Stability of a nonisothermal boundary layer in the presence of periodic perturbations of the exterior flow velocity

The stability of a laminar boundary layer in the presence of high-frequency time-periodic perturbations of the exterior flow velocity, in particular, acoustic vibrations, is investigated in a series of papers which are reviewed in detail in monograph [1]. The mechanisms by which such perturbations influence the stability and transition to the turbulent flow regime can vary. For example, they can lead to the deformation of the averaged field of the basic flow. However, there was good reason not to discuss the effect of this type of perturbation earlier, as it was considered that the change in the basic flow was very small even for perturbations of great amplitude. The aim of the present paper is to demonstrate how perturbations or pulsations in the exterior flow velocity can, by changing the basic flow, have a strong influence on the stability of the laminar boundary layer of a gas under appreciably nonisothermal conditions. Examples of calculations that support this assertion are given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 183–186, September–October, 1984.The authors wish to thank A. A. Maslov for his help with the calculations.     

Investigation of the transitional process of the startup of a gas bearing

In this article we derive equations for transitional conditions of a gas lubricant under nonisothermal conditions. A numerical solution of the Reynolds equation is described for the problem of the pulsed startup of a radial bearing with a fixed geometry, and the results of this solution are given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 156–160, September–October, 1977.     

Nonlinear effects associated with the mutual displacement of two gases in a porous medium

The cyclic bidirectional process of isothermal flow of a binary singlephase compressible gas mixture in a porous medium accompanied by diffusion-dispersion mass transfer is considered. On the basis of the equations of multiphase multicomponent isothermal flow a system of two nonlinear partial differential equations with nonlinear boundary conditions corresponding to a given constant gas injection or takeoff rate is obtained and investigated. A numerical algorithm for solving the boundary-value problem obtained is proposed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 64–71, November–December, 1991.In conclusion, the author wishes to thank V. M. Maksimov for taking a constant interest in the work and discussing the results.     

Symmetric cavitation flow past a wedge in the presence of a source on the wedge or in the flow

A solution is found to the problem of symmetric cavitation flow over a wedge by an ideal incompressible fluid (in accordance with Efros's scheme [1]) in the presence of a point source in the flow or on the wedge. Expressions are obtained for the forces exerted on the source and the wedge by the fluid, the conditions under which there is a negative resistance (thrust) are indicated, and the profiles of the free streamlines are constructed for different values of the flow parameters.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Shidkosti i Gaza, No. 6, pp. 137–141, November–December, 1979.We thank L. I. Sedov for his interest in the work.     

Calculation of the characteristics of a gas-dynamic laser

The dependence of the radiated power on the characteristics of optical cavities in the case of flow systems has been investigated in a number of papers [1–3], in which it is assumed that population inversion of the laser levels is obtained until entry into the cavity. The operation of a cavity is analyzed in [1] in the geometric-optical approximation with allowance for vibrational relaxation in the gas flow. A simplified system of relaxation equations is solved under steady-state lasing conditions and an expression derived for the laser output power on the assumption of constant temperature, density, and flow speed. The vibrational relaxation processes in the cavity itself are ignored in [2, 3]. It is shown in those studies that the solution has a singularity at the cavity input within the context of the model used. In the present article the performance characteristics of a CO₂-N₂-He gas-dynamic laser with a plane cavity are calculated. A set of equations describing the processes in the cavity is analyzed and solved numerically. Population inversion of the CO₂ laser levels is created by pre-expansion of the given mixture through a flat hyperbolic nozzle. The dependence of the output power on the reflectivities of the mirrors, the cavity length, the pressure, and the composition of the active gas medium is determined.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi FiziM, No. 5, pp. 33–40, September–October, 1972.     

