Axially symmetric vortical flow of a nonviscous liquid in the semiinfinite gap between two coaxial circular cylinders

In the framework of the Hromek-Lamb equations we investigate the axially symmetric vortical flow of a nonviscous incompressible liquid in both semiinfinite and infinite gaps between two coaxial circular cylinders. The investigation is carried out for two circulation and flow functions and two different Bernoulli constants which are chosen in the form of a third-order polynomial in the flow function. This makes it possible to determine the effect of the azimuthal velocity component on the flow in an axial plane with radial and axial components of the velocity. It is shown that under certain circumstances wave oscillations in the flow are possible, in agreement with the results of [1–3] which investigated the flow in an infinite tube [1], in a semiinfinite tube with simpler circulation functions and Bernoulli constants [2], and in the two-dimensional case [3]. We determine the dependence of the formation of wave perturbations on the third term of the Bernoulli constant and on the azimuthal velocity component. The results of this work agree with investigations by other authors [1–4].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 38–45, September–October, 1977.The author thanks Yu. P. Gupalo and Yu. S. Ryazantsev for suggesting this problem and for their interest in the work. Thanks are also due to G. Yu. Stepanov for discussions and valuable comments.     

Asymptotic solution of the Orr-Sommerfeld equation in the outer region of the boundary layer with allowance for nonparallelism

There have been many publications devoted to the investigation of the hydrodynamic stability of nonparallel flows on the basis of the modified Orr-Sommerfeld equation [1–4]. Taking into account the additional terms associated with the presence in the flow of a transverse component of velocity and acceleration can lead not only to a significant quantitative discrepancy as compared with calculations based on the usual Orr-Sommer-feld equation but also to qualitatively new results (nonclosure of the neutral curves for flow on a permeable surface in the presence of strong injection [4]). In this paper an asymptotic solution of the Orr-Sommer-feld equation, valid in the outer region of boundary layer flow, is constructed for self-similar gradient flow over a surface (Falkner-Skan flow). The continuity of the eigenvalue spectrum for an unbounded increase in the perturbation propagation velocity is demonstrated on the basis of the solution obtained. For the ordinary Orr-Sommerfeld equation a continuous transition of the spectrum through the value of the perturbation propagation velocity C_r=1 (which coincides with the velocity of the external flow) is impossible [5].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 171–173, January–February, 1987.     

Transition flow of a fibrous suspension in a pipe as the flow of an anisotropic fluid

The transition flow is considered of a fibrous suspension in a pipe. The flow region consists of two subregions: at the center of the flow a plug formed by interwoven fibers and fluid moves as a rigid body; between the solid wall and the plug is a boundary layer in which the suspension is a mixture of the liquid phase and fibers separated from the plug [1–3]. In the boundary region the suspension is simulated as an anisotropic Ericksen—Leslie fluid [4, 5] which satisfies certain additional conditions. Equations are obtained for the velocity profile and drag coefficient of the pipe, which are both qualitatively and quantitatively in good agreement with the experimental results [6–8]. Within the framework of the model, a mechanism is found for reducing the drag in the flow of a fibrous suspension as compared to the drag of its liquid phase.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 91–98, September–October, 1985.     

Propagation of modulated nonlinear waves in a relaxing gas-liquid mixture

The propagation of nonstationary weak shock waves in a chemically active medium is essentially dispersive and dissipative. The equations for short-wavelength waves for such media were obtained and investigated in [1–4]. It is of interest to study quasimonochromatic waves with slowly varying amplitude and phase. A general method for obtaining the equations for modulated oscillations in nonlinear dispersive media without dissipation was proposed in [5–8]. In the present paper, for a dispersive, weakly nonlinear and weakly dissipative medium we derive in the three-dimensional formulation equations for waves of short wavelength and a Schrödinger equation, which describes slow modulations of the amplitude and phase of an arbitrary wave. The coefficients of the equations are particularized for the considered gas-liquid mixture. Solutions are obtained for narrow beams in a given defocusing medium as well as linear and nonlinear solutions in the neighborhood of a diffraction beam. A solution near a caustic for quasimonochromatic waves was found in [9].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 133–143, January–February, 1980.     

