Improving resolution of turbulent flow field prediction using limited measurements and Bayesian inferred physics-informed neural network

The prediction of high-resolution turbulent flow field is often difficult as the experimental measurements are spatially sparse in nature. Due to the limitations of the measurement instruments, the feature at major areas in the flow field could not be captured. The present work uses a Bayesian-inference-based physics-informed neural network framework to reconstruct high-resolution turbulent flow field with high accuracy using sparse particle image velocimetry (PIV) measurements. The periodic hill case is selected to demonstrate the framework, which is trained with the mean flow measurements. The degree of sparsity of the PIV measurement and the locations of measurement data are varied, and it is found that the recirculation zone of the periodic hill requires more sensors for efficient reconstruction of the flow field. The uncertainty in the prediction is quantified at various locations across the flow field. It is identified that the prediction uncertainty is greater where sensors are insufficient, or there is no sensor. However, the overall uncertainty is within acceptable limits. Finally, the robustness of the model is tested against the various noise levels in the measurement and with different sensor arrangements. With the reduction in the number of measurement data points, the effect of noise in measurement becomes significant, and the uncertainty in the prediction increases. The model can accurately (≤±10%) reconstruct the high-resolution flow field with high noise levels (up to 20%) when there are more labeled data points. Further, the adaptability of the framework has been tested for flow over a square cylinder.