Numerical modeling of non-newtonian fluid flows in an apparatus with blade mixers
A numerical simulation of the non-Newtonian fluid flow in a paddle-type mixer is performed in a two-dimensional approximation. The rheological behavior of the medium is described using the Shvedov-Bingham model. The numerical solution is based on the finite volume method and the SIMPLE correction procedure implemented on an orthogonal grid. The singularity of the rheological law associated with the infinite viscosity in the regions with zero strain rates is eliminated using Papanastasiou regularization. The flow kinematics in mixers with one, two, and four blades is demonstrated, characterized by the formation of unyielded regions and stagnant zones near the mixer boundaries and the vessel walls. In addition, the problem of marker-particle redistribution over time is solved, allowing for a qualitative assessment of the mixing dynamics. The characteristic mixing modes of the markers are determined. The mixing process is quantitatively analyzed using the power number and a unique heterogeneity characteristics. Parametric studies of the flow are performed with respect to the main dimensionless parameters of the problem.
Keywords
mixing,
Shvedov-Bingham model,
non-Newtonian fluids,
mixing quality analysisAuthors
| Borzenko Evgeniy I. | Tomsk State University | borzenko@ftf.tsu.ru |
| Garbuzov Dmitriy N. | Tomsk State University | dmitrij.garbuzov.98@mail.ru |
| Efremov. Maksim A. | Tomsk State University | 33murman@gmail.com |
Всего: 3
References
Барабаш В.М., Абиев Р.Ш., Кулов Н.Н. Обзор работ по теории и практике перемешивания // Теоретические основы химической технологии. 2018. V. 52 (4). P. 367-383. doi: 10.1134/ S0040357118040024.
Balmforth N.J., Frigaard I.A., Ovarlez G. Yielding to Stress: Recent Developments in Viscoplastic Fluid Mechanics // Annu. Rev. Fluid Mech. 2014. V. 46 (1). P. 121-146. doi: 10.1146/annurev-fluid-010313-141424.
Russell A.W., Patrick M.P., Paul F.L., Konstantin S.P., Christos N.M. An experimental study of the mixing characteristics of viscoplastic fluids in dual-impeller agitation systems // Chem. Eng. Res. Des. 2025. V. 216. P. 216-229. doi: 10.1016/j.cherd.2025.02.032.
Curran S.J., Hayes R.E., Afacan A., Williams M.C., Tanguy P.A. Experimental Mixing Study of a Yield Stress Fluid in a Laminar Stirred Tank // Ind. Eng. Chem. Res. 2000. V. 39 (1). P. 195202. doi: 10.1021/IE990468E.
Pakzad L., Ein-Mozaffari F., Upreti S.R., Lohi A. Experimental and numerical studies on mixing of yield-pseudoplastic fluids with a coaxial mixer // Chem. Eng.Commun. 2013. V. 200 (12). P. 1553-1577. doi: 10.1080/00986445.2012.751380.
Bercovier M., Engelman M. A finite-element method for incompressible non-Newtonian flows // J.Comput. Phys. 1980. V. 36 (3). P. 313-326. doi: 10.1016/0021-9991(80)90163-1.
Papanastasiou T.C. Flows of Materials with Yield // J. Rheol. (N. Y. N. Y). The Society of Rheology. 1987. V. 31 (5). P. 385-404. doi: 10.1122/1.549926.
Benmoussa A., Pascoa J.C. A Chamfered Anchor Impeller Design for Enhanced Efficiency in Agitating Viscoplastic Fluids // Fluids. 2024. V. 9 (12). Art. 288. doi: 10.3390/fluids9120288.
Kada B., Lakhdar R., Brahim M., Ameur H. Agitation of Complex Fluids in Cylindrical Vessels by Newly Designed Anchor Impellers // Period. Polytech. Mech. Eng. 2022. V. 66 (2). P. 109119. doi: 10.3311/PPme.18438.
Alraddadi I., Yang D., Katbar N.M., Benhanifia K., Rahmani L., Mebarki B., Ameur H. Effect of curved anchor impellers on power consumption and hydrodynamic parameters of yield stress fluids (Bingham-Papanastasiou model) in stirred tanks // Rev. Adv. Mater. Sci. 2023. V. 62. Art. 20230156. P. 1-18. doi: 10.1515/rams-2023-0156.
Mokhefi A. Hydrodynamic and thermal performance analysis of an inclined anchor impeller designed for yield stress food mixing applications // Food Bioprod. Process. 2024. V. 143. P. 255-270. doi: 10.1016/j.fbp.2023.12.006.
Komoda Y., Date T. Enhancement of laminar mixing by an anchor impeller with rotationally reciprocating motion // AIP Adv. 2022. V. 12 (1). doi: 10.1063/5.0075750.
Benhanifia K., Redouane F., Lakhdar R., Brahim M., Al-Farhanu K., Jamshed W., Eid M.R., El Din S.M., Raizah Z. Investigation of mixing viscoplastic fluid with a modified anchor impeller inside a cylindrical stirred vessel using Casson-Papanastasiou model // Sci. Rep. 2022. V. 12 (1). Art. 17534. doi: 10.1038/s41598-022-22415-6.
Брагинский Л.Н., Бегачев В.И., Барабаш В.М. Перемешивание в жидких средах: физические основы и инженерные методы расчета. Л.: Химия, 1984. 336 p.
Патанкар С.В. Численные методы решения задач теплообмена и механики жидкости. М.: Энергоиздат, 1988. 526 p.
Борзенко Е.И., Гарбузов Д.Н. Течение ньютоновской жидкости в смесителях различных конфигураций // Comput. Contin. Mech. 2025. V. 17 (4). P. 486-495. doi: 10.7242/1999-6691/2024.17.4.39.
Brown D.A.R., Jones P.N., Middleton J.C. Experimental Methods // Handbook of Industrial Mixing. New Jersy: Wiley, 2003. P. 145-256.
