A three-dimensional Direct Numerical Simulation (DNS) database of statistically planar turbulent premixed flames covering the wrinkled/corrugated flamelets and the thin reaction zones regimes of premixed turbulent combustion has been utilised to assess the performances of the extrapolation relations, which approximate the stretch rate and curvature dependences of density-weighted displacement speed . It has been found that remains negatively correlated with curvature and exhibits a significantly non-linear relation with stretch rate for all cases considered here. As a result of these behaviours, an extrapolation relation, which assumes a linear stretch rate dependence of density-weighted displacement speed has been found to be inadequate. However, an alternative extrapolation relation which assumes a linear curvature dependence of has been found to be more successful in capturing local behaviour of the density-weighted displacement speed because it allows for a non-linear stretch rate dependence of . The extrapolation relations, which express as non-linear functions of either curvature or stretch rate, have been found to perform better than the linear extrapolation relations. The Markstein length for all the extrapolation relations except for the one, which assumes a linear stretch rate dependence of , has been found to be in good agreement with an analytical expression for . An extrapolation relation which involves solving a non-linear equation in terms of stretch rate has been found to be sensitive to the initial guess and an alternative high-order polynomial-based extrapolation relation gives rise to overshoots and undershoots and thus the goodness of fit of these relations suffers for high turbulence intensities. An alternative extrapolation relation has been proposed in this analysis, which explicitly accounts for the non-linear curvature dependence of the combined reaction and normal diffusion components of and satisfactorily captures the statistical behaviours of for all cases considered here.

中文翻译：

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统计平面湍流预混火焰的曲率和拉伸率依赖于位移速度的外推关系的适用性

覆盖褶皱/波纹小火焰和预混湍流燃烧的薄反应区制度的统计平面湍流预混火焰的三维直接数值模拟 (DNS) 数据库已被用于评估近似拉伸速率的外推关系的性能和密度加权位移速度的曲率依赖性。已经发现，对于这里考虑的所有情况，它与曲率保持负相关并且与拉伸率呈现显着的非线性关系。由于这些行为，已发现假定密度加权位移速度的线性拉伸速率依赖性的外推关系是不充分的。然而，已经发现假设线性曲率相关性的替代外推关系在捕获密度加权位移速度的局部行为方面更成功，因为它允许非线性拉伸速率相关性。外推关系表示为曲率或拉伸率的非线性函数，已发现其性能优于线性外推关系。所有外推关系的马克斯坦长度，除了假设线性拉伸率相关的 ，已发现与 的解析表达式非常一致。已经发现，涉及根据拉伸率求解非线性方程的外推关系对初始猜测很敏感，而另一种基于高阶多项式的外推关系会导致过冲和下冲，从而导致拟合优度这些关系受到高湍流强度的影响。在该分析中提出了另一种外推关系，它明确解释了组合反应和法向扩散分量的非线性曲率依赖性，并令人满意地捕获了此处考虑的所有情况的统计行为。