Machine learning for RANS turbulence modeling of variable property flows

This paper presents a machine learning methodology to improve the predictions of traditional RANS turbulence models in channel flows subject to strong variations in their thermophysical properties. The developed formulation contains several improvements over the existing Field Inversion Machine Learning (FIML) frameworks described in the literature. We first showcase the use of efficient optimization routines to automatize the process of field inversion in the context of CFD, combined with the use of symbolic algebra solvers to generate sparse-efficient algebraic formulas to comply with the discrete adjoint method. The proposed neural network architecture is characterized by the use of an initial layer of logarithmic neurons followed by hyperbolic tangent neurons, which proves numerically stable. The machine learning predictions are then corrected using a novel weighted relaxation factor methodology, that recovers valuable information from otherwise spurious predictions. Additionally, we introduce L2 regularization to mitigate over-fitting and to reduce the importance of non-essential features. In order to analyze the results of our deep learning system, we utilize the K-fold cross-validation technique, which is beneficial for small datasets. The results show that the machine learning model acts as an excellent non-linear interpolator for DNS cases well-represented in the training set. In the most successful case, the L-infinity modeling error on the velocity profile was reduced from 23.4% to 4.0%. It is concluded that the developed machine learning methodology corresponds to a valid alternative to improve RANS turbulence models in flows with strong variations in their thermophysical properties without introducing prior modeling assumptions into the system.