Influence of the liquid layer thickness on the stability of a plane-parallel flow in a two-phase system with evaporation
DOI:
https://doi.org/10.7242/1999-6691/2023.16.2.19Keywords:
evaporative convection, two-phase system, exact solution, stability, numerical solution of spectral problemAbstract
The widespread use of evaporating liquids and gas-vapor mixtures in different technologies and industrial processes causes keen interest in study of convection accompanied by phase transitions. Methods of mathematical modelling present an alternative to the pilot development of technological techniques and experimental investigations of convective heat and mass transfer. In this paper, the problem of evaporative convection in a two-phase liquid–gas system is considered within frame of the Oberbeck–Boussinesq approximation. A partially invariant exact solution of the governing equations is used for description of stationary advective flows occurring under diffusive-type evaporation. The solution allows one to correctly take into account the impact of external thermal load and thermodiffusion effects in the gas-vapor layer. The influence of the liquid layer height on the kinematic and temperature characteristics of arising regimes, as well as on the parameters of phase transitions and vapor content in the carrier gas, is investigated on the basis of the exact solution. The increase of the fluid layer thickness leads to an alteration in the flow regime from the pure thermocapillary flow to the mixed or Poiseuille type flows and to qualitative changes in mass transfer processes at the thermocapillary interface. The linear stability of the exact solution with respect to both plane and spatial normal wave perturbations is investigated by means of the normal mode method. The threshold stability characteristics are obtained, and the evolution of neutral curve topology and instability forms in response to changes in the system geometry is demonstrated. The growth of the liquid layer thickness has destabilizing influence; the oscillatory instability is always realized in this case in the system. The dependencies of the phase velocities of disturbances are presented for the systems of different geometry. The instability forms in the evaporating liquid layer driven by a co-current gas flux, predicted on the basis of the exact solution, coincide with those observed in thermophysical experiments.
Downloads
References
Kabov O.A., Kuznetsov V.V., Kabova Yu.O. Evaporation, dynamics and interface deformations in thin liquid films sheared by gas in a microchannel. Encyclopedia of two-phase heat transfer and flow II: Special topics and applications, ed. J.R. Thome, J. Kim. Singapore, World Scientific Publishing Company, 2015. Pp. 57-108
Worner M. Numerical modeling of multiphase flow in microfluidics and micro process engineering: A review of methods and applications. Microfluid. Nanofluid., 2012, vol. 12, pp. 841-886. https://doi.org/10.1007/s10404-012-0940-8
Sharma A. Level set method for computational multi-fluid dynamics: A review on developments, applications and analysis. Sadhana, 2015, vol. 40, pp. 627-652. https://doi.org/10.1007/s12046-014-0329-3
Eisenschmidt K., Ertl M., Gomaa H., Kieffer-Roth C., Meister C., Rauschenberger P., Reitzle M., Schlottke K., Weigand B. Direct numerical simulations for multiphase flows: An overview of the multiphase code FS3D. Appl. Math. Comput., 2016, vol. 272, pp. 508-517. https://doi.org/10.1016/j.amc.2015.05.095
Qin T. Buoyancy-thermocapillary convection of volatile fluids in confined and sealed geometries. Springer Cham, 2017. 227 p. https://doi.org/10.1007/978-3-319-61331-4
Kupershtokh A.L., Medvedev D.A., Gribanov I.I. Thermal lattice Boltzmann method for multiphase flows. Phys. Rev. E, 2018, vol. 98, 023308. https://doi.org/10.1103/PhysRevE.98.023308
Bekezhanova V.B., Goncharova O.N. Problems of the evaporative convection (review). Fluid Dyn., 2018, vol. 53, pp. S69 S102. http://dx.doi.org/10.1134/S001546281804016X
Shliomis M.I., Yakushin, V.I. Konvektsiya v dvukhsloynoy binarnoy sisteme s ispareniyem [Convection in a two-layers binary system with an evaporation]. Uch. zap. Perm. gos. un-ta. Ser. Gidrodinamika [Proceedings of Perm State University. Hydrodynamics], 1972, vol. 4, pp. 129-140.
