Convective instability of a horizontal fluid layer with a heat-conducting permeable partition

Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 158–161, March–April, 1993.     

Convective heat transfer in a rotating horizontal cylindrical fluid layer

This paper describes the thermal convection and heat transfer in a cylindrical fluid layer rotating around a horizontal axis, with various constant temperatures set at the layer boundaries. The influence of the rotational speed of the cylindrical fluid layer on the convective heat transfer in this layer is studied. The study results are presented as functions of dimensionless parameters that characterize the action of two convective mechanisms: centrifugal and thermal-oscillatory. It is shown that, with low rotational speed, the heat transfer is determined by quasistationary gravitational convection.     

Convective instability of a plane horizontal layer of weakly conducting fluid in alternating and modulated electric fields

The electrothermoconvective instability of a plane horizontal layer of weakly conducting fluid in a modulated vertical electric field is investigated. The analysis is based on the electrohydrodynamic approximation. The stability threshold in the linear approximation is found using Floquet’s theory. The effect of periodic modulation on the fluid behavior is studied in both the presence and the absence of the constant component of the electric field. It is shown that modulation can stabilize the unstable ground state or destabilize fluid equilibrium, depending on the amplitude and frequency. In addition to a synchronous or subharmonic response to an external forcing, the instability may be associated with two-frequency (quasiperiodic) perturbations. The cases of weightlessness and a transversely stratified fluid in a static gravity field are considered. Madrid, Perm’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 31–38, May–June, 2000. The investigations whose results are presented in this paper were supported by the Russian Foundation for Basic Research (project No. 98-01-00507).     

Effect of a permeable partition on convective instability of a horizontal liquid layer

We consider the effect of a thin permeable partition on the static stability of a horizontal liquid layer heated from underneath. The permeable partition is assumed to be plane and situated parallel to the boundary planes in the center of the layer. The resistance of the partition to the flow of liquid from one part of the layer to another leads to an increase in the static stability. We investigate the dependence of the minimum critical Rayleigh number-on the resistance of the partition and the form of the critical motions.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 157–159, January–February, 1977.     

Convective stability of a horizontal rotating fluid layer with helical turbulence

The problem of the corrective stability of a horizontal layer of turbulent fluid rotating about a vertical axis with a fixed heat flow at the boundaries is investigated in the case in which the intensity of the helical background does not depend on the rate of rotation and the degree of heating.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 33–39, January–February, 1992.The author is grateful to S. S. Moiseev for proposing the subject and to G. Z. Gershuni and D. V. Lyubimov for useful discussions.     

Convective stability of a horizontal rotating fluid layer with distributed heat sources

The results of investigating the convective instability of a horizontal layer of rotating fluid, created by a temperature difference applied at the boundaries of the layer and by heat sources distributed according to various laws, are presented. It is shown that, when the other parameters of the problem are fixed, an increase in the internal heat release lowers the limits of both monotonic and oscillatory stability of the layer, increases the wave number and reduces the neutral oscillation frequency. An increase in source concentration towards the center of the layer intensifies the effect. As the strength of the internal heat sources and their concentration towards the center of the layer increase, the oscillating convection that develops at the stability limit when the Prandtl number is low and the rotation fairly fast is first replaced by monotonic convection and then ceases altogether.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 21–28, January–February, 1989.     

Steady convective motions in a plane horizontal fluid layer with permeable boundaries

In a plane horizontal fluid layer bounded by permeable plane surfaces which are heated to different temperatures and between which transverse flow takes place with uniform velocity, convection occurs at a definite critical Rayieigh number. The study of the disturbance spectrum and the convective stability, made within the framework of linear theory in [1], showed that convective instability in the layer with permeable boundaries, just as in the case of the Rayieigh problem, is associated with the development of monotonie disturbances. It turns out that the transverse motion in the layer leads to a considerable increase of the Rayieigh number. Linear theory does not permit analysis of the development of the disturbances in the supercritical region. Analysis of the developed nonlinear motion can be made only on the basis of the complete nonlinear convection equations.In this investigation we made a numerical study of nonlinear motions in the supercritical region. Calculations were made on a computer via the grid method. Solutions are obtained for the nonlinear equations of motion over a wide range of Rayieigh numbers for different values of the Peclet number, whichdefines the intensity of the transverse motion in the layer.The author wishes to thank E. M. Zhukovitskii for his guidance, and G. Z. Gershuni and E. L. Tarunin for their interest and assistance in the study.     

