Труды сотрудников ИВМ СО РАН

/ I.V. Stepanova // Commun. Nonlinear Sci. Numer. Simul. - 2013. - Vol. 18, Is. 6. - P1341-1346, DOI 10.1016/j.cnsns.2012.10.013. - Cited References: 14. - Author thanks Prof. V.K. Andreev for formulation of the problem and attention to the work. This work is supported by the Integrational Grant No 44 and The Ministry of education and science of Russia, project 14.A18.21.2014. . - 6. - ISSN 1007-5704РУБ Mathematics, Applied + Mathematics, Interdisciplinary Applications + Mechanics + Physics, Fluids & Plasmas + Physics, Mathematical

Аннотация: Group classification problem is solved for equations of motion of a binary mixture under the buoyancy force and thermodiffusion effect. These equations are parameterized by five arbitrary functions of two arguments. The admissible Lie symmetry algebras of generators are found depending on arbitrary elements. These results are useful for analytical and numerical modeling of the convection in binary mixtures. (C) 2012 Elsevier B. V. All rights reserved.


Доп.точки доступа:
Stepanova, I.V.; Степанова, Ирина Владимировна

[Text] / Y. Gaponenko, V. Shevtsova // Acta Astronaut. - 2010. - Vol. 66, Is. 01.02.2013. - pp. 174-182, DOI 10.1016/j.actaastro.2009.05.019. - Cited References: 10 . - ISSN 0094-5765РУБ Engineering, Aerospace

Аннотация: We report on a numerical study of the mixing of two miscible fluids in gravitationally stable configuration. In the absence of external forces the diffusion process leads to the mixing of species. The aim of this study is to analyze the physical mechanism by which vibrations affect the mixing characteristic of two stratified miscible fluids. The translational periodic vibrations of a rigid cell filled with different mixtures of water-isopropanol are imposed. The vibrations with a constant frequency and amplitude are directed along the interface. In absence of gravity vibration-induced mass transport is incomparably faster than in diffusion regime. Our results highlight the strong interplay between gravity and vibrational impact, the relative weight of each effect is determined by ratio vibrational and classical Rayleigh numbers. (C) 2009 Elsevier Ltd. All rights reserved.


Доп.точки доступа:
Gaponenko, Y.; Гапоненко, Юрий Анатольевич; Shevtsova, V.

[Текст] : статья / V. K. Andreev // Journal of Siberian Federal University. Mathematics & Physics = Журнал Сибирского федерального университета. Математика и физика. - 2008. - Т. 1, № 4. - С. 349-370
Аннотация: The invariant solution of the equations of thermodiffusional motion is investigated. This solution describes the motion of two immiscible incompressible binary mixtures with a common flat interface under the action of pressure gradient and thermocapillary forces. The stationary flow of such system is found. If the pressure gradient in one of the mixtures tends to zero sufficiently fast, then the motion of mixtures is slowed down by the viscous friction. On the other hand, if there exists a finite limit of pressure gradient when time tends to infinity, then the solution tends to the stationary state.

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Держатели документа:
ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44

Доп.точки доступа:
Андреев, Виктор Константинович

[Text] : статья / V.K. Andreev // Proceeding of the Steklov Institute of Mathematics. - 2008. - Suppl. 1. - p. 1-4


Доп.точки доступа:
Андреев, Виктор Константинович

[Text] : статья / S. Arcidiacono, J. Mantzaras, I. V. Karlin // Physical review E. - 2008. - Vol. 78. - Ст. 046711, DOI 10.1103/PhysRevE.78.046711 . - ISSN 1539-3755
Аннотация: A lattice Boltzmann model is developed to simulate finite-rate catalytic surface chemistry. Diffusive wall boundary conditions are established to account for catalytic reactions in multicomponent mixtures. Implementation of wall boundary conditions with chemical reactions is based on a general second-order accurate interpolation scheme. Results of lattice Boltzmann simulations for a four-component mixture with a global catalytic methane oxidation reaction in a straight channel are in excellent agreement with a finite volume Navier-Stokes solver in terms of both the flow field and species concentrations.

