The convective instability of Maxwell fluid-saturated porous layer using a thermal non-equilibrium model

A linear stability analysis is carried out to study viscoelastic fluid convection in a horizontal porous layer heated from below and cooled from above when the solid and fluid phases are not in a local thermal equilibrium. The modified Darcy–Brinkman–Maxwell model is used for the momentum equation and two-field model is used for the energy equation each representing the solid and fluid phases separately. The conditions for the onset of stationary and oscillatory convection are obtained analytically. Linear stability analysis suggests that, there is a competition between the processes of viscoelasticity and thermal diffusion that causes the first convective instability to be oscillatory rather than stationary. Elasticity is found to destabilize the system. Besides, the effects of Darcy number, thermal non-equilibrium and the Darcy–Prandtl number on the stability of the system are analyzed in detail.     

Convective instability of a horizontal layer of fluid between permeable membranes

The equilibrium stability is investigated of a system consisting of two semi-infinite isothermal masses of fluid divided by a horizontal layer of finite thickness of the same fluid with a vertical temperature gradient directed downwards. The transition layer is separated by thin permeable membranes. Neutral stability curves are constructed for different membrane resistances. In the case of high permeability, the equilibrium is absolutely unstable with respect to monotonic-type longwave perturbations. For low permeability membranes, instability with respect to monotonic finite-wavelength perturbations is characteristic.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 171–173, July–August, 1985.     

Linear stability of relative equilibria with a dominant mass

A criterion for the linear stability of relative equilibria of the Newtoniann-body problem is found in the case whenn–1 of the masses are small. Several stable periodic orbits of the problem are presented as examples.     

The uniqueness of the solution of boundary-value problems of a thermal model of discharge

The paper is devoted to a nonlinear analysis of superheating [1, 2] instability of an electric discharge stabilized by electrodes [3] in the framework of a thermal model [4] where the stability of the discharge relative to the long-wave and short-wave perturbations is proved in a linear approximation. Similar boundary-value problems arise in the theories of chemically and biologically reacting mixtures [5–7], thermal breakdown of dielectrics [8], thermal explosion [9], in the investigation of nonlinear waves in semiconductors and superconductors [10, 11], and in the investigation of Couette flow with variable viscosity [12]. The uniqueness of the one-dimensional steady solutions of the thermal model of discharge and the stability relative to the small spatial perturbations, respectively, for the exponential and step dependence of the electrical conductivity on the temperature are proved in [3, 13]. The uniqueness of the solutions in the one-dimensional case for the same electrode temperature and arbitrary dependences of the electrical and thermal conductivity on the temperature is established in paper [14]. In the present paper, the existence and uniqueness of steady solutions of the thermal model of discharge in a three-dimensional formulation for arbitrary fairly smooth electrical and thermal conductivity functions of the temperature in the case of isothermal isopotential electrodes are proved analytically.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 140–145, January–February, 1986.The author expresses his gratitude to A. G. Kulikovskii and A. A. Barmin for the formulation of the problem and their discussions.     

Investigation of hydrodynamic and heat and mass transfer processes for crystal growing by the Czochralski method

A mathematical model and numerical method are developed and used to investigate nonstationary flow and heat and mass transfer regimes in a melt appropriate to the conditions of Czochralski crystal growth. A study is made of the separate and combined influence of rotation and thermal, concentration, and thermocapillary convection on the distribution of the temperature and the dopant in the range of regime parameters corresponding to large charging masses of the melt with small value of the kinematic viscosity. Large-scale fluctuations are found to occur when rotation and thermal convection interact. Thermocapillary convection is shown to have an important influence on the resulting motion when it interacts with the thermal and concentration forms of convection. A comparison is made with the results of experimental and theoretical investigations of other authors.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 55–65, January–February, 1981.     

Diffusion and thermal slip of a binary gas mixture

Let us note that the phenomenon of diffusion slip at a constant gas-mixture temperature has been considered in [1], for example, and thermal slip for a single-component gas in [2]. The slip velocity of a binary gas mixture has been calculated in a field of the temperature gradient and of the partial pressure gradients. The kinetic equation is solved by an approximate method based on physical considerations. A formula has been obtained analytically for the slip velocity for arbitrary accommodation coefficients as well as for arbitrary gas concentrations and arbitrary molecule masses. The results agree to 1% accuracy with the numerical computations of other authors.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 51–55, July–August, 1970.     

