The generalized diagram of the critical Grashof numbers as functions of the Prandtl number is presented. The diagram shows the zones of occurrence of flow field and temperature fluctuations in the axisymmetric and three-dimensional formulations of the crystal growth model using the pulling from a melt. The structure of thermals at high Prandtl numbers and the distinctive features of the three-dimensional convection structure in the zones of stabilization and hazardous mode changeover at different Prandtl numbers are discussed. The effect of crystal rotation on the flow and temperature field patterns is estimated.

Coupling of two basic mechanisms of gravity-driven convection is named as convective interactions in the paper. Classification of applications of the interaction mechanism with different orientation of input (output) heat flux to the gravity force is suggested. Brief overview and comments are done. For illustration of the classification a number of examples on the basis of experience in technique and technology are presented. Some convective interaction features with change of orientation for a model of differently heated square are shown. Critical value of the angle for bifurcation onset, heat transfer and temperature stratification in dependency of the angle, temperature oscillations onset in dependency of Pr number for inclined square are presented.

One- and two-dimensional thermoacoustic convection was studied numerically in a closed volume, filled with carbon dioxide, under normal conditions (perfect gas) or in the vicinity of the stagnation point (Van der Waals gas) within the range of the Reynolds numbers 103 − 105 on the parallel computer MVC-100K of the Supercomputer Center of Russian Academy of Sciences (RAS). The achieved speedup of calculations equals 60 for the one-dimensional and 300for the two-dimensional problem compared to the single-processor computer. The fields of flow and temperature were investigated depending on the problem parameters. The necessity of using the detailed grid in both directions to resolve the thin boundary layers and fronts (104 grid nodes for the Reynolds number equal to 105) is shown.

Thermal gravitational convection in a bottom-heated layer of near-critical 3He is considered. The range of criteria determining the convection parameters beyond the stability threshold is discussed. The specific features of 2D and 3D supercritical structures, the adiabatic compression effect, and heat transfer are considered.

A new model for spatial convective transport processes conjugated with the measured or calculated realistic quasi‐steady microaccelerations is presented. Rotation around the mass center, including accelerated rotation, gravity gradient, and aerodynamical drag are taken into account. New results of the effect on mixing and concentration inhomogeneities of the elementary convective processes are presented. The mixing problem in spacecraft enclosures, concentration inhomogeneities due to convection induced by body forces in realistic spaceflight, and the coupling of this kind of convection with thermocapillary convection on the basis of this model are discussed.

New numerical results on thermal gravity-driven convection in a layer filled with near-critical 3He and heated from below are presented. Corrections of conditions for convection onset are discussed. The heat transfer calibrations near the critical point are tested using experimental data. Stratification effects are analysed. As found, space environment that suppresses the strong density gradients near the critical point may provoke the enhancement of convection compared to the terrestrial conditions.

We present a review of recent activity of the VIP-CRIT team in analyzing the previous space experiments, developing analytical methods, and carrying out the laboratory and numerical simulations devoted to the study of the effects of microgravity environment on the heat transfer and phase separation in the supercritical and near-critical fluids. The studies complement one another, and the results show that such kind of collective activity is extremely important for both obtaining new basic knowledge and optimizing the future space experiment onboard the ISS.

Thermal gravity convection in a horizontal layer of compressible perfect gas heated from below and a van der Waals gas near the critical state is investigated. The characteristics of the isentropic equilibrium of a compressible medium with a van der Waals equation of state are considered. The known conditions of convection onset in the perfect and van der Waals gases are checked on the basis of a solution of the complete and linearized equations. The restrictions imposed in deriving the known formulas for the adiabatic temperature gradients used in the conditions of absence and onset of convection are discussed. The characteristics of the convective heat transfer are examined, including the causes of the heat-transfer deterioration in the near-critical medium above the hydrostatic equilibrium threshold.

Peculiarities of the isothermal and isentropic equilibrium in highly compressible media with nonperfect state equations are discussed. Formulation of the adiabatic temperature gradient using Schwarzschild criterion and equilibrium equations for nonperfect gas are considered. Criterion for the onset of convection in the van der Waals (VDW) gas is examined using direct numerical modeling on the basis of equation for convection in compressible viscous nonperfect gas. Results of three-dimensional modeling near-critical convection in the vicinity of the convection onset in space flight with quasi-steady microaccelerations are given. A proposal for the microgravity research of the near-critical convection is discussed.