Problem concerning a plane explosion in a heterogeneous atmosphere with account taken of the post-breakthrough stage

The problem is considered concerning a plane explosion in an exponential and standard atmosphere. The heterogeneity of the medium exerts an extremely marked influence on the gas flow. As shown in [1], under the conditions of an exponential atmosphere the upper part of the shock-wave front recedes to an infinite distance, after a finite time. This phenomenon has received the name breakthrough of the atmosphere. A numerical investigation of a powerful plane explosion in an exponential atmosphere at the stage before breakthrough is contained in [2]. In [3], asymptotic boundary conditions are proposed which permit the gas flow after breakthrough to be calculated. In the present paper, a numerical solution of this problem is obtained at an interval of time which exceeds by a factor of 10–15 the time of break-through. The effect of counterpressure and gravity is studied. Some results are given for a plane explosion in a standard atmosphere.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 124–131, May–June, 1976.The authors thank L. A. Chudov for attention to the project and for useful advice.     

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.     

Prediction of amount of entrained droplets in vertical annular two-phase flow

Prediction of amount of entrained droplets or entrainment fraction in annular two-phase flow is essential for the estimation of dryout condition and analysis of post dryout heat transfer in light water nuclear reactors and steam boilers. In this study, air–water and organic fluid (Freon-113) annular flow entrainment experiments have been carried out in 9.4 and 10.2 mm diameter test sections, respectively. Both the experiments covered three distinct pressure conditions and wide range of liquid and gas flow conditions. The organic fluid experiments simulated high pressure steam–water annular flow conditions. In each experiment, measurements of entrainment fraction, droplet entrainment rate and droplet deposition rate have been performed by using the liquid film extraction method. A simple, explicit and non-dimensional correlation developed by Sawant [Sawant, P.H., Ishii, M., Mori, M., 2008. Droplet entrainment correlation in vertical upward co-current annular two-phase flow. Nucl. Eng. Des. 238 (6), 1342–1352] for the prediction of entrainment fraction is further improved in this study in order to account for the existence of critical gas and liquid flow rates below which no entrainment is possible.Additionally, a new correlation is proposed for the estimation of minimum liquid film flow rate at the maximum entrainment fraction condition. The improved correlation successfully predicted the newly collected air–water and Freon-113 entrainment fraction data. Furthermore, the correlations satisfactorily compared with the air–water, helium–water and air–genklene experimental data measured by Willetts [Willetts, I.P., 1987. Non-aqueous annular two-phase flow. D.Phil. Thesis, University of Oxford]. However, comparison of the correlations with the steam–water data available in literature showed significant discrepancies. It is proposed that these discrepancies might have been caused due to the inadequacy of the liquid film extraction method used to measure the entrainment fraction or due to the change in mechanism of entrainment under high liquid flow conditions.     

Analysis of optimum asymmetric plane nozzles with allowance for the moment characteristics

Some properties of the flow in asymmetric plane nozzles producing the maximum moment about a given point [1] are investigated. The maximum moment conditions, which follow from an analysis of the second variation, are obtained. A numerical analysis is carried out for nozzles with a relatively short lower wall.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 103–108, July–August, 1988.The author wishes to thank A. N. Kraiko for discussing the results and for his valuable advice, and V. P. Tenetov and N. A. Vodyanov for participating in the development and refinement of the programs for designing optimum asymmetric nozzles.     

Rarefied gas shear flow between two movable segments of parallel plates

A study is made of the two-dimensional steady-state rarefied gas flow observed between two parallel plane surfaces of finite and different length when one of the surfaces is fixed and the other moves parallel to itself at a constant velocity, while remaining within the bounds of a given segment with fixed ends (the motion is similar to that of a conveyer belt). This flow can be regarded as a twodimensional counterpart of the classical one-dimensional Couette flow. The corresponding problem is formulated in a rectangular domain for the nonlinear kinetic equation with a model collision operator and is solved by a finite-difference method for various boundary conditions. For simplicity's sake, the flow was studied under conditions such that it can be considered near-isothermal. The gas pressures on each side of the gap formed by the plates may be the same or different. If the pressures on both sides of the gap are equal, then a near-zero-gradient flow develops between the plates. In this case, the greater the plate length, the nearer the flow in the middle of the gap to one-dimensional Couette flow. The end effects are examined, together with the conditions in which the flow in the middle of the domain can be assumed to be practically one-dimensional. In the zero-gradient regime, the system operates, in general, as a pump transferring gas from one side of the gap the other. The ability to pump gas also remains if a small counterpressure exists.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 150–155, May–June, 1995.The work was financially supported by the Russian Foundation for Fundamental Research (project No. 93-013-17928).     

