The motion of a gas around a strongly heated body

Maxwell was one of the first to study the thermal slipping and radiometry effects. In particular, he suggested [1] that the thermal stresses which occur in a gas are important in an analysis of the radiometry effect. Interest in these problems has recently increased in connection with the problem of the slow motion of a strongly heated body in a gas. The paper by Galkin et al. [2], for example, is devoted to this question. However, the paper contains certain inaccuracies, and this means that the problem needs to be reconsidered. The present note describes the classification and the general characteristics of the types of motion and gives a statistical example of the state of a nonuniformly heated gas.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 95–98, July–August, 1972.In conclusion the author wishes to thank V. V. Struminskii for a useful discussion of the results.     

Drag of a strongly heated sphere at small Reynolds numbers

Using an asymptotic small-perturbation method, the flow around a strongly heated sphere at small Reynolds numbers Re ≪ 1 is considered with account for thermal stresses in the gas in the higher-order approximations, beyond the Stokes one. It is assumed that the value of the Prandtl number Pr is arbitrary and the temperature dependence of the viscosity is described by a power law with an arbitrary exponent. In the O(Re²) and O(Re³ ln(Re)) approximations, the drag force of a heated sphere is found over a wide range of the ratios of sphere’s temperature to the gas free-stream temperature T _W /T _∞. The limits of applicability of the first (in Re) approximation are investigated, including the negative-drag effect, attributable to the action of the thermal stresses. The results are compared with numerical calculations of the flow around a hot sphere. The limits of applicability of the approximations found are examined. Similar results are obtained for the standard Navier-Stokes equations in which the thermal stresses are neglected.     

Slow gas flow around a nonuniformly heated plate

Slow flow of a rarefied gas over a nonuniformly heated plate is investigated numerically. The interaction of the oncoming stream with the flow due to the variable temperature of the gas near the body is considered.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 181–184, September–October, 1981.     

Investigation of the flow and heat transfer of viscous reacting fluids in long tubes

Heat transfer and resistance in the case of laminar flow of inert gases and liquids in a circular tube were considered in [1–4], the justification of the use of boundary-layer type equations for investigating two-dimensional flows in tubes being provided in [4]. The flow of strongly viscous, chemically reacting fluids in an infinite tube has been investigated analytically and numerically in the case of a constant pressure gradient or constant flow rate of the fluid [5–8]. An analytic analysis of the flow of viscous reacting fluids in tubes of finite length was made in [9, 10]. However, by virtue of the averaging of the unknown functions over the volume of the tube in these investigations, the allowance for the finite length of the tube reduced to an analysis of the influence of the time the fluid remains in the tube on the thermal regime of the flow, and the details of the flow and the heat transfer in the initial section of the tube were not taken into account. In [11], the development of chemical reactions in displacement reactors were studied under the condition that a Poiseuille velocity profile is realized and the viscosity does not depend on the temperature or the concentration of the reactant; in [12], a study was made of the regimes of an adiabatic reactor of finite length, and in [13] of the flow regimes of reacting fluids in long tubes in the case of a constant flow rate. The aim of the present paper is to analyze analytically and numerically in the two-dimensional formulation the approach to the regimes of thermal and hydrodynamic stabilization in the case of the flow of viscous inert fluids and details of the flow of strongly viscous reacting fluids.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 17–25, January–February, 1930.     

Distribution of radiant thermal flux over the surface of a sphere for hypersonic flow of a nonviscous radiating gas past the sphere

