Direct numerical simulation of instabilities in a two-dimensional near-critical fluid layer heated from below

Abstract

An analysis of the hydrodynamic stability of a fluid near its near critical point – initially at rest and in thermodynamic equilibrium – is considered in the Rayleigh–Bénard configuration, i.e. heated from below. The geometry is a two-dimensional square cavity and the top and bottom walls are maintained at constant temperatures while the sidewalls are insulated. Owing to the homogeneous thermo-acoustic heating (piston effect), the thermal field exhibits a very specific structure in the vertical direction. A very thin hot thermal boundary layer is formed at the bottom, then a homogeneously heated bulk settles in the core at a lower temperature; at the top, a cooler boundary layer forms in order to continuously match the bulk temperature with the colder temperature of the upper wall. We analyse the stability of the two boundary layers by numerically solving the Navier–Stokes equations appropriate for a van der Waals' gas slightly above its critical point. A finite-volume method is used together with an acoustic filtering procedure. The onset of the instabilities in the two different layers is discussed with respect to the results of the theoretical stability analyses available in the literature and stability diagrams are derived. By accounting for the piston effect the present results can be put within the framework of the stability analysis of Gitterman and Steinberg for a single layer subjected to a uniform, steady temperature gradient.

Near-critical fluid hydrodynamics

“…to unique features. Firstly, the transient states in cavities heated from below are strongly influenced by the piston effect which heat the bulk phase adiabatically, as shown by numerical simulations [49,50] (Fig. 14) or revealed by high precision measurements in 3 He [15] and well correlated with a recent numerical solution of approximated Navier-Stokes equations [51].…”

“…This layer becomes unstable and gives the original double-instability pattern (right side). Moreover (left side), Rayleigh criteria (decreasing part of the curve) and Schwarzchild criteria (left hand side of the curve) are both accounted for (from [49,50]). to unique features.…”

Thermal gravity-driven convection of near-critical helium in enclosures

“…For example, when e = = 0.03, the experimental values are Ra r = 1.27 . 10 4 and Pr r = 12.4. As following from (9), these magnitudes correspond to Ra = 45.4, Pr = 0.986 which should be entered into the governing equations.…”

“…Parameters of numerical simulation will be estimated on the basis of the physical properties of helium and the approach of the model fluid to the real one will be fulfilled. The Rayleigh-Benard convection was simulated in intensive near-critical flows [4], but we will investigate the onset of convection.…”

Natural convection heat transfer of supercritical binary fluid in a long closed vertical cylinder

“…1 is the specific heat capacity of nitrogen, which pulses to an extreme large value at the critical point and may dramatically change the heat transfer characteristics of the fluid. There already have been some studies focusing on the natural convection of supercritical fluids [1,[18][19][20][21][22]. However, all of them considered pure fluids and only a few parameters were allowed to vary and many others were kept constant.…”