Держатели документа:
ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44

Доп.точки доступа:
Mantzaras, J.; Karlin, I.V.; Карлин, Илья Вениаминович

[Text] : статья / Y. A. Gaponenko, V. Shevtsova // Microgravity Science and Technology. - 2008. - Vol. 20, Iss. 3-4 . - p. 307-311, DOI 10.1007/s12217-008-9075-7 . - ISSN 0938-0108
Аннотация: The aim of this study is to analyze the physical mechanism by which vibrations affect the mixing characteristic of two initially stratified miscible fluids. The translational periodic vibrations of a rigid cell filled with different mixtures (Sc = 7125) are considered. The vibrations with a constant frequency are imposed parallel to the initially planar interface. The ability of the applied vibrations to enhance the flow is examined. At the early stage after imposing the vibrations the Kelvin-Helmholtz instability is observed in absence and at low level of gravity. Later in time the system undergoes a transition to Rayleigh-Taylor instability. With increasing of gravity level the life-time of Kelvin-Helmholtz instability is decreased. We found the critical value of Gr above which this instability do not developed.

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Доп.точки доступа:
Shevtsova, V.; Гапоненко, Юрий Анатольевич

/ I. I. Ryzhkov, V. M. Shevtsova // Microgravity Science and Technology. - 2009. - Vol. 21, Is. 1-2. - P37-40, DOI 10.1007/s12217-008-9081-9 . - ISSN 0938-0108
Аннотация: The model of convection in a multicomponent fluid is considered taking into account the cross-diffusion and the Soret effect. It is shown that the cross-diffusion coefficients can be eliminated by a linear change of composition and the thermal diffusion coefficients. It allows a simple incorporation of cross-diffusion phenomena into the results obtained for the case of diagonal diffusion matrix. Applications to the modelling of multicomponent flows in microgravity and terrestrial conditions are discussed. В© 2008 Springer Science+Business Media B.V.

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Доп.точки доступа:
Shevtsova, V.M.; Рыжков, Илья Игоревич

[Text] : статья / A. N. Gorban, H. P. Sargsyan, H. A. Wahab // Mathematical Modelling of Natural Phenomena. - 2011. - Vol. 6, Iss. 5. - p. 184-262DOI 10.1051/mmnp/20116509 . -
Аннотация: Diffusion preserves the positivity of concentrations, therefore, multicomponent diffusion should be nonlinear if there exist non-diagonal terms. The vast variety of nonlinear multicomponent diffusion equations should be ordered and special tools are needed to provide the systematic construction of the nonlinear diffusion equations for multicomponent mixtures with significant interaction between components. We develop an approach to nonlinear multicomponent diffusion based on the idea of the reaction mechanism borrowed from chemical kinetics. Chemical kinetics gave rise to very seminal tools for the modeling of processes. This is the stoichiometric algebra supplemented by the simple kinetic law. The results of this invention are now applied in many areas of science, from particle physics to sociology. In our work we extend the area of applications onto nonlinear multicomponent diffusion. We demonstrate, how the mechanism based approach to multicomponent diffusion can be included into the general thermodynamic framework, and prove the corresponding dissipation inequalities. To satisfy thermodynamic restrictions, the kinetic law of an elementary process cannot have an arbitrary form. For the general kinetic law (the generalized Mass Action Law), additional conditions are proved. The cell–jump formalism gives an intuitively clear representation of the elementary transport processes and, at the same time, produces kinetic finite elements, a tool for numerical simulation.


Доп.точки доступа:
Sargsyan, H.P.; Wahab, H.A.; Горбань, Александр Николаевич

[Text] : статья / V. Shevtsova [et al.] // Comptes Rendus Mécanique. - 2011. - Vol. 339, Iss. 5. - p. 310–317DOI 10.1016/j.crme.2011.03.007 . -
Аннотация: The IVIDIL (Influence of VIbrations on DIffusion in Liquids) experiment was aimed at utilizing the International Space Station for investigating the effects of vibrations on liquid diffusion and thermodiffusion. The SODI-IVIDIL project of ESA is gathering together European, Canadian and Russian researchers with complementary skills to prepare and carry out the experiment, to process the raw data and perform numerical modeling of the phenomena. The experiment IVIDIL started on the October 5, 2009. In total 55 experimental runs were successfully completed by 20 January, 2010. A general description of the ISS facility related to the diffusion experiments and accessible for European researchers is briefly presented and some details about IVIDIL instrument are given. The scientific interest of this short article is focused on one of the objectives of the experiment: performing precise measurements of diffusion and thermodiffusion coefficients for binary mixtures in the absence of gravity. We demonstrate possibility of the experimental environment and report on the first results related to measurements of mass transport coefficients in the mixture with the negative Soret effect: 10% isopropanol (IPA)–90% water.

