Convective stability of a binary mixture in a fractured porous medium

The effect of the gravity field and the concentration and thermal gradients on the convective stability of a mixture in a nonhomogeneous porous medium containing a system of thin highly permeable fractures separating relatively impermeable blocks is analyzed. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.1, pp. 88–97, January–February, 1994.     

Convective instability of a binary mixture with allowance for the Soret effect

The effect of weak mixture concentration on the threshold of convective instability of a binary mixture filling a cavity of arbitrary shape is investigated. In the case of thermally insulated boundaries in the neighborhood of the critical Rayleigh number monotonicity of perturbations is proved. This makes it possible to express the critical Rayleigh number for the mixture in terms of its analog for a single-component fluid at any values of the Soret parameter. In the general case of boundaries of arbitrary thermal conductivity an estimate of the critical Rayleigh number is obtained for small values of the Soret parameter.Perm'. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 161–165, November–December, 1996.     

Hard excitation of auto-oscillations in a Hagen-Poiseuille flow

Sufficiently powerful perturbations of the flow of a liquid moving in circular pipes results in turbulence, starting with Reynolds numbers of the order of 2200–2300 [1]. It has been established theoretically [2, 3] that the flow of a viscous incompressible liquid in a pipe of circular section (Hagen-Poiseuille flow) is stable with respect to infinitesimally small perturbations for all Reynolds numbers. Attempts to obtain finite-amplitude flow instability by considering only two-dimensional perturbations [4, 5] were also unsuccessful. This paper shows that the considered flow is unstable with respect to three-dimensional perturbations of finite amplitude.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 181–183, September–October, 1984.The author wishes to express sincere gratitude to G. I. Petrov and S. Ya. Gertsenshtein for their interest in his work.     

Suppression of auto-oscillations in wind tunnels with open working part

The results are given of an experimental investigation of the acoustic method of auto-oscillation suppression in wind tunnels of closed type with open working part.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 126–132, January–February, 1982.     

Calculation of auto-oscillations resulting from the loss of stability of a nonisothermal Couette flow

A study is made of the periodic (in time) auto-oscillatory regime (cycle) of azimuthal wave type which branches from a stationary nonisothermal Couette flow between rotating cylinders. Yudovich's method [1, 2] is used. It is shown that the cycle is unique (up to a shift along the axis z of the cylinders and rotation through any angle) and stable against spatially periodic three-dimensional perturbations. The results are given of a numerical calculation of the first two terms in the expansion of the cycle in Lyapunov-Schmidt series. The torque acting on the surface of the inner cylinder is calculated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 25–32, May–June, 1981.I thank V. I. Yudovich for constant interest in the work.     

Jumps in the density and temperature of one of the components of a binary gas mixture over the plane surface of a liquid

We consider a problem concerning the vaporization (or condensation) of one of the components of a binary gas mixture situated over the plane surface of a liquid. The kinetic equation in the model form of [1] is used to describe the system. As is well known, this model agrees well with experiment and is simpler than the Boltzmann equation so far as mathematical relations are concerned. This model fails to describe a number of effects because it is assumed that the collision time of the particles is independent of their velocity. This relates primarily to the phenomenon of thermal diffusion of the gases. Thus the formulas given below are applicable to gas mixtures having a small thermal-diffusion coefficient. The model equation is solved by an approximate method developed in [2]. In [3] the temperature jump of a single-component gas at a solid wall is calculated by this method, and the method is also employed in [4] in the calculation of the slipping rate of a binary gas mixture in the field of a temperature gradient. In both cases the results agree with numerical calculations by other authors within an accuracy of 1.5%.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 142–148, September–October, 1973.     

Boundary conditions for the equations of two-temperature gas dynamics of a binary mixture with strongly differing masses of the components

A study is made of the problem of the boundary conditions for the equations of two-temperature gas dynamics for a binary mixture with strongly differing masses when (m/M)^1/2 Kn 1 (Kn is the Knudsen number, m is the mass of the light molecules, and M the mass of the heavy molecules). The flow structure is established at velocities of the light and heavy components of the order of the velocity of sound of the heavy component. The formulation of the boundary conditions for the gas-dynamic equations is investigated. It is shown that the only closed boundary layer theory is Prandtl's theory taking into account terms of order Kn^1/2.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 93–98, September–October, 1982.I thank M. N. Kogan, N. K. Makashev, and E. S. Asmolov for assistance in the work and valuable discussions.     

Convective Acceleration in Porous Media

Transport in Porous Media - Convective acceleration occurs in porous media flows due to the spatial variations of the nonuniform flow channel geometry of natural pores. This article demonstrates...     

Convective instability in the presence of volume energy release

The problem of the convective instability of a plane fluid layer bounded by rigid walls with heating in a narrow layer running parallel to the walls inside the volume in question is solved. Instability criteria depending on the location of the heated layer and the Rayleigh numbers of the upper and lower layers are found. The results are compared with those for a plane layer with uniform energy release inside the volume. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 8–15, January–February, 1997. The work was carried out with partial support from the Russian Foundation for Fundamental Research (project No. 95-01-00354a).     

