The application of the projection method for constructing the shape of a body with minimum drag

The problem is considered of constructing a semi-infinite axisymmetric body with minimum drag in subsonic flow of an ideal gas. This problem is formulated as the problem of finite-dimensional minimization by prescribing the shape of the body in parametric form and applying the projection method for solving a flow problem.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 108–113, March–April, 1985.     

Effect of supersonic stream parameters on the characteristic time of transient step flow

There have been many studies of viscous compressible gas flow in wakes and behind steps [1–6] in which attention has been focused on the steady-state flow regime. The problem of the supersonic flow of a viscous compressible heat-conducting gas past a plain backward-facing step is considered. The problem is solved numerically within the framework of the complete system of Navier-Stokes equations. The passage of the solution from the initial data to the steady-state regime and the effect of the gas dynamic parameters of the external flow on the characteristic flow stabilization time are investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 137–140, July–August, 1989.     

Nonlinear Antiplane Deformation of an Elastic Body

The antiplane elastic deformation of a homogeneous isotropic prestretched cylindrical body is studied in a nonlinear formulation in actual–state variables under incompressibility conditions, the absence of volume forces, and under constant lateral loading along the generatrix. The boundary–value problem of axial displacement is obtained in Cartesian and complex variables and sufficient ellipticity conditions for this problem are indicated in terms of the elastic potential. The similarity to a plane vortex–free gas flow is established. The problem is solved for Mooney and Rivlin—Sonders materials simulating strong elastic deformations of rubber–like materials. Axisymmetric solutions are considered.     

Quasi-three-dimensional calculation of flow in blade passages of turbines

The flow in turbomachines is currently calculated either on the basis of a single successive solution of an axisymmetric problem (see, for example, [1-A]) and the problem of flow past cascades of blades in a layer of variable thickness [1, 5], or by solution of a quasi-three-dimensional problem [6–8], or on the basis of three-dimensional models of the motion [9–11]. In this paper, we derive equations of a three-dimensional model of the flow of an ideal incompressible fluid for an arbitrary curvilinear system of coordinates based on averaging the equations of motion in the Gromek–Lamb form in the azimuthal direction; the pulsation terms are taken into account in the equations of the quasi-three-dimensional motion. An algorithm for numerical solution of the problem is described. The results of calculations are given and compared with experimental data for flows in the blade passages of an axial pump and a rotating-blade turbine. The obtained results are analyzed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 69–76, March–April, 1991.I thank A. I. Kuzin and A. V. Gol'din for supplying the results of the experimental investigations.     

Determination of relative permeabilities in a three-phase flow in a porous medium

A study is made of the problem of determining the parameters of flow described by the Buckley-Leverett system of equations by using functions that admit direct measurement. The well-known solution to the analogous problem for two-phase flow [1–3] is generalized. In contrast to [4], the general case is considered, when the fractions of the phases in the flow and the phase permeabilities depend on two variables.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 187–189, September–October, 1984.The author wishes to thank B. V. Shalimov for his helpful advice.     

Axisymmetric flow of ideal fluid past a gas bubble

A generalization of the analytic functions is proposed to solve the problem of axisymmetric flow past a gas bubble. By the use of an integral transformation the problem is reduced to that of two-dimensional parallel flow, which can be investigated by the well-known methods of the theory of analytic functions. The problem of plane flow is solved by means of a total approximation for the parametric plane.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 98–103, September–October, 1993.     

Drag of porous cylinders in a viscous fluid at low reynolds numbers

The problem of flow past a permeable cylinder at low Reynolds numbers is of interest for the solution of a number of problems in chemical technology in, for example, the design of porous electrodes and porous catalysts and in the calculation of nonstationary filtration of aerosols by fibrous filters. In the present paper, we solve the problem of transverse flow of a viscous fluid past a continuous cylinder in a porous shell and, in particular, in the case of a porous cylinder under conditions of constrained flow (system of cylinders) and an isolated cylinder at arbitrary permeability. The analogous problem of Stokes flow past permeable spheres has been solved in a number of papers [1–3].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 122–124, November–December, 1979.     

