This article reports an analysis of the first detailed chemistry direct numerical simulation (DNS) of a high Karlovitz number laboratory premixed flame. The DNS results are first compared with those from laser-based diagnostics with good agreement. The subsequent analysis focuses on a detailed investigation of the flame area, its local thickness and their rates of change in isosurface following reference frames, quantities that are intimately connected. The net flame stretch is demonstrated to be a small residual of large competing terms: the positive tangential strain term and the negative curvature stretch term. The latter is found to be driven by flame speed–curvature correlations and dominated in net by low probability highly curved regions. Flame thickening is demonstrated to be substantial on average, while local regions of flame thinning are also observed. The rate of change of the flame thickness (as measured by the scalar gradient magnitude) is demonstrated, analogously to flame stretch, to be a competition between straining tending to increase gradients and flame speed variations in the normal direction tending to decrease them. The flame stretch and flame thickness analyses are connected by the observation that high positive tangential strain rate regions generally correspond with low curvature regions; these regions tend to be positively stretched in net and are relatively thinner compared with other regions. High curvature magnitude regions (both positive and negative) generally correspond with lower tangential strain; these regions are in net negatively stretched and thickened substantially.

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 ($\mathrm{C}{H}_4$ for the freely propagating flames and ${\mathrm{H}}_2$ 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.

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 $\tilde{c}$ and decreasing subgrid turbulent velocity fluctuation $u{\prime }_{\Delta }$ . 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 $\tilde{c}$ and $u{\prime }_{\Delta }$ on the performance of different models for various cases were explored. The algebraic models perform well with large values of $\tilde{c}$ and small values of $u{\prime }_{\Delta }$ 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.