In the present study using the Newtonian approximation [1] we obtain an analytical solution to the problem of flow of a steady, uniform, hypersonic, nonviscous, radiating gas past a sphere. The three-dimensional radiative-loss approximation is used. A distribution is found for the gasdynamic parameters in the shock layer, the withdrawal of the shock wave and the radiant thermal flux to the surface of the sphere. The Newtonian approximation was used earlier in [2, 3] to analyze a gas flow with radiation near the critical line. In [2] the radiation field was considered in the differential approximation, with the optical absorption coefficient being assumed constant. In [3] the integrodifferential energy equation with account of radiation was solved numerically for a gray gas. In [4–7] the problem of the flow of a nonviscous, nonheat-conducting gas behind a shock wave with account of radiation was solved numerically. To calculate the radiation field in [4, 7] the three-dimensional radiative-loss approximation was used; in [5, 6] the self-absorption of the gas was taken into account. A comparison of the equations obtained in the present study for radiant flow from radiating air to a sphere with the numerical calculations [4–7] shows them to have satisfactory accuracy.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 44–49, November–December, 1972.In conclusion the author thanks G. A. Tirskii and É. A. Gershbein for discussion and valuable remarks.     

Two-phase couette flow

A study is made of plane laminar Couette flow, in which foreign particles are injected through the upper boundary. The effect of the particles on friction and heat transfer is analyzed on the basis of the equations of two-fluid theory. A two-phase boundary layer on a plate has been considered in [1, 2] with the effect of the particles on the gas flow field neglected. A solution has been obtained in [3] for a laminar boundary layer on a plate with allowance for the dynamic and thermal effects of the particles on the gas parameters. There are also solutions for the case of the impulsive motion of a plate in a two-phase medium [4–6], and local rotation of the particles is taken into account in [5, 6]. The simplest model accounting for the effect of the particles on friction and heat transfer for the general case, when the particles are not in equilibrium with the gas at the outer edge of the boundary layer, is Couette flow. This type of flow with particle injection and a fixed surface has been considered in [7] under the assumptions of constant gas viscosity and the simplest drag and heat-transfer law. A solution for an accelerated Couette flow without particle injection and with a wall has been obtained in [6]. In the present paper fairly general assumptions are used to obtain a numerical solution of the problem of two-phase Couette flow with particle injection, and simple formulas useful for estimating the effect of the particles on friction and heat transfer are also obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 42–46, May–June, 1976.     

Force acting on a body in a nonuniformly heated magnetizable fluid

The force acting on a spherical particle in a nonuniformly heated magnetizable fluid is calculated in the case in which the permeability of the particle material depends arbitrarily on temperature and the strength of the magnetic field, and the permeability of the fluid on temperature. In calculating the force the difference between the thermal conductivities of the particle material and the fluid and, as distinct from [6], the distortion of the applied magnetic field due to the presence of a temperature gradient are taken into account. Accordingly, the expression for the force differs from that obtained in [6]. It is shown that the expression obtained for the force is correct up to terms of the order of a certain power of a small parameter — the ratio of the particle size to the characteristic interval of variation of the parameters (temperature, strength of magnetic field, etc.). A condition determining the value of this power is derived.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 76–83, March–April, 1989.     

Radiative and convective heat transfer during blowing into a compressed hypersonic layer of two-phase products from the ablation of a covering

The study examines the screening of the radiative heat flux in conditions of hypersonic flow around blunt bodies with ablated carbon-based coverings. In contrast to the studies already known [1–3], allowance is made for the presence of condensed microscopic particles in the products of ablation. In [4] the problem of radiative transfer is considered in a layer of two-phase ablation products with parametrically prescribed dimensions, particle temperature, and layer thickness. The present study uses a closed system of equations which describes the processes of heat and mass transfer. This gives rise to considerable differences in the numerical results, according to the degree of screening.Translated fron Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 161–166, November–December 1985.deceased     

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.     

Motion of a spherical solid particle in a nonuniform flow of a viscous incompressible liquid

The effect of a particle on the basic flow is studied, and the equations of motion of the particle are formulated. The problem is solved in the Stokes approximation with an accuracy up to the cube of the ratio of the radius of the sphere to the distance from the center of the sphere to peculiarities in the basic flow. An analogous problem concerning the motion of a sphere in a nonuniform flow of an ideal liquid has been discussed in [1]. We note that the solution is known in the case of flow around two spheres by a uniform flow of a viscous incompressible liquid [2], and we also note the papers [3, 4] on the motion of a small particle in a cylindrical tube.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 71–74, July–August, 1976.     

