Deep learning based spatio-temporal wall-shear stress quantification from velocity measurements

Wall-shear stress dynamics are of fundamental interest in basic and applied research ranging from biomedical applications to aircraft design and optimization. However, we still lack experimental methods that can simultaneously measure the temporal dynamics of the wall-shear stress with a sufficient spatial resolution and domain size. Neither do we have universal models which adequately mimic the instantaneous wall-shear stress dynamics in numerical simulations of multi-scale systems for which direct numerical simulations are too expensive to be conducted. Working towards filling those gaps, we developed a deep learning architecture that takes wall-parallel velocity fields from the logarithmic layer of turbulent wall-bounded flows as an input and outputs the corresponding 2D wall-shear stress fields. Trained in a supervised fashion using datasets from direct numerical simulations where the true wall-shear stress distributions are known, we demonstrate a zero-shot applicability to experimental data with similar flow conditions. The physical correctness of the wall-shear stress estimation from experimental Particle-Image Velocimetry based velocity fields is verified using wall-shear stress measurements with the Micro-Pillar Shear-Stress Sensor.