Assessment of Extrapolation Relations of Displacement Speed for Detailed Chemistry Direct Numerical Simulation Database of Statistically Planar Turbulent Premixed Flames
Assessment of Extrapolation Relations of Displacement Speed for Detailed Chemistry Direct Numerical Simulation Database of Statistically Planar Turbulent Premixed Flames
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DOI：
10.1007/s10494-021-00283-w
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发表时间：
2021-08
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通讯作者：
N. Chakraborty;A. Herbert;U. Ahmed;H. Im;M. Klein
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作者：
N. Chakraborty;A. Herbert;U. Ahmed;H. Im;M. Klein
利用一个统计平面空气湍流预混火焰的三维直接数值模拟(DNS)数据库，在很大的卡洛维茨数范围内，当量比为0.7，评估了外推关系的性能，该外推关系近似于密度加权置换速度的拉伸率和曲率依赖关系。结果表明，在所有的情况下，伸长率与伸长率之间存在显著的非线性相关关系，而与曲率之间的相关性仍然是负的。因此，假定密度加权驱替速度与拉伸率线性相关的外推关系是不充分的。然而，另一种外推关系被发现在捕捉密度加权位移速度的局部行为方面更成功，该关系假设线性曲率依赖于，但允许非线性拉伸速率依赖于。用曲率或伸长率的非线性函数表示的外推关系比线性外推关系更能定性地反映非线性曲率和伸长率的依赖关系。然而，这种改进是以额外的调谐参数为代价的。对于所有的外推关系，马克斯坦长度LM都表现出对反应进度变量定义的选择的依赖性，对于某些外推关系，LM也随反应进度变量的值而变化。外推关系的预测涉及用拉伸率求解非线性方程，已被发现对初始猜测值敏感，而基于高次多项式的外推关系可能会导致超调和未调。因此，最近提出的一个基于对简单化学解析数据的分析的外推关系，它明确地解释了组合反应和法向扩散组分的非线性曲率相关性，对于这里所考虑的所有情况，都显示出良好的预测效果。
A three-dimensional Direct Numerical Simulation (DNS) database of statistically planarair 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. It has been found that the correlation betweenand curvature remains negative and a significantly non-linear interrelation betweenand 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 ofbut allows for a non-linear stretch rate dependence of, has been found to be more successful in capturing local behaviour of the density-weighted displacement speed. The extrapolation relations, which expressas non-linear functions of either curvature or stretch rate, have been found to capture qualitatively the non-linear curvature and stretch rate dependences ofmore satisfactorily than the linear extrapolation relations. However, the improvement comes at the cost of additional tuning parameter. The Markstein lengthsLMfor all the extrapolation relations show dependence on the choice of reaction progress variable definition and for some extrapolation relationsLMalso 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, has been shown to exhibit promising predictions offor all cases considered here.