Experimental investigation of the internal ballistics of a pulsed water cannon

Measurements were made of the piston velocity and water pressure in the tube of a pulsed water cannon. The results are compared with calculations, which show that the quasistationary formulation of the problem gives sufficient accuracy.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 150–152, May–June, 1979.     

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.     

Flow past a plate under the free surface of a weightless liquid

A study is made of the nonlinear problem of the flow without separation of a perfect weightless liquid past a plate near the free surface. This problem was first posed by Gurevich [1]. At present, there are only a general solution to the problem [2–4] and some numerical calculations [5], which have been made under definite restrictions and are inadequate for detailed information about the interaction between the free surface and the plate. In the present paper, a complete investigation of the problem is given. Convenient computational formulas are obtained together with asymptotic expansions of them, and detailed calculations are made for all depths of the plate.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 158–162, January–February, 1980.     

Optimal vorticity regime in the flow tract of a hydroturbine

A study is made of the problem of maximizing the power taken from the shaft of the working rotor of a hydroturbine for a fixed available energy difference in the framework of a two-dimensional axisymmetric flow model. Necessary conditions of optimality of first and second order are derived and used to set up an algorithm for numerical solution of the problem. The results of calculations are given, and a comparison is made with optimal solutions obtained using two- and one-dimensional models of axisymmetric flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 68–73, May–June, 1984.     

Calculation of supersonic flow around v-shaped wings by the fitting method

The problem of flow around a V-shaped wing with supersonic leading edges is solved. The method employed is that of fitting with respect to a space variable in which the system of equations of motion is hyperbolic, using the computing scheme of V. V. Rusanov, A comparison between the results of these calculations and experimental data in relation to the pressure distribution along the wing span reveals excellent agreement, except for a limited region, in which the compression jump incident on the plane of the wing interacts with the boundary layer. A comparison between the results obtained by means of the oblique-jump equations and by numerical calculations indicates that the method in question is reasonably accurate.Translated from Izvestiya Akademu Nauk SSSE, Mekhanika Zhidkosti i Gaza, No. 3, pp. 180–185, May–June, 1971.The author is grateful to A. L. Gonor and V. V. Rusanov for interest in this work.     

Mass transfer problem for particles,drops and bubbles in a shear flow

A numerical solution of the axisymmetric steady heat and mass transfer problem for spherical particles, drops and bubbles in a linear Stokes shear flow is obtained for the entire range of Péclet numbers. Simple approximate expressions for the average Sherwood number in good agreement with the results of the numerical calculations are proposed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 137–141, July–August, 1990.     

Rolling of a Rigid Cylinder over a Half-Plane with Initial Stresses (Harmonic and Bartenev–Khazanovich Potentials)

An asymmetric quasistationary problem for a prestressed half-plane with harmonic and Bartenev–Khazanovich potentials is solved based of the linearized theory of elasticity. The Mehler–Fock integral transform is used to solve the differential equations that describe the stress–strain state of the half-plane. The dependences of the normal and tangential stresses and stress intensity factors on the elongation are plotted     

Equilibrium theory and stability of a high-current,pinched, varying-current discharge

The characteristics of a quasistationary state of a varying-current discharge are considered when the discharge current can be assumed to be high-frequency relative to hydrodynamic processes and constant relative to electrodynamic processes. It is shown that the quasistationary state of such a discharge is described by the same relations as the equilibrium state of a constant current discharge, but with physical quantities replaced by corresponding effective values. The discharge considered seems as unstable as a constant current discharge.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 21–28, March–April, 1973.The authors are grateful to A. A. Rukhadze for his constant interest and for discussing the results.     

Contact Stress Distribution Under a Rigid Cylinder Rolling Over a Prestressed Strip

A nonsymmetric quasistationary problem for a strip with initial stresses is solved under the linearized theory of elasticity for harmonic and Bartenev–Khazanovich potentials. The Hankel integral transform is used to solve the differential equations that describe the stress–strain state of the strip. The dependences of the normal and tangential stresses and stress intensity factors on the elongation are plotted     

Aerodynamics of an asymmetrically deformed body in nonstationary supersonic motion

A method for making numerical calculations of the stationary and nonstationary aerodynamic characteristics of bodies of variable shape is considered. The results of calculations of the aerodynamic coefficents are given [1]. The results of numerical calculations are compared with the results of Newton's theory.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 162–167, March–April, 1980.     