The results of two series of space experiments carried out onboard the MIR in 1999–2000 are presented. The experiments were undertaken to study the effect of microgravity environment as well as specially excited vibration on heat spread from a point source inside a cell filled with SF 6 near its critical point. New space experiments are proposed to continue the series interrupted by the deorbiting of the MIR. These proposals are the central point of the CRIT project planned for the realization onboard the Russian Segment of the ISS.

Steady-state Rayleigh-Benard convection in a medium with parameters close to the thermodynamic critical point is simulated within the framework of the complete Navier-Stokes equations with a two-scale representation of the pressure and the Van-der-Waals equation of state. A calibration relation is obtained for a realistic Rayleigh number in a compressible stratified medium. The parameters of the numerical simulation are determined from experimental data for near-critical helium on the basis of the calibration relation. The threshold Rayleigh numbers are found without and with allowance for stratification and a comparison with the experimental and theoretical data is carried out. The effect of compressibility of the near-critical fluid on steady-state convection flows is investigated beyond the stability threshold and the effect of adiabatic compression of the medium is analyzed.

Summary Experience in the education and tutorial in modeling of the elementary flows, heat and mass transfer during crystal growth in ground-based and microgravity environment using computer system COMGA is presented. The system supports free and forced convection problems on the basis of the Navier - Stokes equations. The computer laboratory as intellectual shell of this system includes basic double-diffusion gravity-driven and Marangoni problems in enclosures, Bridgman model, and Czochralski model for microgravity and ground-based applications. A basic version of the system and computer laboratory includes most of classical problem of convective heat and mass transfer with different types of the boundary conditions, external forces, and fluid (gas) properties. Initial stage of education starts from the definition of the physical properties of the typical liquids and gases in crystal growth applications and hydrostatic equilibrium. Convection is induced by the buoyancy and gradient of the surface tension (Marangoni convection). A general mechanism of the onset of convection and convective instability is included. Elements of the modeling theory and the basic knowledge of fluid dynamics and numerical methods should be also studied for understanding the options of the finite difference schemes. Classical problems of the gravity-driven convection with side heating, Rayleigh-Bernard convection with rigid and free surfaces, and similar types of the Marangoni convection should be firstly studied. A fragment of the solution of the problem on thermocapillary convection in horizontal layer during bottom heating (Marangoni instability) presented in Fig. 1. The onset of Marangoni convection after the loss of hydrostatic equilibrium stability and formation of the steady- state regime is shown for the classical Pearson problem with zero body force (3). The field of stream function (roll structure) is on the top and isotherms of thermocapillary convection are below. On the right side the temporal evolution of the maximum of stream function is shown. A fragment of Menu of the computer system COMGA_W is shown on the left side. One can see here a title of the problem and items inside the Problem category, which characterizes only a given problem: parameters Ma, Pr, region L/H, body force (g=0 in this case), and type of initial conditions. Study all aspects of the problem with output the information in real time make it possible to use this system (together with interface of the input information, library of the problems, physical properties, references of the related papers etc.) as a computer laboratory. The students can study most of the elementary convection problems in real-time calculation during the tutorial process. Research works related to unsolved classical problems may be carried out in the end of this part of education. As an example of the bachelor degree work the result of analysis of temporal bound of the onset of gravity-driven convection in a horizontal layer with bottom heating is shown in (4).

Our experience in education and tutorials regarding the modeling of elementary flows, heat and mass transfer during crystal growth in ground-based and microgravity environment using the computer system convection in microgravity and applications is presented. The system supports free and forced convection problems on the basis of the Navier–Stokes equations for the Boussinesq approach. The computer laboratory as the intellectual shell of this system includes basic double-diffusion gravity-driven and Marangoni problems in enclosures, a Bridgman model, and a Czochralski model for microgravity and ground-based applications.

A bstract : This paper presents analysis of the different time scales associated with unsteady fluid flow phenomena near the thermodynamical critical point and that are typical for experiments carried out in microgravity. A focus of the paper is modeling the initial stage of convection under low and zero gravity on the basis of the two‐dimensional Navier‐Stokes equations for a compressible gas with the Van der Waals state equation. We also consider a thermoacoustic problem on the basis of three‐dimensional linearized equations for an isentropic inviscid gas near the critical point in zero gravity. We compare the heat transfer due to unsteady convection and the piston effect in an enclosure with side heating in zero and low gravity with pure conductivity. image