Background-oriented-schlieren-based optical velocimetry of low-convective-Mach-number turbulent shear layers

Background-oriented schlieren (BOS)-based velocimetry is a potential method for achieving simultaneous measurements of density and velocity in a flow with density gradients. Similar to schlieren velocimetry, BOS velocimetry relies on (1) refraction of light due to density gradients and (2) the presence of turbulent eddies or contrast by high-/low-density fluid parcels to serve as seeding particles. Previous attempts at BOS velocimetry suffered from compounded noise, error propagation, and significant loss of spatial resolution due to the requirement for an additional round of interrogation. Kymography-based BOS velocimetry has been shown to produce accurate velocity measurements but at the expense of spatiotemporally averaging the flow field. The optical flow displacement estimation method was shown to be ineffective to yield useful velocity information for schlieren velocimetry, due to the large displacements of turbulent eddies between adjacent time instances. In the current work, a novel approach for BOS velocimetry is proposed that uses deformable image registration (DIR) in each of the two interrogation steps to obtain accurate, spatiotemporally resolved velocity fields. Ray-tracing simulations using density fields from CFD of low-convective-Mach-number turbulent mixing layers are leveraged to generate synthetic, experiment-like BOS images. The DIR method using isotropic total variation regularization is first used to reconstruct the instantaneous density gradient fields from the BOS images. Then, DIR using Maxwell’s demons is used in the second round to measure the displacements of turbulent eddies between two adjacent time instances. Comparison of the velocities extracted from BOS against the CFD fluid velocities demonstrates excellent capability of the proposed methodology..