Stability of combustion of powder in a phenomenological model with nonadiabatic flame

A stability criterion for combustion of powder is obtained, taking into account the effect of the processes in the gas phase. It is shown that consideration of the effects of a nonadiabatic flame leads to the stability reserve of combustion being reduced and the natural frequency of vibrations being lowered. The effects thus found are physically explained by the radiation of a part of energy from the combustion zone with thermal and acoustic waves.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 82–87, November–December, 1973.Deceased.     

Stability of Thermocapillary Flow in a Flat Layer with Allowance for the Soret Effect

The stability of thermocapillary two-component liquid flow is studied taking into account thermal diffusion. An explicit expression is obtained to construct neutral Marangoni numbers under the assumption of monotonicity of perturbations. The thermocapillary and hydrodynamic instability mechanisms are considered. It is shown that plane perturbations are the greatest hazard to the stability of return flow.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 5, pp. 86–92, September–October, 2005.     

Effect of condensed powder phase reactions on the stability of steady-state combustion processes

A study has been made of the low-frequency stability of powder combustion in a semiclosed chamber, working within the framework of a linear theory with account taken of condensed-phase (k-phase) inertia and evolution of thermal energy. The case treated is that of the first-order reaction. It is shown that k-phase exothermic chemical decomposition increases the stability of the combustion process. The results of numerical computations are interpreted.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 102–111, September–October, 1973.     

Instability of convective flow of water near 4 °C

A study is made of the stability of the plane-parallel convective flow of water in a plane vertical layer bounded by planes heated to different temperatures in the region of anomalous thermal expansion.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 189–192, March–April, 1979.     

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.     

Convection in mixtures with nonuniform heat release proportional to the density of an active component

A study is made of the stability of a horizontal layer of a two-component mixture with concentration gradient of the active (heat releasing) component directed upward. The nature of the instability depends strongly on the direction of the gradient. In the investigated case, the stability may be either monotonic or oscillatory in nature. The problem is also distinguished by the existence of two independent neutral curves associated with the thermal and concentration instability mechanisms. The regions in which monotonic and oscillatory convection occur are found by stepwise integration. Graphs of the amplitudes of the critical perturbations of the velocity, temperature, and concentration are given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 21–27, November–December, 1980.We thank E. M. Zhukhovitskii for discussing the results.     

The necessary conditions for stable combustion of a powder in a half-closed chamber

The low-frequency stability of the steady-state combustion cycle is investigated in linear approximation for a powder in a half-closed chamber, taking account of incompleteness of combustion, heat losses at the walls, and dynamic erosion. The necessary conditions for stable combustion are obtained. Qualitative conclusions are drawn of the incompleteness of the chemical reactions taking place and of the destabilizing effect of thermal losses and erosion on the combustion process. Only two out of three possible steady-state mechanisms are stable. The existence of limits of combustion with respect to pressure is shown.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 90–98, November–December, 1972.     

Development of two- and three-dimensional perturbations in the case of an ionization instability in a channel with nonconducting walls

An lonization instability of a plasma bounded by nonconducting walls is investigated taking into account electron thermal conduction. The wave vector is considered directed at some angle to the magnetic field direction. Perturbations with a wave vector orthogonal to the magnetic field induction vector turn out to be most unstable. A relatively simple formula to compute the neutral curve separating the stability and instability domains is obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 119–123, May–June, 1976.     

Stability of convective motion caused by inhomogeneously distributed internal heat sources

The stability of steady convective plane-parallel flow in a vertical layer of viscous incompressible liquid of thickness h is investigated. The motion is caused by heat sources distributed in the liquid with volume density Q = Q₀exp (^–x) (the x axis is taken perpendicular to the boundary layer). The region of instability is determined for various values of the Prandtl number and the parameter N = h characterizing the inhomogeneity of the internal sources. It is shown that with increase in N there is qualitative rearrangement of the stability limit for perturbations of hydrodynamic type and incremental thermal waves.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 140–144, May–June, 1977.     