Quasiequilibrium model of the kinetics of coupled modes of CO2 molecules

The correct allowance for the influence of anharmonicity in the vibrational spectrum of CO₂ on the level distribution of molecules under nonequilibrium conditions, when the vibrational temperature departs significantly from the gas temperature, has become especially urgent in connection with obtaining generation on a number of long-wavelength transitions of CO₂ molecules [1, 2]. The shifts in the levels of coupled modes (symmetric and deformation) are due mainly to Fermi resonance and can reach a considerable value, comparable with the gas temperature even for low levels. In [3] the main features of the quasisteady level distribution of coupled modes were clarified within the framework of the Treanor model of vibrational kinetics. The influence of the ascending flux of quanta, excited by VV exchange under nonequilibrium conditions, on the vibrational distribution was considered in [4–6]. In the present paper we propose a quasiequilibrium model of CO₂ kinetics, obtained without presuming quasisteadiness of the ascending flux of quanta, and making it possible, in contrast to [3–6] to describe the dynamics of the variation of the distribution of molecules among multiplets as a result of processes of VV exchange and VT relaxation between multiplets, with allowance for possible processes of pumping by outside sources. With a Boltzmann population distribution within the multiplets, having the translational temperature of the gas, the problem of studying relaxation in coupled modes is reduced to the equations for an effective anharmonic oscillator with levels corresponding to the multiplets of CO₂ molecules. In this case the levels of the effective oscillator are degenerate with a multiplicity equal to the number of levels in the corresponding multiplet, and they have an anharmonicity constant dependent on the gas temperature. The population distribution of the effective oscillator can be studied by methods developed for the investigation cf a one-mode anharmonic oscillator. The proposed quasiequilibrium model was used for a numerical calculations of the temporal evolution of the distribution function of CO₂ molecules over the levels of coupled modes under the conditions of an extremely maintained discharge.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 16–22, May–June, 1986.     

Plastic deformation of metals subjected to intensive sources

The elastoplastic strain of metals being formed when they melt under the effect of a point heat source with a pulse duration greater than 10^–6 sec is considered in this paper. The time development of the plastic strain and pressure domains in the melt is investigated. It is shown that two plastic strain domains occur during the interaction under consideration: a relatively broad domain of mechanical influence and a narrow domain of thermal influence. The stress-strain distributions as well as the hydrostatic pressure in the fluid are determined by a quasistationary temperature distribution starting with times corresponding to half (of the quasistationary) the value of the melt radius X 0.5. It is shown that the dimensions of the weak and strong plastic strain domains formed by heat and acoustic waves grow continuously to the quasistationary values, while the hydrostatic pressure in the fluid reaches the maximum value for X 0.3...0.4. The ratio between the radii of the plastic strain zones and of the liquid bath for a quasistationary temperature distribution in the first domain lies within the range 10–50, and does not exceed 1.7 for Cu, Ni, and Fe in the second. The anomalous nature of the development of the strong plastic strain domain in Al, because of migration of the metal grain boundaries to result in collapse of the domain for the values X 0.5 accompanied by a jumplike diminution in the hydrostatic pressure in the fluid, is noted.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 129–140, May–June, 1976.     

Oscillating flows in capillaries filled with immiscible liquids

Hydrodynamic flows generated by mechanical vibrations of a capillary filled with immiscible liquids are investigated. Air bubbles are contained at the hermetically sealed ends of the capillary. Equations for the change in the volumes of the air bubbles as functions of time and velocity distribution in the liquids are obtained for the case when the radius of the capillary is much less than the lengths of the liquid columns. Results of numerical calculations are given for a capillary filled with two liquids: water and mercury. Amplitude-frequency dependences of the change in volumes of the air bubbles are constructed which have a resonance nature. Graphs of the dependence of the velocity of the water and the mercury on the radial coordinate at different times are given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 13–18, September–October, 1987.     

