IRN AP09259248 «Arising of concentration gravitational convection in multicomponent diffusion in stably stratified medium».

Expected results: During the project development process, the following expected results will be obtained for the first time:

1. An analysis of the stability of mechanical equilibrium and development of computational algorithms will be carried out to determine the optimal thermobaric and concentration conditions of kinetic mixing regimes in multicomponent mixtures in which the diffusion regimes are changed to convective regimes;

2. Spectrum of thermophysical and geometric parameters that cause occurrence of supercritical flows in isothermal multicomponent gas mixtures will be determined;

3. Influence of diffusion mechanisms on the hydrodynamics of mixing multi-component systems getting used to a kinetic transition to the convective phase during mass transfer in cylindrical and flat channels will be studied;

4. Research generation of the initial phase of the supercritical flow in the pulsation regime at different pressures and initial compositions of multicomponent mixtures will be carried out;

5. Behavior of a convective structural formation located between two parallel solid surfaces in a medium of different density with taking into account the movement of the contact line along the solid surface will be studied;

An analysis of the stability of mechanical equilibrium is carried out and computational algorithms are developed, which allow determining the optimal thermobaric and concentration conditions of kinetic mixing regimes in multicomponent mixtures in which the diffusion regimes are changed to convective regimes. It is shown, that in triple gas mixtures, due to the different diffusion velocity of the components, conditions arise for the implementation of convection, which distorts the partial mass transfer expected during isothermal diffusion. It is established, that feature of the organization of concentration fields concluded on, that formed under the condition of a decrease in the density of the mixture with height. Within the framework of the stability theory, the solution of a system of hydrodynamic equations for an isothermal triple mixture is considered. For a flat vertical diffusion channel, a boundary relation is obtained, that allows predicting the transition from a diffusion state to a convective state for specific p – V – T conditions. Critical Rayleigh numbers for even and odd solutions are determined, also characteristic values for the convective mixing velocity are obtained. It is shown, that in the conditions of developed convection, change in the intensity of the transfer of components depending on the pressure is linked with the perturbation mode, that determines various types of convective flows. Work is being down to develop a model of the kinetic transition “diffusion-convection”. Critical Rayleigh numbers will be determined for a vertical cylindrical channel.

Spectrum of thermophysical and geometrical parameters causing the occurrence of supercritical flows in isothermal multicomponent gas mixtures has been determined. Physical interpretation for appearance of convective instability and subsequent development of hydrodynamic disturbances are described in detail in the literature. However, use of the Rayleigh thermal problem formalism to describe isothermal multicomponent mixing under conditions of initial steady-state stratification of the mixture requires influence of already several partial concentration gradients to considered. Importance of such an adjustment has been shown in the work of research group, in which it was found, that in ternary systems with different molecular weights M_i and different diffusion coefficients D_ij damping and increasing convective perturbations occur. The latter can be the cause of structured flows in multicomponent diffusion. However, such approach defines only boundary of “diffusion-convection” mode change in the area of given thermophysical and geometrical parameters. Process of occurrence of structured convective flows and their subsequent evolution at the boundary of “diffusion-convection” regime change can be described numerically. As a result, an algorithm for solution of perturbed equations of diffusion and convection has been developed, which in vertical channel of different geometries allowed to determine spectrum of thermophysical and geometrical parameters causing emergence of supercritical currents in isothermal multicomponent gas mixtures.

2. For ternary systems, where diffusion coefficients differ significantly from each other, isoconcentration distributions in vertical channels are numerically obtained. For ternary systems H₂O + CH₂O₂ – Ar, He + Ar – N₂, He + R12 – Ar, H₂ + CO₂ – N₂, CH₃OH + H₂O – Ar, where diffusion coefficients differ significantly, isoconcentration distributions of components at different mixing times were obtained numerically based on physical parameter splitting scheme. Definition of convective instability can be related to significant curvature of the isoconcentration distributions, which are absent during diffusion. Degree of curvature of concentration distributions depends on the component content of the highest molecular weight in system. At certain compositions the curvature disappears and diffusion is realized in the system. Similar situation appears for system with given initial composition and different pressures. There is certain value of pressure, at which significant curvature of isolines occurs, showing that conditions for occurrence of supercritical flows in the system are formed.

3. The baric dependences of component concentrations in several mixtures at different diffusion coefficient ratios were investigated experimentally. For ternary mixtures H₂ + CO₂ – N₂, He + R12 – Ar where diffusion coefficients are significantly different, the baric mixing speed of components was studied experimentally. It was found, that at certain pressures kinetic “diffusion-convection” transition is observed. Further pressure increase causes the appearance of supercritical currents, implementing the preferential transfer of components with the highest molecular weight. For the system N₂ + CO₂ – Ar, where diffusion coefficients are close to each other, diffusion was observed at all test pressures. Diffusion-convection mode change was not observed in this system.

4. Effect of mixture viscosity and channel geometry has been evaluated. The experimental data are compared with the calculated data. Series of experiments with the following three-component systems 0.440 He (1) + 0.560 CO₂ (2) – N₂ (3) и 0.788 CO₂ (1) + 0.212 C₃H₈ – N₂O (3) were implemented to study the effect of viscosity and diffusion channel geometry on the occurrence of convection currents. The first mixture was studied in a cylindrical diffusion channel with channel diameter equal to 4·10^-3 m as a characteristic influencing parameter, and the second mixture was studied in a flat vertical channel with channel thickness equal to 6·10^-3 m as a characteristic influencing parameter. Thus, increase of characteristic influencing parameter by two orders of magnitude leads to decrease of pressure value, at which transition from diffusive process to unstable one occurs. In the first system, transition from diffusion to convection process occurs at a pressure of 0.58 MPa, and for the second system at pressure of 0.39 MPa, which is also caused by viscosity of diffusing components. In the system 0.440 He (1) + 0.560 CO₂ (2) – N₂ (3) the viscosities of diffusing components are practically identical, whereas in system 0.788 CO₂ (1) + 0.212 C₃H₈ (2) – N₂O (3) the first and the third component have similar viscosities, and viscosity of the second component (propane) is about 2 times less. This difference in viscosities at almost same diffusion coefficients leads to the fact that in the system 0.788 CO2 (1) + 0.212 C3H8 – N2O (3) the instability occurs at much lower pressure values. Thus, the study showed, that intensity of unstable process is influenced not only by diffusion channel shape but also by viscosity of diffusing components. Stability maps were constructed for the considered systems in coordinates (Ra₂, p), where Ra₂ is Rayleigh number of the heaviest component of mixture. The obtained numerical data are in good agreement with the results of experiments. (2022).