Abstract

Accurate modeling of the unresolved flame surface area is critical for the closure of reaction source terms in the flame surface density (FSD) method. Some algebraic models have been proposed for the unresolved flame surface area for premixed flames in the flamelet or thin reaction zones (TRZ) regimes where the Karlovitz number (Ka) is less than 100. However, in many lean combustion applications, Ka is large (Ka > 100) due to the strong interactions of small-scale turbulence and flames. In the present work, a direct numerical simulation (DNS) database was used to evaluate the performance of algebraic FSD models in high Ka premixed flames in the context of large eddy simulations. Three DNS cases, i.e., case L, case M and case H, were performed, where case L is located in the TRZ regime with Ka < 100 and case M and case H are located in the broken reaction zones regime with Ka > 100. A convolutional neural network (CNN) model was also developed to predict the generalized FSD, which was trained with samples of case H and a small filter size, and was tested in various cases with different Ka and filter sizes. It was found that the fraction of resolved FSD increases with increasing filtered progress variable c̃ and decreasing subgrid turbulent velocity fluctuation u′Δ. The performance of CNN and algebraic models was assessed using the DNS database. Overall, the results of algebraic models are promising in case L and case M for a small filter size; the CNN model performs generally better than the algebraic models in high Ka flames and the correlation coefficient between the modeled and actual generalized FSD is greater than 0.91 in all cases. The effects of c̃ and u′Δ on the performance of different models for various cases were explored. The algebraic models perform well with large values of c̃ and small values of u′Δ in high Ka cases, which indicates that they can be applied to high Ka flames in certain conditions. The performance of the CNN model is better than the algebraic models for a large filter size in high Ka cases.

Accurate prediction of temporal evolution of turbulent flames represents one of the most challenging problems in the combustion community. In this work, predictive models for turbulent flame evolution were proposed based on machine learning with long short-term memory (LSTM) and convolutional neural network-long short-term memory (CNN-LSTM). Two configurations without and with mean shear are considered, i.e., turbulent freely propagating premixed combustion and turbulent boundary layer premixed combustion, respectively. The predictions of the LSTM and CNN-LSTM models were validated against the direct numerical simulation (DNS) data to assess the model performance. Particularly, the statistics of the fuel (CH4 for the freely propagating flames and H2 for the boundary layer flames) mass fraction and reaction rate were examined in detail. It was found that generally the performance of the CNN-LSTM model is better than that of the LSTM model. This is because that the CNN-LSTM model extracts both the spatial and temporal features of the flames while the LSTM model only extracts the temporal feature of the flames. The errors of the models mainly occur in regions with large scalar gradients. The correlation coefficient of the mass fraction from the DNS and that from the CNN-LSTM model is larger than 0.99 in various flames. The correlation coefficient of the reaction rate from the DNS and that from the CNN-LSTM model is larger than 0.93 in the freely propagating flames and 0.99 in the boundary layer flames. Finally, the profiles of the DNS values and predictions conditioned on axial distance were examined, and it was shown that the predictions of the CNN-LSTM model agree well with the DNS values. The LSTM model failed to accurately predict the evolution of boundary layer flames while the CNN-LSTM model could accurately predict the evolution of both freely propagating and boundary layer flames. Overall, this study shows the promising performance and the applicability of the proposed CNN-LSTM model, which will be applied to turbulent flames a posteriori in future work.

Large eddy simulation (LES) plays a significant role in turbulent flame modeling. However, accurate prediction of nitrogen oxide (NO x ) formation in turbulent combustion is challenging in LES as the characteristic timescale of the NO reaction is much larger than that of fuel oxidation. In the present work, a machine learning-based model using principal component analysis (PCA) and the convolutional neural network (CNN) was proposed to predict the NO reaction rate in the framework of LES. Direct numerical simulation (DNS) of CH 4 /air freely propagating premixed flames with various turbulent intensities was employed to assess the model performance a priori. The input features of the CNN model include the filtered temperature and species mass fraction related to NO formation. PCA was used to reduce the data dimensions and to remove the noise of the input features. The presented model was trained using samples from a single case and was tested using samples from cases with various turbulent intensities and filter sizes. Various NO pathways, that is, thermal, prompt, N 2 O, and NO 2 pathways, were examined. The distributions of the modeled NO pathways were compared with those of the DNS. It was shown that the model performs well in predicting the thermal, prompt, and N 2 O pathways, with relative errors being smaller than 0.4 for these pathways. As for the NO 2 pathway, non-negligible errors were observed, and the relative errors can be larger than 0.6. The correlations of the actual and modeled total NO reaction rate are evident, with correlation coefficients being higher than 0.98 generally. The conditional means from the CNN model are in good agreement with those from the DNS. Overall, the CNN model performs well for NO prediction in turbulent flames with various turbulent intensities.

Flame stretch and its related quantities are three-dimensional (3D), while most planar imaging techniques, widely used in turbulent combustion, can only provide lower-dimensional information of these quantities. In the present work, based on a direct numerical simulation (DNS) database, artificial neural network (ANN) and random forest (RF) models were developed to predict the 3D flame stretch and its related quantities such as the tangential strain rate, displacement velocity, and curvature from lower-dimensional information that can be accessed experimentally. It was found that the performance of the RF model is better than that of the ANN model. In the RF model, the correlation coefficients between the modeled and actual values are more than 0.97, and the determination coefficients are over 0.95. The model performance deteriorates with increasing turbulent intensity. The probability density functions of various quantities predicted by the RF model are in good agreement with those of the DNS. Compromising the model performance and the computational cost, a simplified RF model was proposed by using a few optimal input features. It was found that the discrepancies between the modeled and actual values mainly occur in highly curved regions, which explains the observation that the prediction errors increase with increasing turbulent intensity. Overall, the predictions of the simplified RF model agree well with the actual values.