Bernard Zappoli

Thermoacoustic and buoyancy-driven transport in a square side-heated cavity filled with a near-critical fluid

The mechanisms of heat and mass transport in a side-heated square cavity filled with a near-critical fluid are explored, with special emphasis on the interplay between buoyancy-driven convection and the Piston Effect. The Navier-Stokes equations for a near-critical van der Waals gas are solved numerically by means of an acoustically filtered, finite-volume method. The results have revealed some striking behaviour compared with that obtained for normally compressible gases : (i) heat equilibration is still achieved rapidly, as under zero-g conditions, by the Piston Effect before convection has time to enhance heat transport ; (ii) mass equilibration is achieved on a much longer time scale by quasi-isothermal buoyant convection ; (iii) due to the very high compressibility, a stagnation-point effect similar to that encountered in highspeed flows provokes an overheating of the upper wall ; and (iv) a significant difference to the convective single-roll pattern generated under the same conditions in normal CO 2 is found, in the form of a double-roll convective structure.

The response of a nearly supercritical pure fluid to a thermal disturbance

The response of a nearly supercritical pure fluid confined in a slablike container to a slowly varying temperature disturbance at the boundary is studied. The matched asymptotic expansion technique is used to describe the core and boundary‐layer flows on the short acoustic time scale. The multiple scale expansion technique is then used to obtain the solution of the equations for longer times. It is found (i) that the acoustic field generated in the bulk is stronger, the closer the initial conditions are to the critical point; (ii) that the heat transport is much faster than the conductive transport owing to the very high compressibility of the fluid; (iii) the scaling laws and the equations describing the flow field on the long time scale confirm both the numerical results obtained previously as well as their interpretation in terms of the piston effect which provokes the enhancement of the heat transport by adiabatic compressive heating of the bulk phase.

Thermoacoustic heating and cooling in near-critical fluids in the presence of a thermal plume

This work brings new insight to the question of heat transfer in near–critical fluids under Earth gravity conditions. The interplay between buoyant convection and thermoacoustic heat transfer (piston effect) is investigated in a two-dimensional non-insulated cavity containing a local heat source, to reproduce the conditions used in recent experiments. The results were obtained by means of a finite-volume numerical code solving the Navier–Stokes equations written for a low-heat-diffusing near-critical van der Waals fluid. They show that hydrodynamics greatly affects thermoacoustics in the vicinity of the upper thermostated wall, leading to a rather singular heat transfer mechanism. Heat losses through this wall govern a cooling piston effect. Thus, the thermal plume rising from the heat source triggers a strong enhancement of the cooling piston effect when it strikes the middle of the top boundary. During the spreading of the thermal plume, the cooling piston effect drives a rapid thermal quasi-equilibrium in the bulk fluid since it is further enhanced so as to balance the heating piston effect generated by the heat source. Then, homogeneous fluid heating is cancelled and the bulk temperature stops increasing. Moreover, diffusive and convective heat transfers into the bulk are very weak in such a low-heat-diffusing fluid. Thus, even though a steady state is not obtained owing to the strong and seemingly continuous instabilities present in the flow, the bulk temperature is expected to remain quasi-constant. Comparisons performed with a supercritical fluid at initial conditions further from the critical point show that this thermalization process is peculiar to near-critical fluids. Even enhanced by the thermal plume, the cooling piston effect does not balance the heating piston effect. Thus, overall piston-effect heating lasts much longer, while convection and diffusion progressively affect the thermal field much more significantly. Ultimately, a classical two-roll convective-diffusive structure is obtained in a perfect gas, without thermoacoustic heat transfer playing any role.

Heat and mass transport in a near supercritical fluid

The analytical solution of the equations describing the propagation of a temperature step at the boundary in a near supercritical van der Waals gas is obtained and discussed. The quantitative properties of the velocity and thermodynamic fields are given on a long‐time scale. Quantitative evidence of the speeding up of the heat transport compared to a purely diffusive process is given. The numerical solution obtained by means of the piso algorithm, which is performed and discussed confirms the validity of the obtained analytical solution.

Heat transfers and related effects in supercritical fluids

This book investigates the unique hydrodynamics and heat transfer problems that are encountered in the vicinity of the critical point of fluids. Emphasis is given on weightlessness conditions, gravity effects and thermovibrational phenomena. Near their critical point, fluids indeed obey universal behavior and become very compressible and expandable. Their comportment, when gravity effects are suppressed, becomes quite unusual. The problems that are treated in this book are of interest to students and researchers interested in the original behavior of near-critical fluids as well as to engineers that have to manage supercritical fluids. A special chapter is dedicated to the present knowledge of critical point phenomena. Specific data for many fluids are provided, ranging from cryogenics (hydrogen) to high temperature (water). Basic information in statistical mechanics, mathematics and measurement techniques is also included. The basic concepts of fluid mechanics are given for the non-specialists to be able to read the parts he is interested in. Asymptotic theory of heat transfer by thermoacoustic processes is provided with enough details for PhD students or researchers and engineers to begin in the field. Key space are described in details, with many comparisons between theory and experiments to illustrate the topics.

