Convection of magnetic fluids in connected channels heated from below

The convective flows of a binary mixture in connected channels heated from below are studied experimentally. In contrast to homogeneous fluids, in magnetic colloids “hard” convection excitation, specific transient flows, and oscillatory convection regimes can be observed. The temperature fields and concentration inhomogeneities are measured.     

Thermocapillary and thermogravitational convection in a two-layer system with curved interface

In an earlier study [1], the present authors used the complete nonlinear hydrodynamic equations to investigate thermocapillary convection in a two-layer system. Oscillatory instability of the equilibrium was established for some ratios of the parameters. In the present paper, a study is made of the influence on the thermocapillary convective motions of two different factors — curvature of the interface and gravity. It is established that curvature of the interface can lead to significant changes in the flow structure and hysteresis transitions between convection regimes. In the case of the joint influence of the thermogravitational and thermocapillary instability mechanisms, many different flow regimes are found: steady motions with different directions of rotation of the vortices and periodic and nonperiodic oscillatory motions with different spatial structures.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 175–179, May–June, 1984.We thank E. M. Zhukovitskii for discussing the results.     

Combined action of anticonvection and thermocapillarity in two- and three-layer systemsAction simultanée d'anticonvection et de thermocapillarité dans des systèmes multi-couches

Anticonvection generated by the joint action of the external heating and heat sources (sinks) on the interface in the layers with finite thicknesses is studied. Anticonvective structures in fluid systems subject to the anticonvective instability only in the presence of heat sources (sinks) on the interface have been obtained. The nonlinear regimes of anticonvection in the system of three immiscible viscous fluids heated from above are investigated. The specific phenomena caused by direct and indirect interaction of anticonvective and thermocapillary mechanisms of instability are considered. In particular, different oscillatory configurations where anticonvection arises mainly near the upper interface and thermocapillary convection appears mainly near the lower interface, have been studied. To cite this article: I.B. Simanovskii, C. R. Mecanique 332 (2004).     

Stability of two-layer systems with respect to convective mixing

The occurrence and development of convection in a two-layer system heated below has been investigated [1–5] under the assumption that the interface of the fluids is horizontal and is not subject to deformations. However, this assumption may not be satisfied if the surface tension on the interface is small and the fluids have either nearly equal densities or the heavier fluid is situated at the top. In the present paper, an attempt is made to study the convection regimes in a two-layer system with deformation of the interface when there is heating from below or above. The simultaneous influence of the convective and Rayleigh-Taylor instability mechanisms is taken into account; the surface tension on the interface is assumed to be infinitesimally small, and thermocapillary effects are ignored. A two-fluid variant of the method of markers and cells [6–9] is used for the numerical solution of the convection equations. A diagram of the regimes is constructed. It is shown that depending on the values of the parameters the system either preserves its two-layer structure, or the development of the conveetive motion leads to the breakup of the interface and complete mixing of the fluids.     

Vibrational Convection in the Hele-Shaw Cell. Theory and Experiment

The influence of high-frequency horizontal vibrations on convection in the Hele-Shaw cell located in a uniform gravity field is considered experimentally and theoretically. Nonlinear regimes of vibrational convection in the supercritical region are examined. It is shown that horizontal vibrations (directed toward the wide sides of the cell) decrease the threshold of quasi-equilibrium stability. Regions of existence of one- and two-vortex steady flows are found, and unsteady regular and random regimes of thermal vibrational convection are considered. New random regimes in the Hele-Shaw cell are found, which result from nonlinear interaction of the “lower” modes responsible for the formation of regular supercritical convective regimes. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 2, pp. 40–48, March–April, 2006.     

Combined action of anticonvective and thermocapillary mechanisms of instability in multilayer systems

The nonlinear regimes of convection in the system of three immiscible viscous fluids heated from above are investigated. The interfaces are assumed to be flat. The boundary value problem is solved by the finite-difference method. Transitions between convective motions with different spatial structures are investigated. The common diagram of instability regimes is constructed. The new phenomena caused by direct and indirect interaction of anticonvective and thermocapillary mechanisms of instability are considered. Specifically, different oscillatory configurations where anticonvection arises mainly near the upper interface and thermocapillary convection appears mainly near the lower interface have been found.     

Mixed Convection of Water at 4°C Along a Wedge with Variable Surface Flux in a Porous Medium

In this study, the mixed convection of water at 4°C along a wedge in a porous medium is investigated numerically using finite difference method. In order to explore the effect of mixed convection, both forced and free convection-dominated regimes are considered. Non-similarity solutions are obtained for the variable wall flux boundary condition. Velocity and temperature profiles as well as local dimensionless skin friction and Nusselt number are obtained and compared with the available numerical results for various values of different parameters. The wedge angle geometry parameter m and mixed convection parameter ξ are ranged from 0 to 1 in both regimes whereas different values of λ are considered for the purpose of comparison of heat transfer results.     

