Inertial obukhov-bolgiano interval in shell models of convective turbulence

The shell model of developed convective turbulence of an incompressible fluid is considered. Regimes developing at high Rayleigh numbers are investigated numerically for three- and two-dimensional motion. It is shown that in the three-dimensional turbulent convection model the inertial Obukhov-Bolgiano interval is developed on large scales, but this interval is unstable and gives way to the Kolmogorov regime in which the temperature behaves as a passive admixture. In the two-dimensional turbulent convection model a finite scale interval on which the buoyancy forces determine the nature of the fluctuations but the spectral laws established differ from those that follow from dimensional considerations for the Obukhov-Bolgiano interval is detected. Perm’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 37–46, November–December, 1998. The work was carried out with financial support from the Russian Foundation for Basic Research (project No. 94-01-00951a).     

Thermal convection in an acoustic field

The linear stability of flow in a horizontal fluid layer is investigated within the framework of thermoacoustic convection. The flow is initiated by a longitudinal temperature gradient and the propagation of an acoustic wave in the fluid. Instability modes corresponding to perturbations of both plane and longitudinal roller and oblique wave type are detected. Using weakly nonlinear analysis, it is shown that these regimes develop softly; the stability of various secondary flows is investigated for small supercriticalities. Perm’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 10–21, May–June, 2000. The work was carried out with partial support from the Program of State Support for Leading Science Schools (grant No. 96-015-96084).     

Thermal convection initiated by the quasistatic component of the microacceleration field on the “Mir” orbital station

The three-dimensional unsteady thermal convection developing in a cubic cavity on board the “Mir” station under the action of the quasistatic component of the microacceleration caused by the earth’s gravity field strength gradient and the motion of the station about the centre of mass is investigated numerically. The calculations are carried out for two real time intervals of motion of the station about the centre of mass using actual values of the quasistatic component. Moscow, Sankt-Peterburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 39–45, May–June, 2000.     

Bifurcation regimes of free convection in the presence of thermal radiation and cavity inclination

The bifurcation regimes of free convection in closed cavities with heating from below have been investigated numerically by many authors [1]. In the situations considered the equilibrium solution conditions were disturbed by only one factor, e.g. the inclination of the cavity to the vertical, the motion of one of the boundaries, a change in the equilibrium temperature distribution, etc. In this paper, the simultaneous influence of two factors that disturb the fluid equilibrium conditions, namely thermal radiation and a slight inclination of the cavity relative to the vertical, are investigated. It is shown that, for the simultaneous action of two destabilizing factors, a near-equilibrium solution is possible. Perm’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 42–47, January–February, 2000. The work received financial support from the Russian Foundation for Basic Research (project No. 96-01-01737).     

Effects of Viscous Dissipation on Unsteady Free Convection in a Fluid Past a Vertical Plate Immersed in a Porous Medium

The effects of viscous dissipation on unsteady free convection from an isothermal vertical flat plate in a fluid saturated porous medium are examined numerically. The Darcy–Brinkman–Forchheimer model is employed to describe the flow field. A new model of viscous dissipation is used for the Darcy–Brinkman–Forchheimer model of porous media. The simultaneous development of the momentum and thermal boundary layers are obtained by using a finite difference method. Boundary layer and Boussinesq approximation have been incorporated. Numerical calculations are carried out for various parameters entering into the problem. Velocity and temperature profiles as well as local friction factor and local Nusselt number are shown graphically. It is found that as time approaches infinity, the values of friction factor and heat transfer coefficient approach steady state.     

Azimuthal wave motions on the surface of a rotating fluid cylinder

Wave motions in a fluid cylinder rotating about the axis are investigated within the framework of the linear theory. The cylinder is assumed to be fairly long. This makes it possible to restrict attention to the study of the plane oscillation pattern. The fluid is assumed to be ideal and incompressible. The models in which the fluid particles are confined by gravitational (body) or/and capillary forces (surface stress forces) are considered. A mode analysis is carried out and the dispersion relations are constructed. Traveling and steady-state waves on the surface of the fluid cylinder are investigated; qualitative effects ("wave inertia") are established. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 128–133, May–June, 1998. The work was carried out with financial support from the Russian Foundation for Basic Research (project No. 96-01-00221). An erratum to this article is available at .     

Linear and nonlinear stability of double diffusive convection in a couple stress fluid–saturated porous layer

The linear and nonlinear stability of double diffusive convection in a layer of couple stress fluid–saturated porous medium is theoretically investigated in this work. Applying the linear stability theory, the criterion for the onset of steady and oscillatory convection is obtained. Emphasizing the presence of couple stresses, it is shown that their effect is to delay the onset of convection and oscillatory convection always occurs at a lower value of the Rayleigh number at which steady convection sets in. The nonlinear stability analysis is carried out by constructing a system of nonlinear autonomous ordinary differential equations using a truncated representation of Fourier series method and also employing modified perturbation theory with the help of self-adjoint operator technique. The results obtained from these two methods are found to complement each other. Besides, heat and mass transport are calculated in terms of Nusselt numbers. In addition, the transient behavior of Nusselt numbers is analyzed by solving the nonlinear system of ordinary differential equations numerically using the Runge–Kutta–Gill method. Streamlines, isotherms, and isohalines are also displayed.     

