Relaxation of a supercritical fluid after a heat pulse in the absence of gravity effects: Theory and experiments

Abstract

We study the response of a fluid in near-critical conditions to a heat pulse, in the absence of gravity effects. The fluid under investigation is CO 2 at critical density. It is enclosed in a thermostated sample cell. We apply a theory that accounts for hydrodynamics and a real equation of state. Comparison with experiments performed under reduced gravity on board the MIR orbital station show quantitative agreement and demonstrate that the dynamics of relaxation is ruled by two typical times, a diffusion time t D and a time t c associated to adiabatic heat transport, the so-called ''Piston effect'' ͑PE͒. Three regions are observed in the fluid. First, a hot boundary layer, developing at the heat source, which shows large coupled density-temperature inhomogeneities. This part relaxes by a diffusive process, whose density and temperature relaxations are slowed down close to the critical point. Second, the bulk fluid, which remains uniform in temperature and density and whose dynamics is accelerated near the critical point and governed by the PE time. At the thermostated walls a slightly cooler boundary layer forms that cools the bulk also by a PE mechanism. The final equilibration in temperature and density of the fluid is governed by the diffusion time t D , which corresponds to the slowest mechanism. Comparison with a one-dimensional model for temperature relaxation is performed showing good agreement with experimental temperature measurements. A brief comparison is given with the situation in the presence of gravity.

Fast heat transfer calculations in supercritical fluids versus hydrodynamic approach

“…As stated in the introduction, we are mainly interested in the description of the early stages of the heating, i.e. on times of the order of the Piston effect time scale [12]. In this regime, the thermodynamic quantities c p , c v , k, .…”

“…In this Appendix we use the traditional notation, so that D and t correspond to D d and τ of Eq. (12). It can be shown [21] that the linear diffusion problem…”

“…The spatially varying fluid temperature T has to be calculated with Eqs. (8,12). SubstitutingT by T , Eq.…”

“…Heat transfer in supercritical fluid involves three characteristic time scales [12,18]: the acoustic time scale defined by t a = L/c 0 (where c 0 is the sound velocity and L is the cell size), the diffusion time scale t D = L 2 /D (D being the thermal diffusivity) and the Piston Effect time scale defined by…”

Thermal vibrational convection in near-critical fluids. Part 1. Non-uniform heating

“…These anomalies result in unexpected behaviour of near-critical fluids such as the existence of a fourth heat transfer mechanism of a thermoacoustic nature, named the piston effect, which allows heat to be transferred much faster than by diffusion or convection (see Boukari et al 1990;Onuki, Hao & Ferrell 1990;Zappoli et al 1990). The piston effect was recently shown to strongly influence the hydrodynamics of near-critical fluids (see Garrabos et al 1998;Polezhaev, Emelianov & Gorbunov 1998).…”