Thermal plumes and convection in highly compressible fluids

Onset of double-diffusive convection in near-critical gas mixtures

Near the thermodynamic critical point, the physical properties of binary fluids exhibit large variations in response to small temperature and concentration differences, whose effects on the onset of double-diffusive convection are reported here. The vertical symmetry is broken, irregular penetrative instability occurs, and cat's eye patterns are identified in the fingering regime and oscillatory regime, respectively. A new parameter Θ is defined which indicates how the variations of physical properties influence flow fields. It is seen through numerical simulations that the Boussinesq approximation with constant physical properties has limited applicability, and that the Boussinesq equations with variable properties and density will describe all features seen. This conclusion is based on comparisons with the fully compressible, variable-property system.

Thermal relaxation and critical instability of near-critical fluid microchannel flow

We present two-dimensional numerical investigations of the temperature and velocity evolution of a pure near-critical fluid confined in microchannels. The fluid is subjected to two sides heating after it reached isothermal steady state. We focus on the abnormal behaviors of the near-critical fluid in response to the sudden imposed heat flux. New thermal-mechanical effects dominated by fluid instability originating from the boundary and local equilibrium process are reported. Near the microchannel boundaries, the instability grows very quickly and an unexpected vortex formation mode is identified when near-critical thermal-mechanical effect is interacting with the microchannel shear flow. The mechanism of the new kind of Kelvin-Helmholtz instability induced by boundary expansion and density stratification processes is also discussed in detail. This mechanism may bring about innovations in the field of microengineering.

Thermoacoustic waves along the critical isochore

Near the liquid-gas critical point, thermal disturbances can generate sounds. We study the acoustic emission over four decades of reduced temperatures [defined as ɛ=(T-T(c))/T(c), with T(c) the critical temperature] along the critical isochore, under linear and nonlinear temperature perturbations, respectively. We identify various thermoacoustic behaviors by numerically solving the governing equations. It is shown that a homogeneous thermoacoustic-wave pattern dominates in the linear case, largely independent of ɛ; whereas under the nonlinear perturbation, variation in ɛ could lead to severe wavefront deformation. The strong nonlinear effect is found to be of a transient nature because, in due time, both cases tend to converge in terms of the energy yield of the adiabatic process.

Thermovibrational instability in supercritical fluids under weightlessness

Low amplitude, high frequency vibrations can induce in fluids under weightlessness behaviors that resemble those induced by gravity. Supercritical fluids (above their gas-liquid critical point) are used in the space industry and also display universal behavior. They are particularly sensitive to gravity effects. When submitted to vibration (typically 0.1 to 0.5mm amplitude, 10 to 50Hz frequency), a Rayleigh-Bénard-like instability is observed in experiments with H2 and CO2 under weightlessness. The thermal boundary layer created during a temperature change displays periodic fingering perpendicular to the vibration direction. A systematic two-dimensional numerical study by the finite volume method is performed in CO2 that shows that the fingering pattern is due to a thermovibrational instability, characterized by a vibrational Rayleigh number. The simulation and a simplified dimensional analysis show that the fingering wavelength and the vibrational Rayleigh number decrease as a power law with the distance in temperature to the critical point. However, due to the oversimplification of the analysis, the exponent in the simulation is found to be somewhat different than in the theoretical approach, calling for a more complete investigation of the problem.

Modeling heat transfer in supercritical fluid using the lattice Boltzmann method

A lattice Boltzmann model has been developed to simulate heat transfer in supercritical fluids. A supercritical viscous fluid layer between two plates heated from the bottom has been studied. It is demonstrated that the model can be used to study heat transfer near the critical point where the so-called piston effect speeds up the transfer of heat and results in homogeneous heating in the bulk of the layer. We have also studied the onset of convection in a Rayleigh-Bénard configuration. It is shown that our model can well predict qualitatively the onset of convection near the critical point, where there is a crossover between the Rayleigh and Schwarzschild criteria.