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Доп.точки доступа:
Shevtsova, V.; Mialdun, A.; Melnikov, D.; Ryzhkov, I.I.; Рыжков, Илья Игоревич; Gaponenko, Y.; Гапоненко, Юрий Анатольевич; Saghir, Z.; Lyubimova, T.; Legros, J.C.

[Text] / Y. . Gaponenko, A. . Mialdun, V. . Shevtsova // Eur. Phys. J. E. - 2014. - Vol. 37, Is. 10. - Ст. 90, DOI 10.1140/epje/i2014-14090-5. - Cited References: 18. - This work is supported by the PRODEX programme of the Belgian Federal Science Policy Office and ESA. . - ISSN 1292-8941. - ISSN 1292-895XРУБ Chemistry, Physical + Materials Science, Multidisciplinary + Physics, Applied + Polymer Science

Аннотация: One of the targets of the experiment IVIDIL (Influence Vibrations on Diffusion in Liquids) conducted on-board ISS was to study the response of binary mixtures to vibrational forcing when the density gradient results from thermal and compositional variations. Compositional variations were created by the Soret effect and can strengthen or weaken the overall density gradient and, consequently, the response to vibrational forcing. We present the results of two experimental runs conducted on-board ISS in the frame of the experiment IVIDIL for low and strong vibrational forcing. The experimental observations revealed that a significant mean flow is set within 2 minutes after imposing vibrations and later in time it varies weakly and slowly due to the Soret effect. A mathematical model has been developed to compute the thermal and concentration fields in the experiment IVIDIL and verify the accuracy of picture processing based on the classical approach used in non-convective systems with the Soret effect. The effect of temperature and concentrations perturbations by joint action of vibrational convection and Soret effect on long time scale are carefully examined. The model demonstrates that image processing used for non-convective systems is suitable for the systems with vibration-affected thermodiffusion experiment.

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Держатели документа:
[Gaponenko, Y.
Mialdun, A.
Shevtsova, V.] Univ Libre Bruxelles, MRC, EP CP 165 62, B-1050 Brussels, Belgium
[Gaponenko, Y.] Inst Computat Modelling SB RAS, Krasnoyarsk 660036, Russia
ИВМ СО РАН

Доп.точки доступа:
Gaponenko, Y.; Гапоненко, Юрий Анатольевич; Mialdun, A.; Shevtsova, V.; PRODEX programme of the Belgian Federal Science Policy Office; ESA

[Text] : статья / I.I. Ryzhkov // Fluid Dynamics. - 2013. - Vol. 48, Iss. 4. - p. 477-490DOI 10.1134/S0015462813040078 . -
Аннотация: Long-wave instability that arises in a plane multicomponent mixture layer with the Soret effect is investigated. The layer is heated from above or below in the gravity field. The solution of the linearized equations of motion is sought in the form of a series in powers of the wave number assumed to be small. For the mixture with an arbitrary number of components the critical parameters of instability are determined. For binary and ternary mixtures the stability maps are plotted. The regions where the long- and short wave perturbations are the most dangerous are distinguished in the space of physical parameters. The analytical results are compared with the numerical solution of the linearized equations over a wide wave number range. As an example, instability in a ternary hydrocarbon mixture is considered.

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Доп.точки доступа:
Рыжков, Илья Игоревич

/ I. I. Ryzhkov, I. V. Stepanova // Int. J. Heat Mass Transf. - 2015. - Vol. 86. - P268-276, DOI 10.1016/j.ijheatmasstransfer.2015.02.069 . - ISSN 0017-9310
Аннотация: The stationary heat transfer and Soret separation of a binary mixture between parallel plates with different constant temperatures is studied allowing for variable transport properties. The mixture is described by non-linear one-dimensional equations of heat and mass transfer, where the density, thermal conductivity, and Soret coefficient depend on temperature and concentration. A general procedure for integrating these equations is proposed. The problem is reduced to the ordinary differential equation of first order, which describes the trajectory of the system in the concentrationerature plane, and implicit dependence of temperature on space coordinate. It is shown that the solution for concentration is unique if the density and thermal conductivity do not depend on concentration. Analytical solutions of the problem are derived in a number of cases, while the most general case is treated numerically. The non-linear temperature and concentration profiles in different binary mixtures (aqueous solutions, colloidal suspensions, polymer blend) are constructed and analyzed. A procedure for extracting the dependence of Soret coefficient on temperature and concentration from the experimentally measured thermal and compositional profiles is suggested. © 2015 Elsevier Ltd.All rights reserved.

