Motion of low-density gaseous bodies in the atmosphere

The problem of motion of low-density deformable bodies in an atmosphere is interesting in reference to the hypothesis that the Tungussk catastrophe of 1908 resulted from atmospheric deceleration of a body of large size and low density (less than 0.01 g/cm³) [1]. Article [2] investigated the region of earth destruction caused by the shock wave formed ahead of a meteorite body. The motion of the meteorite is modeled here by explosion of a linear charge of variable cross section. Article [3] examined deceleration in an exponential atmosphere of a body whose shape and size are given functions of time. It was shown that under certain conditions the shock wave separates from the body and detaches. However, the body shape is not known beforehand, in fact, and a law for its variation can be obtained only by simultaneous consideration of flow in the shock layer, the wake, and the gas cloud. With an initial cloud velocity on the order of 40 km/sec this is a difficult problem. The present author knows of no attempt to solve the problem formulated in this way. The present paper addresses the problem of motion of a gas cloud in an exponential atmosphere with large initial velocity. The cloud gas and the atmospheric gas are assumed to be perfect and ideal. The problem is solved numerically by the direct finite-difference method of Godunov [4], using a moving mesh and isolated discontinuities. The objective of the work is to elucidate the basic aerodynamic effects arising when a low-density body enters the atmosphere.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 89–93, March–April, 1978.The author thanks G. I. Petrov for guidance of the work.     

Axisymmetric cavitation flow around a body in a tube

The problem of the axisymmetric flow around a body in a circular tube with arbitrary shape of the meridian section is reduced to the numerical solution of a system of two integral equations to determine the shape of the cavern and the intensity of the vortex rings arranged on the solid boundaries and the cavern boundary. Results of computations of the cavitation flow around a sphere, ellipsoid of revolution, and cone in a cylindrical tube, and also for a cone in converging and expanding tubes and in a hydrodynamic tunnel with the actual shape of the converging and working sections, are presented.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 50–55, July–August, 1976.     

Asymptotic form of the free surface of a uniformly rotating liquid for large bond numbers

In [1–5] boundary-layer methods were used to solve problems concerned with the equilibrium and motion of a liquid with surface tension in a strong gravitational field (for large Bond numbers Bo). In the present paper we apply these methods to problems involving the equilibrium shape of a uniformly rotating liquid, contained in a cylindrical container of arbitrary cross section or in a container which is a surface of revolution about the z axis. Both of these problems reduce to the asymptotic integration of an equation with a small parameter involving a quasilinear elliptic operator with a nonlinear boundary condition. In the second case, owing to radial symmetry, the equation for the problem goes over into an ordinary equation; however, the wetted boundary is not known beforehand. This boundary, together with the equilibrium shape, is also determined asymptotically.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 3–12, November–December, 1973.The authors thank L. A. Slobozhanin for his help in the preparation of this paper.     

Experimental study of the effect of vertical vibrations on convection in a horizontal cylindrical layer

An experimental study is made of the effect of vertical vibrations on convection in a cylindrical layer formed by two horizontal coaxial cylinders of circular cross section at different temperatures.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 180–183, November–December, 1985.     

Numerical and experimental investigation of a laval nozzle with a cylindrical throat

The results are reported of experimental and numerical investigation of mixed flow and of the parameters of heat transfer in the transonic region of an axisymmetric Laval nozzle whose throat is formed by a cylindrical surface, i.e., the nozzle contour near the minimum cross section contains two bends.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 189–192, September–October, 1984.     

Self-similar solution to a problem of axisymmetric motion of gas through a porous medium in the case of a quadratic law of resistance

The results of solution of the self-similar problem of planar flow of gas through a porous medium in the case of a quadratic law of resistance [1] are generalized to the case of axisymmetric motion. The equation in similarity variables for the velocity of isothermal gas flow is reduced to an equation having cylindrical functions as solution. Analytic dependences of the pressure and the gas velocity on the coordinate and time are obtained for a given flow rate of the gas at the coordinate origin and for zero Initial gas pressure in the porous medium.Translated from Izvestlya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza., No. 4, pp. 168–171, July–August, 1982.     

Longitudinal dispersion associated with the motion of an adsorbed mixture in a column filled with porous granules

The effect of the radial nonuniformity of the linear flow velocity on the radial nonuniformity of the adsorbate concentration distribution over the cross section of a column and on the longitudinal dispersion is estimated for the diffusion model, and the legitimacy (for relatively small adsorber radii) of using a one-dimensional diffusion model for describing the interphase mass transfer in cylindrical adsorbers is thereby determined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 93–101, July–August, 1987.     

