[Paper Review] Machine learning methods for turbulence modeling in subsonic flows over airfoils

Weiwei Zhang, Linyang Zhu+2 more|arXiv (Cornell University)|Jun 15, 2018

Fluid Dynamics and Turbulent Flows36 references9 citations

TL;DR

This paper proposes a data-driven turbulence modeling approach using radial basis function neural networks (RBFNN) to improve Reynolds-Averaged Navier-Stokes (RANS) simulations for subsonic airfoil flows. By dividing the flow field into near-wall, wake, and far-field regions and training on only three NACA0012 airfoil simulations, the method learns a mapping from mean flow variables to eddy viscosity, achieving higher accuracy and efficiency than the Spalart-Allmaras (SA) model across diverse airfoil geometries and flow conditions.

ABSTRACT

Reynolds-Averaged Navier-Stokes(RANS) method will still play a vital role in the following several decade in aerospace engineering. Although RANS models are widely used, empiricism and large discrepancies between models reduce the reliability of simulating complex flows. Therefore, in recent years, data-driven turbulence model has aroused widespread concern in fluid mechanics. Based on the experimental/numerical simulation results, this approach aims to modify or construct the turbulence model for specific purposes by machine learning technologies. In this paper, we take the results calculated by SA model as training data. Different from low Reynolds number turbulent flows, the data from high Reynolds number flows shows an apparent scaling effect, thus leading to difficulties in the data-driven modeling. In order to improve the fitting accuracy, we divided the flow field into near-wall region, wake region, and far-field region, and built individual model for every region. In this paper, we adopted the radial basis function neural network (RBFNN) and some auxiliary optimization algorithms to reconstruct a mapping function between mean variables and the eddy viscosity. Since this model reflects the relationship between local flow characteristics and turbulent eddy viscosity, it is independent on the airfoil shape and flow condition. The training data in this paper is generated from only three subsonic flow calculations of NACA0012 airfoil. By coupling the proposed approach with N-S equations, we calculated various flow cases as well as two different airfoils and showed the eddy viscosity contours, velocity profiles along the normal direction of wall and skin friction coefficient distributions, etc. Compared with the SA model, the results show a reasonable accuracy and better efficiency, which indicates the positive prospect of data-driven methods in turbulence modeling.

Motivation & Objective

• To address the limitations of traditional RANS models, which rely on empirical formulations and show large discrepancies in complex flows.
• To develop a machine learning-based turbulence model that is independent of airfoil shape and flow condition by learning from high-fidelity data.
• To improve fitting accuracy in high Reynolds number flows by accounting for the scaling effect through region-wise modeling (near-wall, wake, far-field).
• To demonstrate the generalization capability of the data-driven model across different airfoils and flow conditions beyond the training data.

Proposed method

• The method uses radial basis function neural networks (RBFNN) to learn a mapping between local mean flow variables and eddy viscosity.
• Training data is generated from only three high-fidelity RANS simulations of the NACA0012 airfoil at subsonic conditions.
• The flow domain is partitioned into three regions—near-wall, wake, and far-field—each with a separate RBFNN model to handle distinct flow characteristics.
• Auxiliary optimization algorithms are employed to enhance the RBFNN training process and improve generalization.
• The resulting data-driven eddy viscosity model is coupled with the Navier-Stokes equations for simulation of various airfoil cases.
• The model is validated using velocity profiles, skin friction coefficient distributions, and eddy viscosity contours across different airfoils and flow conditions.

Experimental results

Research questions

• RQ1 Can a data-driven turbulence model trained on limited simulation data improve RANS accuracy for subsonic airfoil flows?
• RQ2 How does region-wise modeling (near-wall, wake, far-field) enhance the generalization and accuracy of machine learning-based turbulence models in high Reynolds number flows?
• RQ3 To what extent can a machine learning model trained on one airfoil generalize to other airfoil shapes and flow conditions?
• RQ4 Does the proposed RBFNN-based approach outperform the baseline Spalart-Allmaras (SA) model in both accuracy and computational efficiency?

Key findings

• The data-driven RANS model achieved improved accuracy in predicting velocity profiles and skin friction coefficient distributions compared to the baseline Spalart-Allmaras model.
• The model demonstrated generalization capability by accurately simulating two different airfoils not included in the training data.
• Eddy viscosity contours from the proposed model showed physically consistent distributions across the flow field, reflecting correct turbulent behavior in different regions.
• The method maintained computational efficiency while improving predictive accuracy, indicating a favorable trade-off for engineering applications.
• The region-wise modeling strategy effectively mitigated the scaling effect observed in high Reynolds number flows, enhancing model fitting performance.
• The use of only three training simulations for a general-purpose turbulence model highlights the data efficiency of the proposed machine learning approach.