Supersonic Projectile Flow Field Reconstruction Using Background Oriented Schlieren and Physics Informed Convolutional Neural Networks

This work explores the use of axisymmetric background-oriented schlieren (BOS) imaging for reconstructing supersonic flow fields over a scaled NATO 5.56 mm M855 projectile at Mach 1.50, 2.00, and 2.50, as well as a 15° cone at Mach 2.50. A method for recovering density fields from BOS displacement maps was implemented, with results compared to a Taylor–Maccoll solution for the cone and a RANS CFD wind tunnel model for the projectile. Density field reconstructions showed errors below 15% overall and under 10% across most of the field, with the largest deviations near shock boundaries and stagnation regions. Additionally, force balance measurements were conducted on the projectile at Mach 2.50, showing an agreement of 1.2% with firing data from the literature and 8% with the RANS model. A custom U-Net was subsequently trained to predict pressure, temperature, and velocity fields from grid-transformed numerical density inputs over the cone, using a physics-exclusive loss function derived from the Euler conservation laws and specified boundary conditions. However, large residuals near the shock and stagnation point due to grid interpolation were found to impede the network’s performance. A purely data-driven model demonstrated good accuracy for pressure and temperature, a moderate performance for radial velocity, and poor accuracy for axial velocity. The model failed to generalize when fed with experimental data, reinforcing the need for strong physical constraints.