MODELING OF THE CONVECTIVE FLUID FLOWS WITH EVAPORATION IN THE TWO-LAYER SYSTEMS

Abstract

The flows of two fluids (or of a liquid and gas) filled with infinite horizontal layers with a thermocapillary interface are considered. Study of flows caused by impact of various forces on the liquid and gas media is very important nowadays. The increased interest in problems of convection with evaporation is evidenced by the experiments performed at the Institute of Thermophysics SB RAS in the framework of the CIMEX project of the European Space Agency. These investigations focus on the features of convective fluid flows in an open cavity and in an open horizontal layer under conditions of cocurrent gas flows (Lyulin and Kabov, 2013). In this paper a stationary coupled problem of gravitational and thermocapillary convection with respect to a diffusive mass transfer at the interface due to evaporation is studied. Two-layer flows are described with the help of the Oberbeck-Boussinesq approximation of the Navier-Stokes equations. The no-slip conditions are prescribed on the fixed boundaries, which are heated nonuniformly (linear dependencies of temperature on the longitudinal coordinate are given on these rigid boundaries). The kinematic and dynamic conditions, the conditions of continuity of temperature and velocity, and also a mass balance equation are assumed to be fulfilled on the interface. A relation defining a concentration of the saturated vapor at the interface is written on the basis of the Clapeyron-Clausius equation. Closed flow conditions are used to close the problem statement. This paper is devoted to construction of the exact solutions of a special type to illustrate the two-layer flows with evaporation. The exact solutions for two different types of conditions for vapor concentration on the upper rigid boundary have been obtained. The velocity profiles are presented to demonstrate the two-layer flows for liquid-gas systems such as "ethanol-nitrogen" and "benzine-air" under conditions of normal and low gravity.