Solution of the direct problem of the mixed flow of a conducting gas in a laval nozzle with a meridional magnetic field

We consider the direct problem in the theory of the axisymmetric Laval nozzle (including sonic transition) for the steady flow of an inviscid and nonheat-conducting gas of finite electrical conductivity. The problem is solved by numerical integration of the equations of unsteady gas flow using an explicit difference scheme that was proposed by Godunov [1,2], and was used to calculate steady and unsteady flows of a nonconducting gas in nozzles by Ivanov and Kraiko [3]. The subsonic and the supersonic flows of a conducting gas in an axisymmetric channel when there is no external electric field, the magnetic field is meridional, and the magnetic Reynolds numbers are small have previously been completely investigated. Thus, Kheins, Ioller and Élers [4] investigated experimentally and theoretically the flow of a conducting gas in a cylindrical pipe when there is interaction between the flow and the magnetic field of a loop current that is coaxial with the pipe. Two different approaches were used in the theoretical analysis in [4]: linearization with respect to the parameter S of the magnetogasdynamic interaction and numerical calculation by the method of characteristics. The first approach was used for weakly perturbed subsonic and supersonic flows and the solutions obtained in analytic form hold only for small S. This is the approach used by Bam-Zelikovich [5] to investigate subsonic and supersonic jet flows through a current loop. The numerical calculations of supersonic flows in a cylindrical pipe in [4] were restricted to comparatively small values of S since, as S increases, shock waves and subsonic waves appear in the flow. Katskova and Chushkin [6] used the method of characteristics to calculate the flow of the type in the supersonic part of an axisymmetric nozzle with a point of inflection. The flow at the entrance to the section of the nozzle under consideration was supersonic and uniform, while the magnetic field was assumed to be constant and parallel to the axis of symmetry. The plane case was also studied in [6]. The solution of the direct problem is the subject of a paper by Brushlinskii, Gerlakh, and Morozov [7], who considered the flow of an electrically conducting gas between two coaxial electrodes of given shape. There was no applied magnetic field, and the induced magnetic field was in the direction perpendicular to the meridional plane. The problem was solved numerically in [7] using a standard process. However, the boundary conditions adopted, which were chosen largely to simplify the calculations, and the accuracy achieved only allowed the authors [7] to make reliable judgments about the qualitative features of the flow. Recently, in addition to [7], several papers have been published [8–10] in which the authors used a similar approach to solve the direct problem in the theory of the Laval nozzle (in the case of a nonconducting gas).Translated from Izvestiya Akademiya Nauk SSSR, Mekhanika Zhidkosti i Gaza., No. 5, pp. 14–20, September–October, 1971.In conclusion the author wishes to thank M. Ya. Ivanov, who kindly made available his program for calculating the flow of a conducting gas, and also A. B. Vatazhin and A. N. Kraiko for useful advice.     

Unsteady-state flow of a gas in a channel,resulting from the motion of a piston,with magnetohydrodynamic offtake of energy and luminescence of the gas

The present paper discusses the one-dimensional unsteady-state flow of a gas resulting from the motion of a piston in the presence of weak perturbing factors, with which the investigation of the perturbed (with respect to the usual self-similar conditions) motion reduces to the solution of ordinary differential equations, is indicated. The distributions of the parameters of the gas between the piston and the shock wave are found. The conditions under which there is acceleration or slowing down of the shock front are clarified. As an example, this paper considers the unsteady-state motion of a conducting gas in a channel with solid electrodes under conditions where electrical energy is generated, and the flow of a gas taking radiation into account, under the assumption of optical transparency of the medium. The theory developed is used to solve the problem of the motion of a thin wedge with a high supersonic velocity in an external axial magnetic field, taking account of the luminescence of the layer of heated gas between the wedge and the shock wave.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 17–25, September–October, 1970.     