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Держатели документа:
Institute of Computational Modelling SB RASAkademgorodok,Krasnoyarsk, Russian Federation
ИВМ СО РАН

Доп.точки доступа:
Stepanova, I.V.; Степанова, Ирина Владимировна; Рыжков, Илья Игоревич

/ I. I. Ryzhkov, S. P. Tsarev // Phys. Fluids. - 2015. - Vol. 27, Is. 7. - Ст. 072103, DOI 10.1063/1.4926891 . - ISSN 1070-6631
Аннотация: The linear stability of mechanical equilibrium in a two-layer system formed by different phases of the same binary mixture is investigated. The temperature difference is applied to the layers by heating and cooling the opposite rigid boundaries. In the state of mechanical equilibrium, the applied temperature gradient induces concentration gradients due to the Soret effect. The conservation of mass for the mixture components leads to the dependence of layer thicknesses on the applied temperature difference. In weightlessness, the main mechanisms of instability in the considered system are related to phase change and Marangoni effect. The calculations are performed for cyclohexane-methanol binary mixture, which has a liquid-liquid miscibility gap. The analytical solution of amplitude equations for monotonic perturbations is found and expression for the critical temperature difference is derived. It is shown that the phase change instability is long-wave and favoured when the difference between interfacial concentrations in the basic state decreases. When the Marangoni effect is taken into account, additional monotonic and oscillatory modes appear. They result from the interplay between thermocapillarity and phase change with latent heat release/absorption. The most unstable monotonic and oscillatory modes are identified depending on the heating regime and relative thickness of the layers. © 2015 AIP Publishing LLC.

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Держатели документа:
Institute of Computational Modelling SB RAS, Akademgorodok, Krasnoyarsk, Russian Federation
Institute of Space and Information Technologies, Siberian Federal University, 79 Svobodny pr., Krasnoyarsk, Russian Federation

Доп.точки доступа:
Tsarev, S.P.; Рыжков, Илья Игоревич

/ J. C. Legros [et al.] // Phys. Chem. Chem. Phys. - 2015. - Vol. 17, Is. 41. - P27713-27725, DOI 10.1039/c5cp04745e . - ISSN 1463-9076
Аннотация: We present a comprehensive experimental study of isothermal Fickian diffusion in the ternary and binary liquid mixtures of water, ethanol, and triethylene glycol over the entire ternary composition space. 21 ternary mixtures inside the composition triangle have been investigated by means of the Taylor dispersion technique and 30 binary mixtures by Taylor dispersion and/or optical beam deflection in a Soret cell. The scalar binary diffusion coefficient has been determined along all three binary boundaries of the composition space and compared with estimations based on the Stokes-Einstein relation using stick or slip boundary conditions. The four elements of the ternary diffusion matrix and the diffusion eigenvalues were determined over a large portion of the composition triangle. The pseudo-binary diffusion coefficients obtained in Taylor dispersion experiments with either one of the two independent concentrations kept constant are comparable to the two diffusion eigenvalues. One of the two off-diagonal elements of the diffusion matrix is of the same order as the diagonal ones and, hence, not negligible, whereas the other one is approximately one order of magnitude smaller. Where available, our results compare well with literature data. The investigated compositions also comprise the five compositions that are scheduled for microgravity experiments in the ESA DCMIX3 project. This journal is © the Owner Societies 2015.

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Держатели документа:
Microgravity Research Center, Universite Libre de Bruxelles (ULB), CP-165/62 Av. F.D. Roosevelt 50, B-1050 Brussels, Belgium
Institute of Computational Modelling SB RAS, Krasnoyarsk, Russian Federation
Physikalisches Institut, Universitat Bayreuth, Bayreuth, Germany
National Research Tomsk Polytechnic University, Russian Federation

Доп.точки доступа:
Legros, J. C.; Gaponenko, Y.; Гапоненко, Юрий Анатольевич; Mialdun, A.; Triller, T.; Hammon, A.; Bauer, C.; Kohler, W.; Shevtsova, V.