Cavitation flow around a plate in a channel by a stream of heavy liquid

The nonlinear problem of cavitation flow around a plate by a stream of heavy liquid is investigated in precise formulation; the plate is located on the horizontal floor of a channel when the gravity vector is directed perpendicular to the wall of the channel. Two flow systems are considered-Ryabushinskii's and Kuznetsov's system [1]. This problem was investigated in linear formulation in [2], Similar problems were considered earlier in [3–7] for unrestricted flow. Below, on the basis of a method proposed by Birkhoff [8, 9], all the principal hydrodynamic and geometric characteristics are calculated for the problem being considered.Translated from Ivestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 3, pp. 3–9, May–June, 1973.     

Impact of a figure of revolution in a stream of incompressible fluid with separation of a jet

The impact interaction of bodies with a fluid in a flow with jet separation has been considered in [1–3], for example. This investigation was in the two-dimensional formulation. The present paper considers the three-dimensional problem of impact of a figure of revolution in a stream of an ideal incompressible fluid with separation of a jet in accordance with Kirchhoff's scheme. A boundary-value problem is formulated for the impact flow potential and solved by the Green's function method. A method for constructing the Green's function is described. Expressions are given for the coefficients of the apparent masses. The results are given of computer calculations of these coefficients in the case of a cone using the flow geometry of the corresponding two-dimensional problem.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 176–180, November–December, 1980.     

Calculation of limiting configuration of stagnant zones when viscoplastic oil is displaced by water

A study is made of the problem of determining the position of the limiting equilibrium portions of unrecovered viscoplastic oil displaced by water from a porous stratum in a many-well system. This problem was formulated by Bernadiner and Entov [1] and is of interest in connection with the obtaining of estimates of the volume of displaced oil. For two-dimensional isothermal flow in a homogeneous undeformed stratum and certain restrictions on the geometry of the flow region, the problem can be investigated by the methods of the theory of analytic functions [1–3]. An approximate solution of one problem with complicated flow geometry has been obtained [4] by means of potential theory. In the present paper the methods of the theory of jets are used to construct and analyze an exact analytic solution to the problem for three possible flow schemes.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 77–81, March–April, 1991,We thank M. M. Alimov for discussing the work.     

Unsteady displacement of an oil deposit in a flow of stratal water

Unsteady problems concerning the displacement of gas and oil deposits in a seepage flow of stratal water are of specific interest to oil and gas hydrogeology, and in the planning and analysis of the processes of reservoir exploitation. Firstly, a change of the hydrogeological environment in a region of already formed deposits involves their displacement. Secondly, when one of two adjacent deposits is developed, a displacement of the other occurs in the artificial flow of stratal water which is produced. Papers [1–3] investigate the steady configuration of gas—water or water—oil contacts in the presence of a seepage flow of stratal water under the deposit. The unsteady problem considered below is a generalization of the problem in paper [3]. Its characteristic property is the presence of mobile boundaries separating the regions with flow of different fluids in the horizontal plane.Translated from Izvestiya Akademii Nauk SSSR, Mekh. Zhidk. Gaza, No. 2, pp. 177–179, March–April, 1985.     

Stability of the motion of a rigid body in an unsteady flow

The problem of rigid-body motion in an unsteady gas flow is considered using a flow model [1] in which the motion of the body is described by a system of integrodifferential equations. The case in which among the characteristic exponents of the fundamental system of solutions of the linearized equations there are not only negative but also one zero exponent is analyzed. The instability conditions established with respect to the second-order terms on the right sides of the equations are noted. The problem may be regarded as a generalization of the problem of the lateral instability of an airplane in the critical case solved by Chetaev [2], pp. 407–408.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 18–22, May–June, 1989.     