A whirlwindlike Chaplygin vortex

The motion due to a cylindrical vortex of annular cross section with flow in the core is investigated.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.4, pp. 52–59, July–August, 1992.     

Helical flows with multiple circulation in channels of simple shape

A general solution is obtained for the problem of the helical motion of an incompressible liquid along a channel with a cross section in the shape of an annular sector or a triangle. The possible use of the solutions so obtained in order to describe secondary flows with repeated circulation in channels of simple shape (ring, circle, square, rhomb, rectangle, equilateral triangle) is demonstrated. The theory is in agreement with experiment. In one particular setting, problems as to the helical motion of an ideal incompressible liquid in channels of simple configuration were solved in [1, 2]. In this paper flows of a more general form with repeated circulation are considered, several vortices occurring inside the tube cross section.Deceased.Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 32–38, March–April, 1973.     

Effect of the form of the electrodes on the current distribution in a magnetogasdynamic channel

A solution is given to the plane problem of the flow of a conducting gas across a homogeneous magnetic field in a magnetogasdynamic channel taking account of the Hall effect at small magnetic Reynolds numbers. The channel is formed by two long electrodes, and the cross section of the channel varies slightly and periodically along the gas flow. It is assumed that the electromagnetic forces are small. It is shown that the current distribution in the channel is nonuniform to a consider able degree and that inverse currents can form at the electrodes, with both subsonic and supersonic flows of the conducting gas. Transverse motion of the gas, due to a change in the cross section of the channel, leads to an increase of Joule energy losses. In [1] the current distribution was obtained in a flat channel formed by infinite dielectric walls, with the flow of a steady-state stream of plasma through the channel across a homogeneous magnetic field. With interaction between the flow and the magnetic field, closed current loops develop in the channel.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 26–33, November–December, 1970.     

Distortion of the shock front in a shock tube with a divergent conical transition section

The profile of the leading shock front in a gas has been experimentally investigated in shock tubes of variable cross section. It is shown that the presence of a conical transition section between the high-pressure and low-pressure chambers leads to the retention of inhomogeneities on the surface of the wave front (slopes, twists, and bends) over a length of 20–30 diameters.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 141–147, July–August, 1991.     

Stress Analysis of Orthotropic Noncircular Cylindrical Shells of Variable Thickness in a Refined Formulation

An approach is developed to solve stress–strain problems in a refined formulation for orthotropic cylindrical shells of variable thickness and noncircular cross section. It is shown, as an example, how the distributions of deflections and stresses depend on changes in the shell thickness at constant weight     

Stationary flow of a conducting liquid in a rectangular channel with two nonconducting walls and two walls having an arbitrary conductivity parallel to an external magnetic field

The flow of a conducting liquid in a channel of rectangular cross section with two walls (parallel to the external magnetic field) having an arbitrary conductivity, the other two being insulators, is considered. The solution of the problem is presented in the form of infinite series. The relationships obtained are used for numerical calculations of the velocity distribution and the distribution of the induced magnetic field over the cross section for several modes of flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkostt i Gaza, No. 5, pp. 46–52, September–October, 1970.     

Unsteady natural convection in a toroidal vessel of arbitrary cross section

Unsteady natural convection in toroidal vessels, whose meridional cross section is a quadrangle with arbitrary curvilinear boundaries, is considered. The gravity vector is parallel to the axis of symmetry. The Navier-Stokes and energy equations are reduced to a universal form that describes the convective processes in both the plane and axisymmetric cases. A numerical solution of the problem is obtained on the basis of a multistep implicit finite-difference method. The unsteady natural convection in a toroidal vessel whose cross section is formed by segments of straight lines is calculated. The need to investigate natural convection processes in vessels of toroidal shape has arisen in connection with the expansion of design work on solar collectors and vessels used in cryogenic engineering. An experimentally based system of similarity criteria, which makes it possible to estimate the principal thermodynamic characteristics of the convection process in a toroidal reservoir partially filled with cryogenic fluid, was constructed in [1, 2].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. A, pp. 16–22, July–August, 1990.     

