Mathematical Modeling of Three-Layer Flows in a Horizontal Channel with Consideration of Inhomogeneous Evaporation
УДК 536.25:519.688
Abstract
The paper studies a three-layer flow in a horizontal channel under the action of gravitational and thermocapillary forces, as well as a thermal load on solid impermeable channel walls. The lower and middle layers in the channel are filled with liquids, and a mixture of gas and vapors of a light liquid moves above them. A mass transfer, which depends linearly on the longitudinal coordinate, is considered at the liquid — gas interface. Also, heat transfer is modeled at the liquid — liquid and liquid-gas interfaces. The effects of thermal diffusion and diffusion heat conduction in the upper layer of the system are considered. Flows in liquid layers are simulated using the Boussinesq approximation of the Navier-Stokes equations, which are supplemented by the diffusion equation for the upper layer. Exact solutions of a special form describe the flows in each layer of the system. Codependences of unknown parameters of the problem are identified using boundary conditions. The influence of the system geometry on the flow structure and the mass transfer intensity at the liquid — gas interface is investigated. The paper demonstrates the obtained profiles of the longitudinal velocity, temperature distributions, and graphs of the mass evaporation rate for different values of thickness of the upper and lower layers of the system.
Downloads
Metrics
References
Lyulin Yu.V, Feoktistov D.V, Afanasyev I.A., Chachilo E.S., Kabov O.A., Kuznetsov G.V Measurement of the Evaporation Rate from the Local Surface of the Liquid Layer under the Action of a Gas Flow // Pis'ma v ZHTF. 2015. Vol. 41. No 14. P. 1-7. (In Russ.). DOI: 10.1134/S1063785015070251
Bekezhanova V.B., Goncharova O.N, Ivanova N.A., Klyuev D.S. Instability of a Two-layer System with Deformable Interface under Laser Beam Heating // Journal of Siberian Federal University. Mathematics and Physics. 2019. Vol. 12. No 5. P. 543-550. DOI: 10.17516/1997-1397-2019-12-5-543-550
Shliomis M.I., Yakushin VI. Convection in a Two-layer Binary System with Evaporation // Uchenyye Zapiski Perm-skogo Gosuniversiteta, Seriya Gidrodinamika. 1972. No 4. P. 129-140. (In Russ.).
Bekezhanova V.B., Goncharova O.N. and Shefer I.A. Analysis of an Exact Solution of Problem of the Evaporative Convection (Review). Part I. Plane cases // Journal of Siberian Federal University. Mathematics and Physics. 2018. Vol. 11. No 2. P. 178-190. DOI: 10.17516/1997-1397-2018-11-2-178-190
Goncharova O., Rezanova E., Lyulin Yu., Kabov O. Analysis of a Convective Fluid Flow with a Concurrent Gas Flow with Allowance for Evaporation // High Temperature. 2017. Vol. 55. No 6. P 887-897. DOI: 10.1134/S0018151X17060074
Andreev V.K., Gaponenko Yu.A., Goncharova O.N., Pukhnachev V.V. Mathematical Models of Convection. Berlin ; Boston: De Gruyter, 2012. 432 p. DOI: 10.1515/9783110258592
Остроумов Г.А. Свободная конвекция в условиях внутренней задачи. М.: Гос. изд-во технико-теоретической литературы, 1952. 256 с.
Бирих РВ. О термокапиллярной конвекции в горизонтальном слое жидкости // ПМТФ. 1966. № 3. С. 69-72.
Antonov G.N. Sur la Tension Superficielle '{a} la Limite de Deux Couches // Journal de Chimie Physique. 1907. Vol. 5. P. 372-385. DOI: 10.1051/jcp/1907050372
Rezanova E.V. Construction of Exact Solution Describing Three-layer Flows with Evaporation in a Horizontal Channel // Journal of Siberian Federal University. Mathematics and Physics. 2021. Vol. 14. No 1. P 57-68. DOI: 10.17516/19971397-2021-14-1-57-68
Ghezzehei T.A., Trautz R.C., Finsterle S. et al. Modeling Coupled Evaporation and Seepage in Ventilated Cavities // Vadose Zone J. 2004. Vol. 3. P. 806-818. DOI: 10.2113/3.3.806
Ласковец Е.В. Изучение влияния геометрических параметров системы на характер трехслойных течений в горизонтальном канале // Известия Алтайского государственного университета. 2023. Вып. 129. № 1. С. 124-129. DOI: 10.14258/izvasu(2023)1-20
Кипер Р.А. Физико-химические свойства веществ. Хабаровск, 2013. 1016 с.
Гороновский И.Т., Назаренко Ю.П., Некряч Е.Ф. Краткий справочник по химии. Киев: Наукова думка, 1987. 833 с.
Lyulin Y.V, Kabov O.A. Evaporative Convection in a Horizontal Liquid Layer under Shearstress // International Journal Heat and Mass Transfer. 2014. Vol. 70. P. 599-609. DOI: 10.1016/j.ijheatmasstransfer.2013.11.039
Copyright (c) 2024 Екатерина Валерьевна Ласковец
This work is licensed under a Creative Commons Attribution 4.0 International License.
Izvestiya of Altai State University is a golden publisher, as we allow self-archiving, but most importantly we are fully transparent about your rights.
Authors may present and discuss their findings ahead of publication: at biological or scientific conferences, on preprint servers, in public databases, and in blogs, wikis, tweets, and other informal communication channels.
Izvestiya of Altai State University allows authors to deposit manuscripts (currently under review or those for intended submission to Izvestiya of Altai State University) in non-commercial, pre-print servers such as ArXiv.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License (CC BY 4.0) that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
