On evolution of a pure supercritical droplet near the critical point
Résumé
The evolution of pure super critical "droplet" in an hotter atmosphere of the same fluid is investigated here.
Numerical calculations show that for small values of the density ratio between the atmosphere and the spherical droplet, the quasi steady hypothesis which is usually applied in clearly subcritical vaporization of liquid droplet leads in our case to analytical results less accurate than expected. A new quasi-steady hypothesis is assumed: the density is supposed stationary in a reference frame such that the distance between the droplet surface and the maximum unit mass flow rate surface is held constant. Corrections to the quasi-steady expansions are then worked out by considering the unsteady area far from the droplet. Numerical and analytical results are in good agreement for density ratios ranging approximately from 0.05 to 0.5.
For density ratios close to 1, the near-critical density relaxation theory should rather be adapted and applied. For very small values of density ratios, second order effects in the density boundary layer similar to those analyzed in Aria Zugasti M. et al, Combust. Sci. Technol. 60, 2000 are likely to be involved.