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.     

Example of parametric resonance in a rotating flow

Parametric resonance is one of the common types of instability of mechanical systems [1]. A standard example of the equations describing parametric oscillations is the Mathieu equation and its generalizations. In hydrodynamics these oscillations have been closely studied in connection with the problem of the vertical oscillations of a vessel containing an incompressible fluid in a uniform gravity field [1–5]. In this paper a new example of a flow whose stability problem reduces to the Mathieu equation is given. This is a flow of special type in a rotating cylindrical channel. The direction of the angular velocity is perpendicular to the channel axis, and its magnitude varies periodically with time. Flows with this geometry are of potential interest in technical applications [6, 7].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 175–177, March–April, 1987.     

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.     

Forced oscillations of pressure in tubes of active material

A study is made in the quasione-dimensional inertialess approximation of the axisymmetric flow of a Newtonian fluid in a tube of finite length made of a nonlinear active material with the capability of reducing deformations in response to an increase in tensile stresses [1, 2]. A study is made of the influence of the frequency and amplitude of forced oscillations of pressure at the entrance of the tube on its flow rate characteristics and on the behavior of the tube, depending on its length and certain rheological parameters. The first attempts at a study within the framework of this model of flow for unsteady conditions at the ends of the tube and in the ambient medium are described in [3, 4]. A general solution of this problem for external periodic disturbances of low amplitude is constructed in [5]. The present study gives an analysis of certain results of the numerical solution of an analogous problem for a wide range of variations in the frequency and amplitude of the pressure oscillations at the entrance to the tube.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 88–90, March–April, 1985.     

Plug flow of a fibrous suspension

A model of a fibrous suspension with plug flow is constructed. A solution to the problem of the flow of a suspension in a straight round tube is obtained for two partial cases and is compared with experiment. With the flow of a fibrous suspension in a round tube, several sets of flow conditions can be distinguished [1–3]. If the flow rate is relatively small, the so-called plug flow is established. It is characterized by the fact that two flow regions are formed in the tube: the core of the flow, or the plug [1–3], in which the mass of the fibers is concentrated, and a layer near the wall in which only the liquid phase of the suspension flows. When the suspension has attained a determined velocity, the plug starts to break down, and the flow ceases to be of the plug type.Petrozavodsk. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 65–71, July–August, 1972.     

Numerical simulation of flow of multicomponent mixtures in porous media

A study is made of the isothermal flow of multicomponent mixtures in a porous medium, accompanied by phase transitions, interphase mass exchange, and change in the physicochemical properties of the phases [1–3], It is assumed that at each point of the flow region, phase equilibrium is established instantaneously and the flow velocities of the separate phases conform to Darcy's law. Approximate solutions of problems of displacing oil by high-pressure gas were obtained in [1]. By generalizing the theory developed in [4], a study is made in [5] of the structure of the exact solutions of the problems of the flow of three-component systems which describe the displacement of oil by different reactants (gases, solvents, micellar solutions). The numerical solutions of the problems of multicomponent system flow are considered in [2, 3, 6, 7]. This paper presents a numerical method which is distinguished from the well-known ones [2, 3, 6, 7] by the following characteristics. The flow equations are approximated by a completely conservative finite-difference scheme of the implicit pressure-explicit saturation type, the calculation being carried out using Newton's method of iteraction with spect to both the pressure and the composition of the mixture. The minimum derivative principle [8] is used in the approximation of the divergence terms of the equations. The phase equilibrium is calculated using the equation of state.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 101–110, July–August, 1985.     

Electric arc in hydrogen flow at high pressure

The interaction of an electric arc with laminar hydrogen flow at a pressure of 100 atm is examined with account for the transverse flows. Results of calculations are presented for a current strength of 30 A and tube radius 0.3 cm. It is shown that for these parameters radiation plays the defining role in the heat transfer process.The electric arc in a gas stream without account for radiation has been studied previously in [1–4] and with account for radiation in [5]. However, in these studies only the longitudinal velocity component was taken into account in the energy equation.The authors wish to thank A. T. Onufriev for his interest in this study.     