/ O. A. Khlybov, I. I. Ryzhkov, T. P. Lyubimova // Eur. Phys. J. E. - 2015. - Vol. 38, Is. 4, DOI 10.1140/epje/i2015-15029-0 . - ISSN 1292-8941
Аннотация: Abstract: The paper is devoted to processing the data of DCMIX 1 space experiment. In this experiment, the Optical digital interferometry was used to measure the diffusion and Soret coefficients in the ternary mixture of 1,2,3,4-tetrahydronaphthalene, isobutylbenzene and n-dodecane at mass fractions of 0.8/0.1/0.1 and at 25°C. The raw interferometric images were processed to obtain the temporal and spatial evolution of refractive indices for two laser beams of different wavelengths. The method for extracting the diffusion and thermal diffusion coefficients originally developed for optical beam deflection was extended to optical digital interferometry allowing for the spatial variation of refractive index along the diffusion path. The method was validated and applied to processing the data for Soret and diffusion steps in 5 experimental runs. The obtained results for the Soret coefficients and one of the eigenvalues of diffusion matrix showed acceptable agreement within each step. The second eigenvalue was not determined with sufficient accuracy. Graphical abstract: [Figure not available: see fulltext.]. © 2015, EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg.

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Держатели документа:
Institute of Continuous Media Mechanics, UB RAS, Koroleva St. 1Perm, Russian Federation
Institute of Computational Modelling, SB RASAkademgorodok, Krasnoyarsk, Russian Federation

Доп.точки доступа:
Ryzhkov, I.I.; Рыжков, Илья Игоревич; Lyubimova, T.P.

/ M. M. Bou-Ali [et al.] // Eur. Phys. J. E. - 2015. - Vol. 38, Is. 4, DOI 10.1140/epje/i2015-15030-7 . - ISSN 1292-8941
Аннотация: Abstract: With the aim of providing reliable benchmark values, we have measured the Soret, thermodiffusion and molecular diffusion coefficients for the ternary mixture formed by 1,2,3,4-tetrahydronaphthalene, isobutylbenzene and n-dodecane for a mass fraction of 0.8-0.1-0.1 and at a temperature of 25°C. The experimental techniques used by the six participating laboratories are Optical Digital Interferometry, Taylor Dispersion technique, Open Ended Capillary, Optical Beam Deflection, Thermogravitational technique and Sliding Symmetric Tubes technique in ground conditions and Selectable Optical Diagnostic Instrument (SODI) in microgravity conditions. The measurements obtained in the SODI installation have been analyzed independently by four laboratories. Benchmark values are proposed for the thermodiffusion and Soret coefficients and for the eigenvalues of the diffusion matrix in ground conditions, and for Soret coefficients in microgravity conditions. Graphical abstract: [Figure not available: see fulltext.]. © 2015, EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg.

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Держатели документа:
Mechanical and Industrial Manufacturing Department, MGEP Mondragon Goi Eskola Politeknikoa, Loramendi 4 Apdo 23Mondragon, Spain
Dept. of Mechanical and industrial Engineering, Ryerson UniversityToronto, Canada
MRC, EP CP 165/62, Universite libre de Bruxelles (ULB)Brussels, Belgium
Physikalisches Institut, Universitat BayreuthBayreuth, Germany
Institute of Continuous Media Mechanics UB RASPerm, Russian Federation
Institute of Computational Modelling SB RASKrasnoyarsk, Russian Federation

Доп.точки доступа:
Bou-Ali, M.M.; Ahadi, A.; Alonso de Mezquia, D.; Galand, Q.; Gebhardt, M.; Khlybov, O.; Kohler, W.; Larranaga, M.; Legros, J.C.; Lyubimova, T.; Mialdun, A.; Ryzhkov, I.I.; Рыжков, Илья Игоревич; Saghir, M.Z.; Shevtsova, V.; Van Vaerenbergh, S.

[Текст] : статья / В. К. Андреев // Некоторые актуальные проблемы современной математики и математического образования. Герценовские чтения - 2015 : материалы 68-ой научной конференции. - 2015. - Т. LXVIII. - С. 12-18 . - ISBN 978-5-8064-2095-5
   Перевод заглавия: On the existence conditions of a binary mixtures unidirectional flows

УДК

517.9

Аннотация: Рассматриваются уравнения однонаправленных стационарных течений бинарных смесей. Условия существования таких течений накладывают ограничения на уравнения состояния смеси и представления решений. В случае модели Обербека - Буссинеска анализ условий совместности проведён полностью. Построены новые точные решения, показывающие их существенное отличие от классических.
The unidirectional steady flows of a binary mixtures equations are considered. The study is focused on the conditions for the buoyancy force function admits above flows. For the Oberbeck -Boussinesq model the problem is complete solved. Some new exact solutions are found. Comparison with the classical well-known solutions are given.

