Analysis of an Exact Solution of Problem of the Evaporative Convection (Review). Part II. Three-dimensional Flows

In the paper the review of exact solutions of the three-dimensional convection problems is presented. The solutions allow one to model the two-layer convective fluid flows with evaporation at the thermocapillary interface

Analysis of an Exact Solution of Problem of the Evaporative Convection (Review). Part I. Plane Case

Development of theory describing the convection under conditions of "liquid – gas" phase transition, is caused by the active experimental study of the convective phenomena accompanied by evaporation/condensation at interphase. Results of the analytical and numerical investigation of new nonstandard problems of heat and mass transfer in domains with free surfaces or interfaces allow one to evaluate the adequacy of new mathematical models and to derive new characteristic criteria. The obtained fundamental knowledge on physical mechanisms of the studied processes provides the basis of modification and improvement of the fluidic technologies using the evaporating liquids and gas-vapor mixtures as working media. In the paper the analysis of the exact solution of the convection equations, which gives a possibility to model the two-layer convective fluid flows with evaporation, is presented

Long-Wave Instability of Advective Flows in Inclined Layer with Solid Heat Conductive Boundaries

We investigate the stability of the steady convective flow in a plane tilted layer with ideal thermal conductivity of solid boundaries in the presence of uniform longitudinal temperature gradient. Analytically found the stability boundary with respect to the long-wave perturbations, find the critical Grashof number for the most dangerous among them of even spiral perturbation.Comment: in Russian, 18 pages, 5 figures, submited to Appl. mechanics and physics, RAS Siberian brunch, Novosibirsk, Russia; Key words: advective flow, oblique layer, a longitudinal temperature gradient, long-wave instabilit

Analysis of the characteristic perturbations spectrum of the exact invariant solution of the microconvection equations

The properties of an exact invariant solution of the equations of microconvection of isothermally incompressible liquids have been investigated. The solution describes a stationary fluid flow in a vertical channel. The temperature or heat flux can be given at the solid boundaries of the channel. A classification of the solutions and their physical interpretation are suggested. In accordance with the classification the solutions describe different types of flows. The solution of the stability problem of all classes of flows in the vertical channel with the given temperature on the walls is presented. The structure of the spectrum of small non-stationary spatial perturbations for the model medium (silicon dioxide melt) has been studied, depending on the configuration of the perturbation wave, thickness channel, thermal and gravitational effects. The formation regularities of different types of the thermal and hydrodynamic disturbances have been determined. The interaction of the thermal and hydrodynamic perturbations leads to the formation of various convective structures. Typical patterns of the velocity and temperature perturbations and relations of critical characteristics of the instability are presented, depending on the problem parameters. The most dangerous mechanisms change from hydrodynamic to thermal ones with the variation of the viscous and thermal liquid properties

Impact of Gravity on the Flow Pattern in a Locally Heated Two-Layer System

Problem of thermocapillary convection is studied to analyze peculiarities of the flows arising in a gas-liquid system under action of an intense local thermal exposure. The "stream function-vorticity" formulation of the Navier-Stokes equations in the Boussinesq approximation is used to describe the fluid flows. The kinematic and dynamic conditions on the free boundary are stated in terms of tangential and normal velocities, while temperature conditions at the lower or upper boundary of the system take into account the presence of finite size heaters. Special attention is given to the study of the influence of the gravity intensity on the dynamics of heat and mass transfer in fluid layers and character of the interface deformations. Theoretical study of the thermocapillary convection includes development of the mathematical model and effective numerical algorithm. The results of numerical study of features of convective flows in the cavity being in the terrestrial or microgravity conditions and of the evolution of the interface allow one to validate the developed mathematical model, and to specify dominant mechanisms determining the flow regimes

Analysis of Characteristics of Two-Layer Convective Flows with Diffusive Type Evaporation Based on Exact Solutions

The theoretical approaches for mathematical modelling of the convective flows with mass transfer through the liquid-gas interface are discussed. The special attention is payed to modelling with use of the classical Boussinesq approximation of the Navier-Stokes equations. The diffusion equation and the effects of thermodiffusion and thermal diffusivity (the Soret and Dufour effects) are taken into account additionally to describe vapor and heat transfer processes in the gas-vapor phase. The use of the Oberbeck-Boussinesq equations allows one to apply the group-analytical methods in the theory of the evaporative convection and to construct the exact solutions of special type of the governing equations. Joint flows of the evaporating liquid and gas-vapor mixture are studied with the help of a partially invariant solution for the convection equations. The 2D and 3D solutions are demonstrated to simulate two-phase flows in the infinite channels with interface being under action of a longitudinal temperature gradient and perpendicularly directed gravity field. In the present paper the fluid flows with diffusive evaporation/condensation in the terrestrial and microgravity conditions are studied in the steady case. The new results obtained for combined thermal regime on the external rigid boundaries are presented