Solution of some variational problems of two-phase gas dynamics

The problem of constructing an optimal-profile nozzle for a two-phase medium is considered in the one-dimensional approximation. A problem of this type to find an optimal-thrust nozzle was considered by Kraiko, Starkov, and Sternin [1]. In contrast to their study, a more complete model of the two-phase medium is used in the present paper, and the nozzles are optimized with respect to the efficiency, gas velocity, and velocity of the suspended particles. The problem is solved using the formalism of optimal control theory [2, 3]. The change in the vapor concentration and phase transitions are taken into account. A method of numerical solution of the problem is proposed. It has been realized on a computer. The method can be used to solve similar problems for a more complicated model of the two-phase medium.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 52–58, January–February, 1982.     

Far nonlinear field of a nonlifting airfoil for a generalised equation of transonic flow

The transonic flow equation [1] for plane unsteady irrotational idealgas flows is extended to the case of subsonic, transonic or supersonic flows in a region with an almost constant value of the velocity using orthogonal flow coordinates (family of equipotential lines and streamlines). A solution for the nonlinear far field of steady transonic flow past an airfoil has been obtained for the transonic equation [2]. In this paper it is obtained for a generalized transonic equation and its asymptotic expansion is given. In using difference methods of calculating the flow past an airfoil in the transonic regime a knowledge of the nonlinear field makes it possible to reduce the dimensions of the calculation region (near field) as compared with the region determined by the far field of the linear theory.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 87–91, January–February, 1986.     

Exact solutions of boundary-value problems for nonlinear flow in porous media

Exact solutions for flow problems in porous media with a limiting gradient in the case when the flow region in the hodograph plane is a half-strip with a longitudinal cut [1] are known only for two models of the resistance law [2–6]. The present study gives a one-parameter family of flow laws, and argues the possibility of effective determination of exact and approximate analytical solutions on the basis of successive reduction to boundary-value problems for the Laplace equation or for the equation studied in detail in [1]. It should be noted that the characteristics of the flow are determined without additional quadratures.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 107–112, May–June, 1985.     

Drag associated with transitional flow regime of a fiber suspension in a tube

A semlempirical model is constructed of the flow of a fiber suspension of low and medium concentration in regimes that are usually called mixed and undeveloped turbulent regimes [1–4]. It is shown that although the flow of fiber suspensions in these regimes has features similar to those of the turbulent flow of a Newtonian fluid, for example, a logarithmic velocity profile, the characteristic features of the flow in both regimes can be better explained, not by turbulence of the flow, but by orientation of the fibers in it and by plastic flow of the fiber continuum. For this reason, to distinguish the mixed and undeveloped turbulent regimes from a truly turbulent regime it is proposed here to describe them by a general name — transitional flow. The obtained expressions agree qualitatively and quantitatively with the experimental results of Lee and Duffy [2], Sanders and Meyer [3], and Mih and Parker [4].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 40–45, May–June, 1984.I thank V. N. Nikolaevskii and A. N. Golubyatnikov for interest in the work and helpful comments.     

Self-similar problems of propagation of an extended hydrofracture in a permeable medium

The propagation of an extended hydrofracture in a permeable elastic medium under the influence of an injected viscous fluid is considered within the framework of the model proposed in [1, 2]. It is assumed that the motion of the fluid in the fracture is turbulent. The flow of the fluid in the porous medium is described by the filtration equation. In the quasisteady approximation and for locally one-dimensional leakage [3] new self-similarity solutions of the problem of the hydraulic fracture of a permeable reservoir with an exponential self-similar variable are obtained for plane and axial symmetry. The solution of this two-dimensional evolution problem is reduced to the integration of a one-dimensional integral equation. The asymptotic behavior of the solution near the well and the tip of the fracture is analyzed. The difficulties of using the quasisteady approximation for solving problems of the hydraulic fracture of permeable reservoirs are discussed. Other similarity solutions of the problem of the propagation of plane hydrofractures in the locally one-dimensional leakage approximation were considered in [3, 4] and for leakage constant along the surface of the fracture in [5–7].Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 91–101, March–April, 1992.     

