Olga Goncharova

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

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.

Numerical investigation of the tangential stress effects on a fluid flow structure in a partially open cavity

Mathematical and numerical modeling of fluid flows in the domains with free boundaries under co-current gas flow is widely investigated nowadays. A stationary problem of fluid motion in a rectangular cavity with a non-deformed free boundary is studied in a two-dimensional statement. The tangential stresses created on the free boundary by an adjoint gas flow are considered to be a driving force for a fluid motion. The influence of the cavity geometry (cavity aspect ratio) and of the free boundary (length of the open part of the boundary) on the velocity field is investigated numerically. The simulations are carried out for different values of the gas Reynolds numbers. The characteristic values for the flow parameters as well as geometrical characteristics described in this paper are motivated by the main features of the CIMEX-1 experiments prepared for the International Space Station. The paper presents examples of the fluid flow structure in the open cavities and conclusions.

Modeling of Two-layer Fluid Flows with Evaporation at the Interface in the Presence of the Anomalous Thermocapillary Effect

Stationary convectiveows of two immiscible viscous incompressibleuids (liquid and gas) under action of the transverse gravityeld and longitudinal temperature gradient along the interface are studied ana- lytically. Mathematical model of theuidows with the effects of evaporation at the interface is based on exact solutions to the Navier-Stokes equations in the Oberbeck-Boussin esq approximation. The effects of the thermodiffusion and diffusive heat conductivity in the gas-vapor layer are taken into consideration. The obtained solutions are used to model theows in the two-layer gas-liquid system in the case when a liquid exhibits the anomalous thermocapillary effect. Examples of the two-layeruidows are presented for various values of the gasow rate, longitudinal temperature gradient at the interface and the gravity force acceleration.

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

Victoria B. Bekezhanova∗ Institute of Computational Modeling SB RAS Academgorodok, 50/44, Krasnoyarsk, 660036 Institute of Mathematics and Computer Science Siberian Federal University Svobodny, 79, Krasnoyarsk, 660041 Russia Olga N.Goncharova† Institute of Thermophysics SB RAS Lavrentieva, 1, Novosibirsk, 630090 Altai State University Lenina, 61, Barnaul, 656049 Russia Ilia A. Shefer‡ Institute of Mathematics and Computer Science Siberian Federal University Svobodny, 79, Krasnoyarsk, 660041 Russia

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

In the second part of the review we present application of exact solutions of the classical convection equations to description of the two-layer flows in three-dimensional case, among other flows with evaporation. The Ostroumov – Birikh exact solutions of the Oberbeck−Boussinesq equations allow one to study characteristic features of interaction of various mechanisms of the evaporative convection in gravitational field and in weightlessness. The solutions consider the thermodiffusion and diffusive thermal conductivity effects in the gas – vapor phase. In the paper the trajectories of fluid particle motion, temperature fields in a rectangular channel are presented.

Numerical Investigation of a Dependence of the Dynamic Contact Angle on the Contact Point Velocity in a Problem of the Convective Fluid Flow

Received 07.12.2015, received in revised form 09.02.2016, accepted 20.06.2016 A two-dimensional problem of the fluid flows with a dynamic contact angle is studied in the case of an uniformly moving contact point. Mathematical modeling of the flows is carried out with the help of the Oberbeck-Boussinesq approximation of the Navier-Stokes equations. On the thermocapillary free boundary the kinematic, dynamic conditions and the heat exchange condition of third order are fulfilled. The slip conditions (conditions of proportionality of the tangential stresses to the difference of the tangential velocities of liquid and wall) are prescribed on the solid boundaries of the channel supporting by constant temperature. The dependence of the dynamic contact angle on the contact point velocity is investigated numerically. The results demonstrate the contact angle behavior and the different flow characteristics with respect to the various values of the contact point velocity, friction coefficients, gravity acceleration and an intensity of the thermal boundary regimes.

Conditions on Thermocapillary Surface with Consideration of Liquid Evaporation and Transfer Coefficient Temperature Dependence

Конвективные течения жидкостей под действием сопутствующего потока газа и вызываемого им испарения активно изучаются в настоящее время аналитически, численно и экспериментально. Задача математического моделирования конвективных процессов с учетом испарения является чрезвычайно сложной. Принципиальным вопросом остается формулировка граничных условий на поверхности раздела жидкости и газопаровой смеси. На основе законов сохранения и соотношений на сильном разрыве выписываются обобщенные кинематическое, динамическое и энергетическое условия на термокапиллярной границе раздела. Данные условия формулируются с учетом зависимости от температуры коэффициентов переноса. Гипотезы, принимаемые при выводе условий на поверхности раздела с испарением, включают в себя отождествление свободной поверхностной энергии с коэффициентом поверхностного натяжения, закон Стокса для несжимаемой жидкости, законы Фурье и Фика для определения потока тепла и пара, установление скрытой теплоты испарения как скачка внутренней потенциальной энергии. Предполагается непрерывность касательных скоростей и температуры на границе раздела, а поток испаряющейся жидкости определяется исходя из кинетической теории.

Convection under low gravity: Correctness of mathematical models

The alternative mathematical models of convective fluids flows (the microconvection model of isothermally incompressible fluid, the model of convection of weakly compressible fluid) and the classical Oberbeck-Boussinesq model with temperature dependent viscosity are applicable to investigation of many applied problems of convection: convection under low gravity, in small scales and at fast changes of the boundary thermal regimes. A characteristic property of the alternative mathematical models is the nonsolenoidality of the velocity fields.Principal issues relating to well/ill posed initial boundary value problems for the mathematical models of convection are considered. For the convection equations of weakly compressible fluid the initial boundary value problem with general temperature condition on the boundary is studied. The analytical result concerning the correctness of this problem is presented: the local theorem of existence of a smooth solution in the classes of the Hoelder functions is proved.