Data-driven Turbulence Modeling using Field Inversion and Machine Learning

Abstract

In order to predict turbulent flows numerically, the Reynolds-Averaged Navier-Stokes (RANS) model is broadly used in many practical engineering fields because of its relatively low computational cost. The RANS model, however, loses its reliability when flow separation occurs or compressible effect becomes stronger. In this study, the data-driven turbulence modeling method is considered in order to overcome the RANS limitations. Among them, the field inversion and machine learning (FIML) method is selected. In the FIML process, RANS model discrepancy is inferred as a correction term, which is a function of location, in the RANS model equation, and by building Neural Network in the machine learning process, the correction term is represented as a function of flow features, not location. Then, one can utilize the FIML method for improving RANS performance to the flow simulations that are not used for the machine learning process. Two simulation cases of S809 airfoil and axisymmetric base flow are numerically investigated applying the FIML method. For the S809 airfoil case, it is checked that the FIML method can enhance the RANS performance in the flow separation region. The field inversion process is performed to the one post-stall angle AoA=14.2º simulation where occurs flow separation. Neural Network is trained by the inversed result at AoA=14.2º, and the test is performed to the unseen angles AoA={6.2º, 12.2º, 16.2º}. As a result of the airfoil case, it is observed that the FIML method can capture flow separation and improve RANS prediction performance at the post-stall angles whereas rarely affects the low angle result which has no flow separation. For the axisymmetric base flow case, the flow separation occurs due to the sharp corner at the base. The field inversion process is performed to the various simulation cases in the Mach number range 0.11 ≤ M ≤ 2.5. In order to save computational cost, the source terms are added to both Navier-Stokes and turbulence equations in the 2D Cartesian form to imitate axisymmetric simulation. It is checked that the FIML method can be applied even if the source terms are added to the governing equations. Through Neural Network that is trained by various simulation cases according to Mach number, the prediction performance for the unseen cases compared to original RANS results is improved. It is shown that the FIML method can be used to overcome the RANS drawbacks: flow separation and strong compressibility.