Data-informed characterization of spatio-temporal scales in experiments of microconfined high-pressure transcritical turbulence

The spatio-temporal scales of microconfined high-pressure transcritical turbulence are characterized in relation to the resolution capabilities of present time-resolved two-dimensional $\mu$PIV technology. Utilizing ${\mathrm{CO}}_2$ as the working fluid, the physical scales are examined by considering the main dimensionless groups of the problem, which correspond to the Reynolds, Brinkman, and Stokes numbers and the mass fraction of particles in the fluid. In detail, the methodology employed leverages direct numerical simulation data to inform the estimation of hydrodynamic, thermophysical, and particle-related scales, and selects a state-of-the-art $\mu$PIV setup to describe the optical performance of the current technology. The results indicate that the temporal scales can be experimentally captured for a wide range of operating conditions. However, the scenario becomes much more complex when trying to capture the spatial scales of microconfined high-pressure transcritical turbulent flow. Particularly, the Kolmogorov and Batchelor spatial scales can be captured for bulk Reynolds numbers below $O\left(10^3\right)$. Otherwise, the spatial scales can only be partially captured and/or remain completely masked due to insufficient resolution, like for example in the case of boundary layer viscous scales and fluid density variations. This limitation is not imposed by the tracer behavior of microparticles, as the Stokes number remains significantly low for all the system configurations studied. Instead, the limitation is mainly a result of the optical capabilities of present $\mu$PIV systems. Finally, given the generalizable properties of dimensionless numbers, the results and insight obtained can be extended to other experiments of $\mu$PIV-based visualization/quantification of microconfined multiscale flows involving large thermophysical variations.