[Paper Review] Uncovering wall-shear stress dynamics from neural-network enhanced fluid flow measurements

Esther Lagemann, Steven L. Brunton+1 more|arXiv (Cornell University)|Oct 17, 2023

Anomaly Detection Techniques and ApplicationsComputer Science3 citations

TL;DR

This paper presents WSSflow, a deep learning framework that enhances particle image velocimetry (PIV) data using a physics-informed optical flow network to estimate high-resolution velocity and wall-shear stress (WSS) fields. By preserving original image resolution and enforcing physical consistency, WSSflow achieves superior spatial and temporal resolution in WSS dynamics, outperforming traditional PIV and state-of-the-art methods in synthetic and real-world fluid flows.

ABSTRACT

Friction drag from a turbulent fluid moving past or inside an object plays a crucial role in domains as diverse as transportation, public utility infrastructure, energy technology, and human health. As a direct measure of the shear-induced friction forces, an accurate prediction of the wall-shear stress can contribute to sustainability, conservation of resources, and carbon neutrality in civil aviation as well as enhanced medical treatment of vascular diseases and cancer. Despite such importance for our modern society, we still lack adequate experimental methods to capture the instantaneous wall-shear stress dynamics. In this contribution, we present a holistic approach that derives velocity and wall-shear stress fields with impressive spatial and temporal resolution from flow measurements using a deep optical flow estimator with physical knowledge. The validity and physical correctness of the derived flow quantities is demonstrated with synthetic and real-world experimental data covering a range of relevant fluid flows.

Motivation & Objective

• To address the critical lack of experimental methods capable of capturing instantaneous, high-resolution wall-shear stress (WSS) dynamics in turbulent flows.
• To overcome the resolution limitations of conventional PIV, which averages velocity over interrogation windows and smoothes gradients near walls.
• To develop a data-driven framework that integrates physical laws with deep learning to produce physically consistent, high-resolution WSS estimates from PIV measurements.
• To enable accurate, real-time WSS monitoring for applications in aeronautics, vascular health, and energy systems.
• To validate the method across diverse flow configurations, including complex geometries like elastic blood vessels and canonical boundary layers.

Proposed method

• The method employs a physics-informed deep optical flow network, WSSflow, trained end-to-end on synthetic PIV data to estimate per-pixel velocity fields from image pairs.
• The network is trained using a loss function that enforces physical consistency by minimizing the divergence of the velocity field and ensuring correct wall-normal velocity gradients at the wall boundary.
• WSSflow operates directly on the original image resolution, avoiding the spatial averaging inherent in traditional PIV, thus preserving fine-scale velocity gradients.
• The framework incorporates a wall-normal averaging strategy over the viscous sublayer, using a minimum of three pixels to improve WSS accuracy and reduce sensitivity to sub-pixel wall misalignment.
• A multi-scale, multi-grid approach with iterative refinement and subpixel displacement estimation is used during training and inference to ensure high-accuracy velocity fields.
• The model is evaluated against a high-performance in-house PIV code (SOTA), using standard PIV metrics and physical validation on both synthetic and experimental data.

Experimental results

Research questions

• RQ1 Can a deep learning framework enhance PIV data to recover wall-shear stress with higher spatial and temporal resolution than conventional PIV?
• RQ2 How does the integration of physical constraints (e.g., no-slip condition, divergence-free flow) improve the accuracy and generalization of WSS estimation?
• RQ3 To what extent does preserving original image resolution in velocity estimation improve the resolution of wall-shear stress dynamics near the wall?
• RQ4 How does WSSflow perform across diverse flow configurations, including canonical boundary layers and complex geometries like elastic blood vessels?
• RQ5 Can the method reliably estimate instantaneous WSS dynamics from limited, real-world PIV measurements without requiring additional sensors or calibration?

Key findings

• WSSflow achieves a spatial resolution of 64 times higher than standard PIV, yielding $1024 \times 1024$ velocity vectors from a $1024 \times 1024$ px² image pair.
• The method reduces velocity gradient smoothing near the wall, enabling accurate estimation of wall-normal velocity gradients critical for WSS computation.
• Using at least three pixels in the viscous sublayer improves WSS accuracy and reduces sensitivity to sub-pixel wall misalignment and optical artifacts.
• WSSflow outperforms the state-of-the-art in-house PIV code (SOTA) in both synthetic and real experimental data, particularly in resolving transient WSS dynamics.
• The framework successfully recovers instantaneous WSS fields in complex flows, including those with strong unsteadiness and separation, demonstrating robustness and generalization.
• Training on a single GPU node with four A100s took approximately 22 hours for 200 epochs, with a global batch size of 8, demonstrating feasible computational cost for practical deployment.