Influence of the Dufour and Soret effects on the characteristics of evaporating liquid flows

Текст статьи не публикуется в открытом доступе в соответствии с политикой журнала.The characteristics of regimes of two-layer flows with diffuse evaporation in an infinite channel are studied in the frame of the Boussinesq approximation for the Navier - Stokes equations. A joint flow of an evaporating liquid and a co-current gas flux is simulated with the help of the exact solution of a special type for the convection equations. The effects of thermodiffusion and diffusive thermal conductivity are additionally taken into account to model the flow in the gas phase and in the boundary conditions on the thermocapillary interface and upper solid wall of the channel. The character and extent of the impact of the Soret and Dufour effects on the structure of the appearing regimes of evaporative convection is investigated at the example of HFE-7100 - nitrogen and ethanol - nitrogen systems. It is shown that these effects do not influence the topological structure of the flows but can lead to a qualitative change of the regime pattern. The Soret effect can cause significant variations of the vapor content in the system upon changing the liquid layer thickness and external thermal load, and result in the transformation of the phase transition mode (evaporation/condensation). The influence of the Dufour effect can be neglected. Critical characteristics of the stability for the flow under study are determined depending on the intensity of the thermodiffusion effects. The weak destabilizing influence of the Soret effect is ascertained for all the considered configurations

Influence of Gravity on the Stability of Evaporative Convection Regimes

The characteristics of convective regimes in a two-layer system have been investigated in the framework of the Boussinesq approximation of the Navier–Stokes equations. An exact invariant solution of the convection equations is used to describe a joint stationary flow of an evaporating liquid and a gas-vapor mixture in a horizontal channel. Thermodiffusion effects in the gas-vapor phase are additionally taken into account in the governing equations and interface conditions. The influence of gravity and thickness of the liquid layer on the hydrodynamical, thermal and concentration characteristics of the regimes has been investigated. Flows of the pure thermocapillary, mixed and Poiseuille’s types are specified for different values of the problem parameters. The linear stability of the evaporative convection regimes has been studied. The types and properties of the arising perturbations have been investigated and the critical characteristics of the stability have been obtained. Disturbances can lead to the formation of deformed convective cells, vortex and thermocapillary structures. The change of the instability types and threshold thermal loads occurs with the increasing thickness of the liquid layer and gravity action

Influence of Heat Defect on the Characteristics of a Two-layer Flow with the Hiemenz Type Velocity

Текст статьи не публикуется в открытом доступе в соответствии с политикой журнала.An exact solution is derived in the frame of the creeping flow model to describe thermocapillary convection in a two-layer system with heat defect when the heat is transferred through the interface. The solution is characterized by the Hiemenz-type velocity and temperature distribution which is quadratic in the longitudinal coordinate. The heat defect is connected with changes in the internal energy of the interface caused by the action of thermocapillary forces on the transformation of the area and shape of the surface. A model linear problem is studied to estimate the impact of this effect on the formation of typical flow regimes and stability of these regimes. There is only a nonlinear term in the energy balance condition at the interface corresponding to the heat defect in the model problem. Depending on the values of a parameter defining the character of thermal load on the lower boundary of the system this problem may not have any solution, or it may have one or two exact solutions obtained in an explicit form. In the frame of the linear theory the stability of one of these exact solutions is investigated both taking into account the heat defect and under classical condition of heat balance at the interface setting an equality of heat fluxes on this surface. The interface position and velocity and temperature perturbation fields are calculated. With the decrease of the liquid layer thickness the changes in the internal energy of the interface can result in oscillations of the surface and saw-shaped deformations. Such behavior of the interface does not appear in the system without the heat defect

Stability of two-layer fluid flows with evaporation at the interface

Текст статьи не публикуется в открытом доступе в соответствии с политикой журнала.The problem of stability of two-layer (fluid-gas) flows with account of evaporation at the thermocapillary interface is studied under the condition of a fixed gas flow rate. In the upper gas-vapor layer, the Dufour effect is taken into account. A novel exact solution of the Navier–Stokes equations in the Boussinesq approximation is constructed. The effects of longitudinal temperature gradients, gravity, thicknesses of the gas and fluid layers, and the gas flow rate on the flow structure, the onset of recirculated flows near the interface, the evaporation rate, and the properties of characteristic disturbances are investigated