Upper and lower bounds for constitutive relation of crack-weakened rock masses under dynamic compressive loads

A micro-mechanics-based model is proposed to investigate the rate-dependent constitutive relation for crack-weakened rock masses subjected to dynamic compressive loads. The present micro-mechanical model reveals that the nucleation, growth and coalescence of sliding cracks dominate the failure and macroscopic properties of crack-weakened rock masses subjected to dynamic compressive loads. The interactions among multiple parallel sliding cracks in crack-weakened rock masses subjected to dynamic compressive loads are examined asymptotically in an explicit and quantitative manner in order to reveal fully their so-called shielding and magnification effects on the stress–strain relation. Based on the micro-mechanical framework and the asymptotic analysis, analytical upper and lower bounds are proposed for the rate-relation for rock masses containing multiple rows of echelon cracks subjected to dynamic compressive loads. The factors that affect the rate-dependent properties of crack-weakened rock masses have been analyzed. The strain energy density factor approach, which is related to crack growth velocity and dynamic fracture toughness of rock material, is employed in the analysis. The rate-dependent constitutive relation of crack-weakened rock masses is derived from micro-mechanical framework and the asymptotic analysis. The closed-form explicit expression for the rate-dependent constitutive relation of rock masses containing echelon cracks subjected to dynamic compressive loads is obtained. Finally, the present model is used to analyze the complete stress–strain relation and strength for jointed rock masses at shiplock slope of the Three Gorges Dam.     

Convective stability of a weakly conducting liquid in an electric field

In an inhomogeneously heated weakly conductive liquid (electrical conductivity 10^–12–1 cm^–1) located in a constant electric field a volume charge is induced because of thermal inhomogeneity of electrical conductivity and dielectric permittivity. The ponderomotive forces which develop set the liquid into intense motion [1–6]. However, under certain conditions equilibrium proves possible, and in that case the question of its stability may be considered. A theoretical analysis of liquid equilibrium stability in a planar horizontal condenser was performed in [2, 4]. Critical problem parameters were found for the case where Archimedean forces are absent [2]. Charge perturbation relaxation was considered instantaneous. It was shown that instability is of an oscillatory character. In [4] only heating from above was considered. Basic results were obtained in the limiting case of disappearingly small thermal diffusivity in the liquid (infinitely high Prandtl numbers). In the present study a more general formulation will be used to examine convective stability of equilibrium of a vertical liquid layer heated from above or below and located in an electric field. For the case of a layer with free thermally insulated boundaries, an exact solution is obtained. Values of critical Rayleigh number and neutral oscillation frequency for heating from above and below are found Neutral curves are constructed. It is demonstrated that with heating from below instability of both the oscillatory and monotonic types is possible, while with heating from above the instability has an oscillatory character. Values are found for the dimensionless field parameter at which the form of instability changes for heating from below and at which instability becomes possible for heating from above.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 16–23, September–October, 1976.In conclusion, the author thanks E. M. Zhukhovitskii for this interest in the study and valuable advice.     

Nonisothermal instability of high-velocity elastoplastic flows

An important feature of the high-velocity deformation of solids is the localization of deformation, one of the causes of which may be the nonisothermal instability of plastic flow [1–6]. In connection with the intensive development of high-velocity technology in the treatment of materials, the investigation of the criteria for nonisothermal stability of processes of plastic deformation is of fundamental interest, since in certain cases they determine the optimum technological regimes [5]. The critical values of deformation velocities, above which the effects of thermal instability becomes decisive in the process of deformation of solids, are estimated by semiempirical methods in [1]. The non-boundary-value problem of the criteria for nonisothermal instability is analyzed in [2] for the point of view of flow stability in the so-called coupled formulation. The latter means that the heat-conduction equation is added to the basic equations determining the dynamics of an elastoplastic medium. The problem is solved in [6] in an analogous formulation, but for flow averaged over the spatial coordinate. The solution of the boundary-value problem for one-dimensional flow in this formulation is given in the present paper.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 133–138, May–June, 1986.     

Container for Localization of an Explosion of a Compact High–Explosive Charge with an Inert Shell

Results of an experimental study of fragmentation effects in the explosion and the piercing power of the fragments of inert masses in the form of hemispherical aluminum and soft–steel shells enclosing the spherical charge of a high explosive under their action on flat steel, aluminum, steel–net, and claydite—concrete barriers are given. A design of the lightest spherical explosion–proof container with a load–carrying steel or glass–reinforced plastic shell protected by a splinter–proof layer capable of withstanding an explosion of a high–explosive charge (with a twofold safety factor) with an inert steel shell is proposed.     

Vibrational thermal convection in a cavity executing high-frequency rocking motions

The vibrational thermal convection in a cavity executing high-frequency rocking motions is investigated. The equations of vibrational convection are obtained by the method of averaging. It is shown that rocking motions lead to some new and distinctive effects. The convective stability in a plane layer in the presence of such vibrations is investigated on the basis of the obtained equations. A comparison with known experimental data is made. The results of experiments confirm the theoretical conclusions drawn on the basis of the averaged equations of vibrational convection.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 138–144, May–June, 1988.I thank E. M. Zhukhovitskii for helpful discussion.