РИНЦ

Держатели документа:
Институт вычислительного моделирования СО РАН

Доп.точки доступа:
Andreev V.K.; Некоторые актуальные проблемы современной математики и математического образования (2015 ; 13.04 - 17.04 ; Санкт-Петербург)

/ I. V. Stepanova // Comm. Nonlinear Sci. Numer. Simul. - 2015. - Vol. 20, Is. 3. - P684-691, DOI 10.1016/j.cnsns.2014.06.043 . - ISSN 1007-5704
Аннотация: Three-dimensional equations describing heat and mass transfer in fluid mixtures with variable transport coefficients are studied. Using Lie group theory the forms of unknown thermal diffusivity, diffusion and thermal diffusion coefficients are found. The symmetries of the governing equations are calculated. It is shown that cases of Lie symmetry extension arise when arbitrary elements have the power-law, logarithmic and exponential dependencies on temperature and concentration. An exact solution is constructed for the case of linear dependence of diffusion and thermodiffusion coefficients on temperature. The solution demonstrates differences in concentration distribution in comparison with the same distribution under constant transport coefficients in the governing equations. © 2014 Elsevier B.V.

Scopus

Держатели документа:
Institute of Computational Modeling SB RAS, 50/44, Krasnoyarsk, Akademgorodok, Russian Federation

Доп.точки доступа:
Stepanova, I. V.

[Text] / V. K. Andreev, I. V. Stepanova // Fluid Dyn. - 2016. - Vol. 51, Is. 2. - P136-147, DOI 10.1134/S0015462816020022. - Cited References:17. - The work was supported financially by the Russian Foundation for Basic Research (project No. 14-01-00067). . - ISSN 0015-4628. - ISSN 1573-8507РУБ Mechanics + Physics, Fluids & Plasmas

Аннотация: Existence conditions are investigated for the unidirectional flows of binary mixtures describable by the equations of motion in the Oberbeck-Boussinesq approximation with account for the thermodiffusion effect. Possible solutions are classified, known and novel classes of exact solutions being distinguished. For the solutions obtained different formulations of boundary-value problems are proposed. Flows between two rigid walls with given heat distribution laws are described.

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Держатели документа:
Russian Acad Sci, Siberian Branch, Inst Computat Modelling, Akademgorodok 50,Str 44, Krasnoyarsk 660036, Russia.
Siberian Fed Univ, Inst Math & Fundamental Informat, Pr Svobodnyi 79, Krasnoyarsk 660041, Russia.

Доп.точки доступа:
Andreev, V. K.; Stepanova, I. V.; Russian Foundation for Basic Research [14-01-00067]

/ S. V. Kozlova, I. I. Ryzhkov // Phys. Fluids. - 2016. - Vol. 28, Is. 11, DOI 10.1063/1.4966640 . - ISSN 1070-6631
Аннотация: This work studies the stationary separation of a multicomponent mixture in a thermogravitational column (TGC). The existing theory for a flat-plate column is extended to the case of a cylindrical column. The equations of motion and heat/mass transfer are written in cylindrical coordinates to take into account the impact of the cylinders curvature and the ratio of their radii on the separation process. To characterize the impact of each component on convective motion induced by thermal diffusion, the dimensionless separation ratios are used. A multicomponent system as a whole is described by the net separation ratio. The approximation neglecting vertical diffusion in the column is employed and conditions for its validity are analyzed. The profiles of velocity, temperature, composition, and density in the column with a multicomponent mixture are found and their dependence on the separation ratios and the ratio of cylinders radii is analyzed. The vertical separation is described by the solutal Rayleigh numbers, which are proportional to the vertical concentration gradients. It is shown that the key relation of TGC theory, which relates the net solutal Rayleigh number to the net separation ratio, essentially depends on the ratio of cylinders radii. The working formulas for the thermal diffusion coefficients are derived and the importance of forgotten effect is discussed. It is found that the vertical separation in the column increases with decreasing the ratio of inner and outer cylinders radii. A detailed comparison of results with the case of a flat-plate column is performed. Example of a ternary hydrocarbon mixture is analyzed on the basis of obtained solution and numerical simulation. © 2016 Author(s).

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Держатели документа:
Institute of Computational Modelling SB RAS, 50/44 Akademgorodok, Krasnoyarsk, Russian Federation
Siberian Federal University, 79 Svobodny pr., Krasnoyarsk, Russian Federation

Доп.точки доступа:
Ryzhkov, I.I.; Рыжков, Илья Игоревич; Козлова, Софья Владимировна