[Paper Review] Self-critical machine-learning wall-modeled LES for external aerodynamics

Adrián Lozano-Durán, H. Jane Bae|arXiv (Cornell University)|Dec 18, 2020

Fluid Dynamics and Turbulent Flows40 references22 citations

TL;DR

This paper proposes a self-critical machine-learning wall model (SCMv1) for wall-modeled large-eddy simulation (WMLES) in external aerodynamics, using a dual neural network architecture that classifies flow regimes and predicts wall stress with confidence scores. The model outperforms a standard equilibrium wall model in predicting mean velocity profiles across complex flow regions like wing-body junctions, with improved accuracy and robustness due to its ability to flag uncertain predictions.

ABSTRACT

The prediction of aircraft aerodynamic quantities of interest remains among the most pressing challenges for computational fluid dynamics. The aircraft aerodynamics are inherently turbulent with mean-flow three-dimensionality, often accompanied by laminar-to-turbulent transition, flow separation, secondary flow motions at corners, and shock wave formation, to name a few. However, the most widespread wall models are built upon the assumption of statistically-in-equilibrium wall-bounded turbulence and do not faithfully account for the wide variety of flow conditions described above. This raises the question of how to devise models capable of accounting for such a vast and rich collection of flow physics in a feasible manner. In this work, we propose tackling the wall-modeling challenge by devising the flow as a collection of building blocks, whose information enables the prediction of the stress as the wall. The model relies on the assumption that simple canonical flows contain the essential flow physics to devise accurate models. Three types of building block units were used to train the model: turbulent channel flows, turbulent ducts and turbulent boundary layers with separation. This limited training set will be extended in future versions of the model. The approach is implemented using two interconnected artificial neural networks: a classifier, which identifies the contribution of each building block in the flow; and a predictor, which estimates the wall stress via non-linear combinations of building-block units. The output of the model is accompanied by the confidence in the prediction. The latter value aids the detection of areas where the model underperforms, such as flow regions that are not representative of the building blocks used to train the model. The model is validated in a unseen case representative of external aerodynamic applications: the NASA Juncture Flow Experiment.

Motivation & Objective

• To address the lack of robustness and accuracy in existing wall-modeled LES (WMLES) for complex external aerodynamic flows with diverse flow physics.
• To develop a data-driven wall model that can generalize across multiple flow regimes—such as separation, three-dimensionality, and transitional flows—beyond the assumptions of equilibrium wall-bounded turbulence.
• To incorporate confidence estimation into wall-stress predictions, enabling detection of out-of-distribution or poorly represented flow conditions.
• To validate the model on a realistic industrial benchmark: the NASA Juncture Flow Experiment at Re = 2.4×10⁶.
• To lay the foundation for a scalable, physics-informed machine-learning framework that can be extended by adding new canonical flow building blocks.

Proposed method

• The model uses two interconnected artificial neural networks: a classifier that assigns a flow to one or more canonical building blocks (e.g., turbulent channel, duct, separated boundary layer) and outputs a confidence score.
• The predictor network estimates wall stress based on the weighted contribution of each identified building block, using non-linear combinations of their characteristics.
• Training data consists of DNS results from flat-plate boundary layers, turbulent ducts, and separated flows at various Reynolds numbers.
• The model is self-critical by providing a confidence value for each prediction, which drops when inputs deviate from known flow regimes (e.g., shock waves or non-boundary layer flows).
• The approach relies on instantaneous velocity and flow gradient data as input, with non-dimensionalization used to improve generalization.
• The model is validated on the NASA Juncture Flow Experiment, comparing mean velocity profile predictions against a standard equilibrium wall model (EQWM).

Experimental results

Research questions

• RQ1 Can a machine-learning wall model trained on canonical flows generalize to complex, industrial-scale external aerodynamic flows with strong three-dimensionality and separation?
• RQ2 Can confidence scores in predictions effectively identify regions where the model is uncertain or outside its training distribution?
• RQ3 Does a self-critical, flow-classification-based approach improve accuracy and robustness compared to traditional equilibrium wall models in complex flow configurations?
• RQ4 How does the inclusion of multiple building blocks (e.g., channel, duct, separated flow) enhance the model’s predictive capability across diverse flow regimes?
• RQ5 To what extent can the model’s performance be improved by expanding the set of training building blocks and refining input feature selection?

Key findings

• SCMv1 outperforms the equilibrium wall model (EQWM) in predicting mean velocity profiles at all three test locations on the NASA Juncture Flow configuration: upstream fuselage, wing-body juncture, and trailing-edge juncture.
• The model demonstrates superior accuracy in regions with strong mean-flow three-dimensionality and flow separation, where the EQWM fails to capture key flow features.
• The confidence score provided by the model reliably decreases in regions with unmodeled physics, such as shock waves or non-boundary layer flows, indicating effective uncertainty quantification.
• The model successfully identifies and classifies complex flow regimes using only instantaneous flow data, suggesting its potential for real-time or industrial-scale LES applications.
• The self-critical nature of the model enables detection of prediction failures, which is critical for reliable deployment in engineering design workflows.
• Despite promising results, the model’s performance is limited by the current scope of training data, and further validation across multiple grid resolutions and configurations is required.