Entrainment of dispersed impurities into the atmosphere by a rising thermal

The ascent of a dusty turbulent thermal in a nonuniform compressible atmosphere is numerically investigated. The dispersed phase is described in the one-velocity and one-temperature approximation. A comparative calculation of the entrainment of active and passive impurities into the stratosphere is made, the vertical aerosol density distribution in the hanging cloud is obtained, and the maximum amount of active impurity that can be carried beyond the tropopause by a thermal of given energy is determined. The ascent of a thermal formed in an air blast is contrasted with that of a thermal formed in a surface blast, and the results of the calculations are compared with previously published data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 123–130, January–February, 1990.     

Self-similar axisymmetric thermal in a variable-density medium

A model of a turbulent axisymmetric thermal rising in a medium whose density varies with height is proposed. An analytic solution describing the self-similar stage of ascent of the thermal is constructed. The effect of the density stratification of the atmosphere on the structure of the thermal during its motion is analyzed, and relations describing the characteristic points of the thermal and the smearing of its leading edge are obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 45–53, July–August, 1991.     

Drift of large-scale hot thermals in stratified air flows

A difference method developed for the calculation of the three-dimensional unsteady flows of a viscous heat-conducting gas is used to investigate the influence of a horizontal wind, stratified with respect to height, on the motion of the eruption clouds of a volcano. It is shown that as the intensity of the air flow rises and its stratification increases the rate of ascent of the thermal decreases. Data are obtained for the features of the motion of the vortex rings formed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 173–176, November–December, 1984.     

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.     

Nonlinear problems of the thermal conductivity equation

The asymptotic behavior of solutions of parabolic equations at infinite times has been investigated for various cases [1–6]. Two initial boundary-value problems are considered in this paper. The solution of the thermal conductivity equation with a nonlinear right-hand side is found, including also nonlinear boundary conditions. It is shown that the solution of the corresponding problem tends either to a stable, steady-state solution, or to a periodic solution, depending on the initial values of the functions and constants appearing in the conditions of the problem. Other papers [7, 8] are devoted to finding the periodic solutions of these two problems encountered in hydrodynamics (diffusion, underground hydrodynamics), and to studying the asymptotic behavior of the corresponding initial boundary problems.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 123–128, May–June, 1972.     

Modeling of Heat and Mass Transfer in Absorption in Two–Phase Binary Systems used in Heat Pumps

Results of modeling of heat– and mass–transfer processes proceeding simultaneously in vapor absorption on tube banks are described. Theoretical models of film absorption are presented. The calculation results are compared with experimental data on steam absorption by the lithium bromide solution on a vertical tube. In calculation of transfer processes in absorption on horizontal tubes, the possibility of using solutions for the initial thermal length and for the section with a linear temperature profile is substantiated. The calculations are illustrated by the example of a multipass absorber.     

Numerical modeling of the ascent of surface thermals

The problem of the ascent of large-scale hemispherical clouds of hot gas from the vicinity of a rigid, thermally insulated surface is investigated numerically.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 129–135, March–April, 1989.     

Conservation of the resultant force vector in the plane of the angle of attack for slender star-shaped bodies in supersonic flows

At high supersonic flight speeds bodies with a star-shaped transverse and power-law longitudinal contour are optimal from the standpoint of wave drag [1–3]. In most of the subsequent experimental [4–6] and theoretical [6–9] studies only conical star-shaped bodies have been considered. For these bodies in certain flow regimes ascent of the Ferri point has been noted [10]. In [11] the boundary-value problem for elongated star-shaped bodies with a power-law longitudinal contour was solved for the case of supersonic flow. The present paper deals with the flow past these bodies at an angle of attack. It is found that for arbitrary star-shaped bodies with any longitudinal (in particular, conical) profile the aerodynamic forces can be reduced to a wave drag and a lift force, the lateral force on these bodies being equal to zero for any position of the transverse contour.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 135–141, November–December, 1989.     

Laws of ascent of two volumes of hot gas

The three-dimensional interaction of a pair of thermals spaced a certain distance apart in the horizontal direction is numerically investigated. It is found that the distance between the thermals has a determining effect on the interaction pattern, the height of ascent of the pair, and the structure of the airstreams in the troposphere and atmosphere which they initiate.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 48–51, May–June, 1996.     

Electric arc in a submerged gas jet

The results of photographic studies of the behavior of an electric arc in a submerged gas jet, using both regular photography and still and cine shadow photography, are presented. The interaction of the arc with the turbulent portion of the jet and the development of disturbances in the arc and the thermal layer around the arc dependent on initial jet velocity are noted. Experimentally obtained values for extent of the arc laminar zone, radius of arc thermal layer, and electric field intensity are compared with calculated values.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 17–23, September–October, 1971.     

Differential equation for a stratified fluid and its particular solutions

The plane steady motion of a stratified ideal incompressible fluid in a gravity field is examined. Considering that the parameter characterizing the fluid particles — their density ₀ — is constant along the streamline, it is convenient to take the stream function as one of the independent variables and, in view of the presence of the gravity force, the Cartesian coordinate as the other. In this study, on the basis of Lavrent'eva's equation [1, 2, 3], the differential equation is derived for a single unknown function — the vertical displacement of the streamline y(y₀, x), where y₀ is its initial position and x is the horizontal coordinate. The particular solutions corresponding to a wave guide, cnoidal and solitary waves and, moreover, waves of the type corresponding to a smooth ascent to a new level are presented. A similar coordinate system was used in [4], but there the problem was reduced to a system of partial differential equations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 83–87, September–October, 1986.The authors are grateful to A. A. Barmin for discussing their results.     

