基于离散伴随的流场反演在湍流模拟中的应用

精确模拟湍流流动是学术界和工业界均普遍关注的问题。采用数据驱动湍流建模的思路，建立了基于离散伴随方法的流场反演框架。通过为SA模型涡黏性输运方程的生成项乘以非均匀分布的系数，并利用有限的观测数据对该系数进行推断，实现对SA模型的修正。为了提高带有物理约束的离散伴随优化的效率，发展了约束增广的伴随方法，其高效性在本文得到了验证。选取了结冰翼型和周期山2个分离算例进行分析，所得结果在2个算例中均能以很高的精度拟合观测数据，并能借助湍流模型的修正将有限的观测信息泛化到整个流场。分析表明，流场反演所推断出的修正区域具有较为明确的物理意义，能够指导湍流模型的进一步改进。

Application of field inversion based on discrete adjoint method in turbulence modeling

Accurate simulation of turbulent flow is a common problem in engineering and academic fields. In this paper, the idea of data-driven turbulence modeling is adopted, and a framework of flow field inversion based on discrete adjoint is established. The SA model is modified by multiplying the production term of its eddy viscosity transport equation and a coefficient with non-uniform distribution, which is inferred with limited observation data. To improve the efficiency of discrete adjoint optimization under physical constraints, the constraint-augmented adjoint method is used, and its efficiency is verified in this paper. Two cases of iced airfoil and periodic hill are selected for analysis. The results obtained in both cases are highly consistent with the observed data, and the limited observation information can be generalized to the whole flow field with the help of the correction of the turbulence model. The analysis shows that the correction region deduced from field inversion has a certain physical significance and can guide further development of the turbulence model.