基于当地变量的一方程转捩预测模型
A One-Equation Transition Model Based on Local Variables

引入适用于边界层内的湍流度及压力梯度因子求解公式,构造Reθc和Flength经验关系式,实现对γ-Reθt转捩模型中两输运方程的简化得到一方程转捩预测模型。将其与SST湍流模型进行耦合并利用Schubauer and Klebanoff平板标定各参数。此外,经过分析SST与SA湍流模型输运方程间的联系,修正SA湍流模型中的ft2函数,通过其对源项的控制实现文中一方程转捩预测模型与SA湍流模型的耦合。最后,利用得到的分别基于SST和SA的一方程转捩预测模型对S809低速翼型、DLR-F5机翼进行数值模拟。结果表明:由S809翼型的计算数据可得出文中构建的一方程转捩模型在线性区与实验数据吻合很好,力系数在8°迎角范围内均达到了3%以内的预测精度;DLR-F5机翼在中翼段和外翼段的转捩预测位置与实验较接近,吻合良好。2个算例均表明改进后的一方程转捩模型取得了良好的预测效果。
In order to simplify the transition model by substituting two equations with one,the local turbulence intensity and pressure gradient parameter are introduced to construct the new empirical correlations for Reθc and Flength. The new model can be coupled with SST turbulence model, whose parameters are calibrated by the Schubauer and Klebanoff flat plate. Furthermore, by analyzing the relations of transport equations between SST and SA, ft2 function, a part of the source terms, is corrected to realize the coupling of one equation transition model and SA turbulence model. Finally, numerical analysis are conducted on S809 airfoil and DLR F5 wing, and the results indicate that: simulations using one-equation transition models agree well with experiments in linear region, and the error of force coefficients is less than 3% for S809 foil; for DLR-F5 wing, the transition locations also meet well with the experiments except for the root part. Both of the cases demonstrate that the polished model performs quite accurately in the prediction of transition