Establishment of circumfluence (steady-state flow) when a shock wave strikes a cylinder or a sphere

The problem of the diffraction of a shock wave at a stationary sphere or cylinder is considered. The finite-difference method proposed by S. K. Godunov [1, 2] is employed Numerical solutions are obtained for the stage of the diffraction of the shock wave and for the subsequent steady state of flow around the object (circumfluence). Cases of sub-, trans-, and supersonic flow behind the shock wave are considered. When strong shock waves undergo diffraction, zones of reverse flow appear in the neighborhood of the tail part of the obstacle.Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 97–103, September–October, 1972.     

Instability of combined convective flow in a vertical layer

In the present paper, a study is made of the stability of plane-parallel flow induced by a transverse temperature difference between the boundaries of a layer and a longitudinal pressure gradient. This problem was solved earlier by the author [3] in a purely hydrodynamic formulation without allowance for thermal factors; the results then obtained correspond to the limiting case of small Prandtl numbers. In the paper, a numerical solution to the problem with the complete formulation is given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 3–9, May–June, 1982.I thank G. Z. Gershuni for supervising the work, and also M. A. Gol'dshtik and V. N. Shtern for a helpful discussion.     

A method for calculating the two-dimensional temperature field of a reservoir with thermal injection

In [1–3] and other studies devoted to the determination of the temperature field of an oil reservoir when injecting into it a fluid with a temperature different from that of the initial reservoir temperature, the one-dimensional fluid flow (linear or radial) was considered in the case of an injection gallery or a single injection well in the reservoir. The problem was formulated in [4] with an arbitrary distribution of wells, but the solution was obtained only for the integral thermal-loss characteristic. To evaluate the coverage of the reservoir by the thermal effect, we must know the temperature distribution in the multi-well reservoir system at any instant of time. In this paper we propose a method for calculating the reservoir temperature field in the case of two-dimensional fluid flow using the simplifying assumptions which were used earlier by Lauwerier [1] and other authors to describe the thermal phenomena in a reservoir.     

Nonisothermal Couette flow of a non-Newtonian fluid under the action of a pressure gradient

Nonisothermal Couette flow has been studied in a number of papers [1–11] for various laws of the temperature dependence of viscosity. In [1] the viscosity of the medium was assumed constant; in [2–5] a hyperbolic law of variation of viscosity with temperature was used; in [6–8] the Reynolds relation was assumed; in [9] the investigation was performed for an arbitrary temperature dependence of viscosity. Flows of media with an exponential temperature dependence of viscosity are characterized by large temperature gradients in the flow. This permits the treatment of the temperature variation in the flow of the fluid as a hydrodynamic thermal explosion [8, 10, 11]. The conditions of the formulation of the problem of the articles mentioned were limited by the possibility of obtaining an analytic solution. In the present article we consider nonisothermal Couette flows of a non-Newtonian fluid under the action of a pressure gradient along the plates. The equations for this case do not have an analytic solution. Methods developed in [12–14] for the qualitative study of differential equations in three-dimensional phase spaces were used in the analysis. The calculations were performed by computer.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 26–30, May–June, 1981.     

Calculation of the kinetics of propagation of a powerful light beam in a transparent dielectric with impurities

