of velocity, temperature and composition data with experiments and a well-investigated combustion model in literature reveals competitive performance of the new model. Especially in the near-field of the bluff body flame, corresponding to thin and moderately thickened flame regions, its ability to capture the flame structure is highly promising. The chosen, partly explicit approach to recover the temperature from the transported sensible enthalpy, involving a strong coupling between filtered reaction and heat release rate, also shows advantages over obtaining the temperature from presumed probability density functions.

A Priori Analysis on Deep Learning of Filtered Reaction Rate

A filtered reaction rate model driven by deep learning is proposed and analyzed a priori in the context of large eddy simulation (LES). A deep artificial neural network (ANN) is trained on the explicitly filtered reaction rate source term extracted from a database comprised of turbulent premixed planar flame direct numerical simulations (DNSes) employing single-step chemistry. The filtered DNS database to be used for the training of the ANN covers a wide range of turbulence intensities and LES filter widths. An interpretation technique of deep learning is employed to search the principal input parameters in the high dimensional database to alleviate the model complexity. The deep learning filtered reaction rate model is then tested on the unseen filtered planar flames featuring untrained turbulence intensities and LES filter widths, in conjunction with another canonical type of flame configuration that it has not been trained on. The deep learning filtered reaction rate model achieves good agreement with the filtered DNS results and also provides a quantitatively accurate surrogate model when compared to existing algebraic models and other combustion models from the literature.

On the blow‐off correlation for swirl‐stabilised flames with a precessing vortex core

Large eddy simulations of turbulent swirl-stabilised flames gradually approaching blow-off conditions in a gas turbine model combustor are undertaken. The global equivalence ratio of the flames is reduced by increasing and decreasing the air and fuel flow rates respectively. The filtered reaction rate for partially premixed combustion is modelled using a presumed joint probability density function flamelet model. The average position of the flame is closer to the fuel nozzle when the global equivalence ratio is decreased, contrary to what is expected. Comparisons are made with simultaneous particle image velocimetry, and acetone and OH planar laser induced fluorescence imaging for the corresponding simulated case. It is demonstrated that the mechanisms leading to local extinction are well captured in the simulation and insufficient mixing induced by the precessing vortex core leads to local extinction. Further analysis of the simulations shows that including heat loss effects within the modelling is important for flames near or approaching blow-off. The non-adiabatic simulation influences the re-stabilisation of the flame after lift-off and shows that the flame leading edge follows the rotation of the PVC. A blow-off correlation based on the Damköhler number is proposed using the PVC rotation frequency and a chemical time scale. Analysis shows that the simulated flames respond to the correlation and including non-adiabatic flamelets is important for flames approaching blow-off.

Generalization Capability of Convolutional Neural Networks for Progress Variable Variance and Reaction Rate Subgrid-Scale Modeling

Deep learning has recently emerged as a successful approach to produce accurate subgrid-scale (SGS) models for Large Eddy Simulations (LES) in combustion. However, the ability of these models to generalize to configurations far from their training distribution is still mainly unexplored, thus impeding their application to practical configurations. In this work, a convolutional neural network (CNN) model for the progress-variable SGS variance field is trained on a canonical premixed turbulent flame and evaluated a priori on a significantly more complex slot burner jet flame. Despite the extensive differences between the two configurations, the CNN generalizes well and outperforms existing algebraic models. Conditions for this successful generalization are discussed, including the effect of the filter size and flame–turbulence interaction parameters. The CNN is then integrated into an analytical reaction rate closure relying on a single-step chemical source term formulation and a presumed beta PDF (probability density function) approach. The proposed closure is able to accurately recover filtered reaction rate values on both training and generalization flames.

Conventional anddata‐drivenmodeling of filtered drag, heat transfer, and reaction rate ingas–particleflows

AbstractThis study presents conventional and artificial neural network‐based data‐driven modeling (DDM) methods to model simultaneously the filtered mesoscale drag, heat transfer and reaction rate in gas–particle flows. The dataset used for developing the DDM is filtered from highly resolved simulations closed by our recently formulated microscopic drag and heat transfer coefficients (HTCs). Results reveal that the filtered drag correction is nearly independent of filter size when including the filtered gas phase pressure gradient. We further find that the filtered HTC correction critically depends on the added filtered temperature difference marker while the filtered reaction rate correction shows weak dependence on the additional markers. Moreover, compared with conventional correlations, DDM predictions agree better with filtered resolved data. Comparative analysis is also conducted between existing HTC corrections and our work. Finally, the applicability of conventional and data‐driven models coupled with coarse‐grid computational fluid dynamics simulations for pilot‐scale (reactive) gas–particle flows is validated comprehensively.

