Reconstructing a Turbulent Compressible Jet From Multi-Camera BOS Measurements Using Data Assimilation*

We present a neural data assimilation (DA) method for 4D background-oriented schlieren (BOS) tomography that can accurately reconstruct density, velocity, and pressure fields. Scale-resolving simulations of turbulent mixing in a compressible flow are computationally costly. A RANS or LES approach is often used to lower the cost, but limitations of the turbulence model can lead to large errors. BOS measurements of compressible mixing, paired with DA, have the potential to produce high-fidelity datasets to study the mixing system, validate computational models, and perform data-driven modeling. In single-camera BOS, a camera records images of a pattern positioned behind the flow; a reference image and image distorted by refraction are processed by a computer vision algorithm to estimate the 2D deflection field. BOS tomography (usually) involves multiple cameras and backgrounds, and synchronous images are used to reconstruct the density field, which involves a series of ill-posed problems that require regularization. DA algorithms produce better estimates than tomography algorithms by including the governing equations in the reconstruction. We apply this treatment to synthetic measurements of a Mach 0.9 turbulent jet using the compressible Navier–Stokes equations.