Assessment of Neural Network Augmented Reynolds Averaged Navier Stokes Turbulence Model in Extrapolation Modes

Abstract

A machine-learned (ML) model is developed to enhance the accuracy of turbulence transport equations of Reynolds Averaged Navier Stokes (RANS) solver and applied for periodic hill test case, which involves complex flow regimes, such as attached boundary layer, shear-layer, and separation and reattachment. The accuracy of the model is investigated in extrapolation modes, i.e., the test case has much larger separation bubble and higher turbulence than the training cases. A parametric study is also performed to understand the effect of network hyperparameters on training and model accuracy and to quantify the uncertainty in model accuracy due to the non-deterministic nature of the neural network training. The study revealed that, for any network, less than optimal mini-batch size results in overfitting, and larger than optimal batch size reduces accuracy. Data clustering is found to be an efficient approach to prevent the machine-learned model from over-training on more prevalent flow regimes, and results in a model with similar accuracy using almost one-third of the training dataset. Feature importance analysis reveals that turbulence production is correlated with shear strain in the free-shear region, with shear strain and wall-distance and local velocity-based Reynolds number in the boundary layer regime, and with streamwise velocity gradient in the accelerating flow regime. The flow direction is found to be key in identifying flow separation and reattachment regime. Machine-learned models perform poorly in extrapolation mode, wherein the prediction shows less than 10% correlation with Direct Numerical Simulation (DNS). A priori tests reveal that model predictability improves significantly as the hill dataset is partially added during training in a partial extrapolation model, e.g., with the addition of only 5% of the hill data increases correlation with DNS to 80%.

arXiv comment50 pages, 18 figures

References in corpus (21)

• A Unified Approach to Interpreting Model Predictions
• Machine Learning for Fluid Mechanics
• Turbulence Modeling in the Age of Data
• On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima
• Physics-informed neural networks for solving Reynolds-averaged Navier$\unicode{x2013}$Stokes equations
• Hyperparameter Search in Machine Learning
• Sub-grid modelling for two-dimensional turbulence using neural networks
• Discovery of Algebraic Reynolds-Stress Models Using Sparse Symbolic Regression
• Searching for turbulence models by artificial neural network
• Committee neural network potentials control generalization errors and enable active learning
• Data-Driven Modelling of the Reynolds Stress Tensor using Random Forests with Invariance
• CFDNet: a deep learning-based accelerator for fluid simulations
• Formulating turbulence closures using sparse regression with embedded form invariance
• Feature selection and processing of turbulence modeling based on an artificial neural network
• Prediction of Reynolds Stresses in High-Mach-Number Turbulent Boundary Layers using Physics-Informed Machine Learning
• An Iterative Machine-Learning Framework for RANS Turbulence Modeling
• Data-driven turbulence modeling in separated flows considering physical mechanism analysis
• Deep Structured Neural Networks for Turbulence Closure Modelling
• Machine-learning accelerated turbulence modelling of transient flashing jets
• Robust deep learning for emulating turbulent viscosities
• Finding Closure Terms Directly from Coarse Data for 2D Turbulent Flow