Percolation model of two-phase equilibrium flow in a porous medium with microheterogeneous wettability

The percolation model of two-phase flow described in [1, 2] is used as a basis for examining the problem of the behavior of the characteristics of two-phase equilibrium flow in a porous medium when the capillaries have a radius distribution and differ with respect to the wettability properties of their surfaces. Analytic expressions describing the dependence of the relative phase permeability coefficients on the saturation of the medium by the displacing phase and the microinhomogeneous wettability parameters are obtained. A qualitative comparison shows the theoretical results to be consistent with the data of a direct numerical computer calculation of a grid model [3]. The effect of the microinhomogeneity parameters and the form of the capillary radius distribution function on the phase permeabilities is analyzed within the framework of the approach developed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 86–93, September–October, 1989.     

Effect of viscoelastic properties of a liquid on the dynamics of small oscillations of a gas bubble

A series of papers has been devoted to questions of gas bubble dynamics in viscoeiastic liquids. Of these papers we mention [1–4]. The radial oscillations of a gas bubble in an incompressible viscoeiastic liquid have been studied numerically in [1, 2] using Oldroyd's model [5]. Anexact solution was found in [3], and independently in [4], for the equation of small density oscillations of a cavity in an Oldroyd medium when there is a periodic pressure change at infinity. The analysis of bubble oscillations in a viscoeiastic liquid is complicated by properties of limiting transitions in the rheological equation of the medium. These properties are of particular interest for the problem under investigation. These properties are discussed below, and characteristics of the small oscillations of a bubble in an Oldroyd medium are investigated on the basis of a numerical analysis of the exact solution obtained in [3].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 82–87, May–June, 1976.The authors are grateful to V. N. Nikolaevskii for useful advice and for discussing the results.     

Nonisothermal instability of high-velocity elastoplastic flows

An important feature of the high-velocity deformation of solids is the localization of deformation, one of the causes of which may be the nonisothermal instability of plastic flow [1–6]. In connection with the intensive development of high-velocity technology in the treatment of materials, the investigation of the criteria for nonisothermal stability of processes of plastic deformation is of fundamental interest, since in certain cases they determine the optimum technological regimes [5]. The critical values of deformation velocities, above which the effects of thermal instability becomes decisive in the process of deformation of solids, are estimated by semiempirical methods in [1]. The non-boundary-value problem of the criteria for nonisothermal instability is analyzed in [2] for the point of view of flow stability in the so-called coupled formulation. The latter means that the heat-conduction equation is added to the basic equations determining the dynamics of an elastoplastic medium. The problem is solved in [6] in an analogous formulation, but for flow averaged over the spatial coordinate. The solution of the boundary-value problem for one-dimensional flow in this formulation is given in the present paper.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 133–138, May–June, 1986.     

The boundary layers of a fully ionized two-temperature plasma with given component temperatures at an electrode

The flow of a plasma with different component temperatures in the boundary layers at the electrodes of an MHD channel is investigated without any assumptions as to self-similarity. For the calculation of the electron temperature, the full energy equation for an electron gas [1] is solved with allowance for the estimates given in [2]. In contrast to [3, 4], the calculation includes the change in temperature of electrons and ions along the channel caused by the collective transport of energy, the work done by the partial pressure forces, and the Joule heating and the energy exchange between the components. The problem of the boundary layers in the flow of a two-temperature, partially ionized plasma past an electrode is solved in simplified form by the local similarity method in [5–7]. In these papers, either the Kerrebrock equation is used [5, 6] or the collective terms are omitted from the electron energy equation [7].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 3–10, September–October, 1972.The author thanks V. V. Gogosov and A. E. Yakubenko for interest in this work.