Development of a filtered reaction rate model for reactive gas–solid flows based on fine‐grid simulations

AbstractThe filtered reaction rate for the coarse‐grid simulations of reactive gas–solid flows can be obtained via a correction to its microscopic reaction rate. The correction term is defined as the mesoscale effectiveness factor ηΔ, which is the ratio of the reaction rate obtained from the fine‐grid simulations to that obtained from the coarse‐grid simulations. The considered reaction is an isothermal, solid‐catalyzed surface reaction with a power law reaction rate model. The simulation results show that the mean ηΔ is almost invariant with the reaction orders at the same Damköhler number. A closure correlation for the mean ηΔ is formulated. However, the standard deviation of ηΔ is found to be quite large. A presumed probability density function model is proposed to capture the fluctuating properties of ηΔ. The predictability of the closure correlations are evaluated via performing the filtered two fluid model simulations in circulating fluidized beds of ozone decomposition.

Application of machine learning for filtered density function closure in MILD combustion

Abstract A machine learning algorithm, the deep neural network (DNN) 1 , is trained using a comprehensive direct numerical simulation (DNS) dataset to predict joint filtered density functions (FDFs) of mixture fraction and reaction progress variable in Moderate or Intense Low-oxygen Dilution (MILD) combustion. The important features of the DNS cases include mixture fraction variations, turbulent mixing lengths, exhaust gas recirculation (EGR) dilution levels, etc., posing a great challenge for data-driven modelling. The DNN architecture is built and optimised with extreme care to achieve high robustness and accuracy, resorting to dimensionality reduction techniques such as principal component analysis (PCA) to identify and remove the outliers in the training data. To better interpret the predictive ability of the DNN, two analytical joint FDF models respectively using two independent β and copula distributions, are also employed for a detailed comparison with the DNS data. The FDFs in MILD combustion behave differently compared to those in conventional flames because the reaction zones are more distributed. They generally exhibit non-regular (neither Gaussian nor bi-modal) distributions and strong cross correlations, which cannot be captured adequately by the analytical models. However, the DNN is well suited for this physico-chemically complex problem and its predictions are in excellent agreement with the DNS data for a broad range of mixture conditions and filter sizes. Furthermore, a priori assessment is conducted for filtered reaction rate closure. It is found that the DNN model significantly outperforms the analytical models for all cases showing very good predictions for the filtered reaction rate for a range of filter sizes. The DNN prediction improves as the filter size becomes larger than the characteristic reaction zone thickness while the analytical models works relatively better for smaller filter sizes. This is a clear advantage for the DNN to be used in practical LES applications.

A priori evaluation of the Double-conditioned Conditional Source-term Estimation model for high-pressure heptane turbulent combustion using DNS data obtained with one-step chemistry

An evaluation of the submodels constituting the Double-Conditioned Source-term Estimation (DCSE) method for utilization in Large Eddy Simulation (LES) is presented which makes use of a single realization of a turbulent high-pressure reactive-flow database obtained from Direct Numerical Simulation (DNS). A filtered and coarsened DNS (FCDNS) field is first created to mimic a real LES field, and the FCDNS values for thermodynamic variables (temperature, density and species mass fractions) are used as inputs to the DCSE model to predict the FCDNS reaction rates. It is found that there are significant errors in the predictions of the filtered reaction rate compared to the template. These errors are attributed to three important aspects of the model. First, the conditional-filtered values of the thermodynamic variables are found by an inversion of an integral equation, but this inversion requires the definition of spatial ensembles in which it must be performed; these ensembles are a subset of the entire spatial domain containing the LES volumes. A drastic reduction in the number of ensembles from the number of LES volumes (i.e. the largest possible number of such ensembles) deteriorates the model, whereas a further and smaller such reduction has a small effect. Second, the procedure for the integral inversion introduces problems related to the method selected to regularize the inversion. Third, by far the largest source of error was found to be due to the modelling of the joint probability density function of the conditioning variables: assuming a β-PDF for the marginal PDF of the reaction progress variable is shown to be a particularly poor choice, as is the assumption that the conditioning variables are statistically independent.

New Dynamic Scale Similarity Based Finite-Rate Combustion Models for LES and a priori DNS Assessment in Non-premixed Jet Flames with High Level of Local Extinction

In this work, the performances of two recently developed finite-rate dynamic scale similarity (SS) sub-grid scale (SGS) combustion models (named DB and DC) for non-premixed turbulent combustion are a priori assessed based on three Direct Numerical Simulation (DNS) databases. These numerical experiments feature temporally evolving syngas jet flames with different Reynolds (Re) numbers (2510, 4487 and 9079), experiencing a high level of local extinction. For comparison purposes, the predicting capability of these models is compared with three classical non-dynamic SS models, namely the scale similarity resolved reaction rate model (SSRRRM or A), the scale similarity filtered reaction rate model (SSFRRM or B), and a SS model derived by the “test filtering” approach (C), as well as an existing dynamic version of SSRRRM (DA). Improvements in the prediction of heat release rates using a new dynamic model DC are observed in high Re flame case. By decreasing Re, dynamic procedures produce results roughly similar to their non-dynamic counterparts. In the lowest Re, the dynamic methods lead to higher errors.