Motion of a cylinder below the free surface of a fluid at large froude numbers

A method of solving the problem of the motion of a cylinder of given shape below the free surface of an infinitely deep heavy fluid is perfected for large Froude numbers. The motion of a circular cylinder is investigated at small distances from the free surface. Solutions of the problem are given for cylinders with noncircular cross-sections. Kazan. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 34–45, July–August, 2000. The work was carried out with financial support from the Russian Foundation for Basic Research (projects Nos. 99-01-00169 and 99-01-00173).     

Bifurcation of self-similar solutions describing a thermocapillary flow of a fluid in a thin layer

Thermocapillary flows of a fluid in a lamina with a rigid lower wall and a free upper surface, along which the temperature gradient is given in the radial direction, are investigated for large Marangoni numbers. Self-similar solutions which describe the axisymmetric flow regimes of a fluid without the circumferential velocity component are constructed numerically and asymptotically for a system of Prandtl equations. It is shown that a pair of new self-similar flow regimes of a fluid with rotation branches off from the regimes obtained. The new regimes ere calculated numerically and asymptotically. Rostov State University, Rostov-on-Don 344090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 3, pp. 137–142, May–June, 1999.     

Effects of Temperature-Dependent Viscosity on Forced Convection Inside a Porous Medium

Considering the exponential viscosity–temperature relation, effect of temperature-dependent viscosity on forced convection of a liquid through a porous medium, bounded by isoflux parallel plates, is investigated numerically based on the general model of momentum transfer. Local effects of viscosity variation on the distribution of velocity and temperature are analyzed. Moreover, global aspects of the problem are investigated where corrections are proposed for total pressure drop and the fully developed Nusselt number, in the form of out/in viscosity ratio. Results are obtained over a wide range of permeabilities from clear (of solid material) fluid to very low permeability, where for constant properties one expects a nearly slug flow.     

Thermal convection in an acoustic field

Thermal vibrational convection is considered for an acoustic wavelength at the vibration frequency comparable with the dimensions of the cavity. Equations of the pulsatory and average motions of a medium that generalize the well-known equations of thermovibrational convection are obtained. Effective boundary conditions for average fields on rigid boundaries are formulated. The quasi-equilibrium stability problem for a plane horizontal layer heated from below and executing high-frequency oscillations is solved. It is shown that the compressibility effects can be significant even when the acoustic wavelength substantially exceeds the length of the layer. A destabilizing compressibility effect which can lead to instability of the layer even under conditions of weightlessness is established. Perm’, e-mail: lyubimov@psu.ru. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 28–36, March–April, 2000. The work was carried out with partial financial support from the Program of State Support for Leading Science Schools (project No. 96-015-96084).     

Stability of a fluid interface under tangential vibrations

The stability of the interface between two immiscible fluids of different density which occupy a plane horizontal layer performing harmonic horizontal oscillations is considered. Within the framework of the ideal fluid model a transformation reducing the problem of small plane perturbations to the Mathieu equation is found. Resonance instability domains associated with the formation of capillary-gravitational waves are investigated. A model which takes into account dissipation processes due to the presence of viscous friction is constructed. The role of the viscous dissipation in suppressing resonance instability is discussed. Perm’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 25–31, May–June, 1998. The work was carried out with partial support from the Russian Foundation for Basic Research (project No. 95-01-00386).     

Interaction of a supersonic pulse jet with an obstacle

The nonstationary interaction between a supersonic pulse jet and a flat plate perpendicular to the jet axis is studied experimentally and numerically. The time dependences of the pressure and heat flux at various points on the obstacle and the spatial distribution of the density are obtained experimentally. The nonstationary flow is calculated numerically by the Godunov method. The experiments and calculations reveal the effect of the reflected starting shock wave and the front part of the swirled gas outflow on the distribution of the dynamic and thermal loads acting on the plate, in both time and space. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 45–51, March–April, 1998. This research was carried out with partial financial support from the Russian Foundation for Fundamental Research (project No. 96-02-16170).     

