Effects of Body Forces on the Statistics of Flame Surface Density and Its Evolution in Statistically Planar Turbulent Premixed Flames

Body forces such as buoyancy and externally imposed pressure gradients are expected to have a strong influence on turbulent premixed combustion due to the considerable changes in density between the unburned and fully burned gases. The present work utilises Direct Numerical Simulation data of three-dimensional statistically planar turbulent premixed flames to study the influence of body forces on the statistical behaviour of the flame surface density (FSD) and its evolution within the flame brush. The analysis has been carried out for different turbulence intensities and normalised body force values (i.e., Froude numbers). A positive value of the body force signifies an unstable density stratification (i.e., body force is directed from the heavier unburned gas to the lighter burned gas) and vice versa. It is found that for a given set of turbulence parameters, flame wrinkling increases with an increase in body force magnitude in the unstable configuration. Furthermore, higher magnitudes of body force in the unstable density stratification configuration promote a gradient type transport of turbulent scalar and FSD fluxes, and this tendency weakens in the stable density stratification configuration where a counter-gradient type transport is promoted. The statistical behaviours of the different terms in the FSD transport equation and their closures in the context of Reynolds Averaged Navier–Stokes simulations have been analysed in detail. It has been demonstrated that the effects of body force on the FSD and the terms of its transport equation weakens with increasing turbulence intensity as a result of the diminishing relative strength of body force in comparison to the inertial force. The predictions of the existing models have been assessed with respect to the corresponding terms extracted from the explicitly averaged DNS data, and based on this evaluation, suitable modifications have been made to the existing models to incorporate the effects of body force (or Froude number).

Data-Driven Combustion Modeling for a Turbulent Flame Simulated With a Computationally Efficient Solver

The use of machine learning (ML) for modeling is on the rise. In the age of big data, this technique has shown great potential to describe complex physical phenomena in the form of models. More recently, ML has frequently been used for turbulence modeling while the use of this technique for combustion modeling is still emerging. Gene expression programming (GEP) is one class of ML that can be used as a tool for symbolic regression and thus improve existing algebraic models using high-fidelity data. Direct numerical simulation (DNS) is a powerful candidate for producing the required data for training GEP models and validation. This paper therefore presents a highly efficient DNS solver known as HiPSTAR, originally developed for simulating non-reacting flows in particular in the context of turbo-machinery. This solver has been extended to simulate reacting flows. DNSs of two turbulent premixed jet flames with different Karlovitz numbers are performed to produce the required data for training. GEP is then used to develop algebraic flame surface density models in the context of large-eddy simulation (LES). The result of this work introduces new models which show excellent performance in prediction of the flame surface density for premixed flames featuring different Karlovitz numbers.