Computer simulation of oscillatory Marangoni flow

Ohnishi, Mitsuru; Azuma, Hisao; Doi, Takao

doi:10.1016/0094-5765(92)90158-f

Cited by 35 publications

(10 citation statements)

References 5 publications

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“…The profiles obtained practically coincide with the analogous profiles from [ 19]. Thus the results obtained for Marangoni numbers not larger than 100 are in good agreement with the data of [19], while for Ma = 400 they agree with [18].…”

Section: Results Of Numerical Computations For the R-r Casesupporting

confidence: 92%

“…At Ma -400 a vortex forms in the left lower part of the region rotating in the opposite direction. A similar picture holds in [18]. Figure 12 gives profiles of the horizontal velocity in the section x = .4 / 2 with different Marangoni numbers.…”

Section: Results Of Numerical Computations For the R-r Casesupporting

confidence: 59%

“…The problem of Marangoni convection. In this section we study the problem of thermocapillary convection of a viscous incompressible liquid in the absence of gravitation (~, = 0) [18], [19]. A large number of studies have been conducted on this problem, since the surface of a liquid (melt) is free in many processes of space engineering (directed crystallization, extra-crucible zonal melting), and it is the thermocapillary effect that leads to the appearance of convective motion in the melt.…”

Section: Results Of Numerical Computations For the R-r Casementioning

confidence: 99%

“…The results of the computations were compared with the data of [18], where this problem was computed using the Navier-Stokes equations by the finite-difference method on uniform grids of sizes 25 x 100, 32 x 128, 40 x 160, and 50 x 200, and with the data of [19].…”

Section: Results Of Numerical Computations For the R-r Casementioning

confidence: 99%

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Computation of convective flows using the quasihydrodynamic equations

Елизарова¹,

Kalachinskaya²,

Klyuchnikova³

et al. 1999

Comput Math Model

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We discuss the results of numerical modeling of problems of gravitational and thermocapillary convection in rectangular cavities with small Prandtl numbers. The results are obtained using the quasihydrodynamic system of equations and compared with the results of computations using the Navier-Stokes system. Three tables, 12figures. Bibliography: 19 titles.Introduction. The Navier-Stokes equations are widely used to describe the convective flow of a viscous incompressible liquid [1], [2]. In the present paper we consider a different approach based on the use of quasihydrodynamic equations. The quasihydrodynamic system was introduced to describe the flow of a viscous incompressible liquid and studied in [3]-[5]. This system is dissipative and has a number of exact physically meaningful solutions. Mathematical analysis of the quasihydrodynamic system that models the flow of a viscous compressible heat-conducting medium was given in [4]. In particular, the equation for balance of thermodynamic entropy with a nonnegative dissipative function was obtained, the theorem on increase of total thermodynamic entropy in adiabatically isolated regions was proved, and a laminar boundary layer approximation was constructed. A physical derivation of quasihydrodynamic systems with an explanation of the meaning of all quantities and parameters occurring in them was published in [5].The possibility of using quasihydrodynamic equations for numerical modeling of flows of a viscous incompressible liquid in a cavern [6] and to study the Boussinesq convection in a square cavity [7] had been demonstrated previously.A system of quasihydrodynamic equations related to the quasihydrodynamic system has been successfully applied in numerical modeling of flows of a rarefied gas [8].The quasihydrodynamic system of equations. The quasihydrodynamic system in Boussinesq approximation was derived in [5] and has the form div ~ = div ~,Po P0 T t + div (fiT) = div (fiT) + r div (VT).(3) Here P0 is the mean value of the density, ~ = ~(.~,t) is the hydrodynamic velocity, p = p(Y,t) is the excess of pressure above the hydrostatic value, T = T(.Tc, t) is the deviation of the temperature from its mean value To, fl > 0 is the coefficient of thermal expansion of the liquid, ~, is the acceleration of gravity, r=zl(PoCp) is the coefficient of thermal diffusivity, and Z is the coefficient of thermal conductivity. The quantity po E is interpreted as the mean momentum of a unit volume of liquid. The vector ~ is computed from the formula As boundary conditions for the system (1)-(4) in a closed region we use the conditions for velocity and temperature adopted in the Navier-Stokes theory, supplemented by the condition of mass impermeability in the form Translated from Problemy Matematicheskoi Fiziki, 1998, pp. 193-208. 160 1046-283X/99/t002-0160522.00 9 Kluwer Academic/Plenum Publishers

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Section: Results Of Numerical Computations For the R-r Casesupporting

confidence: 92%

Section: Results Of Numerical Computations For the R-r Casesupporting

confidence: 59%

Section: Results Of Numerical Computations For the R-r Casementioning

confidence: 99%

Section: Results Of Numerical Computations For the R-r Casementioning

confidence: 99%

See 2 more Smart Citations

Computation of convective flows using the quasihydrodynamic equations

Елизарова¹,

Kalachinskaya²,

Klyuchnikova³

et al. 1999

Comput Math Model

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show abstract

“…We consider below the problem on the thermocapillary convection of a viscous incompressible fluid under the absence of gravitation (see [152,166]). A large number of studies are devoted to this problem, since in many problems of cosmic technology (directed crystallization and crucibleless zone melting), the surface of the fluid (melt) is free and the thermocapillary effect leads to the appearance of convective motion in the melt.…”

Section: Marangoni Convection In the Zero Gravitymentioning

confidence: 99%

Quasi-Gas Dynamic Equations

Елизарова

2009

Computational Fluid and Solid Mechanics

174

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The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: deblik, BerlinPrinted on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) PrefaceThe monograph is devoted to modern mathematical models and numerical methods for solving gas-and fluid-dynamic problems based on them. Two interconnected mathematical models generalizing the Navier-Stokes system are presented; they differ from the Navier-Stokes system by additional dissipative terms with a small parameter as a coefficient. The new models are called the quasi-gas-dynamic and quasi-hydrodynamic equations. Based on these equations, effective finite-difference algorithms for calculating viscous nonstationary flows are constructed and examples of numerical computations are presented. The universality, the efficiency, and the exactness of the algorithms constructed are ensured by the fulfillment of integral conservation laws and the theorem on entropy balance for them.The book is a course of lectures and is intended for scientists and engineers who deal with constructing numerical algorithms and performing practical calculations of gas and fluid flows and also for students and postgraduate students who specialize in numerical gas and fluid dynamics. Moscow Tatiana Elizarova December 2008 v Contents

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Steady and oscillatory buoyant thermocapillary convection

Mundrane

Zebib

1994

Computational Mechanics

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Computer simulation of oscillatory Marangoni flow

Cited by 35 publications

References 5 publications

Computation of convective flows using the quasihydrodynamic equations

Computation of convective flows using the quasihydrodynamic equations

Quasi-Gas Dynamic Equations

Steady and oscillatory buoyant thermocapillary convection

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