Construction of asymmetric nozzles of maximum moment given additional conditions on the geometrical and force characteristics

A solution is given to the variation problem of constructing asymmetric plane nossles which realize the maximum moment relative to some point. The contours of the nozzle are assumed to be noninteracting. The method of the undetermined control contour is used [1]. The solution of this problem contains as a special case the solution to the problem of constructing a nozzle of maximum thrust, including also the case of a given lifting force [1–3]. It is shown that the construction of a nozzle of maximum moment under additional conditions on the thrust and the lifting force, or on the moment relative to another point, reduces to the construction of a nozzle of maximun moment relative to some auxiliary point.Translated from Izvestiya Akademi Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 148–152, September–October, 1984.The author thanks A. N. Kraiko for useful discussions and for his appraisal of the study.     

Role of two-dimensional acoustic wave cutoff in the instability of subsonic MHD flows

One of the important factors affecting the structure of the natural vibrations and the conditions under which they build up in an inhomogeneous subsonic flow may be the cutoff of non-one-dimensional sound waves expressed in the strong reflection of such waves from the critical sections (caustics). In this study the case of natural two-dimensional acoustic perturbations in an inhomogeneous subsonic conducting gas flow in the presence of critical sections is subjected to an asymptotic analysis. Special attention is paid to the conditions of growth of the two-dimensional acoustic perturbations in the internal resonator formed by two critical sections and the walls of an MHD channel.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 26–36, March–April, 1988.The authors are grateful to seminar participants L. M. Biberman and G. A. Lyubimov for useful discussions.     

Induced flow close to the entry of a jet into a channel

The flow investigated here appears as a result of the ejecting action of a turbulent jet in conditions when a jet, after emerging from a cylindrical nozzle, impinges into a gas flow channel. Such conditions occur in gas distribution systems. A review of the investigations of flows induced by jets and the solution of a number of problems are contained in [1]. A distinctive feature of the problem investigated below is the stronger development of local characteristics and the specific flow geometry, and also its spatial inhomogeneity. The method of integral transforms is used and formulas for determining the velocity about the nozzle and the flow in the vicinity of jet entry into the gas channel are obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 126–133, January–February, 1976.The author thanks T. Kh. Sedel'nikov for valuable suggestions.     

Slip boundary conditions on a catalytic surface in a multicomponent gas flow

The boundary conditions for the velocity slip and temperature and concentration jumps on the surface of a body in a rarefied multicomponent gas flow are obtained. The mathematical treatment is given in detail because of the need to examine critically some previous results which disagree with each other in spite of the fact that the initial premises and the methods of solution were the same. The results of this study, which are given in a convenient form, represent the boundary conditions for both the simplified and the complete Navier-Stokes equations in problems of hypersonic rarefied gas flow past bodies with a catalytically active surface.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 159–168, January–February, 1996.     

Deformation of liquid jets and drops injected into a gas stream

The process of deformation of liquid drops and jets is examined on a broad interval of two-phase flow parameters. The shape of a jet penetrating a gas stream directed at an angle to the jet-particle velocity vector is determined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 82–88, May–June, 1971.In conclusion the authors thank A. K. Simonovskii for his useful comments.     

Motion of a shock wave through a gas of variable density

A successive approximation method is used to solve the self-similar problem of gas flow accompanying a shock wave propagated through a polytropic gas of variable density. The method is based on a special choice of independent variables and the use of Whitham's approximation [1] as the initial approximation for the motion of the discontinuity. A first approximation for the self-simulation index is calculated which is in good agreement with exact values.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 68–72, September–October 1970.The author wishes to thank S. V. Fal'kovich for suggesting this problem and for his help in the work.     

Flow of a gas behind a Chapman-Jouguet detonation wave in the vicinity of a line of discontinuity of a surface wave curvature

This paper discusses questions of constructing a solution of the gasdynamic equations near a line of curvature discontinuity at the surface of a detonation wave, propagating under Chapman—Jouguet conditions. It describes the construction of the solution in two cases: in a flow arising with the initiation of a detonation along a half-plane in a quiescent homogeneous combustible gas and in a flow arising with the initiation of a detonation along a half-line under these same conditions.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 120–126, January–February, 1978.     

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.