Supercritical density relaxation as a new approach of droplet vaporization

Abstract

The isobaric density relaxation of a cold, slightly supercritical, fluid package in a hotter atmosphere of this same fluid at a near critical pressure is studied in this paper. We solve the Navier-Stokes equations describing the evolution of an initial density inhomogeneity in a supercritical van der Waals fluid. These numerical simulations allow exploring the whole range of surrounding conditions, including the slightly supercritical ones. Strong discrepancies are found from the classical decay of the squared diameter of the droplet observed in clearly subcritical conditions. We present a quasisteady analysis that allows neglecting unsteady terms in the equations that describe the problem, provided that the moving reference frame is well defined. The strong density gradient that follows the "droplet" as well as the time dependant mass flow rate location are considered with a particular attention. The obtained solutions of the equations match with the numerical results and generalize to near critical conditions the classical subcritical quasisteady analysis of droplet vaporization performed in the combustion science field.

Interfaces et fluides critiques

“…Le cas où la goutte initialement sphérique se trouve dans les conditions critiques et s"épand de façon isobare, en restant sphérique, dans le même fluide au repos de température à l"infini très supérieure à la température critique, a été étudié [S. Préau et al, 2004]. On se propose d"étendre ici l"étude au cas où la température initiale de la goutte est inférieure à la température critique et où la pression ambiante est supérieure à la pression critique (figure 9).…”

A Study of Droplet Evaporation

“…We introduce the nondimensional num- The use of two characteristic times and two characteristic densities in the dimensional analysis yields the two nondimensional numbers and % and the thermal Peclet number ) based on the characteristic quantities of the gas phase. The asymptotic studies conducted on this topic [2], [4], [9], generally use either or % as small parameter. The form (3) of the nondimensional equations of conservation of the mass and the conservation of energy shows that unsteady phenomena are governed by the ratio 1 2 ' % .…”