Plane problem of uniform flow of a two-layer fluid past a circular cylinder

An explicit solution is found for the problem of uniform horizontal flow of a two-layer fluid of infinite depth past a circular cylinder. The cylinder axis is perpendicular to the flow. The problem is solved within a linear formulation. The solution of the problem is expressed in the form of rapidly converging series with coefficients determined from a recurrence relation. The first seven terms of the series yield the values of the hydrodynamic loads with a relative accuracy of 10^–6. The results are in good agreement with the known values for similar problems in a homogeneous fluid. Tables of the lift and wave drag are given for homogeneous and two-layer fluids.Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 91–97, January–February, 1996.     

Instability of a film of viscous liquid under the influence of an adjacent gas flow

A study is made of the instability of a film of viscous liquid adjacent to a gas flow. Despite a number of investigations, there is no unified theory of this problem capable of explaining the experimental results of different authors. The present paper gives a solution of the problem that is valid for a large class of flows of liquid films in the case of laminar and turbulent flow of the gas.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 28–36, March–April, 1979.     

Hypersonic flow past a wing at large angles of attack with detached shock wave

The thin shock layer method [1–3] has been used to solve the problem of hypersonic flow past the windward surface of a delta wing at large angles of attack, when the shock wave is detached from the leading edge (but attached to the apex of the wing) and the velocity of the gas in the shock layer is of the same order as the speed of sound. A classification of the regimes of flow past a delta wing at large angles of attack has been made. A general solution has been obtained for the problem of three-dimensional hypersonic flow past the wing allowing for nonequilibrium physicochemical processes of thermal radiation of the gas at high temperatures.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 149–157, May–June, 1985.     

Laminar flow between the surfaces of two eccentric circular cylinders

The problem of laminar fluid flow in an asymmetric annular gap has been solved in earlier work in an approximation with error difficult to gauge. In the present paper, the problem is solved exactly. The velocity distribution of the flow is obtained, the mean velocity is determined, and an exact expression is found for the coefficient which determines the flow rate. An approximate expression proposed for this coefficient holds asymptotically at small eccentricities. The results are compared with experimental data.Translated from Izvestiya Akademil Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 16–20, January–February, 1984.     

Approximate solution of the problem of the bottom zone in a rarefied gas

The problem of the steady-plane monatomic rarefied gas flow around a semiinfinite bar is considered (the plane stationary case of the problem about the bottom zone). The problem is solved numerically at the level of the Krook relaxation model [1, 2]. A depenence of the gas density, velocity, and temperature in the whole flow domain on the space coordinates is obtained for supersonic and subsonic gas streams flowing around a body by using calculations on an M-20 electronic calculator.Khar'kov. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 139–143, January–February, 1972.     

Flow past a sphere of two co-axial supersonic streams

We investigate the flow past a sphere of a parallel supersonic stream which is nonuniform in magnitude; such a flow can be considered as two co-axial streams of an ideal gas. The problem is solved numerically by the method of establishment [1]. Supersonic flow of nonuniform magnitude and direction past blunt bodies and a plane wall was investigated in [2–5],Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 89–94, September–October, 1970.The author wishes to thank G. F. Telenin for his attention to the paper.     

Influence of sound waves on steady duct flow

The article discusses the problem of determining the secondary steady flow in a plane duct when a sound field is superimposed on an undisturbed compressible laminar flow. It is shown that under certain simplifying conditions the velocity distribution of the secondary flow in the wall region is given by a simple analytical expression. In the rest of the duct the problem is reduced to the solution of a linear fourth-order ordinary differential equation (in complex variables); this problem is solved numerically. The indicated equation is transformed to an Airy equation for large Reynolds numbers Re of the undisturbed flow. The results are presented graphically.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 57–64, March–April, 1976.The author is indebted to V. E. Nakoryakov for valuable comments and interest.     

Interaction of a cylinder with a free surface and a jet

The problem of the asymmetric flow around a cylinder of a nonviscous jet is considered and, in particular, of flow with one free boundary. The problem of the choice of circulation is posed, based on a generalization of the Zhukovskii-Chaplygin postulate. Several possibilities are considered and the principle of the minimum of the maximum velocity on a contour is proposed, which qualitatively and quantitatively truly reflects certain aspects of the interaction of the cylinder with the flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 50–58, September–October, 1977.