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The statistical behaviour and closure of sub-grid scalar fluxes in the context of turbulent premixed combustion has been assessed based on an a priori analysis of a detailed chemistry Direct Numerical Simulation (DNS) database consisting of three hydrogen air flames spanning the corrugated flamelets (CF), thin reaction zones (TRZ) and broken reaction zones (BRZ) regimes of premixed turbulent combustion. The sub-grid scalar fluxes have been extracted by explicit filtering of DNS data. It has been found that the conventional gradient hypothesis model is not appropriate for the closure of sub-grid scalar flux for any scalar in the context of a multi-species system. However, the predictions of the conventional gradient hypothesis exhibit a greater level of qualitative agreement with DNS data for the flame representing the BRZ regime. The aforementioned behaviour has been analysed in terms of the properties of the invariants of the anisotropy tensor in the Lumley triangle. The flames in the CF and TRZ regimes are characterised by a pronounced two dimensional anisotropy due to strong heat release whereas a three dimensional and more isotropic behaviour is observed for the flame located in the BRZ regime. Two sub-grid scalar flux models which are capable of predicting counter-gradient transport have been considered for a priori DNS assessment of multi-species systems and have been analysed in terms of both qualitative and quantitative agreements. By combining the latter two sgs flux closures a new modelling strategy is suggested where one model is responsible for properly predicting the conditional mean accurately and the other model is responsible for the correlations between model and unclosed term. Detailed physical explanations for the observed behaviour and an assessment of existing modelling assumptions have been provided. Finally, the classical Bray-Moss-Libby theory for the scalar flux closure has been extended to address multispecies transport in the context of Large Eddy Simulations (LES).

The statistical behaviours of the principal strain rates and its evolution in turbulent premixed flames have been analysed using a three-dimensional Direct Numerical Simulations dataset of statistically planar turbulent premixed flames with different turbulence intensities spanning from the corrugated flamelets regime to the thin reaction zones regime. It has been found that the scalar gradient predominantly aligns collinearly with the most extensive principal strain rate within the flame for large Damköhler numbers and small values of turbulence intensities and Karlovitz numbers. However, this tendency weakens with increasing turbulence intensity, which for a given integral length scale, amounts to a decrease (an increase) in Damköhler (Karlovitz) number. Moreover, it has been observed that the terms due to molecular diffusion, pressure Hessian and the correlation between pressure and density gradients play key roles in the evolution of principal strain rates for flames with large Damköhler number and small values of Karlovitz number. However, the relative importance of the terms arising from the correlation between pressure and density gradients and the pressure Hessian relative to the strain rate and vorticity contributions of the principal strain rate transport diminishes with increasing Karlovitz number and decreasing Damköhler number. The statistical behaviours of the mean values of the terms of the transport equation of the principal strain rate have been explained based on the relative alignments of principal strain rate eigenvectors with vorticity, pressure gradient and the eigenvectors of the pressure Hessian tensor. The findings of the current analysis suggest that the pressure gradient and pressure Hessian tensor play key roles in the evolution of principal strain rates within premixed turbulent flames, and their influences need to be accounted for high fidelity modelling of the tangential strain rate and scalar-turbulence interaction terms of the Flame Surface Density and Scalar Dissipation Rate transport equations, respectively. This provides possible explanations for the modification in the alignment of the reactive scalar gradient with local principal strain rates in premixed flames in comparison to that in non-reacting turbulent flows.

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International licence Newcastle University ePrints -eprint.ncl.ac.uk Klein M, Kasten C, Chakraborty N. A-priori Direct Numerical simulation assessment of models for generalized sub-grid scale turbulent kinetic energy in turbulent premixed flames. Computers and Fluids 2017, 154, 123-131.

In the present study, Gene Expression Programming (GEP) will be used for training a model for subgrid scale (SGS) scalar dissipation rate (SDR) for a large range of filter widths, using a database of statistically planar turbulent premixed flames, featuring different turbulence intensities and heat release parameters. GEP is based on the idea to iteratively improve a population of model candidates using the survival-of-the-fittest concept. The resulting model is a mathematical expression that can be easily implemented, shared with the community and analyzed for physical consistency, as illustrated in this work. Efficient evaluation of the cost function and a smart choice of basis functions have been found to be essential for a successful optimization process. The GEP based model has been found to outperform an existing algebraic model from the literature. However, the optimization process was found to be quite intricate and the SGS SDR closure turned out to be difficult. Some of these problems have been explained using the model-agnostic interpretation method which requires the existence of a trained artificial neural network (ANN). ANNs are known for their ability to represent complex functional relationships and serve as an additional benchmark solution for the GEP based model.

The statistical behaviors of the evolutions of the components of the strain rate tensor and Favre-averaged dissipation rate of kinetic energy are analyzed using direct numerical simulations of statistically planar turbulent premixed flames propagating into forced unburned gas turbulence for different turbulence intensities spanning a range of different Karlovitz numbers. The pressure Hessian contribution and the combined molecular diffusion and dissipation terms are found to play dominant roles in the transport equations of diagonal strain rate components and the Favre-averaged dissipation rate of kinetic energy for flames with small Karlovitz numbers. By contrast, the leading order balance is maintained between the strain rate, vorticity, and molecular dissipation contributions for flames with large Karlovitz numbers, similar to non-reacting turbulent flows. The contributions of the terms arising from the correlation between pressure and density gradients and pressure Hessian in the strain rate and dissipation rate of kinetic energy transport equations weaken in comparison to the magnitude of the molecular dissipation contribution with an increase in Karlovitz number. These behaviors have been explained in terms of the alignments of vorticity, pressure gradient, and pressure Hessian eigenvectors with strain rate eigendirections. The magnitudes of the terms in the transport equation of the Favre-averaged dissipation rate of kinetic energy are also found to increase with increasing Karlovitz number, which is explained with the help of a detailed scaling analysis. This scaling analysis also explains the leading order contributions to the dissipation rate of kinetic energy for different combustion regimes.

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