Tomographic reconstruction of combustion flow fields from density measurements based on physics-informed neural networks

Achieving stable, low-emission combustion with green hydrogen is crucial for climate-neutral ground-based power generation in turbomachinery. Lean combustion modes with green hydrogen reduce fuel consumption but increase unsteadiness. Thus, multimodal detection techniques for parameters like density and flow velocity are essential to understand the interconnected behavior of combustion, advection velocity and noise production. We previously introduced a high-speed camera-based laser interferometric vibrometer system to detect thermoacoustic oscillations and record advection velocities, using interferometric detection of density fluctuations and correlation-based velocity estimation. However, this method only estimates integral velocity fields, necessitating the solution of the inverse problem. This is relying on iterative optimization, which is computationally expensive and struggles with high dimensional, noisy or limited data. Physics-Informed Neural Networks offer an innovative and efficient approach to these problems, combining neural network flexibility with physical law constraints to unravel intricate cause-effect relationships. Here an approach for reconstructing local velocity fields from a single projection velocity calculated from integral density data is presented. Using a U-net and model assumptions for coupling local and integral velocity fields, the training minimizes errors between measured integral input fields and the predicted local field integrals. The comparison of measured local velocity and the network prediction achieved a relative mean squared error of 3 %.