Convective instability of a rotating fluid

A physical system may be in thermodynamic equilibrium when participating as a whole in uniform rotational motion [1]. In particular, mechanical equilibrium of a liquid in a cavity rotating about a stationary axis with the constant angular velocity (solid-body rotation of the liquid) is possible. If the liquid is uniform in composition and isothermal, then such equilibrium, as shown in [2], is stable for all . However, in the case of a nonuniformly heated liquid, stability of the solid-state rotation is, generally speaking, impossible.The appearance of two steady-state force fields is associated with uniform rotation: the centrifugal field and the Coriolis force field. The former field forces the liquid elements which are less heated and therefore more dense to move away from the axis of rotation, displacing the less dense liquid layers (centrifugation). If we maintain in the liquid a temperature gradient which prevents the establishment of equilibrium stratification of the liquid, then with a suitable value of this gradient (the magnitude obviously depending on ) undamped flows—convection—will develop in the liquid. Thus, while in conventional gravitational convection the gravity field is the reason for the appearance of the Archimedes buoyant forces, in the rotating cavity the mixing of the nonuniformly heated liquid is caused by the centrifugal field. As soon as the convective flows arise the Coriolis forces come into play. Account for the latter, as is shown below, prevents reducing in a trivial fashion the study of convective stability of rotating liquid to the well-studied problems of gravitational convection.     

Vibrational-convective instability of a horizontal fluid layer with internal heat sources

The convective motion of a nonisothermal fluid in a gravity field in a vibrating cavity is caused by two mechanisms: the usual static mechanism and a vibrational mechanism. The same mechanisms are also responsible for mechanical equilibrium crisis under the conditions in which such equilibrium is possible. The research on these questions is reviewed in [1]. The problems of vibrational-convective stability examined so far relate to cases in which the nonisothermicity was created by specifying the temperature at the boundaries of the region. The present study is concerned with the vibrational-convective stability of a fluid in which the temperature nonuniformity is created by internal heat generation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 3–7, September–October, 1985.     

Convective instability in a rapidly rotating fluid layer in the presence of a non-uniform magnetic field

Magnetoconvective instabilities in a rapidly rotating, electrically conducting fluid layer heated from below in the presence of a non-uniform, horizontal magnetic field are investigated. It was first shown by Chandrasekhar that an overall minimum of the Rayleigh number may be reached at the onset of magnetoconvection when a uniform basic magnetic field is imposed. In this paper, we show that the properties of instability can be quite different when a non-uniform basic magnetic field is applied. It is shown that there is an optimum value of the Elsasser number provided that the basic magnetic field is a monotonically decreasing or increasing function of the vertical coordinate. However, there exist no optimum values of the Elsasser number that can give rise to an overall minimum of the Rayleigh number at the onset of magnetoconvection if the imposed basic magnetic field has an inflexion point. The project supported by the National Natural Science Foundation of China (40174026 and 40074041)     

Vibrational and convective instability of a plane horizontal fluid layer at finite vibration frequencies

The vibrational-convective instability of a plane horizontal fluid layer subject to longitudinal harmonic vibrations of finite frequency and transverse stratification in a static gravity field is studied. The analysis is based on the complete convection equations in the Boussinesq approximation. It is demonstrated that in the limiting case of high-frequency vibrations the results thus obtained coincide with those obtained earlier on the basis of the averaged equations. In the limiting low-frequency case the nature of the instability is quite different being due to the instability of oscillating counterstreams.Perm'. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 44–51, September–October, 1996.     

Convective stability of fluid in a rotating horizontal annulus

The convective stability of quasi-equilibriumof a fluid layer formed by two horizontal coaxial cylindrical surfaces which have different temperatures and rotate at the same angular velocity about the axis of symmetry is investigated theoretically and experimentally. Consideration is carried out from the standpoint of thermal vibrational convection caused by the average lifting force generated as a result of vibrations of a nonisothermal fluid with respect to the cavity. The vibrations are induced by an external field. The action of the centrifugal force field is also taken into account. Stability of mechanical quasi-equilibrium with respect to monotonic plane perturbations, which are, as shown experimentally, the most dangerous, is studied within the framework of the linear analysis. The stability boundaries are constructed for layers of various relative thickness in the plane of control parameters, the centrifugal and vibrational Rayleigh numbers. The thresholds of excitation of two-dimensional convective structures obtained experimentally are in good agreement with the theoretical ones.     

