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Abstract: This Note describes an acoustic filtering of the equations governing the supercritical fluid buoyant flow driven by a weak heating. The resulting low Mach number approximation takes into account the compressibility of the fluid with respect to the hydrostatic pressure. Using the direct numerical simulation of a supercritical fluid flow in the Rayleigh–Bénard configuration, we show that the density stratification may be taken into account without further numerical effort and is fundamental for the prediction of the convective instability threshold induced by a weak heating. To cite this article: G. Accary et al., C. R. Mecanique 333 (2005). [Copyright &y& Elsevier] more...

We consider a closed Rayleigh–Bénard cell containing a fluid near its gas–liquid critical point (CP). Due to the divergence of several physical properties near the CP, large Rayleigh numbers can be obtained even for small temperature differences. In the convective regime, the heat flow which is obtained on long time scales exhibits some characteristics of that observed in turbulent convection in normally compressible fluids: it is composed of plumes in thermal boundary layers, jets on lateral walls and a large-scale flow. Our results show that, as it is the case in turbulent convection, this large-scale flow can suddenly change its orientation. To cite this article: I. Raspo et al., C. R. Mecanique 332 (2004). [Copyright &y& Elsevier] more...

A numerical solution of the Navier–Stokes equations coupled with the energy and linearised equation of state has been performed in the unsteady Rayleigh–Bénard configuration for nearly supercritical 3He in the exact conditions with which Meyer and Kogan (Phys. Rev. E 63 (2002) 056310) performed their experiments. We propose an interpretation of the observed unexpected temperature oscillations at the convection onset in terms of coupled hot and cold piston effects. We have also considered the stability of two layers (hot and cold) of a same supercritical fluid in an unstable configuration. The first results show an analogy between the diffusion of species (Rayleigh–Taylor like instability) and thermal diffusion considered in this study. To cite this article: S. Amiroudine, B. Zappoli, C. R. Mecanique 332 (2004). [Copyright &y& Elsevier] more...

A review is presented on the advances in understanding equilibration phenomena in compressible pure fluids near the liquid–vapor critical point. The important role of the piston effect is stressed. The equilibration of temperature and density of a fluid sample, kept in a constant volume, are described. Examples are given both above and below the critical point under Earth''s gravity (1 g) and microgravity conditions. The good agreement between experimental results and simulations demonstrate the present understanding of the process. The convection onset of a compressible pure fluid in a Rayleigh–Bénard cell at 1 g is described. The impact of the piston effect on the transient, which leads to damped oscillations on the way to reaching a steady state convection, is also described. Here again the results of experiments and numerical simulations are compared. To cite this article: H. Meyer, F. Zhong, C. R. Mecanique 332 (2004). [Copyright &y& Elsevier] more...

This paper describes the unsteady convective flow of a supercritical fluid in the Rayleigh–Be´nard configuration. Two-dimensional earlier studies reported fast temperature equilibrium due to the piston effect and the development of a convective instability when the local Rayleigh number exceeds a critical value. In the present work, a high order 3D finite volume method has been developed and optimized, and to our knowledge, we show for the first time a three-dimensional convective instability in a supercritical fluid. Inspecting the time-evolution of temperature field patterns, we exhibit corner effects and a three-dimensional behavior of the flow. To cite this article: G. Accary et al., C. R. Mecanique 332 (2004). [Copyright &y& Elsevier] more...