Numerical investigation of two-phase flows in axisymmetric laval nozzles with allowance for processes of coagulation and division of condensed particles

In the framework of a model in which a polydisperse two-phase medium is represented as a multivelocity continuum [1, 2] a numerical investigation is made into the features of two-phase flows in axisymmetric Laval nozzles with allowance for processes of coagulation and division of particles. Calculations were made for a step distribution of the condensed particles with respect to their diameters (Lagrange's method [3, 4]). The flow pattern as a whole was determined, and also the most important integrated characteristics of the nozzles, including the unit impulse loss. Some qualitative results of calculations of such two-dimensional flows were obtained earlier in [6], but systematic investigations have been made only in the quasione-dimensional approximation (see [3, 4] and the bibliography there).Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 82–90, January–February, 1980.I thank A. A. Glazunov for great assistance in the calculations and am indebted to I. M. Vasenin for his interest in the work and also for a number of comments of a critical nature.     

Natural convection in a vertical cylindrical vessel with heat supplied to its side and free surfaces

A study was made in [4] of convective flow and heat transfer in a vertical cylindrical vessel with heat supplied to the free surface of the fluid, using the numerical simulation method. The results of this study were obtained for a comparatively short heating time for a fixed ratio of heat fluxes to the side and free surfaces. The present study is a continuation of the one in [4]. By using a more precise numerical simulation method, calculations could be made over a fairly wide range of determining parameters, and results were obtained for both short and long heating times.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 51–56, November–December, 1984.     

Formation and decay of a quasisteady detonation complex in a nonuniformly heated combustible gas

This work is a continuation of the study of explosive reaction regimes associated with an initial nonuniformity of the reaction induction period. Relations determining the time and place of formation and decay of a quasisteady detonation complex are obtained for a linear nonuniformity. These are compared with the results of numerical calculations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 161–168, March–April, 1991.     

Optimization of the action of a pulsed water cannon with powder drive

The system of equations of the internal ballistics of a pulsed water cannon with powder drive is obtained. The variational problem of determining the combustion surface of the powder charge for the purpose of obtaining the pressure pulse giving a maximum jet dynamic pressure coefficient is formulated. A numerical solution algorithm is constructed and an example of the calculations is presented.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.6, pp. 156–159, November–December, 1993.     

Stationary flow past the lower surface of a piecewise planar delta wing with supersonic leading edges

The considered wing has any finite number of inflections in its plane with lines of inflection intersecting at the point of inflection of the leading edge. In the present paper, this generalizes the author's earlier work [1] on flow past the undersurface of a flat wing at unite angle of attack with finite angle of slip and supersonic leading edges. In [1], calculations were not given. The special case of flow without slip in the same situation was considered later in [2], However, this paper contains errors, indicated at the end of the present paper. The calculations given in [2] are not correct. In the quoted papers, the gas flow is assumed to be a perturbation of a homogeneous flow behind a plane oblique shock wave. Such flows are treated systematically in [3]. Here and in [1], we use and generalize the representation of the linearized conservation laws across the shock front as the conditions of a boundary-value problem for an analytic function of a complex variable as obtained in [4, 5]. Calculations are given of the pressure distribution over the span for a number of different flow regimes and the pressure coefficients in the middle of the wing are compared with a numerical solution presented partly in [6].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 80–90, September–October, 1979.I am very grateful to V. I. Lapygin for making available a large number of variants of his numerical solution, and to L. E. Pekurovskii for assistance in the calculations.     

Cathode electric-field-intensity-distribution function

The behavior of the distribution function for the electric field intensity at the cathode is considered including only nearest-neighbor effects and is compared with the behavior of the distribution function obtained when including the effects of many ions. Motion of ions in the near-cathode region and their nonuniform density there are taken into account in the calculations of the distribution function. It is shown that for a broad range of parameters the resultant distribution function differs little from the distribution function found when constant density is assumed.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 29–34, May–June, 1973.     

Asymptotic structure of inviscid disturbances in a thin shock layer

The WKB method, used in [4] to analyze the short-wave instability of a supersonic mixing layer, is employed to investigate various types of inviscid three-dimensional short-wave disturbances in a thin shock layer of perfect gas with arbitrary velocity and temperature distributions across the layer. Simple analytic expressions for the dispersion relations are obtained for neutral disturbances. The results of an asymptotic analysis are compared with direct numerical calculations for a simple model of the shock layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 72–79, November–December, 1988.