Thermoacoustic effects in supercritical fluids near the critical point: Resonance, piston effect, and acoustic emission and reflection

We present a general theory of thermoacoustic phenomena in one phase states of one-component fluids. Singular behavior is predicted in supercritical fluids near the critical point. In a one-dimensional geometry we start with linearized hydrodynamic equations taking into account the effects of heat conduction in the boundary walls and the bulk viscosity. We introduce a coefficient Z(omega) characterizing reflection of sound with frequency omega at the boundary in a rigid cell. As applications, we examine acoustic eigenmodes, response to time-dependent perturbations, and sound emission and reflection. Resonance and rapid adiabatic changes are noteworthy. In these processes, the role of the thermal diffusion layers is enhanced near the critical point because of the strong critical divergence of the thermal expansion.

Thermoconvectional phenomena induced by vibrations in supercritical SF6 under weightlessness

The effect of a linear harmonic vibration on heat propagation is investigated in near-critical SF6 under weightlessness conditions in space. Heat was issued from a pointlike source (thermistor), a situation representative of an industrial use of pressurized supercritical fluid storage. Two kinds of vibrations were used, large amplitude (64 mm) at 0.2 Hz and low amplitude (0.8 mm) at 1.6 Hz, with temperatures from 5 K to 20 mK from the critical temperature. The vibrations are seen to strongly affect the evolution and shape of the hot boundary layer (HBL), the heat exchange between the heat source and the fluid, and the bulk thermalization process by the adiabatic piston-effect process. The HBL is initially convected as symmetrical plumes over a distance that only depends on the vibration velocity and which corresponds to a Rayleigh-Bénard-like instability where the vibration acceleration acts as the earth gravity. Then the extremities of the plumes are convected perpendicularly to the direction of oscillation as two "pancakes," a process encountered in the vibrational Rayleigh-Bénard instability. When the vibration velocity is small, only one pancake centered at the hot source is observed. Temperature evolutions of the hot source and the fluid are studied in different locations. Convection flows and adiabatic piston effect compete to determine the thermal dynamics, with the latter being the most efficient near the critical point. The experimental results are compared with a two-dimensional numerical simulation that highlights the similarities and differences between the very compressible van der Waals gas and an ideal gas.

Reverse transition to hydrodynamic stability through the Schwarzschild line in a supercritical fluid layer

We consider a fluid close to its gas-liquid critical point in a bottom-heated cavity. Due to strong density stratification, both the Schwarzschild and the Rayleigh stability criteria are relevant at the same space scale. Taking advantage of the competition between these two limits of the convection-onset criterion, we numerically exhibit striking non-Boussinesq effects: the reverse transition to stability through the Schwarzschild line of a heat diffusing layer subjected to convection, and the convection onset inside a few-millimeters-thick layer according to the Schwarzschild criterion.

Numerical simulation studies of the convective instability onset in a supercritical fluid

Numerical simulation studies in 2D with the addition of noise are reported for the convection of a supercritical fluid, 3He , in a Rayleigh-Bénard cell. The noise addition is to accelerate the instability growth after starting the heat flow across the fluid, so as to bring simulations into better agreement with published experimental observations. Homogeneous temperature noise and spatial longitudinal periodic temperature variations in either top or bottom plates were programmed into the simulations. The second method was the most effective in speeding up the instability onset. For a small amplitude of the longitudinal perturbations, a semiquantitative agreement with the observations was obtained. The results are discussed in relation to predictions by El Khouri and Carlès.

Convection in a very compressible fluid: comparison of simulations with experiments

The time profile DeltaT(t) of the temperature difference, measured across a very compressible fluid layer of supercritical 3He after the start of a heat flow, shows a damped oscillatory behavior before steady-state convection is reached. The results for DeltaT(t) obtained from numerical simulations and from laboratory experiments are compared over a temperature range where the compressibility varies by a factor of approximately 40. First the steady-state convective heat current j(conv) as a function of the Rayleigh number Ra is presented, and the agreement is found to be good. Second, the shape of the time profile and two characteristic times in the transient part of DeltaT(t) from simulations and experiments are compared, namely (1) t(osc), the oscillatory period, and (2) t(p), the time of the first peak after starting the heat flow. These times, scaled by the diffusive time tau(D) versus Ra, are presented. The agreement is good for t(osc)/tau(D), where the results collapse on a single curve showing a power-law behavior. The simulation hence confirms the universal scaling behavior found experimentally. However for t(p)/tau(D), where the experimental data also collapse on a single curve, the simulation results show systematic departures from such a behavior. A possible reason for some of the disagreements, both in the time profile and in t(p), is discussed.