A large number of studies have been dedicated to the interaction of powerful optical radiation with transparent dielectrics in the prebreakdown or breakdown regimes. However, the mechanism by which the material is destroyed has not been determined decisively, as indicated by the constant flow of new publications on this theme. Attempts to obtain destruction as the result of electron avalanche [1] give threshold power values orders of magnitude greater than experiment [2]. In connection with this, in recent years the accent has been to deal with the concept of microimpurities of foreign particles or inhomogeneities within the medium having dimensions so small that their presence and concentration is difficult to monitor. As it absorbs optical radiation, the microimpurity (inhomogeneity) is heated and warms the areas of the medium adjacent to itself, which areas then commence to absorb light with significantly more intensity than they did in the initial state [3]. As a result, increase in absorption within the medium commences, terminating in breakdown or destruction of the material around the inhomogeneity. In [4, 5] it was noted that an important role may be played in such a destruction mechanism by thermoelastic stresses in the medium, which factor was not considered in [3]. In [4, 5] it was proposed that the basic effect of thermoelastic stresses reduces to development of microfissures in the medium. However, thermoelastic stresses can lead to yet another effect — narrowing of the forbidden zone of the medium and increase (together with the analogous action of temperature growth) in the coefficient of absorption of the medium. In the present study, the kinetics of interaction of optical radiation with a dielectric medium containing spherical metal particles as an impurity will be calculated, and it will be shown that thermoelastic stresses produce a significant contribution to the increase in light absorption by the medium around a particle.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 60–66, September–October, 1978.     

Rarefied gas flow past a sphere with injection

Hypersonic rarefied gas flow over the windward face of a sphere is considered in the presence of distributed injection from the surface of the body. A similar problem was previously solved in [1–3] within the framework of continuum mechanics and in [4] on the basis of model kinetic equations. In the present study the calculations were carried out using the Monte Carlo method of direct statistical modeling [5, 6]. The injected gas was the same as the free-stream gas. A simple monatomic gas model with a rigid sphere interaction potential was employed. The reflection of the molecules from the surface of the body was assumed to be diffuse with total energy accommodation. The calculation procedure using weighting factors is described in [7]. The influence of injection on the mechanical and thermal effect of the gas flow on the body is investigated for various degrees of rarefaction of the medium and injection rates.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 175–179, July–August, 1990.     

The influence of a uniformly compressed floating elastic plate on the development of three-dimensional waves in a homogeneous fluid

A study is made in the linear formulation of the influence of a uniformly compressed floating elastic plate on the unsteady three-dimensional wave motion of a homogeneous fluid of finite depth. Waves are excited by a region of normal stresses which moves on the surface of the plate. Three-dimensional flexural-gravity waves were studied in [1, 2] without allowance for compressing forces. Plane waves under conditions of longitudinal compression were considered in [3, 4].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 78–83, November–December, 1984.     

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.     

Thermocapillary instability of the equilibrium of a flat layer containing internal heat sources

In the absence of body forces, a factor which has a strong influence on the equilibrium stability of a nonuniformly heated liquid is the dependence of the coefficient of surface tension on the temperature and the thermocapillary effect generated by it. If the equilibrium temperature gradient is sufficiently great, then the presence of the thermocapillary forces on the free surface can lead to the occurrence of convective motion. The monotonie instability of the equilibrium of a flat layer was investigated in [1–3]. Analysis of nonmonotonic disturbances [4] showed that in the case of an undeformable free surface there is no oscillatory instability. In [5] it was found that oscillatory instability is possible if there is a nonlinear dependence of the coefficient of surface tension on the temperature. The present paper is devoted to numerical investigation of the equilibrium stability of a flat layer with respect to arbitrary disturbances. It is shown that for a deformable free boundary there appears an additional neutral curve, which corresponds to monotonie capillary instability. In addition, when the capillary convection mechanism is taken into account, there appears an oscillatory instability, which becomes the most dangerous in the region of small Prandtl and wave numbers.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 27–31, March–April, 1991.I thank V. K. Andreev for a helpful discussion of the work.     

Nonlinear regimes of current flow through a weakly ionized boundary layer and their stability

The problem of steady states and stability of current flow in low-temperature plasma with allowance for the Joule heat release have been considered repeatedly for the case of confined stationary plasma (see, for example, [1]). The present paper is devoted to the asymptotic solution of this problem for the case of a laminar boundary layer of weakly ionized plasma. A similar problem was previously considered in [2] in a zero-dimensional approximation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 153–163, July–August. 1986.The author thanks G. A. Lyubimov and the participants in the seminar he directs, I. M. Rutkevich and V. D. Khait for their discussion of the work and their useful observations.