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).

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The effects of body forces (alternatively Froude number) on both vorticity and enstrophy evolutions within the flame brush have been analysed using Direct Numerical Simulations (DNS) data of freely propagating statistically planar turbulent premixed flames subjected to different turbulence intensities.The turbulence parameters are taken to represent the thin reaction zone regime of premixed turbulent combustion. The enstrophy has been found to decay significantly from the unburned to the burned gas side of the flame brush for high turbulence intensities and this trend is particularly prominent for the strengthening of the body force promoting unstable stratification. However, local instances of enstrophy generation have been observed and in some cases the decay of enstrophy is arrested across the flame brush for small turbulence intensities. This trend strengthens with the increasing magnitude of the body force promoting stable stratification. The enstrophy generation due to the baroclinic torque is primarily responsible for this local enstrophy generation for small turbulence intensities especially under the body force promoting stable stratification. This baroclinic torque contribution is also found to be responsible for anisotropic behaviour of vorticity components within the flame brush. The vortex stretching and viscous dissipation terms have been found to be the leading order source and sink terms, respectively, in the enstrophy transport for high turbulence intensities especially in the case of body force promoting unstable stratification. However, baroclinic torque, and the sink term due to dilatation rate continue to play significant roles even for high turbulence intensity cases considered here but their relative importance increases with decreasing turbulence intensity especially under the body force promoting stable stratification. The surface-weighted entrainment velocity has been found to be mostly unaffected by the body force in this analysis, and a minor influence can be discerned in the case of small turbulence intensities where an unstable stratification tends to promote high negative values of entrainment velocity only towards the unburned gas side of the flame brush.

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The influence of the ratio of integral length scale to flame thickness on the statistical behaviours of flame surface density (FSD) and its transport has been analysed using a Direct Numerical Simulation database of three-dimensional statistically planar turbulent premixed flames for different turbulence intensities. It has been found that turbulent burning velocity based on volume-integration of reaction rate and flame surface area increase but the peak magnitudes of the FSD and the terms of the FSD transport term decrease with an increase in length scale ratio for a given turbulence intensity. The flame brush thickness and flame wrinkling increase with an increase in length scale ratio for all turbulence intensities. However, the qualitative behaviours of the unclosed terms in the FSD transport equation remain unaltered by the length scale ratio and in all cases the tangential strain rate term and the curvature term act as leading order source and sink, respectively. A decrease in length scale ratio for a given turbulence intensity leads to a decrease in Damköhler number and an increase in Karlovitz number. This has an implication on the alignment of reactive scalar gradient with local strain rate eigenvectors, which in turn increases positive contribution of the tangential strain rate term with a decrease in length scale ratio. Moreover, an increase in Karlovitz number increases the likelihood of negative contribution of the curvature term. Thus, the magnitude of the negative contribution of the FSD curvature term increases with a decrease in length scale ratio for a given turbulence intensity. The model for the tangential strain rate term, which explicitly considers the scalar gradient alignment with local principal strain rate eigenvectors, has been shown to be more successful than the models that do not account for the scalar gradient alignment characteristics. Moreover, the existing model for the curvature and propagation term needed modification to account for greater likelihood of negative values for higher Karlovitz number. However, the models for the unclosed flux of FSD and the mean reaction rate closure are not significantly affected by the length scale ratio.