Field Inversion Machine Learning for Time-Resolved Unsteady Flows in Airfoil Dynamic Stall

TL;DR

This paper advances turbulence modeling for time-resolved unsteady flows by embedding a temporally evolving augmentation field $β$ into the production term of the Spalart–Allmaras model and solving an inverse problem to minimize prediction errors. A four-layer neural network maps local flow features $η$ to $β$, enabling online predictions within the open-source DAFoam framework. The unsteady-FIML approach outperforms steady-FIML in predicting dynamic stall phenomena on a NACA0012 airfoil, accurately capturing drag, lift, moment, surface pressure, and velocity fields, and demonstrating robust generalization to unseen pitch rates. The work provides a data-efficient, physically consistent pathway toward generalizable unsteady turbulence closures for RANS, with potential for extension to LES-informed references and broader aeroelastic applications.

Abstract

While many existing machine learning studies have focused on augmenting Reynolds averaged Navier Stokes (RANS) turbulence models for steady or time averaged unsteady flows, this paper takes a first step toward extending such augmentation to time resolved unsteady flows. An unsteady field inversion and machine learning (FIML) method is developed, in which a temporally evolving correction field (beta) is incorporated into the production term of a RANS turbulence model. The inverse problem is solved by optimizing the spatial temporal distribution of beta to minimize the regularized prediction errors. The resulting optimized beta field is then used to train a multi layer neural network that learns the time dependent relationship between local flow features and beta. The approach is demonstrated using the unsteady flow over a NACA0012 airfoil undergoing dynamic stall. Results show that the unsteady FIML model, trained using only the time series of drag data at a given pitch rate, can accurately reproduce the spatial temporal evolution of reference drag, lift, pitching moment, surface pressure, and velocity fields at both identical and different pitch rates. The unsteady FIML is integrated into the open source DAFoam framework, enabling a pathway toward developing accurate and generalizable RANS turbulence models for time resolved unsteady flows.

Figures (16)

• Figure 1: Schematic of field inversion machine learning (FIML) framework for the augmented turbulence modeling.
• Figure 2: Schematic of the multi-layer neural network (machine learning) model in the offline stage for augmentation field computation.
• Figure 3: Incorporation of a trained neural network model into the unsteady CFD solver for predictive simulation (online stage).
• Figure 4: Structured mesh for the unsteady flow over a NACA0012 airfoil with 12,060 cells (initial pitch: $4^{\circ}$).
• Figure 5: Steady-state field inversion for the NACA0012 airfoil at angles of attack $\alpha$ = $10^{\circ}$, $12^{\circ}$, $14^{\circ}$, $16^{\circ}$, and $18^{\circ}$.