Convective diffusion in fissured-porous media

The mixing of a dynamically neutral admixture added to a stream flowing through a homogeneous porous medium is described by an equation of the diffusion type with some effective diffusion coefficient which varies linearly with the filter velocity in the flow region in which Darcy's law is obeyed [1]. According to the ideas developed in a whole series of papers [2–4] this process, also called convective diffusion, is due to the irregular nature of the porous canals through which the liquid moves. Molecular effects also play a definite role in the mechanism of mixing, and their relative contribution is greater, the lower the filter velocity.This paper proposes equations for convective diffusion in fissuredporous media with due regard to the specific nature of mixing in these media. The solutions of some problems are given. In conclusion the author thanks Yu. P. Zheltov for suggesting the theme and guidance in the work, and G. I. Barenblatt and V. M. Entov for valuable comments.In conclusion the author thanks Yu. P, Zheltov for suggesting the theme and guidance in the work, and G. I. Barenblatt and V. M. Entov for valuable comments.     

Convective instability of air in snow

Convective instability of air in the pores between ice crystals in snow is considered. In the Boussinesq approximation, a system of equations that describes the origin of thermal convection within the snow thickness is derived. It is shown that for snow, as for a liquid, there is a criterial number analogous to the Rayleigh number that determines the origin of air instability in snow. The contribution of natural convection of air to the heat- and mass-transfer processes in snow is estimated and possible reasons for the considerable scatter of reported experimental data on the thermal conductivity and diffusivity of snow are discussed. Kabardino-Balkarian State University, Nal'chik 360004. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 6, pp. 54–59, November–December, 1999.     

Convective oscillations in interconnected containers

We study an oscillating Instability of a nonuniformly heated liquid in interconnected containers. We examine the influence of the conditions of heat transfer and the geometric parameters on the critical Rayleigh number and the frequency of the stationary oscillations. We make a comparison of the theoretical results obtained with experimental results.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 4–9, July–August, 1974.     

Convective combustion of aerosuspensions in fuel that contains the oxidant

The convective combustion of porous gunpowder and high explosives is an intermediate stage in the transition from layered combustion to detonation [1, 2]. The theory of convective combustion of such systems is developed in [3–6]. It has now become necessary to analyze the possibility of convective combustion of aerosuspensions. The present paper develops the theory of the combustion of such systems on the basis of an analysis of the equations of gas dynamics with distributed supply of mass and heat; the problem of nonstationary motion of a convective combustion front is formulated. In the homobaric approximation [7], when the pressure is assumed to be spatially homogeneous, an analytic solution to the problem is found; this determines the law of motion of the front and the distribution of the parameters that characterize the gas and the particles in the combustion zone. Necessary conditions for the transition from convective combustion to explosion are obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 49–56, September–October, 1980.I thank R. I. Nigmatulin for helpful comments and advice, and also V. A. Pyzh and V. K. Khudyakov for discussing the work.     

Some Pitfalls in the Modelling of Convective Flows in Porous Media

Some modelling deficiencies in various recent papers, on convective flows in porous media, are pointed out and discussed. These deficiencies are related to the Forchheimer coefficient, mixed double-diffusive convection, magnetohydrodynamic mixed convection, convection in a rarefied gas, and geophysical phenomena.     

Spatial structures and scaling in the Convective Boundary Layer

We performed an investigation on spatial features of the Convective Boundary Layer (CBL) of the atmosphere, which was simulated in a laboratory model and analyzed by means of image analysis techniques. This flow is dominated by large, anisotropic vortical structures, whose spatial organization affects the scalar transport and therefore the fluxes across the boundary layer. With the aim of investigating the spatial structure and scaling in the Convective Boundary Layer, two-dimensional velocity fields were measured, on a vertical plane, by means of a pyramidal Lucas–Kanade algorithm. The coherent structures characterizing the turbulent convection were educed by analyzing the Finite-Time Lyapunov Exponent fields, which also revealed interesting phenomenological features linked to the mixing processes occurring in the Convective Boundary Layer. Both velocity and vorticity fields were analyzed in a scale-invariance framework. Data analysis showed that normalized probability distribution functions for velocity differences are dependent on the scale and tend to become Gaussian for large separations. Extended Self Similarity holds true for velocity structure functions computed within the mixing layer, and their scaling exponents are interpreted well in the phenomenological framework of the Hierarchical Structure Model. Specifically, β parameter, which is related to the similarity between weak and strong vortices, reveals a higher degree of intermittency for the vertical velocity component with respect to the horizontal one. On the other hand, the analysis of circulation structure functions shows that scaling exponents are fairly constant in the lowest part of the mixed layer, and their values are in agreement with those reported in Benzi et al. (Phys Rev E 55:3739–3742, 1997) for shear turbulence. Moreover, the relationship between circulation and velocity scaling exponents is analyzed, and it is found to be linear in the bottom part of the mixing layer. The investigation of the CBL spatial features, which has seldom been studied experimentally, has important implications for the comprehension of the mixing dynamics, as well as in turbulence closure models.     

Convective heat transfer in laser-irradiated graphite

The gas dynamic and thermal processes developing near the surface of graphite after exposure to a 20-nsec laser pulse with an energy E- 0.1–1 J and a wavelength of 0.6943 m are investigated experimentally and by mathematical modeling. The times required for the shock wave to degenerate into an acoustic wave are also considered. Typical density profiles over the axial section of the inhomogeneity are presented for various moments of time. It is noted that the rate of ascent of the thermal inhomogeneity is much higher than the free convection velocity. The convective heat-transfer processes are studied in detail through numerical solution of the system of two-dimensional Navier-Stokes equations. The results of the calculations are in satisfactory agreement with the experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 180–182, May–June, 1989.