Reconstruction of the mean velocity, pressure, and turbulent viscosity fields from background-oriented schlieren measurements using a physics-informed neural network

A data assimilation technique for turbulent flows, based on the use of the physics-informed neural network (PINN), is presented. Mean temperature fields, measured with the nonintrusive background-oriented schlieren (BOS) method, and sparse velocity measurements are used as input data. The velocity, pressure, turbulent viscosity, and thermal conductivity fields are reconstructed using PINN. PINN searches for the flow field, which approximately satisfies the governing equations while remaining close to the available experimental data. Reconstruction is performed for the free and impinging subsonic axisymmetric turbulent jets of hot air. The results are compared with conventional Reynolds-averaged Navier–Stokes simulations. The feasibility of taking into account the spatial variation of the turbulent Prandtl number is demonstrated. However, due to a large number of unknown parameters, accurate reconstruction of the turbulent Prandtl number field requires velocity data measured with high spatial resolution.