Numerical Simulation of the Poiseuille-Rayleigh-Benard Instability for a Supercritical Fluid in a Mini-Channel

Abstract

The Poiseuille-Rayleigh-Bénard problem, involving the onset of thermoconvective structures in channels heated from below, was the subject of many theoretical, numerical and knowledge, this problem was never studied for supercritical fluids. The objective of this paper is to study the influence of the specific properties of such fluids on thermoconvective instability phenomena compared with those observed in the perfect gas case. The effect of the distance to the critical point is also investigated. The numerical approach used is based on the Navier-Stokes equations in the framework of the low Mach number approximation.

On the modeling and simulation of coupled adsorption and thermosolutal convection in supercritical carbon dioxide

“…Since the thermal expansion coefficient diverges near the critical point, this boundary layer strongly expands and adiabatically compresses the bulk fluid leading to a fast and homogenous increase of pressure and bulk temperature. The same phenomenon occurs in mixtures near the solvent's critical point and it was shown in [15,32] that the strong pressure increase induced by the piston effect has important consequences on the solubility of solids and on adsorption equilibrium constants near the LCEP. The critical properties of naphthalene and CO 2 together with those of the mixture at the LCEP are reported in Table 1.…”

“…Naphthalene is the species adsorbed on the bottom plate. It was selected as a model solute because of the wide experimental data of its solubility in scCO 2 available in the literature, allowing an easier validation of the thermodynamic model [15]. Moreover, the naphthalene-CO 2 mixture can be considered as a reference system, representative of binary mixtures of interest for SFE and adsorption.…”

“…For temperatures ranging between T LCEP and T UCEP , the mixture exhibits equilibrium between a solute solid phase and a mixture fluid phase. In the vicinity of the LCEP, solid solubility and adsorption equilibrium constants are highly sensitive to temperature and pressure variations [15,32], which points out the reason why SFE and adsorption processes are customarily carried out in the aforementioned phase diagram region. Moreover, near the gas-liquid critical point of a pure compound, fast thermal equilibration is achieved by a thermoacoustic effect, named the piston effect, while thermal diffusion becomes extremely slow [36][37][38].…”

“…Moreover, we designate by T cm , ρ cm , and H respectively the characteristics temperature, density, and length. Additionally, we consider the piston effect time scale [41] t PE = t d /(γ − 1) 2 as being the characteristic time, where t d and γ are respectively the characteristic time of thermal diffusion and the mixture specific heat ratio (computed from the equation of state [15]), while the corresponding velocity V PE = H/t PE denotes the characteristic velocity.…”

“…Supercritical carbon dioxide (scCO 2 ) significance has grown fairly quickly in the past decades. It has been extensively investigated in most SCF deposition (SFD) or crystal growth processes and has been the subject of several researches and publications [15][16][17][18][19]. In fact, SFD is a rising technique for the purpose of depositing metals and metaloxides on surfaces, and is notably relevant for technological processes aiming to prepare supported metallic nanoparticles or metallic films [16,17].…”