Data-augmented Correction Of Turbulence Modeling

With the development of high-performance computer,computational fluid dynamics is more and more widely used in aircraft design and other fields.RANS calculation has high computational efficiency while lack of satisfied prediction accuracy.High-precision DNS or LES method could gain flow data with high resolution,but they cost a lot in computing and still have difficulty in the application in industry.Thus,we adopt a data-driven correction method,a modified S-A turbulence model in RANS calculation is constructed taking advantage of those high-resolution data.It is hoped to improve the pridiction accuracy of turbulence model while taking into account the efficiency of RANS calculation.In order to overcome the dependence of data-driven modeling on the number and quality of data samples,this paper proposes a correction method based on physical knowledge constraints.In turbulent friction decomposition,direct viscous dissipation term is independent of Reynolds number and compressibility,and it has an unified analogy relationship in the inner layer of turbulent boundary layer.In the process of modeling,this physical knowledge is used to restrict the boundary and search space of the model.A spatially-distributed correction factor is introduced in the production term of S-A turbulence model equation as design variable.The objective function with physical knowledge constraints is constructed,and the derivatives of objective function with respect to the design variable is solved by discrete adjoint method.The distribution of the correction factor is obtained through gradient-based iteration.In this paper,the advantages of data-driven modeling method with physical knowledge constraints are verified in channel flow,and the influence of physical knowledge constraints on the prediction accuracy of turbulent friction resistance is analyzed.We adopt this method towards the correction of NACA0012 airfoil under low Reynolds number.The skin friction coefficient and pressure coefficient distribution of the airfoil are taken as the objective function.The results show that the modified S-A turbulence model could obtain a more accurate pressure coefficient distribution and skin friction coefficient distribution on the airfoil surface,and the modified turbulence model can capture the flow separation phenomenon better and the effectiveness of the data-augmented turbulence model correction is verified.