湍流模型系数不确定度对翼型绕流模拟的影响

使用非嵌入式多项式混沌方法研究了湍流模型系数的不确定度对RAE2822跨声速翼型绕流模拟的影响。计算中关注了数值模拟的积分量（升力系数、阻力系数）和局部量（壁面压力、摩擦系数和空间马赫数分布）的不确定度量化结果。首先，从单输入变量入手，研究卡门常数的不确定度对数值模拟的影响。然后，同时考虑Spalart-Allmaras模型中9个参数的不确定度带来的影响。通过多项式混沌展开，得到系统输出对不确定输入变量的响应，由此可以得到输出的统计特性，包括平均值、方差和极值等信息。最后，在多变量不确定度量化过程中，通过Sobol指标来量化每个输入变量的不确定度对输出不确定度的贡献程度。本文计算只考虑了RAE2822跨声速翼型模拟的单一计算状态，影响规律是否可以推及其他工况和算例需要进一步检验。

Effects of uncertainty in turbulence model coefficients on flow over airfoil simulation

The effects of uncertainty in the turbulence model closure coefficients on the simulation of flow over RAE2822 airfoil are investigated in this paper using a non-intrusive polynomial chaos method. The integral values (including lift and drag coefficients) and local flow field variables (e.g. pressure coefficient, skin friction coefficient, and Mach number) are considered as the output quantities of interest. The investigation begins with a single stochastic input variable, the von Karman constant. Then the uncertainty in nine closure coefficients of the Spalart-Allmaras model is taken into account. The system response is thus obtained, including the mean value, variance and extreme values. Finally, Sobol indices are used to evaluate the relative contributions of each closure coefficient to the variation of the output quantities. Since the conclusion in this paper is drawn from one single test case of the RAE2822 airfoil, further verification through the simulations of other cases is still needed.