Binary-mixture convection in connected channels heated from below

Supercritical binary-mixture flows in connected channels of finite depth are studied theoretically and experimentally. It is shown that, in contrast to uniform fluids, in the mixture the convection excitation is “hard” and specific transient flows and oscillation regimes are observed. A mechanism explaining the phenomena observed is proposed and confirmed by a theoretical solution of the problem. The amplitude curves and the channel distributions of the velocity, temperature, and admixture concentration are obtained. These illustrate the competition between the thermodiffusion and thermo-gravitational convection mechanisms.     

Investigation of thermogravitational-thermocapillary steady-state convective flow stability at low Prandtl numbers

The stability of gravitational-capillary flow in a square cavity with isothermal vertical and adiabatic horizontal boundaries is investigated. The region of stable regimes in the Grashof number-Marangoni number plane is determined for a fluid with a Prandtl number equal to 0.02. In [1] the stability of steady-state thermogravitational convection regimes in a laterally heated square cavity was numerically investigated. The Galerkin method with a system of coordinate functions constructed as proposed in [2] was used to solve the system of equations of free convection in the Oberbeck-Boussinesq approximation. Below, the variant of the Galerkin method described in [2] is used to investigate the stability of steady-state regimes of free convection flow developing under the combined influence of thermogravitational and thermocapillary forces.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 8–13, March–April, 1990.     

Stability and slightly supercritical oscillatory regimes of natural convection in a 8:1 cavity: solution of the benchmark problem by a global Galerkin method

The global Galerkin method is applied to the benchmark problem that considers an oscillatory regime of convection of air in a tall two‐dimensional rectangular cavity. The three most unstable modes of the linearized system of the Boussinesq equations are studied. The converged values of the critical Rayleigh numbers together with the corresponding oscillation frequencies are calculated for each mode. The oscillatory flow regimes corresponding to each of the three modes are approximated asymptotically. No direct time integration is applied. Good agreement with the previously published results obtained by solution of the time‐dependent Boussinesq equations is reported. Copyright © 2004 John Wiley & Sons, Ltd.     

Criteria of hydrodynamic instability of a phase interface in hydrothermal systems

The loss of stability of a vertical phase flow in a geothermal system in which a liquid layer overlies a vapor layer is considered. The loss of stability criteria are obtained in explicit form. It is found that when the physical parameters of the system are varied the transition to phase interface instability can be realized by means of one of the following mechanisms: the transition occurs spontaneously for any perturbation wavenumber (degenerate case); an unstable wavenumber arises at infinity; the instability threshold is determined by a double zero wavenumber. In the latter case the transition to instability is accompanied by simple resonance bifurcation. As a result of this bifurcation, secondary regimes dependent on the horizontal coordinate branch off from the basic regime describing the horizontally-homogeneous vertical phase flows.Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, 2004, pp. 100–109. Original Russian Text Copyright © 2004 by Ilichev and Tsypkin.     

Kinematic regimes of convection at high Prandtl number in a shallow cavityRégimes cinématiques de la convection à haut nombre de Prandtl dans une cavité allongée.

We consider free convection in a horizontal shallow cavity with different end temperatures, filled with a high Prandtl number fluid. From scaling analysis, we find two kinematic regimes resulting from the competition of heat transfer by conduction and by convection. Numerical simulations realized for a large range of Rayleigh number and aspect ratio confirm the phenomenological analysis and provide the threshold between the two regimes. The conductive and convective regimes occur at $\mathit{Ra}{A}^2$ smaller and larger than 443 respectively, where Ra is the Rayleigh number and A is the aspect ratio. In the convective regime, the characteristic velocity is independent of depth of the cavity. To cite this article: J.-M. Flesselles, F. Pigeonneau, C. R. Mecanique 332 (2004).     

Weakly Nonlinear Analysis of Convection of a Two-Layer System with a Deformable Interface

The onset of convection in a two-layer system heated from above and below is considered within the framework of the generalized Boussinesq approximations. In the longwave approximation an amplitude equation describing large-scale convective motions accompanied by a deformation of the interface is derived. Two types of steady-state regimes are revealed and their stability is studied.The presence of deformable interfaces and nonuniform heating can initiate instability of the fluid in the gravity field. The interaction between these mechanisms is of considerable theoretical interest. This explains the numerous publications devoted to these themes.     