Turbulent Rayleigh–Bénard convection in a near-critical fluid by three-dimensional direct numerical simulation

This paper presents state of the art three-dimensional numerical simulations of the Rayleigh-Benard convection in a supercritical fluid. We consider a fluid slightly above its critical point in a cube-shaped cell heated from below with insulated sidewalls; the thermodynamic equilibrium of the fluid is described by the van der Waals equation of state. The acoustic filtering of the Navier-Stokes equations is revisited to account for the strong stratification of the fluid induced by its high compressibility under the effect of its own weight. The hydrodynamic stability of the fluid is briefly reviewed and we then focus on the convective regime and the transition to turbulence. Direct numerical simulations are carried out using a finite volume method for Rayleigh numbers varying from 10 6 up to 10 8 . A spatiotemporal description of the flow is presented from the convection onset until the attainment of a statistically steady state of heat transfer. This description concerns mainly the identification of the vortical structures in the flow, the distribution of the Nusselt numbers on the horizontal isothermal walls, the structure of the temperature field and the global thermal balance of the cavity. We focus on the influence of the strong stratification of the fluid on the penetrability of the convective structures in the core of the cavity and on its global thermal balance. Finally, a comparison with the case of a perfect gas, at the same Rayleigh number, is presented.

Convection in a supercritical fluid : A reduced model for geophysical flows

Convection in a fluid, slightly above its gas-liquid critical point, is numerically investigated in two configurations where the strong stratification of the fluid—induced by its high compressibility—controls the development and/or the onset of convection: (i) the evolution of a thermal plume in a stable environment where the penetrative convection is found to be blocked by the fluid stratification, and (ii) the convection onset and outset in a supercritical fluid layer according to the Schwarzschild criterion, which usually occurs in the atmosphere when the local temperature gradient exceeds the adiabatic temperature one. Hence, two situations, commonly encountered in large-scale geophysical flows, are reproduced in a centimetric cell containing a supercritical fluid.

Stability of a supercritical fluid diffusing layer with mixed boundary conditions

We consider a fluid close to its gas-liquid critical point in the Rayleigh-Benard configuration. Owing to thermoacoustic effects, the bottom heating induces thermal boundary layers along both the lower and the upper horizontal plates. The hydrodynamic stability of these diffusing layers, whose bounding conditions are interchanged, is studied numerically in a two-dimensional (2D) approximation. As far as the convection onset criterion and the critical wave number are concerned, some discrepancies are found between the simulations and the predictions obtained by means of linear analysis. The extension of the study to three-dimensional configurations confirms the validity of the 2D approximation for the analysis of the hydrodynamic stability and shows its inadequacy when the layers become convection dominated.

Interaction between convection and surface reactions in physical vapor transport in rectangular, horizontal enclosures

Abstract The introduction of mixed boundary conditions on active surfaces allows us to introduce non-equilibrium interfacial surface kinetics together with its coupling to the convective motion of the bulk. The Navier-Stokes equations are used with both thermal and solutal source term in the momentum equation. The boundary conditions on the active surfaces are derived from the conservation equations for the specific properties of the interface. Based on these boundary conditions, a 1D description of diffusive transport in closed ampoules is given. Numerical solutions of the 2D non-steady transport equations were obtained by a finite difference method, carried out as a function of the chemical surface reaction rate, the diffusion coefficient and the gravity level values. It is found that: (a) the model with boundary conditions based on interfacial equilibrium is a zeroth order asymptotic description for infinite surface reaction rates of the present theory; (b) high diffusion coefficients lead to a uniform concentration field and vanishing solutal convection; (c) the concentration on the active surfaces may be affected by convection: it is quite uniform for low gravity level and is strongly disturbed for earth level gravity; (d) the surface concentration profile is the more coupled with convection the smaller the reaction rate is; (e) the concentration field, obtained for neither reaction nor diffusion-limited surface kinetics, exhibits quite new behaviours, compared with the ones previously obtained.

The unexpected response of near‐critical fluids to low‐frequency vibrations

The response of a slab‐shaped container filled with a near‐critical fluid and subjected to mechanical vibrations is studied by means of matched asymptotic expansions applied to the Navier–Stokes equations. The different characteristic regimes of the fluid’s vibration are explored and described. In particular, a specific low‐frequency regime is highlighted, in which the mechanical response couples with thermo‐acoustic convection (piston effect). In this particular regime, the bulk part of the fluid behaves almost like a solid which bounces back and forth between two highly compressible thermal boundary layers. Such a response is entirely specific to near‐critical fluids and is never witnessed in perfect gases.