Abstract
In this paper, we study the exact stationary solution of the Oberbeck–Boussinesq equations describing the joint flow of a viscous heat-conducting liquid and the cocurrent flow of a gas-vapor mixture in a flat horizontal layer. The initial formulation of the problem takes into account mass transfer through the interphase interface due to evaporation, vapor diffusion in the gas phase in the presence of diffusion heat conduction, and a longitudinal temperature gradient at the solid impermeable boundaries of the channel. The effect of the layer thickness of working media on the characteristics of the main flow under conditions of equal thermal load on the channel walls was studied. Based on the linear theory, the stability of the exact solution is studied, typical forms of perturbations and their dynamics are determined with a change in the linear dimensions of a system, and neutral curves and maps of the instability regimes are plotted.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Lyulin, Y. and Kabov, O., Evaporative convection in a horizontal liquid layer under shear-stress gas flow, Int. J. Heat Mass Transfer, 2014, vol. 70, pp. 599–609.
Kabov, O.A., Zaitsev, D.V., Cheverda, V.V., and Bar-Cohen, A., Evaporation and flow dynamics of thin, sheardriven liquid films in microgap channels, Exp. Therm. Fluid Sci., 2011, vol. 35, no. 5, pp. 825–831.
Iorio, C.S., Goncharova, O.N., and Kabov, O.A., Study of evaporative convection in an open cavity under shear stress flow, Microgravity Sci. Technol., 2009, vol. 21, no. 1, pp. 313–320.
Iorio, C.S., Goncharova, O.N., and Kabov, O.A., Heat and mass transfer control by evaporative thermal pattering of thin liquid layers, Comput. Therm. Sci., 2011, no. 3 (4), pp. 333–342.
Andreev, V.K. and Kuznetsov, V.V., The liquid film and gas flow motion in a microchannel with evaporation, Thermophys. Aeromech., 2013, no. 1, pp. 17–28.
Goncharova, O.N. and Rezanova, E.V., Example of an exact solution of the stationary problem of two-layer flows with evaporation at the interface, J. Appl. Mech. Tech. Phys., 2014, vol. 55, no. 2, pp. 247–267.
Goncharova, O.N., Rezanova, E.V., and Tarasov, Ya.A., Mathematical simulation of thermocapillary flows in thin liquid layer by considering evaporation, Izv. Altai. Gos. Univ., 2014, no. 81 (1/1), pp. 47–52.
Rodionova, A.V. and Rezanova, E.V., Stability of two-layer fluid flow, J. Appl. Mech. Tech. Phys., 2016, vol. 57, no. 4, pp. 588–595.
Bekezhanova, V.B., Goncharova, O.N., Rezanova, E.V., and Shefer, I.A., Stability of two-layer fluid flows with evaporation at the interface, Fluid Dyn., 2017, vol. 52, no. 2, pp. 189–200.
Lyulin, Yu.V. and 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, no. 9, pp. 795–797.
Lyulin, Yu.V., Feoktistov, D.V., Afanas’ev, I.A., Chachilo, E.S., Kabov, O.A., and Kuznetsov, G.V., Measuring the rate of local evaporation from the liquid surface under the action of gas flow, Tech. Phys. Lett., 2015, vol. 41, no. 7, pp. 665–667.
Goncharova, O.N., Hennenberg, M., Rezanova, E.V., and Kabov, O.A., Modeling of the convective fluid flows with evaporation in the two-layer systems, Interfacial Phenom. Heat Transfer, 2013, vol. 1, no. 3, pp. 317–338.
Goncharova, O.N., Rezanova, E.V., Lyulin, Yu.V., and Kabov, O.A., Modeling of two-layer liquid-gas flow with account for evaporation, Thermophys. Aeromech., 2015, vol. 22, no. 5, pp. 631–638.
Bekezhanova, V.B. and Goncharova, O.N., Stability of exact solutions describing two-layer flows with evaporation at the interface, Fluid Dyn. Res., 2016, vol. 48, no. 6, p. 061408.
Mizev, A.I., How gas phase thickness influences onto stability and structure of flow in liquid-gas two-layer system: experimental research, Prikl. Mekh. Tekh. Fiz., 2004, vol. 45, no. 6, pp. 14–18.
Joseph, D.D., Stability of Fluid Motions I and II, New York: Springer, 1976.
Ostroumov, G.A., Svobodnaya konvektsiya v usloviyakh vnutrennei zadachi (Gravitational Convection under the Conditions of Internal Problem), Moscow: Gos. Izd. Tekhniko-Teoreticheskoi Literatury, 1952.
Birikh, R.V., On thermocapillary convection in horizontal liquid layer, Prikl. Mekh. Tekh. Fiz., 1966, no. 3, pp. 69–72.
Shliomis, M.I. and Yakushin, V.I., Convection in two-layer binary system with evaporation, Uch. Zap. Permsk. Univ. Ser.: Gidrodin., 1972, no. 4, pp. 129–140.
Godunov, S.K., On numerical solution of boundary problems for systems of linear ordinary equations, Usp. Mat. Nauk, 1961, vol. 16, no. 3 (99), pp. 171–174.
Gaponov, S.A. and Maslov, A.A., Razvitie vozmushchenii v szhimaemykh potokakh (Perturbations Development in Compressible Flows), Novosibirsk: Nauka, 1980.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © I.A. Shefer, 2018, published in Prikladnaya Matematika i Mekhanika, 2018, Vol. 82, No. 2, pp. 207–218.
Rights and permissions
About this article
Cite this article
Shefer, I.A. Effect of the System Geometry on the Flow Stability of an Evaporating Liquid. Fluid Dyn 53 (Suppl 1), S59–S68 (2018). https://doi.org/10.1134/S0015462818040225
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0015462818040225