Prediction and understanding of the wall-shear stress modulation by non-linear interactions based on novel machine learning techniques

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Turbulent wall-bounded fluid flows are of significant importance for numerous engineering and biomedical applications. However, they are typically characterized by high-dimensional, non-linear, and unsteady dynamics that exhibit rich multi-scale phenomena in space and time. Due to such challenging characteristics, we still lack a comprehensive understanding of these complex fluids. One key ingredient necessary for a majority of applications is the spatially and temporally resolved wall-shear stress. Besides providing a measure for the friction drag - a quantity of utmost importance in the transportation sector - it also gives insight into the dynamic loads imposed onto rigid/flexible walls, which can be crucial in human medicine. Despite its significance, it is still exceptionally difficult to measure instantaneous and spatially well-resolved wall-shear stress distributions. Most existing measurement sensors are single-direction and/or single-dimension devices that can only detect one wall-shear stress component at a fixed location. Moreover, the spatial resolution and the maximum number of jointly deployed sensors is typically limited due to experimental constraints arising from secondary electronic devices. As a result, the overwhelming majority of recent studies targeting the investigation of multi-scale phenomena that modulate the wall-shear stress dynamics are limited to time-dependent data without spatial resolution and consequently, cannot provide a comprehensive picture of the complex physics. Therefore, the overarching objective of this proposal is the development of modern deep learning based algorithms for the prediction of the wall-shear stress based on easily accessible velocity measurements. The envisioned neural networks are specifically designed to capture - without limiting assumptions - the complex non-linear and unsteady interactions that are responsible for the wall-shear stress dynamics and to make them interpretable for the human kind. In particular, this proposal targets the development of a deep learning based architecture specifically designed to learn a mapping function from two-dimensional velocity fields located in the outer layer of a turbulent wall-bounded flow to the instantaneous spatially resolved wall-shear stress distribution. Complementary, an interpretable mathematical expression, which corresponds to the inherently learnt transfer function, is extracted from the derived latent representation via symbolic regression. This expression is further investigated to gain deeper insight into the non-linear interactions that result in the modulation of the wall-shear stress. Trained on direct numerical simulation data, the generalization of the envisioned learner is evidenced based on simultaneous particle-image velocimetry measurements in the outer layer and wall-shear stress measurements using the Micro-Pillar Shear-Stress Sensor.