Air Flow Predictions in Converging-Diverging Nozzles Using Fourier Neural Operators

Sammanfattning

This thesis investigates the potential of using Fourier neural operators to predict subsonic and supersonic flows in converging-diverging nozzles, which includes complex flow phenomena such as shock waves. Two different data sets were generated using the Euler equations for fluid flow, one based on analytical relations for a quasi one-dimensional nozzle and another one which was created by numerically solving the governing equations on a planar two-dimensional geometry. Both data sets were generated with a wide range of input conditions, including diverse nozzle shapes and various combinations of boundary conditions. Based entirely on the set of input conditions, the model could be trained to output the solution fields for temperature, pressure and velocity. The trained Fourier neural operator's final results showcase great generalization across various combinations of input conditions and nozzle shapes, while accurately distinguishing between different flow regimes in both one and two dimensions. Furthermore, the presence of normal shock waves as well as their magnitude and location in the diverging section of the nozzle were predicted with high accuracy. Lastly, by including the conservation of mass and energy as a part of the loss function, it was demonstrated that the generalization could be drastically improved for small data sets, essentially filling potential gaps in data with prior knowledge of the problem. However, for larger data sets, the addition of physics proved to be rather ineffective in terms of improving the generalization.