Assimilating Shear Stress Distributions from Sparse Measurement Data and Flow Visualizations Using Deep Neural Networks

• Measurements of surface shear stress with high spatial resolution are typically very challenging. In contrast, oil-film visualizations are easy to implement even for complex geometries, and evaluating a sequence of images with optical flow algorithms can yield a qualitative shear stress vector field. However, without extensive calibration, the magnitude of the obtained vectors does not match the desired shear stress. Our goal is to combine the two measurement techniques to reconstruct a spatially resolved, quantitative shear stress distribution. To achieve this, we use deep neural networks that map spatial coordinates to the shear stress components. The networks are trained using a data loss that compares the unit vectors of the predicted shear stress with the processed oil-film visualization, as well as a boundary loss where sparse sensor measurements are directly compared with the network output. Our flow case is a subsonic half diffuser that features a turbulent separation bubble and strong 3D effects due to sidewall influence. In the first part of our work, we use a RANS simulation of the diffuser to study the influence of the number of sensors and their distribution on the accuracy of the predicted shear stress distributions. Afterwards, we demonstrate the method on an experimental dataset composed of sparse shear stress measurements using MEMS sensors and a processed sequence of oil-film visualizations.