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).

由于未燃烧和完全燃烧的气体之间的密度发生相当大的变化，预计浮力和外部施加的压力梯度等体力会对湍流预混燃烧产生很大影响。目前的工作利用三维统计平面湍流预混火焰的直接数值模拟数据来研究体力对火焰表面密度 (FSD) 统计行为的影响及其在火焰刷内的演变。已经针对不同的湍流强度和归一化的体力值（即弗劳德数）进行了分析。体力的正值表示不稳定的密度分层（即，体力从较重的未燃烧气体导向较轻的燃烧气体），反之亦然。发现对于给定的一组湍流参数，在不稳定配置中，火焰起皱随着体力大小的增加而增加。此外，不稳定密度分层配置中较高的体力促进了湍流标量和 FSD 通量的梯度类型传输，而这种趋势在稳定密度分层配置中减弱，其中促进了反梯度类型传输。详细分析了 FSD 输运方程中不同项的统计行为及其在雷诺平均 Navier-Stokes 模拟的背景下的闭包。已经证明，与惯性力相比，由于体力的相对强度减小，体力对 FSD 及其输运方程项的影响随着湍流强度的增加而减弱。已根据从显式平均 DNS 数据中提取的相应项对现有模型的预测进行了评估，并在此评估的基础上，对现有模型进行了适当的修改，以纳入体力（或弗劳德数）的影响.