Dynamics of a vortex column of supercritical fluid across the pseudo-boiling line

Abstract

The evolution of an axisymmetric vortex column in a weakly compressible supercritical fluid is analysed. A thermal layer is imposed to radially stratify the fluid and uncover effects of the large fluid property variations across the pseudo-boiling line. A multi-dimensional flow solver based on a low-Mach approximation is employed. Using supercritical carbon dioxide as the fluid, we examine axisymmetric configurations at low Reynolds number with the vortex core hotter or colder than the surrounding fluid and for different thermodynamic pressures close to the critical pressure. Vorticity evolution depends strongly on the core temperature and ambient pressure, differing substantially from the classical Oseen solution during the thermal mixing process under highly varying fluid properties. Viscous effects dominate the vorticity evolution. Beyond diffusion, three additional viscous mechanisms are identified, which become significant across the pseudo-boiling line: (1) a vorticity stretching term, (2) an alignment of vorticity and viscosity/density gradients, and (3) a vorticity source due to the interaction between the fluid swirl and the viscosity and density gradients. The first two mechanisms alter existing vorticity, while the latter injects new vorticity. In fact, the third mechanism can generate reverse vorticity, locally increasing circulation and substantially modifying the temporal evolution of the vortex.