Deep learning for presumed probability density function models

In this work, we use machine learning (ML) techniques to develop presumed probability density function (PDF) models for large eddy simulations (LES) of reacting flows. The joint sub-filter PDF of mixture fraction and progress variable is modeled using various ML algorithms and commonly used analytical models. The ML algorithms evaluated in the work are representative of three major classes of ML techniques: traditional ensemble methods (random forests), deep learning (deep neural network (DNN)s), and generative learning (conditional variational autoencoder (CVAE)). The first two algorithms are supervised learning algorithms, and the third is an unsupervised learning algorithm. Data from direct numerical simulation (DNS) of the low-swirl burner[1] are used to develop training data for sub-filter PDF models. Models are evaluated on predictions of the sub-filter PDF as well as predictions of the filtered reaction rate of the progress variable, computed through an integral of the product of the sub-filter PDF and the conditional means of the reaction rate. This a-priori modeling study demonstrates that deep learning models for presumed PDF modeling are three times more accurate than analytical β–β PDF models and linear regression models. These models are as accurate as random forest models while using five times fewer trainable parameters and being 25 times faster for inference. In this work, conditional unsupervised learning did not present additional advantages beyond supervised learning with a feed-forward neural network. We illustrate how models generalize to other regions of the flow and develop criteria based on the Jensen–Shannon divergence to quantify the performance of a model on new data.

Filtered Reaction Rate Modelling in Moderate and High Karlovitz Number Flames: an a Priori Analysis

Direct numerical simulations (DNS) of statistically planar flames at moderate and high Karlovitz number (Ka) have been used to perform an a priori evaluation of a presumed-PDF model approach for filtered reaction rate in the framework of large eddy simulation (LES) for different LES filter sizes. The model is statistical and uses a presumed shape, based here on a beta-distribution, for the sub-grid probability density function (PDF) of a reaction progress variable. Flamelet tabulation is used for the unfiltered reaction rate. It is known that presumed PDF with flamelet tabulation may lead to over-prediction of the modelled reaction rate. This is assessed in a methodical way using DNS of varying complexity, including single-step chemistry and complex methane/air chemistry at equivalence ratio 0.6. It is shown that the error is strongly related to the filter size. A correction function is proposed in this work which can reduce the error on the reaction rate modelling at low turbulence intensities by up to 50%, and which is obtained by imposing that the consumption speed based on the modelled reaction rate matches the exact one in the flamelet limit. A second analysis is also conducted to assess the accuracy of the flamelet assumption itself. This analysis is conducted for a wide range of Ka, from 6 to 4100. It is found that at high Ka this assumption is weaker as expected, however results improve with larger filter sizes due to the reduction of the scatter produced by the fluctuations of the exact reaction rate.

The modeling of the turbulent reaction rate under high-pressure conditions: A priori evaluation of the Conditional Source-term Estimation concept

With the goal of obtaining an accurate model of the turbulent reaction rate for Large Eddy Simulations (LESs), the modeling of turbulence-chemistry-thermodynamic interaction is addressed through an a priori study of a Direct Numerical Simulation (DNS) database representing high-pressure turbulent combustion. The DNS database consists of simulations of a temporal mixing layer in which a single-step chemical reaction occurs. The potential of the single-conditioned Conditional Source-term Estimation (CSE) approach to model the filtered turbulent reaction rate needed for conducting LES is examined. Evaluations conducted with the mixture fraction as a conditioning variable at two filter widths and with the probability density function (PDF) extracted from the DNS database that represents the mixture fraction, show that the deviation between the model and template is large and substantially increases with filter width. To address this deviation, the Double-conditioned CSE (DCSE) approach is explored with two different second conditioning variables, the first conditioning variable still being the mixture fraction; four filter widths are considered. The first choice of the second conditioning variable is a normalized progress variable based on the CO2 mass fraction and the second choice of the second conditioning variable is a normalized temperature. With each second conditional variable, the DCSE results represent a substantial improvement over CSE, by as much as an order of magnitude when measured by the relative error from the DNS-extracted filtered reaction rate. A quantitative test based on a root mean square identifies the reason for the DCSE success compared to CSE: unlike in CSE, the DCSE is able to substantially reduce the fluctuations of the modeled reaction rate from the filtered reaction rate over the entire range of the filtered reaction rate values, and particularly at the larger reaction rate values for which the DCSE model has higher fidelity. The results are shown to be equally favorable for the two conditioning variables. Consideration of DNS realizations at higher free-stream pressure or larger Reynolds number shows that the results are essentially equally successful at other pressure or Reynolds number values.