Convective instability of a fluid in two-layer saturated strata

The problem of convective instability of a fluid in a system consisting of two horizontal porous strata with different permeabilities and a permeable common boundary is considered. The problem is investigated in parametric form as a function of the stratum thickness ratio and stratum permeabilities. As distinct from a uniform stratum, in this case the neutral curve can have one or two minima depending on the relationship between the parameters. The case of two minima is characterized by the condition of loss of stability of the fluid in the system as a whole and in the thinner stratum with greater permeability. These minima correspond to significantly different wave numbers. Makhachkala. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 165–169, January–February, 1999.     

Convective instability of a system of horizontal layers of slightly compressible liquids

The convective stability of a system of two immiscible liquids with close densities is studied. The densities of the liquids depend nonlinearly on temperature and pressure. It is shown that the state of mechanical equilibrium is unstable. Neutral curves are plotted, and the critical values of the Rayleigh number are found. The calculations are performed for physical parameters characteristic of various northern, central, and southern zones of lake Baikal. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 4, pp. 15–22, July–August, 2007.     

Taylor instability in a thin fluid layer

Summary The Stokes-Taylor instability of a thin fluid layer is studied by the usual first order perturbation method. The density of the layer is assumed to be constant or to vary exponentially through it. It is bounded on either side by media of constant density. Particular attention is paid to determining the exponential rates of growth of perturbations at the two interfaces, and the effect of the layer in reducing the instability of the interface between the bounding media formed in the absence of the layer. When the layer is of variable density and the acceleration acts in the direction of increasing density, there is an infinity of modes of internal instability which do not affect the interfaces. There are also two modes of interfacial instability which are similar to those occurring when the layer is of constant density.     

Convective stability of a horizontal binary-mixture layer on temperature gradient modulation

The free convection of a binary mixture in a horizontal cavity is numerically investigated on modulation of the temperature gradient about a certain mean value. The binary mixture stability diagrams are plotted in the modulation amplitude/frequency plane. It is shown that the modulation of the equilibrium temperature gradient may be both a stabilizing and a destabilizing factor in relation to the case in which the modulation is absent. The influence of the skin layer effect on the convective stability of the mechanical equilibrium of the mixture is studied by comparing the solution of this problem in the approximation of a low modulation frequency with that in a more accurate formulation. The skin effect is shown to be a stabilizing factor at high modulation frequencies; with decrease in the frequency it starts to play a destabilizing role, while at fairly low frequencies its effect is negligible.     

Heat mass transfer in a turbulent layer above permeable membranes

The temperature and concentration fields in a boundary layer above perforated membranes are presented, and their relationship with the velocity fields given in [1] is established. Measurements of the thermal state of membranes are made with various geometric and thermophysical properties and various coolant drafts. Empirical formulas are also presented for thermal flux and temperature of the permeable walls.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 22–31, July–August, 1973.     

Convective stability of a nonisothermal fluid in a rotating horizontal coaxial gap

The thermal fluid convection in a coaxial horizontal gap uniformly rotating about its axis is investigated. The threshold above which convective flows are excited and the structure of these flows are studied. It is found that convection ensues irrespective of whether the inner or outer boundary temperature is higher. Convection manifests itself in the threshold development of rolls elongated in the direction of the rotation axis and is determined by two different mechanisms. If the layer is heated from outside, the centrifugal convection mechanism plays a leading part and the diameter of the convective rolls is comparable with the layer thickness. If the higher is the temperature of the inner boundary of the layer, the centrifugal inertia force has a stabilizing effect and convection development is related with the action of thermal vibrational mechanism. The latter is determined by gravity-generated oscillations of the nonisothermal fluid relative to the cavity. The wave number of the vibrational convective structures is several times smaller than under centrifugal convection. The results obtained broaden our understanding of thermal convection in systems rotating in external static force fields.