The Occurrence of the Phenomenon of Elastic Return During Unsteady Flow of a Rheologically Complex Fluid in a Flat Channel within the Oldroyd-B Model
DOI:
https://doi.org/10.71310/pcam.1_71.2026.02Keywords:
pressure gradient, Laplace transform, unsteady flow, hydrodynamic effects, rheologically complex fluidAbstract
This article examines unsteady flows of rheologically complex fluids in a flat channel using the Oldroyd-B model after the actuator is switched off. It is assumed that until the actuator is switched off, the fluid flow is steady under a constant pressure gradient. From a given point in time, the pressure gradient in the system is assumed to be zero. The problem is solved analytically using the Laplace transform. Based on the solutions obtained, the corresponding hydrodynamic regularities are determined, which are important for technical and technological processes.
References
Shul'man Z.P., Khusid B.M. Nestatsionarnyye protsessy konvektivnogo perenosa v nasledstvennykh sredakh. – Minsk, 1983. – 256 s.
Navruzov K., KhakberdiyevZH.B. Dinamika nen'yutonovskikh zhidkostey. – Tashkent: Fan, 2000. – 246 s.
Navruzov K. Biomekhanika krupnykh krovenosnykh sosudov. – Tashkent: Fan va texnologiya, 2011. – 144 s.
Passoni S., Carraretto I.M., Mereu R., Colombo L.P.M. Two-phase stratified flow in horizontal pipes: A CFD study to improve prediction of pressure gradient and void fraction // Chemical Engineering Research and Design. – 2023. – Vol. 189. – P. 38-49.
Wu M., et al. Advances in the modeling of multiphase flows and their application in nuclear engineering: A review // Experimental and Computational Multiphase Flow. – 2024. – Vol. 6, №4. – P. 287-352.
Pozorski J., Olejnik M. Smoothed particle hydrodynamics modelling of multiphase flows: An overview // Acta Mechanica. – 2024. – Vol. 235. – P. 1685-1714. – doi: http://dx.doi.org/10.1007/s00707-023-03763-4.
Senapati A., Dewangan S.K. Comparison of performance of different multiphase models in predicting stratified flow // Computational Thermal Sciences. – 2017. – Vol. 9, №6. – P. 529-539.
Taitel Y., Dukler A.E. A model for predicting flow regime transitions in horizontal and near-horizontal gas-liquid flow // AIChE Journal. – 1976. – Vol. 22, №1. – P. 47-55. – doi: http://dx.doi.org/10.1002/aic.690220105.
Hirt C., Nichols B. Volume of fluid (VOF) method for the dynamics of free boundaries // Journal of Computational Physics. – 1981. – Vol. 39. – P. 201-225. – doi: http://dx.doi.org/10.1016/0021-9991(81)90145-5.
Lakehal L. Advances in turbulence modelling for multiphase flows // International Journal of Multiphase Flow. – 2012. – Vol. 38. – P. 1-16.
Issa R. Solution of the implicitly discretised fluid flow equations by operator splitting // Journal of Computational Physics. – 1986. – Vol. 62. – P. 40-65.
Elghobashi S. On predicting particle-laden turbulent flows // Applied Scientific Research. – 1994. – Vol. 52. – P. 309-329.
Borzenko Ye.I., Yakutenok V.A. Evolyutsiya svobodnoy poverkhnosti pri zapolnenii ploskikh kanalov vyazkoy zhidkost'yu // Izvestiya RAN. Mekhanika zhidkosti i gaza. – 2008. – №1. – S. 24-30.
Astarita Dzh., Marruchchi Dzh. Osnovy gidromekhaniki nen'yutonovskikh zhidkostey. – M.: Mir, 1978. – 309 s.
Akilov ZH.A. Nestatsionarnyye dvizheniya vyazkouprugikh zhidkostey. – Tashkent: Fan, 1982. – 104 s.
Popov D.N. Nestatsionarnyye gidromekhanicheskiye protsessy. – M.: Mashinostroyeniye, 1982. – 424 s.
Nosova L.I. Tablitsy funktsiy Tomsona i ikh pervykh proizvodnykh. – M.: Izd-vo AN SSSR, 1960. – 423 s.
Kuznetsov D.S. Spetsial'nyye funktsii. – M.: Vysshaya shkola, 1965. – 423 s.
Navruzov K., Turaev M., Shukurov Z. Pulsating flows of viscous fluid in channel for given harmonic fluctuation of flow rate // E3S Web of Conferences. – 2023. – Vol. 401. – Art. no. 02010.
Navruzov K., Rajabov S., Ashirov M. Mathematical modeling of hydrodynamic resistance in an oscillatory flow of a viscoelastic fluid // E3S Web of Conferences. – 2023. – Vol. 401. – Art. no. 02026. – doi: http://dx.doi.org/10.1051/e3sconf/202340102026.
Yakhshibayev D.S., Khudaykulov S.I., Usmanov A.Kh. A mathematical model of the diffusion process of sewage and channel waters mixing // 2019 International Conference on Information Science and Communications Technologies (ICISCT). – 2019. – P. 1-5. – doi: http://dx.doi.org/10.1109/ICISCT47635.2019.9011948.
Djumanov J.Kh., Karimov A.B., Yaxshibayev D.S. Monitoring va gidrogeologik tizimlarni matematik modellashtirish // TATU Xabarlari. – 2021. – №4(60). – B. 77-88.
Yakhshibayev D.S. Modelirovaniye konvektivnoy ustoychivosti stratifikatsionnykh techeniy, primenyayemykh v atomnykh stantsiyakh // Potomki Mukhammeda al'-Khorezmi. – 2023. – №3(25). – S. 190-194.
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