A stabilized Nitsche‐type extended embedding mesh approach for 3D low‐ and high‐Reynolds‐number flows

This paper presents a stabilized extended finite element method (XFEM) based fluid formulation to embed arbitrary fluid patches into a fixed background fluid mesh. The new approach is highly beneficial when it comes to computational grid generation for complex domains, as it allows locally increased resolutions independent from size and structure of the background mesh. Motivating applications for such a domain decomposition technique are complex fluid‐structure interaction problems, where an additional boundary layer mesh is used to accurately capture the flow around the structure. The objective of this work is to provide an accurate and robust XFEM‐based coupling for low‐ as well as high‐Reynolds‐number flows. Our formulation is built from the following essential ingredients: Coupling conditions on the embedded interface are imposed weakly using Nitsche's method supported by extra terms to guarantee mass conservation and to control the convective mass transport across the interface for transient viscous‐dominated and convection‐dominated flows. Residual‐based fluid stabilizations in the interior of the fluid subdomains and accompanying face‐oriented fluid and ghost‐penalty stabilizations in the interface zone stabilize the formulation in the entire fluid domain. A detailed numerical study of our stabilized embedded fluid formulation, including an investigation of variants of Nitsche's method for viscous flows, shows optimal error convergence for viscous‐dominated and convection‐dominated flow problems independent of the interface position. Challenging two‐dimensional and three‐dimensional numerical examples highlight the robustness of our approach in all flow regimes: benchmark computations for laminar flow around a cylinder, a turbulent driven cavity flow at Re = 10000 and the flow interacting with a three‐dimensional flexible wall. Copyright © 2016 John Wiley & Sons, Ltd.     

Effects of a barrier on temperature structure and mixing in thermally stratified water cooled from above

A Mach-Zehnder interferometer was used to study the unsteady temperature structure in radiation stratified water cooled from above. Temperature distribution measurements in a test cell filled with distilled water provide conclusive evidence that the thermal structure between the air-water interface and the stable region is controlled by buoyancy induced natural convection. The cooling from above produces a complex vertical temperature profile which can be divided into several distinct regimes. Introduction of a thin, rigid transparent (glass) plate into the water before thermal stratification by radiation and cooling confines the natural convection driven flow and reduces the intensity of mixing. As a result, the energy transport from the interior of the water layer to the interface is decreased. However, under the experimental conditions tested use of rigid, horizontal plates introduced in the fluid were not very effective in reducing the transport of heat from the warm interior to the cooler interface.     

Numerical analysis of natural convection in a thin-walled cylindrical vessel with hemispherical end-plates completely filled with liquid

The results are given of calculations of convection in a thin-walled cylindrical vessel with hemispherical end-plates over the range of Rayleigh and Fourier numbers that correspond to the main regimes of unsteady laminar convection in the presence of a given heat flux.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 204–203, September–October, 1984.     

Vibrational thermal convection in a rectangular cavity

Vibrational thermal convection in a rectangular cavity under conditions of weightlessness is studied. Some equilibrium configurations were obtained in earlier papers of two of the authors [1, 2] and their linear stability investigated. In the present paper, a numerical investigation is made of the developed vibrational convection which arises under conditions when equilibrium is impossible. The structure of the average vibrational-convective flows and the characteristics of the heat transfer are determined. The change of regimes and the connection with the stability problem are discussed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 94–99, July–August, 1982.     

No slip boundary effects in non-Darcian mixed convection from a vertical wall in saturated porous media. Analytical solution

An analytical study is made for wall effects in non-Darcy mixed convection from vertical impermeable surfaces embedded in a saturated porous medium. The governing equations are transformed into a dimensionless form by non-similar transformation to cover both forced and natural convection dominated regimes. Two different dimensionless parameters that measure the strength of mixed convection were found in both regimes. The parameters of forced convection dominated regime can be related to those of natural convection dominated regime. An approximate analytical solution for the governing equations was obtained. Temperature and velocity profiles for both regimes are presented. Received on 9 September 1997     

Level‐set based numerical simulation of a migrating and dissolving liquid drop in a cylindrical cavity

In the present paper the dissolution of a binary liquid drop having a miscibility gap and migrating due to thermo‐solutal capillary convection in a cylindrical cavity is studied numerically. The interest in studying this problem is twofold. From a side, in the absence of gravity, capillary migration is one of the main physical mechanisms to set into motion dispersed liquid phases and from the other side, phase equilibria of multi‐component liquid systems, ubiquitous in applications, often exhibit a miscibility gap. The drop capillary migration is due to an imposed temperature gradient between the cavity top and bottom walls. The drop dissolution is due to the fact that initial composition and volume values, and thermal boundary conditions are only compatible with a final single phase equilibrium state. In order to study the drop migration along the cavity and the coupling with dissolution, a previously developed planar two‐dimensional code is extended to treat axis‐symmetric geometries. The code is based on a finite volume formulation. A level‐set technique is used for describing the dynamics of the interface separating the different phases and for mollifying the interface discontinuities between them. The level‐set related tools of redistancing and off‐interface extension are used to enhance code resolution in the critical interface region. Migration speeds and volume variations are determined for different drop radii. Copyright © 2004 John Wiley & Sons, Ltd.