Simulation of concentration convection at different pressures and compositions of a three-component gas mixture

Abstract

This article discusses the mathematical and computer modeling of the influence of pressure and composition of a three-component gas mixture on concentration convection based on the solution of the Navier-Stokes equations system, the continuity equation and equations for the concentration of the mixture components. The process is investigated when heavy gas and light gas are in the upper part of the parallelepiped, and gas with intermediate density in the lower part. Numerical calculations were carried out for the systems 0.55Ar+0.45He-N2, 0.66Ar+0.34He-N2, 0.55CO2+0.45He-N2 on a uniform rectangular grid. The dynamics of changes in the concentrations of argon and carbon dioxide for these systems at various pressures were presented in the form of figures. The results of the numerical study were obtained using a 3D numerical algorithm implemented on the basis of the D3Q27 model Lattice Boltzmann equations method with Batnagar-Gross-Crook (BGK) approximation. The performed calculations show that complex mass transfer is possible, associated with the occurrence of convective disturbances in three-component gas mixtures at certain pressures and compositions. To test the numerical algorithm, the results obtained in this article were compared with the results obtained experimentally and showed good agreement.

References

[1] Miller L., Spurling Т.Н., Mason E.A., "Instabilities in ternary diffusion", Phys. Fluids, 10:8(1967), 1809-1811.
[2] Zhavrin Y.I., Kossov N.D., Belov S.M., Semidotskaya N.I., "O primenenii metoda effektivnykh koeffitsiyentov k opisaniyu diffuzii v mnogokomponentnykh gazovykh smesyakh pri povyshennykh davleniyakh [On the application of the effective coefficient method to the description of diffusion in multicomponent gas mixtures at elevated pressures]", Teplomassoperenos v zhidkostyakh i gazakh: sb. nauch. tr. (1982), 3-12 [in Russian].
[3] Belov S.M., Zhavrin YU.I., Kosov N.D., Diffuzionnaya neustoychivost’ gazovoy smesi geliy-argon-azot pri razlichnykh davleniyakh i kontsentratsiyakh [Diffusion instability of a helium-argon-nitrogen gas mixture at various pressures and concentrations](Dep. in KazNIINTI 10/14/85. - №1073. Alma-Ata: KazGU, 1985), 13 [in Russian].
[4] Zhavrin YU.I., Kosov V.N., "Vliyaniye dliny kanala na ustoychivost’ diffuzionnogo protsessa v mnogokomponentnykh gazovykh smesyakh. [Influence of the channel length on the stability of the diffusion process in multicomponent gas mixtures]", Vest. AN KazSSR 10 (1991), 63-65 [in Russian].
[5] Kosov V.N., Kul’zhanov D.U., Zhavrin YU.I., Krasikov S.A., Fedorenko O.V., Osobennosti razdeleniya uglevodorodnykh gazovykh smesey pri konvektivnoy diffuzii [Features of the separation of hydrocarbon gas mixtures during convective diffusion] (Almaty: MV-Print, 2014), 144 [in Russian].
[6] Asembaeva M.K., Kosov V.N., Krasikov S.A., Fedorenko O.V., "Effect of the Channel Inclination Angle on Convective Mixing Caused by Instability of Mechanical Equilibrium of Ternary Gas Mixture at Isothermal Diffusion", Technical Physics Letters 45:11 (2019), 1071–1074.
[7] Kassem Ghorayeb, Abdelkader Mojtabi, "Double diffusive convection in a vertical rectangular cavity", Phys. Fluids 9:8(1997), 2339 - 2348.
[8] Qinlong Ren, Cho Lik Chan, "Numerical study of double-diffusive convection in a vertical cavity with Soret and Dufour effects by lattice Boltzmann method on GPU", International Journal of Heat and Mass Transfer 93(2016), 538–553.
[9] Pascale Garaud, "Double-Diffusive Convection at Low Prandtl Number", Annu. Rev. Fluid Mech. 50(2018), 275-298.
[10] Hongtao Xu, Zhuqing Luo, Qin Lou, Shuanyang Zhang, Jun Wang, "Lattice Boltzmann simulations of the double-diffusive natural convection and oscillation characteristics in an enclosure with Soret and Dufour effects", International Journal of Thermal Sciences. 136(2019), 159-171.
[11] Kosov V.N., Zhakebayev D.B., Fedorenko O.V., "Chislennyy analiz konvektivnykh dvizheniy, voznikayushchikh pri izotermicheskoy diffuzii v vertikal’nykh kanalakh v trekhkomponentnykh gazovykh smesyakh. [Numerical analysis of convective motions arising from isothermal diffusion in vertical channels in three-component gas mixtures]", News of the National Academy of Sciences of the Republic of Kazakhstan - physico-mathematical series 5(2017), 134-142 [in Russian].
[12] Kosov V.N., Fedorenko O.V., Zhakebayev D.B., Kizbayev A.P., "Osobennosti vozniknoveniya strukturirovannykh formirovaniy na granitse smeny rezhimov «diffuziya – kontsentratsionnaya konvektsiya» pri izotermicheskom smeshenii binarnoy smesi v ravnoy stepeni razbavlennoy tret’im komponentom [Features of the emergence of structured formations at the boundary of the change of the "diffusion - concentration convection" modes during isothermal mixing of a binary mixture equally diluted with the third component]", Teplofizika i aeromekhanika (2019), 31-40 [in Russian].
[13] T. Kru¨ger, H. Kusumaatmaja, A. Kuzmin, O. Shardt, G. Silva, E.M. Viggen, The Lattice Boltzmann Method (Switzerland: Springer International Publishing, 2017), 293.
[14] Bird B.R., Stewart W.E., Lightfoot E.V., Transport phenomenon (New York: John Wiley and Sons, Inc., 2002), 914.
[15] Guo Z., Zheng C., Shi B., "Discrete lattice effects on the forcing term in the lattice Boltzmann method", Phys. Rev. E. 65(2002), 1-6.
[16] Seta T., "Implicit temperature-correction-based immersed-boundary thermal lattice Boltzmann method for the simulation of natural convection", Phys. Rev. E. 87(2013).
How to Cite
ZHUMALI, A. S. et al. Simulation of concentration convection at different pressures and compositions of a three-component gas mixture. Journal of Mathematics, Mechanics and Computer Science, [S.l.], v. 108, n. 4, p. 108-119, dec. 2020. ISSN 2617-4871. Available at: <https://bm.kaznu.kz/index.php/kaznu/article/view/825>. Date accessed: 20 jan. 2021. doi: https://doi.org/10.26577/JMMCS.2020.v108.i4.09.
Keywords diffusion, concentration convection, pressure, instability, Lattice Boltzmann method