Bekezhanova V.B., Goncharova O.N. Stability of the exact solutions describing the two-layer flows with evaporation at interface. Fluid Dyn. Res., 2016, vol. 48, 061408. https://doi.org/10.1088/0169-5983/48/6/061408
Goncharova O.N., Kabov O.A. Investigation of the two-layer fluid flows with evaporation at interface on the basis of the exact solutions of the 3D problems of convection. J. Phys.: Conf. Ser., 2016, vol. 754, 032008. https://doi.org/10.1088/1742-6596/754/3/032008
Grigoriev R.O., Qin T. The effect of phase change on stability of convective flow in a layer of volatile liquid driven by a horizontal temperature gradient. J. Fluid Mech., 2018, vol. 838, pp. 248-283. https://doi.org/10.1017/jfm.2017.918
Bekezhanova V.B., Goncharova O.N., Rezanova E.V., Shefer I.A. Stability of two-layer fluid flows with evaporation at the interface. Fluid Dyn., 2017, vol. 52, pp. 189-200. https://doi.org/10.1134/S001546281702003X
Bekezhanova V.B., Shefer I.A. Influence of gravity on the stability of evaporative convection regimes. Microgravity Sci. Technol., 2018, vol. 30, pp. 543-560. https://doi.org/10.1007/s12217-018-9628-3
Shefer I.A. Influence of the transverse temperature drop on the stability of two-layer fluid flows with evaporation. Fluid Dyn., 2019, vol. 54, pp. 603-613. https://doi.org/10.1134/S0015462819040098
Lyulin Yu.V., Kabov O.A. Measurement of the evaporation mass flow rate in a horizontal liquid layer partly opened into flowing gas. Tech. Phys. Lett., 2013, vol. 39, pp. 795-797. https://doi.org/10.1134/S1063785013090095
Lyulin Y., Kabov O. Evaporative convection in a horizontal liquid layer under shear-stress gas flow. Int. J. Heat Mass Tran., 2014, vol. 70, pp. 599-609. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2013.11.039
Bekezhanova V.B., Goncharova O.N. Influence of the Dufour and Soret effects on the characteristics of evaporating liquid flows. Int. J. Heat Mass Tran., 2020, vol. 154, 119696. https://doi.org/10.1016/j.ijheatmasstransfer.2020.119696
Godunov S.K. O chislennom reshenii krayevykh zadach dlya sistem lineynykh obyknovennykh differentsial’nykh uravneniy. UMN – Russ. Math. Surv., 1961, vol. 16, no. 3(99), pp. 171-174.
Peng C.-C., Cerretani С., Braun R.J., Radke C.J. Evaporation-driven instability of the precorneal tear film. Adv. Colloid Interface Sci., 2014, vol. 206, pp. 250-264. https://doi.org/10.1016/j.cis.2013.06.001
Tiwari N., Davis J.M. Linear stability of a volatile liquid film flowing over a locally heated surface. Phys. Fluids, 2009, vol. 21, 022105. https://doi.org/10.1063/1.3068757
Chernous’ko Yu.L., Shumilov А.V. Ispareniye i mikrokonventsiya v tonkom poverkhnostnom sloye [Evaporation and microconvection in thin superfacial layer]. Okeanologiya – Oceanology, 1971, vol. 11, no. 6, pp. 982-986.
Kabov O.A., Zaitsev D.V., Cheverda V.V., Bar-Cohen A. Evaporation and flow dynamics of thin, shear-driven liquid films in microgap channels. Exp. Therm. Fluid Sci., 2011, vol. 35, pp. 825-831. https://doi.org/10.1016/j.expthermflusci.2010.08.001
Downloads
Published
Issue
Section
License
Copyright (c) 2023 Computational Continuum Mechanics
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.