Blast wave propagation in air from a gaseous charge

In the point explosion problem it is assumed that an instantaneous release of finite energy causing shock wave propagation in the ambient gas occurs at a space point. The results of the solution of the problem of such blasts are contained in [1–4]. This point model is applied for the determination of shock wave parameters when the initial pressure in a sphere of finite radius exceeds the ambient air pressure by 2–3 orders of magnitude. The possibility of such a flow simulation at a certain distance from the charge is shown in papers [4, 5] as applied to the blast of a charge of condensed explosive and in [6, 8] as applied to the expansion of a finite volume of strongly compressed hot gas. In certain practical problems the initial pressure in a volume of finite dimensions exceeds atmospheric pressure by a factor 10–15 only. Such cases arise, for example, in the detonation of gaseous fuel-air mixtures. The present paper considers the problem of shock wave propagation in air, caused by explosion of gaseous charge of spherical or cylindrical shape. A numerical solution is obtained in a range of values of the specific energy of the charge characteristic for fuel-air detonation mixtures by means of the method of characteristics without secondary shock wave separation. The influence of the initial conditions of the gas charge explosion (specific energy, nature of initiation, and others) is investigated and compared with the point case with respect to the pressure difference across the shock wave and the positive overpressure pulse.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 110–118, May–June, 1986.     

Formula for the Flow Resistance Factor in a Pipe with a Sudden Expansion at Small Reynolds Numbers

A formula for the flow resistance factors in a pipe with a sudden expansion of the cross section at Reynolds numbers of 0.2 to 10 is obtained by numerical solution of the complete Navier–Stokes equations for incompressible fluids. The flow resistance factors obtained using the derived formula are compared to those found by numerical solution of the Navier–Stokes equations.     

Flow of viscous gas out of a cylindrical channel into vacuum

A study is made of the exhausting of a jet of viscous gas from a cylindrical channel into vacuum in the presence of a flat bounding surface outside the channel in the plane of its exit section. The problem is solved numerically using the complete system of Navier—Stokes equations. The developed flow model makes it possible to take into account the influence of an external medium into which the jet exhausts on the structure of the flow in the exit section of the channel, and also the influence of the subsonic part of the boundary layer in the channel on the flow field of the jet.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 122–128, January–February, 1981.     

Convective flow with uniform vorticity in a vertical layer

The free convective circulation of liquid in plane vertical slits of circular and square cross section with a longitudinal horizontal temperature gradient at the boundaries was investigated experimentally. It was found that under such heating conditions there is a uniform-vorticity flow with a region of quasirigid rotation, which has the shape of a disk in a circular slit and the shape of a cross in a square slit; in each longitudinal section of this zone the liquid moves along concentric trajectories with constant angular velocity. Dimensionless numbers for the problem were established by tests with various liquids and cavities of different dimensions. In dimensionless form, the angular velocity of the vortex and the temperature gradient in it depend linearly on the temperature difference at the boundaries of the layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 160–165, May–June, 1984.     

Methods of calculation and numerical analysis of conducting-gas flow in high-current electric arcs

The mechanism of conducting-gas acceleration in an electric arc by intrinsic magnetic field was first investigated in [1]. Further theoretical study of this question was associated with the numerical calculation of arcs [2–7]. A more general approach to the solution of the problem was realized in [4], where the finite-difference method was used. Integral calculational models were developed in [5–7]. The present work proposes a modified version of the difference method [4] and a series of integral methods for the calculation of the conducting-gas flow in a high-current electric arc. The development of integral methods is of interest in that they are usually associated with adequate accuracy in determining integral values and values averaged over the cross section by a relatively simple calculation, and also allow the solution of the problem to be obtained in a number of situations when the realization of a difference method is complicated. The results of different calculation methods are compared. The effect of conditions in the initial cross section of the calculation region of the arc on its characteristics is investigated and a numerical analysis of the heating and acceleration of conducting gas is carried out.Translated from Izvestiya Akademiya Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 103–110, September–October, 1978.     

Problem of gas motion in tubes of variable cross section and its application to solar wind perturbations

A qualitative study of self-similar flows with consideration of possible initial gas motion is performed for the problem of motion of a variable density gas in shock tubes with varying cross section. Asymptotic formulas are obtained near the contact discontinuity, and a numerical solution is obtained for the case of finite density on the contact surface. The equations are applied to the problem of gas motion in solar flares, and the parameters of the disturbed magnetic field are calculated. The results of the computation are compared with data from shock-wave observation in outer space.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 84–89, May–June, 1976.The author thanks V. P. Korobeinikov for his valuable advice and interest in the study.