Machine Learning-augmented Predictive Modeling of Turbulent Separated Flows over Airfoils (1608.03990v3)

Abstract: A modeling paradigm is developed to augment predictive models of turbulence by effectively utilizing limited data generated from physical experiments. The key components of our approach involve inverse modeling to infer the spatial distribution of model discrepancies, and, machine learning to reconstruct discrepancy information from a large number of inverse problems into corrective model forms. We apply the methodology to turbulent flows over airfoils involving flow separation. Model augmentations are developed for the Spalart ALLMaras (SA) model using adjoint-based full field inference on experimentally measured lift coefficient data. When these model forms are reconstructed using neural networks (NN) and embedded within a standard solver, we show that much improved predictions in lift can be obtained for geometries and flow conditions that were not used to train the model. The NN-augmented SA model also predicts surface pressures extremely well. Portability of this approach is demonstrated by confirming that predictive improvements are preserved when the augmentation is embedded in a different commercial finite-element solver. The broader vision is that by incorporating data that can reveal the form of the innate model discrepancy, the applicability of data-driven turbulence models can be extended to more general flows.

• The paper introduces a novel machine learning method to correct turbulence model discrepancies through inverse modeling using sparse experimental data.
• The paper employs neural networks to reconstruct corrective factors for the Spalart-Allmaras model, significantly improving lift coefficient and pressure predictions.
• The paper demonstrates the model's portability across solvers, achieving enhanced predictive accuracy with less than 10% additional computational cost.

Machine Learning-Augmented Predictive Modeling of Turbulent Separated Flows over Airfoils

The paper by Singh, Medida, and Duraisamy introduces a sophisticated modeling framework designed to enhance the predictive performance of turbulence models, specifically targeting turbulent flow separations over airfoils. This is achieved by integrating machine learning methodologies with conventional turbulence models to mitigate deficiencies prevalent in standard simulation approaches, particularly in complex flow phenomena such as flow separation which are poorly predicted by existing models.

Core Contributions and Methodology

The authors propose a novel data-driven modeling methodology that leverages limited experimental data to improve turbulence model predictions through a combination of inverse modeling and machine learning. The key process involves:

1. Inverse Modeling: Inverse modeling is employed to infer spatial distribution discrepancies in the baseline turbulence model. This approach uses adjoint-based optimization to extract field correction factors from discrepancies observed in lift coefficients derived from experimental data.
2. Machine Learning Augmentation: Once discrepancies are identified, they are reconstructed using neural networks into corrective forms that can be applied within existing turbulence models—in this case, the Spalart-ALLMaras (SA) model. The integration of these corrections fundamentally enhances the model's ability to predict flow accurately across conditions and geometries not included in the initial data set.
3. Portability Across Solvers: The resultant NN-augmented models exhibit portability, retaining improved accuracy when transferred between different computational solvers, including a shift from the proprietary, structured solver (ADTURNS) to a commercial unstructured solver (AcuSolve).

Results and Implications

The paper provides robust numerical evidence demonstrating the effectiveness of the machine learning-augmented SA model in predicting lift coefficients and surface pressure distributions for a range of airfoil geometries and Reynolds numbers. Notably, the augmented model shows enhanced accuracy in pre- and post-stall predictions without compromising computational efficiency, a limitation commonly associated with more sophisticated turbulence models.

• Numerical Performance: Consistent improvements in lift predictions and drag rise occur over baseline SA results. This indicates a successful integration of machine learning corrections to improve the model's predictive power.
• Generalization Across Conditions: The model has shown significant predictive improvements under varied aerodynamic conditions and airfoil geometries, underscoring its robustness and adaptability.
• Computational Overhead: The implementation of NN corrections incurs minimal computational overhead (less than 10% additional compute time), maintaining a feasible computation cost for practical applications.

Theoretical and Practical Implications

This approach signifies a pivotal advancement in data-driven turbulence modeling. It emphasizes the use of sparse experimental data to systematically infer and rectify model discrepancies, bridging the gap between high-fidelity numerical simulations and empirical model adjustments typically required in traditional CFD turbulence modeling.

Practically, such advancements are poised to have significant impacts on aerospace and energy industries, where accurate simulation of turbulent flows is crucial in designing efficient and effective systems. The capability to integrate machine learning-based corrections into existing models seamlessly, and across different simulation platforms, empowers researchers and engineers to extend predictive modeling capabilities to a broader class of turbulent flows.

Future Research Directions

Future work could aim to generalize the framework to a more diverse set of turbulence models and flow regimes, exploring broader sets of feature inputs and alternative machine learning algorithms. Integrating uncertainty quantification methods to fully understand the model's sensitivity to training data and its potential limitations remains an area ripe for exploration. Additionally, pushing the framework's boundaries into specific engineering applications where traditional CFD approaches struggle could yield further insights and modeling breakthroughs.

In conclusion, the integration of machine learning for augmenting turbulence models represents a promising direction in computational fluid dynamics, with the potential to improve both the accuracy and applicability of predictive models across various industries. This paper provides a compelling demonstration of how data-driven techniques can enhance traditional model frameworks, nudging them towards better performance with minimal reliance on extensive parametric adjustments.