[Paper Review] A wall model based on neural networks for LES of turbulent flows over periodic hills

Zhideng Zhou, Guowei He+1 more|arXiv (Cornell University)|Nov 9, 2020

Fluid Dynamics and Turbulent Flows57 references4 citations

TL;DR

This paper proposes a data-driven wall model for large-eddy simulation (LES) of turbulent flows over periodic hills using a feedforward neural network (FNN) trained on wall-resolved LES (WRLES) data. The FNN predicts wall shear stress using near-wall velocity, pressure gradient, and wall-normal distance as inputs, achieving high accuracy and generalization across Reynolds numbers, with correlation coefficients >0.7 for instantaneous shear stress and excellent agreement for mean shear stress.

ABSTRACT

In this work, a data-driven wall model for turbulent flows over periodic hills is developed using the feedforward neural network (FNN) and wall-resolved LES (WRLES) data. To develop a wall model applicable to different flow regimes, the flow data in the near wall region at all streamwise locations are grouped together as the training dataset. In the developed FNN wall models, we employ the wall-normal distance, near-wall velocities and pressure gradients as input features and the wall shear stresses as output labels, respectively. The prediction accuracy and generalization capacity of the trained FNN wall model are examined by comparing the predicted wall shear stresses with the WRLES data. For the instantaneous wall shear stress, the FNN predictions show an overall good agreement with the WRLES data with some discrepancies observed at locations near the crest of the hill. The correlation coefficients between the FNN predictions and WRLES predictions are larger than 0.7 at most streamwise locations. For the mean wall shear stress, the FNN predictions agree very well with WRLES data. More importantly, overall good performance of the FNN wall model is observed for different Reynolds numbers, demonstrating its good generalization capacity.

Motivation & Objective

• To develop a wall model for LES that accurately captures non-equilibrium turbulent flows over periodic hills, where traditional equilibrium-based models fail.
• To overcome the limitations of conventional wall models in predicting flow separation and reattachment in complex, non-equilibrium boundary layers.
• To leverage high-fidelity WRLES data and machine learning to create a generalizable, physics-informed wall model for high Reynolds number flows.
• To evaluate the performance of the FNN-based wall model across varying Reynolds numbers and streamwise locations, particularly near flow separation and reattachment points.

Proposed method

• A feedforward neural network (FNN) is trained using near-wall flow data from wall-resolved LES (WRLES) simulations of turbulent flow over periodic hills.
• Input features include wall-normal distance, streamwise and wall-normal velocities, and streamwise pressure gradient; output is the wall shear stress.
• The training dataset combines near-wall data from all streamwise locations to enhance generalization across the domain.
• The FNN architecture includes multiple hidden layers with ReLU activation functions, and the output is computed via weighted summation of hidden layer outputs.
• Model weights and biases are initialized randomly (truncated normal distribution) and trained using backpropagation to minimize prediction error against WRLES data.
• Generalization is tested across different Reynolds numbers, with performance evaluated using correlation coefficients and relative errors.

Experimental results

Research questions

• RQ1 Can a data-driven FNN wall model accurately predict instantaneous and mean wall shear stress in turbulent flows over periodic hills?
• RQ2 How well does the FNN wall model generalize across different Reynolds numbers and streamwise locations, especially near flow separation and reattachment?
• RQ3 Does the FNN wall model outperform traditional equilibrium-based wall models in capturing non-equilibrium effects in separated flows?
• RQ4 What input features (e.g., velocity, pressure gradient, wall-normal distance) are most critical for accurate wall shear stress prediction?
• RQ5 How does the FNN wall model compare to high-fidelity WRLES data in predicting key flow statistics like skin friction and pressure coefficients?

Key findings

• The FNN wall model predicts instantaneous wall shear stress with a correlation coefficient >0.7 at most streamwise locations, showing strong agreement with WRLES data.
• The model shows excellent agreement with WRLES for mean wall shear stress, with minimal deviation across the domain.
• Discrepancies in instantaneous shear stress predictions are observed near the hill crest, where flow non-equilibrium effects are most pronounced.
• The FNN wall model generalizes well across different Reynolds numbers, indicating robustness and adaptability to varying flow conditions.
• Relative errors in turbulence kinetic energy and Reynolds shear stress are below 12% when compared to DNS data, validating the fidelity of the WRLES baseline.
• The skin friction and pressure coefficients from the FNN wall model agree closely with DNS results, confirming the model's predictive capability for key flow features.