Numerical and experimental study of the heat transfer and fluid flow by thermocapillary convection around gas bubbles

 At liquid–gas or liquid–liquid interfaces thermocapillary or Marangoni convection develops in the presence of a temperature or concentration gradient along the interface. This convection was not paid much attention up to now, because under terrestrial conditions it is superimposed by the strong buoyancy convection. In a microgravity environment, however, it is the remaining mode of natural convection. During boiling in microgravity it was observed at subcooled conditions. Therefore the question arises about its contribution to the heat transfer. Thus the thermocapillary convection was intensively studied at single gas bubbles in various liquids both experimentally and numerically. Inside a temperature gradient chamber, the overall heat transfer around single bubbles of different volume was measured with calorimetry and the liquid flow with PIV and LDV. In parallel to the experiment, a 2-dimensional mathematical model was worked out and the coupled heat transfer and fluid flow was simulated with a CV-FEM method both under earth gravity level and under microgravity. The results are described in terms of the dimensionless Nusselt-, Peclet-, Marangoni-, Bond- and Prandtl-number. Received on 23 August 1999     

Flow structures and heat transfer in anisotropic annular porous interlayers

The results of calculating the flow and heat transfer in annular porous interlayers are presented as functions of the Rayleigh number, the geometry of the interlayer, and the anisotropy of the permeability. The existence of single-vortex and multivortex convection regimes depending on the permeability anisotropy coefficient is established and their importance for the effectiveness of the heat-insulating properties of cylindrical interlayers is shown. Nizhnii Novgorod. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 122–128, July–August, 1998. The work was carried out with support from the Russian Foundation for Basic Research (project No. 96-01-000584).     

Numerical analysis of supersonic viscous gas flow past axisymmetric nonpointed bodies

Supersonic viscous homogeneous gas flow past axisymmetric smooth nonpointed bodies is analyzed numerically for widely varying Mach and Reynolds numbers and flow geometry. The initial equations of a viscous shock layer are solved by the stabilization method. The effect of the determining parameters on the flow character and the heat transfer distribution along the surface is analyzed. The accuracy and domain of applicability of several approximate approaches to the solution of the problem are estimated. Tomsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 107–117, January–February, 1999. This research was carried out with financial support from the Russian Foundation for Basic Research (project No. 98-01-00298).     

Multiphase Thermohaline Convection in the Earth’s Crust: II. Benchmarking and Application of a Finite Element – Finite Volume Solution Technique with a NaCl–H2O Equation of State

We present the benchmarking of a new finite element – finite volume (FEFV) solution technique capable of modeling transient multiphase thermohaline convection for geological realistic p-T-X conditions. The algorithm embeds a new and accurate equation of state for the NaCl–H₂O system. Benchmarks are carried out to compare the numerical results for the various component-processes of multiphase thermohaline convection. They include simulations of (i) convection driven by temperature and/or concentration gradients in a single-phase fluid (i.e., the Elder problem, thermal convection at different Rayleigh numbers, and a free thermohaline convection example), (ii) multiphase flow (i.e., the Buckley–Leverett problem), and (iii) energy transport in a pure H₂O fluid at liquid, vapor, supercritical, and two-phase conditions (i.e., comparison to the U.S. Geological Survey Code HYDROTHERM). The results produced with the new FEFV technique are in good agreement with the reference solutions. We further present the application of the FEFV technique to the simulation of thermohaline convection of a 400°C hot and 10 wt.% saline fluid rising from 4 km depth. During the buoyant rise, the fluid boils and separates into a high-density, high-salinity liquid phase and a low-density, low-salinity vapor phase.     

Modeling of heat and mass transfer in a hydrocarbon fluid under inductive heating

Results of numerical simulations of the thermal action on a high-viscosity hydrocarbon fluid with temperature-dependent viscosity and thermal conductivity are presented. A system of equations of thermal convection in the Boussinesq approximation is used as the constitutive equations to describe the convection of the hydrocarbon fluid. The dynamics of the temperature field and convective structures in the fluid is studied. The spatial motion of the fluid is found to be locally nonuniform; the motion is accompanied by vortex flows; as a result, two regions with significantly different temperatures are formed in the medium. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 1, pp. 95–100, January–February, 2009.     

Equations of convective instability of a two-phase medium with modulation of the gravity force

Thermal convection in a heterogeneous medium consisting of a fluid and solid particles is studied under conditions of finite-frequency vibrations. Equations of convection are derived within the framework of the generalized Boussinesq approximation, and the problem of stability of a horizontal layer to infinitesimal perturbations under the condition of vertical vibrations is considered. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 2, pp. 21–28, March–April, 2008.     

Anomalous gravitational instability of mechanical equilibrium during diffusion mixing in isothermal three-component gas mixtures

A theoretical model determining the condition of onset of free gravitational convection in an isothermal ternary gas mixture with inhomogeneous concentrations and stable vertical density stratification (the density is lower at the top than at the bottom) is developed. The model is in satisfactory agreement with the experimental data on the determination of the boundaries between diffusion zones under conditions of mechanical equilibrium and convective mixing in a gravity force field in a vertical capillary connecting two vessels with ternary gas mixtures. Almaty. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 185–192, May–June, 2000. The work was carried out with financial support from the Science Foundation of the Kazakhstan Republic and the Russian Foundation for Basic Research (project No. 98-01-00879).