Fast heat transfer calculations in supercritical fluids versus hydrodynamic approach

This study investigates the heat transfer in a simple pure fluid whose temperature is slightly above its critical temperature. We propose an efficient numerical method to predict the heat transfer in such fluids when the gravity can be neglected. The method, based on a simplified thermodynamic approach, is compared with direct numerical simulations of the Navier-Stokes and energy equations performed for CO2 and SF6. A realistic equation of state is used to describe both fluids. The proposed method agrees with the full hydrodynamic solution and provides a huge gain in computation time. The connection between the purely thermodynamic and hydrodynamic descriptions is also discussed.

Piston-effect-induced thermal oscillations at the Rayleigh-Bénard threshold in supercritical 3He

We perform a Navier-Stokes numerical simulation of the transient Rayleigh-Bénard convection onset in nearly supercritical 3He in the exact conditions in experiments performed by Kogan, Murphy, and Meyer [Phys. Rev. Lett. 82, 4635 (1999)]Phys. Rev. E 63, 056310 (2001)]]. We find an interpretation of the observed unexpected temperature oscillations at the convection onset in terms of the piston effect. This is our first result towards the exploration of the whole instability diagram as recently mapped in those experiments.

Scenarios for the onset of convection close to the critical point

We perform a theoretical analysis of the onset of convection in a layer of near-critical 3He submitted to an unsteady bottom heating. A theoretical model previously presented [P. Carlès, Physica D 147, 36 (2000)] is adapted to the corresponding physical conditions, and a method is proposed to solve the associated equations. We predict, for different intensities of heating and different initial temperatures, when convection will start and what will be the shape of the dominant growing perturbations. A systematic parametric analysis shows that the onset of convection in a supercritical fluid can take place following four distinct scenarios, depending on the initial temperature and the intensity of the heating. Two of these scenarios are entirely specific to near-critical fluids, being impossible to observe in classical Boussinesq fluids.

Onset of convection in a very compressible fluid: the transient toward steady state

We analyze the time profile deltaT(t) of the temperature difference, measured across a very compressible supercritical 3He fluid layer in its convective state. The experiments were done along the critical isochore in a Rayleigh-Bénard cell after starting the vertical constant heat flow q. For q sufficiently well above that needed for the convection onset, the transient deltaT(t) for a given epsilon identical with (T-T(c))/T(c), with T(c)=3.318 K, shows a damped oscillatory profile with period t(osc) modulating a smooth base profile. The smooth profile forms the exponential tail of the transient which tends to the steady-state deltaT( infinity ) with a time constant tau(tail). The scaled times t(osc)/t(D) and tau(tail)/t(D) from all the data could be collapsed onto two curves as a function of the Rayleigh number over approximately 3.5 decades. Here t(D) is the characteristic thermal diffusion time. Furthermore, comparisons are made between measurements of a third characteristic time t(m) between the first peak and the first minimum in the deltaT(t) profile and its estimation by Onuki et al. Also, comparisons are made between the observed oscillations and the two-dimensional simulations by Onuki et al. and by Amiroudine and Zappoli. For epsilon<9 x 10(-3), the experiments show a crossover to a different transient regime. This regime, which we briefly describe, is not understood at present.

Convective heat transport in compressible fluids

We present hydrodynamic equations of compressible fluids in gravity as a generalization of those in the Boussinesq approximation used for nearly incompressible fluids. They account for adiabatic processes taking place throughout the cell (the piston effect) and those taking place within plumes (the adiabatic temperature gradient effect). Performing two-dimensional numerical analysis, we reveal some unique features of plume generation and convection in transient and steady states of compressible fluids. As the critical point is approached, the overall temperature changes induced by plume arrivals at the boundary walls are amplified, giving rise to overshoot behavior in transient states and significant noise in the temperature in steady states. The velocity field is suggested to assume a logarithmic profile within boundary layers. Random reversal of macroscopic shear flow is examined in a cell with unit aspect ratio. We also present a simple scaling theory for moderate Rayleigh numbers.