A transport equation for the flame displacement speed evolution in premixed flames is derived from first principles, and the mean behaviours of the terms of this equation are analysed based on a Direct Numerical Simulation database of statistically planar turbulent premixed flames with a range of different Karlovitz numbers. It is found that the regime of combustion (or Karlovitz number) affects the statistical behaviour of the mean contributions of the terms of the displacement speed transport equation which are associated with the normal strain rate and curvature dependence of displacement speed. The contributions arising from molecular diffusion and flame curvature play leading order roles in all combustion regimes, whereas the terms arising from the flame normal straining and reactive scalar gradient become leading order contributors only for the flames with high Karlovitz number values representing the thin reaction zones regime. The mean behaviours of the terms of the displacement speed transport equation indicate that the effects arising from fluid-dynamic normal straining, reactive scalar gradient and flame curvature play key roles in the evolution of displacement speed. The mean characteristics of the various terms of the displacement speed transport equation are explained in detail and their qualitative behaviours can be expounded based on the behaviours of the corresponding terms in the case of 1D steady laminar premixed flames. This implies that the flamelet assumption has the potential to be utilised for the purpose of any future modelling of the unclosed terms of the displacement speed transport equation even in the thin reaction zones regime for moderate values of Karlovitz number.

根据第一原理推导了预混火焰中火焰位移速度演化的输运方程，并基于具有一系列不同卡洛维茨数的统计平面湍流预混火焰的直接数值模拟数据库分析了该方程项的平均行为。研究发现，燃烧状态（或卡洛维茨数）影响位移速度传输方程项的平均贡献的统计行为，这些项与法向应变率和位移速度的曲率依赖性相关。分子扩散和火焰曲率产生的贡献在所有燃烧状态中都起着主导作用，而火焰法向应变和反应标量梯度产生的项仅对于代表薄反应区状态的具有高卡洛维茨数值的火焰成为主导作用。位移速度传输方程项的平均行为表明，流体动力法向应变、反应标量梯度和火焰曲率产生的影响在位移速度的演化中起着关键作用。详细解释了位移速度传输方程各项的平均特征，并可以根据一维稳态层流预混火焰情况下相应项的行为来阐述它们的定性行为。这意味着小火焰假设有可能被用于位移速度传输方程的未封闭项的任何未来建模，即使是在卡洛维茨数中等值的薄反应区区域中。