**Relevace of the project:** The relevance of proposed project is high. Modern technologies for production of materials, extraction of hydrocarbon raw materials, forecasting of natural phenomena require adequate description of heat and mass transfer processes in liquids and gases, which, as a rule, are mixtures of different substances with a large number of components. Difficulties in the description of multicomponent mixtures are determined by presence of several heat and mass transfer mechanisms (convection, thermal conduction, diffusion, thermodiffusion, diffusive thermal conduction). For systems consisting of three or more components need to account for cross-diffusion effects. To control the behaviour of such systems new knowledge of features of combined mass transfer both in diffusion and convective stages of multicomponent mixing and at the boundary of change “diffusion – concentration gravitational convection” modes is required.

Principal distinguishing feature of research from existing analogues is: obtaining new experimental and computational data on determination of stability boundaries for three- and four-component gas mixtures containing components with different thermophysical properties; study of supercritical flows at the initial stage of their formation; verification of numerical results with experimental data obtained by different methods in the laboratory.

The work envisaged in project refers to fundamental research, which will result in fundamentally new and world-class results in the field of stability and nonlinear dynamics of multicomponent hydrodynamic systems, new methods of controlling their behaviour have been developed. Results of research on multicomponent transfer can be used in technologies to reduce the environmental load, such as separation technologies, which corresponds to the national priorities of socio-economic development of Kazakhstan.

Project uses the following main research approaches to achieve its objectives and justifications:

Research approaches used in the project are based on fundamental laws of physical kinetics and hydrodynamics and multi-component mass transfer. Experimental approaches are based on the application of the two-column method and diffusion bridge method. Observations of stationary, quasi-stationary and non-stationary processes of multicomponent diffusion and convective mixing in experimental benches implementing the mentioned methods will allow to investigate special modes and properties of gas mixtures under study. As a result, spectrum of experimental data characterising the main features of combined mass transfer will be obtained.

Computational – theoretical and numerical methods used in the project are new tools to investigate the effects of thermal and geometrical parameters on a multi-component mixture. Numerical modelling is based on the combined solution of a system of unsteady hydrodynamic equations, particle number conservation of the mixture and components, taking into account the condition of independent diffusion and the equation of state. For the numerical computations, efficient parallel numerical methods and algorithms will be used, and obtained results will be compared with the computational data of other authors and experimental results. In order to prove the adequacy of the developed mathematical models, test problems will be calculated. Results of numerical modelling will be combined with experimental studies, which is an important methodological feature in performing the tasks of this project.

**The aim of the project is: **Numerical research of mechanical equilibrium of isothermal ternary gas mixtures, determination of dynamic characteristics of emerging concentration gravity currents under different conditions (pressure, mixture composition, relationship between diffusion coefficients), obtaining calculated data on the effect of cross-effects on determination of “diffusion-convection” transition boundaries. Conducting experiments to verify the results.

Expected results: 2021 | Results achieved: 2021 |

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. |

Expected results: 2022 | Results achieved: 2022 |

The following expected results will be obtained for the first time in the process of project development: spectrum of thermophysical and geometrical parameters causing supercritical flows in isothermal multicomponent gas mixtures will be determined; isoconcentration distributions in vertical channels will be obtained numerically for the selected triple systems; the experimental baric dependences of concentrations in several mixtures with different relations between diffusion coefficients will be investigated; the influence of diffusion mechanisms on hydrodynamics of mixing multicomponent systems undergoing kinetic transition into convective phase during mass transfer in cylindrical and flat channels will be studied; the conditions of emergence and development of convective flows in vertical channels of given geometry at different pressures and presence of component impurities will be studied experimentally and numerically; the critical time required for formation of supercritical flows will be estimated numerically depending on the problem parameters: diffusion coefficients, partial flow rates of components and concentrations. (2022). |
D 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._{ij}2. 3. 4. |

**Composition of the research team:**

(Researcher ID Web of Science: E-4057-2015; Scopus ID: 7003898941; ORCID ID:0000-0002-8001-1644) – Member-correspondent NAS RK, a foreign member of the Russian Academy of Natural Sciences, Foreign member of the Russian Academy of Natural Sciences, a well-known scientist in the field of gas physics. Hirsch index for the Scopus and Web of Science citation databases is 6/4.*Project manager, Kossov V.N.,*(Researcher ID Web of Science: N-4847-2014), candidate of Physical and Mathematical Sciences. Research activity: diffusion and convective heat and mass transfer, separation effects in multicomponent systems. Hirsch index for the Scopus and Web of Science citation databases is 5/3.*Fedorenko O.V.*(Researcher ID Web of Scopus: 6506553349), doctor of Physical and Mathematical Sciences, professor, project executor. Research activity: thermophysics, heat and mass transfer in gases. Hirsch index for the Scopus and Web of Science citation databases is 2/3.*Kulzhanov D.U.*(Researcher ID Web of Science: O-2430-2017), candidate of Physical and Mathematical Sciences, professor, project executor. Research activity: thermophysics, heat and mass transfer in gases. Author of more than 20 scientific papers. Hirsch index for the Scopus and Web of Science citation databases is 2.*Mukamedenkyzy V.*(Researcher ID Scopus: 563666282000), PhD, project executor. Research activity: thermophysics, architectonics of physical education. Hirsch index for the Scopus and Web of Science citation databases is 2.*Akzholova A.A.*Master, PhD candidate of the third year of study in the specialty “Physics”, project executor.*Kalimov A.B.,*project executor. Research activities: radiation technologies, materials science. The Hirsch index for the Scopus and Web of Science citation databases is 2.*Khodarina N.N.,*project executor, Master’s degree.*Bondareva P.V.,*Master’s degree, PhD candidate of the third year of study, project executor.*Zhusanbayeva A.K.,*

**List of publications for 2022:**

* 3 scientific papers have been published in journals indexed by the Scopus database:*

1 Kossov V., Fedorenko O., Asembaeva M., Mukamedenkyzy V., Moldabekova M. Intensification of the separation of isothermal ternary gas mixtures containing carbon dioxide // Chem. Eng. Technol. – 2021. – Vol. 44, No. 11. – P. 2034 – 2040. DOI:10.1002/ceat.202100241. (percentile – 61%). (Article was not included in the 2021 report).

2 Kossov V., Fedorenko O., Zhakebayev D., Mukamedenkyzy V., Kulzhanov D. Convective mass transfer of a binary gas mixture in an inclined channel // Z Angew Math Mech. – 2022. – Vol. 102, No. 1. – e201900197. https://doi.org/10.1002/zamm.20190019. (percentile – 64%).

3 Kossov V.N., Fedorenko O.V., Zhaneli M., Mukhatova K. Multicomponent mixing on the “diffusion – convection” transition boundary at elevated pressures // Journal of Physics: Conference Series. 2022. – Vol. 2150, No. 1. – 012014. DOI:10.1088/1742-6596/2150/1/012014. (percentile – 18%).

* The thesis of the international conference has been published:*

4 Kosov V.N., Fedorenko O.V., Meirambekuly E. Features of the emergence of structured flows at the boundary of regime change “diffusion – concentration convection” XI International Scientific Conference “Problems of evolution of open systems PEOS – 21”. – Kazakhstan, Almaty, – 2021 – pp. 17-19. (The thesis was not included in the report of 2021).