Convective transport of combustion products in the atmosphere above large fires

A nonstationary axisymmetric model of the development of a turbulent convective combustion product column above a fire in a stratified atmosphere is proposed. The model takes into account the compressibility of the gas and the diffusion of the aerosol particles and makes it possible to predict the dynamics of ascent of the convective column, the height of the cloud and the distribution of the aerosol in the atmosphere. The numerical and experimental data are compared.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 47–52, July–August, 1990.     

Unsteady thermocapillary convection in a nonuniformly heated fluid layer

In many technological processes, thin extended layers of nonuniformly heated fluid are used [1–3]. If they are sufficiently thin, thermocapillary forces have a decisive influence on the occurrence and development of motion of the fluid [4–6]. Investigation of convective motion in such a layer is of great interest for estimating the intensity of heat and mass transfer in technological processes. This paper is a study of unsteady thermocapillary motion in a layer of viscous incompressible fluid with free surface in which a thermal inhomogeneity is created at the initial time. Approximate expressions are obtained for the fields of the velocity, temperature, and pressure in the fluid, and also for the shape of the free surface.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 17–25, May–June, 1991.     

Effects of reagent consumption and heat loss in ignition in a vessel

Two approximate analytical methods are widely used in research on thermal ignition: the stationary theory [1] and the nonstationary one [2]. The first predicts the critical explosion conditions very closely. Direct numerical integration has been used [3] to obtain a solution for thermal ignition, which indicated that ignition near the heated walls can accompany ignition at the center. The difference between the critical conditions for ignition at the wall and self-ignition can be defined only from the interaction between the initial and boundary conditions. The extent of combustion is substantial in both cases [1], and it subsequently plays a substantial part in setting up the temperature conditions in the vessel. A study is made here of the thermal decomposition of methyl nitrate vapor, which incorporates the diffusion and finite reaction rate. Monte Carlo simulation is used with a planar electrically conducting medium [4].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 192–196, January–February, 1975.     

Air streams in the atmosphere induced by multiple near-surface heat sources

On the basis of the complete system of unsteady Navier-Stokes equations for a compressible heat-conducting gas the authors have developed a numerical method for solving the three-dimensional problem of the theory of convection designed for an EC 1037-EC 2706 vector pipeline system. The problem of the ascent and interaction in the atmosphere of seven large-scale thermals generated close to the ground is solved.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 20–26, September–October, 1993.     

The behavior of a gas bubble in a shock wave

The phenomenon of thermal relaxation of the gas bubbles in a fluid behind a shock front is analyzed. The approach to solving the problem of heat transfer between a gas bubble and a fluid developed by the author is used to obtain a solution describing the initial stage of bubble collapse behind the shock front.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 187–189, September–October, 1993.     

Dynamics of a liquid with gas bubbles

The hydrodynamics and diffusion of an admixture near an isolated bubble, which simulates the rise of either a chain of identical bubbles or a system of regularly arranged bubbles of the same volume, are analyzed by solving the Navier-Stokes equations numerically. Data are presented for a specific liquid. It is shown that in both cases the maximum flow velocity on the surface of identical bubbles is practically the same, although in the former case the ascent velocity is considerably higher. The stationary admixture diffusion from a bubble also proves to be nearly the same.In relation to the bubbling of a gas through a liquid layer, it is shown that the total admixture diffusion is maximum for regularly arranged bubbles whose diameter is comparable with the liquids capillary constant. Although the flow past the bubble remains continuous, the values of the hydrodynamic parameters are no longer small.Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 75–88, May–June, 1996.     

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.     

Growth of bubbles in a fluidized bed with a nonlinear interphase interaction

An approximate solution is obtained to the problem of the motion and growth of a spherical bubble in a fluidized bed of particles of sufficiently large dimension, i.e., taking account of a nonlinear law of interphase interaction. A system of ordinary differential equations is obtained for the radius of a bubble and the rate of its ascent depending on the time, and the laws of its growth are found in the case where the dimensions differ only slightly from equilibrium, corresponding to a rise of the bubble without a change in its volume, and in the case where the radius of the bubble considerably exceeds the equilibrium (the latter, as a rule, occurs when the rate of ascent considerably exceeds the rate of fluidization).Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 66–73, November–December, 1977.     

Vortex flows of a viscous heat-conducting gas in a slightly divergent tube with volume energy supply

The results of a numerical investigation of viscous vortex flow in a slightly divergent tube with thermal energy supplied to the flow are presented. The initial stage of vortex flow development is considered for two different longitudinal velocity distributions simulating the velocity profiles in jet-like and wake-like vortex flows in the vicinity of the vortex axis. The first type of flow can be considered as a model for the near-axis region of the vortex formed in the flow around a delta wing at incidence. The second type can serve as a model for the near-axis region of the trailing vortex downstream of a high-aspect-ratio wing. The development of the two flows is studied for a constant area tube, a slightly divergent tube, and in the case of thermal energy supply from a volume energy source at a constant wall temperature.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 90–97, September–October, 1996.