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.@en

Direct numerical simulation (DNS) data of freely propagating turbulent premixed flame of stoichiometric hydrogen air mixture inside a closed vessel is analysed to study a sub-grid combustion closure based on unstrained flamelet approach. This modeling framework needs closures for the sub-grid scale (SGS) reaction rate and scalar dissipation rate. The results show that the closure models for these two SGS quantities work quite well. The dissipation rate closure involves a scale dependent parameter, βc, which is related to the flame curvature induced effects. The reactivity of reactant mixture increases with time in isochoric combustion because the mixture temperature and pressure increase with time. This also influences the parameter βc and thus the dynamic evaluation of this parameter is investigated using the DNS data.@en

Direct numerical simulation (DNS) data of freely propagating turbulent premixed flame of stoichiometric hydrogen air mixture inside a closed vessel is analysed to study a sub-grid combustion closure based on unstrained flamelet approach. This modeling framework needs closures for the sub-grid scale (SGS) reaction rate and scalar dissipation rate. The results show that the closure models for these two SGS quantities work quite well. The dissipation rate closure involves a scale dependent parameter, βc, which is related to the flame curvature induced effects. The reactivity of reactant mixture increases with time in isochoric combustion because the mixture temperature and pressure increase with time. This also influences the parameter βc and thus the dynamic evaluation of this parameter is investigated using the DNS data.@en

Direct numerical simulation (DNS) data of freely propagating turbulent premixed flame of stoichiometric hydrogen air mixture inside a closed vessel is analysed to study a sub-grid combustion closure based on unstrained flamelet approach. This modeling framework needs closures for the sub-grid scale (SGS) reaction rate and scalar dissipation rate. The results show that the closure models for these two SGS quantities work quite well. The dissipation rate closure involves a scale dependent parameter, βc, which is related to the flame curvature induced effects. The reactivity of reactant mixture increases with time in isochoric combustion because the mixture temperature and pressure increase with time. This also influences the parameter βc and thus the dynamic evaluation of this parameter is investigated using the DNS data.@en

The classical energy cascade in turbulence as described by Richardson and Kolmogorov is predominantly a conjecture relying on the locality of interactions between scales of turbulence. This picture is generally accepted and assumes that energy and enstrophy transfers occur between neighboring scales of turbulence and that vortex stretching plays a major role in the dynamics of this energy cascade. Direct numerical simulation data for Reλ ranging from 37 to 1131 is used to gather evidence for the cascade by investigating the energy and enstrophy fluxes between scales and the interplay between vorticity at one scale and strain at an adjacent scale. This is achieved by using a bandpass filter to educe the turbulent structures at various length scales, allowing one to determine the fluxes between these scales and to interrogate the role of nonlocal (in physical space) vortex stretching. It is shown that the structures of a length scale L mostly transfer their energy to structures of size 0.3L and that most of the enstrophy flux goes from structures of scale L to 0.3L. Furthermore, vortical structures of a length scale Lω are stretched mostly by straining structures of size 3Lω to 5Lω, and the stretching by eddies of sizes larger than 10Lω is negligible. The stretching is dominated by the most extensive principal strain rate of the straining structures. These observations are found to be independent of Reλ for the range investigated in this study. These results provide strong evidence for the classical view of an energy cascade transferring energy from large to small scales through a hierarchy of steps, each step consisting of the stretching of vortices by somewhat larger structures.@en