Mathematical modelling of particle settling and concentration stratification in a two-phase dispersed mixture flow
Article Sidebar
Main Article Content
Abstract
This work develops a complete three-dimensional mathematical model for the gravitational settling of a two-phase dispersed mixture and the vertical stratification of concentration in a water reservoir, formulated within the framework of Kh.A. Rakhmatulin’s theory of interpenetrating and interacting multiphase media. The system of mass and momentum conservation equations is written in Reynolds-averaged form and supplemented with the Boussinesq closure for turbulent diffusion and effective viscosity, together with the Stokes-Richardson-Zaki hindered settling law. The closure of the system is demonstrated by matching the eight unknown scalar functions with eight governing equations; physically grounded conditions are imposed on all six faces of the computational domain as well as at the initial time. Numerical computations carried out using a four-stage algorithm based on operator splitting and a finite-difference scheme on a staggered grid reproduce both qualitatively and quantitatively the time evolution of the concentration field, the formation of the clear-water/turbid interface, and the accumulation of the sediment layer.
Article Details
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
Rakhmatulin Kh.A. Fundamentals of the gasdynamics of interpenetrating motions of compressible media // Journal of Applied Mathematics and Mechanics. – 1956. – Vol. 20, No. 2. – P. 184–195. [in Russian]
De Vita F., De Lillo F., Bosia F., Onorato M. A generalized multiphase modelling approach for multiscale flows // Journal of Computational Physics. – 2021. – Vol. 436. – Art. 110321. – DOI: 10.1016/j.jcp.2021.110321.
Richardson J.F., Zaki W.N. Sedimentation and fluidisation. Part I // Transactions of the Institution of Chemical Engineers. – 1954. – Vol. 32. – P. 35–53.
Brzinski T.A. III, Durian D.J. The hindered settling function at low Re has two branches // arXiv:1710.09314 [cond-mat.soft]. – 2018.
Batchelor G.K. Sedimentation in a dilute polydisperse system of interacting spheres. Part 1. General theory // Journal of Fluid Mechanics. – 1982. – Vol. 119. – P. 379–408.
Vowinckel B., Withers J., Luzzatto-Fegiz P., Meiburg E. Settling of cohesive sediment: particle-resolved simulations // Journal of Fluid Mechanics. – 2019. – Vol. 858. – P. 5–44.
Chen L., Heitkam S., Eckert K., Fröhlich J. Hindered settling in polydisperse suspensions: experimental and numerical study // International Journal of Multiphase Flow. – 2023. – Vol. 162. – Art. 104408.
Ariff S., Climent E., Pedrono A. Hindered settling of log-normally distributed particulate suspensions: theoretical models vs. Stokesian simulations // arXiv:2404.17392 [physics.flu-dyn]. – 2024.
Kynch G.J. A theory of sedimentation // Transactions of the Faraday Society. – 1952. – Vol. 48. – P. 166–176.
Bürger R., Diehl S., Farås S., Nopens I., Torfs E. A consistent modelling methodology for secondary settling tanks: a reliable numerical method // Water Science and Technology. – 2013. – Vol. 68, No. 1. – P. 192–208.
Miles J.W. On the stability of heterogeneous shear flows // Journal of Fluid Mechanics. – 1961. – Vol. 10. – P. 496–508.
Petropoulos N., de Bruyn Kops S.M., Caulfield C.P. Modelling dispersion in stratified turbulent flows as a resetting process // Journal of Fluid Mechanics. – 2025. – Vol. 1002. – Art. A48. – DOI: 10.1017/jfm.2024.1194.
Akhmadi B., Akhmedov D. Sedimentation of reservoirs in Uzbekistan: a case study of the Akdarya reservoir, Zerafshan River basin // Lakes & Reservoirs: Research and Management. – 2011. – Vol. 16, No. 4. – P. 295–310.
Tursunov A., Bazarov D.R., Vatin N.I. Field studies of the bottom sediments movement in the Tuyamuyun hydraulic engineering complex lower reaches of the Amu Darya river // Global Journal of Researches in Engineering. – 2020. – Vol. 20, No. 1. – P. 1–8.
Mouris K., Schwindt S., Haun S., Wieprecht S. An interdisciplinary model chain quantifies the footprint of global change on reservoir sedimentation // Scientific Reports. – 2023. – Vol. 13. – Art. 20160. – DOI: 10.1038/s41598-023-47501-1.