A three-dimensional Direct Numerical Simulation (DNS) database of statistically planar \(H_{2} -\) air turbulent premixed flames with an equivalence ratio of 0.7 spanning a large range of Karlovitz number has been utilised to assess the performances of the extrapolation relations, which approximate the stretch rate and curvature dependences of density-weighted displacement speed \(S_{d}^{*}\). It has been found that the correlation between \(S_{d}^{*}\) and curvature remains negative and a significantly non-linear interrelation between \(S_{d}^{*}\) and stretch rate has been observed for all cases considered here. Thus, 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 \(S_{d}^{*}\) but allows for a non-linear stretch rate dependence of \(S_{d}^{*}\), has been found to be more successful in capturing local behaviour of the density-weighted displacement speed. The extrapolation relations, which express \(S_{d}^{*}\) as non-linear functions of either curvature or stretch rate, have been found to capture qualitatively the non-linear curvature and stretch rate dependences of \(S_{d}^{*}\) more satisfactorily than the linear extrapolation relations. However, the improvement comes at the cost of additional tuning parameter. The Markstein lengths L_M for all the extrapolation relations show dependence on the choice of reaction progress variable definition and for some extrapolation relations L_M also varies with the value of reaction progress variable. The predictions of an extrapolation relation which involve solving a non-linear equation in terms of stretch rate have been found to be sensitive to the initial guess value, whereas a high order polynomial-based extrapolation relation may lead to overshoots and undershoots. Thus, a recently proposed extrapolation relation based on the analysis of simple chemistry DNS data, which explicitly accounts for the non-linear curvature dependence of the combined reaction and normal diffusion components of \(S_{d}^{*}\), has been shown to exhibit promising predictions of \(S_{d}^{*}\) for all cases considered here.

当量比为 0.7的统计平面\(H_{2} -\)空气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外推的性能关系，它近似于密度加权位移速度\(S_{d}^{*}\)的拉伸率和曲率依赖性。已经发现\(S_{d}^{*}\)和曲率之间的相关性仍然为负，并且\(S_{d}^{*}\)之间存在显着的非线性相互关系并且在此处考虑的所有情况下都观察到了拉伸率。因此，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，另一种外插的关系，其中假定的线性曲率依赖\（S_ {d} ^ {*} \） ，但是允许的非线性拉伸率依赖\（S_ {d} ^ {*} \） ，已发现在捕捉密度加权位移速度的局部行为方面更为成功。已发现将\(S_{d}^{*}\) 表示为曲率或拉伸率的非线性函数的外推关系定性地捕获了\(S_{ d}^{*}\)比线性外推关系更令人满意。然而，改进是以增加额外的调整参数为代价的。所有外推关系的马克斯坦长度L _M显示依赖于反应进程变量定义的选择和一些外推关系L _M也随着反应进程变量的值而变化。已经发现涉及根据拉伸率求解非线性方程的外推关系的预测对初始猜测值敏感，而基于高阶多项式的外推关系可能导致过冲和下冲。因此，最近提出的基于简单化学 DNS 数据分析的外推关系，明确解释了\(S_{d}^{*}\)的组合反应和法向扩散分量的非线性曲率依赖性，具有对于这里考虑的所有情况，已显示出对\(S_{d}^{*}\) 的有希望的预测。