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.     

Interaction between the boundary layer and a supersonic flow when part of the wall is rapidly heated

There have been many theoretical studies of aspects of the unsteady interaction of an exterior inviscid flow with a boundary layer [1–9]. The mathematical flow models obtained in these studies by the method of matched asymptotic expansions describe a wide range of phenomena observed experimentally. These include boundary layer separation near the hinge of a flap, the flow in the neighborhood of the trailing edge of an oscillating airfoil [1–2], and the development and propagation of perturbations in a boundary layer excited by an oscillating wall or some other way [3–5]. The present paper studies the interaction of an unsteady boundary layer with a supersonic flow when a small part of the surface of a body in the flow is rapidly heated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 66–70, January–February, 1984.     

Visual study of the three-dimensional flow diagram around a delta wing in a subsonic stream

Experimental methods, particularly visualization methods, permit a sufficiently detailed representation of the flow around bodies of complex shape, whose analysis meets with a considerable number of difficulties. The flow around a delta wing in the 1–90-m/sec free-stream velocity range is studied in this paper by using three-dimensional visual methods. Since stream separation and vortex-system formation play the main role in the flow formation over a wing surface, the main purpose of the experiment was to trace the physical process of dynamic development of the flow resulting in separation and vortex formation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 190–194, March–April, 1976.     

Determination of the vorticity on a wing of small aspect ratio in a hypersonic stream

The theory of a thin shock layer [1–3] is used to obtain a formula for calculating the component of the vorticity in the direction of the flow on a wing of small aspect ratio in a hypersonic gas stream. It is shown that for definite shapes of the wing and flow regimes zones may occur with large local values of the vorticity, which, as is well known, have a significant influence on the structure of the flow field.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 175–178, September–October, 1980.     

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.     

Transverse subsonic flow past a cylinder

At around the critical Reynolds number Re = (1.5–4.0)·10⁵ there is an abrupt change in the pattern of transverse subsonic flow past a circular cylinder, and the drag coefficient C_x decreases sharply [1]. A large body of both experimental and computational investigations has now been made into subsonic flow past a cylinder [1–4]. A significant contribution to a deeper understanding of the phenomenon was made by [4], which gives a physical interpretation of a number of theoretical and experimental results obtained in a wide range of Re. Nevertheless, the complicated nonstationary nature of flow past a cylinder with separation and the occurrence of three-dimensional flows when two-dimensional flow is simulated in wind tunnels do not permit one to regard the problem as fully studied. The aim of the present work was to make additional experimental investigations into transverse subsonic flow past a cylinder and, in particular, to study the possible asymmetric stable flow regimes near the critical Reynolds number.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 154–157, March–April, 1980.     

Fluid motion near the surface of a cylinder in a cross flow

An attempt is made to reconstruct the instantaneous flow structures near the surface of a cylinder from measurements of the various characteristics in the precritical self-similar regime, at the moment of crisis and beyond. Information concerning these structures is of decisive importance in connection with the construction of numerical flow models [1–4] and the reliability and accuracy of the calculation results.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 65–71, July–August, 1989.     

Wave flow of a liquid film together with a flow of gas

The wave flow of a thin layer of viscous liquid in conjunction with a flow of gas was considered in a linear formulation earlier [1, 2]. In this paper the problem of the wave flow of a liquid film together with a gas flow is solved in a nonlinear setting. On this basis relationships are derived for calculating the parameters of the film and the hydrodynamic quantities.Ivanovo. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 12–18, January–February, 1972.     

Nonisothermal Couette flow of a non-Newtonian fluid under the action of a pressure gradient

Nonisothermal Couette flow has been studied in a number of papers [1–11] for various laws of the temperature dependence of viscosity. In [1] the viscosity of the medium was assumed constant; in [2–5] a hyperbolic law of variation of viscosity with temperature was used; in [6–8] the Reynolds relation was assumed; in [9] the investigation was performed for an arbitrary temperature dependence of viscosity. Flows of media with an exponential temperature dependence of viscosity are characterized by large temperature gradients in the flow. This permits the treatment of the temperature variation in the flow of the fluid as a hydrodynamic thermal explosion [8, 10, 11]. The conditions of the formulation of the problem of the articles mentioned were limited by the possibility of obtaining an analytic solution. In the present article we consider nonisothermal Couette flows of a non-Newtonian fluid under the action of a pressure gradient along the plates. The equations for this case do not have an analytic solution. Methods developed in [12–14] for the qualitative study of differential equations in three-dimensional phase spaces were used in the analysis. The calculations were performed by computer.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 26–30, May–June, 1981.     

Calculation of interaction of a turbulent near-wake behind a step with a supersonic jet

Existing computational methods [1–5] do not enable one to calculate complex flows behind steps, accounting for nonuniformity of the incident supersonic flow and the effect of compression and expansion waves arriving in the near-wake region. For example, computational methods based on the methods of [1] or [2] are used mainly in uniform supersonic flow ahead of the base edge and, for the most part, cannot be used to calculate flow in annular nozzles with irregular conditions. An exception is reference [6], which investigated flow in an annular nozzle behind a cylindrical center-body. The present paper suggests a method, based on references [7, 8] for calculating the base pressure behind two-dimensional and three-dimensional steps, washed by a supersonic jet.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 43–51, November– December 1977.     

Solute dispersion in a pulsating flow

The one-dimensional model proposed by Taylor [1] of the dispersion of soluble matter describes approximately the distribution of the solute concentration averaged over the tube section in Poiseuille flow. Aris [2] obtained more accurately the effective diffusion coefficient in Taylor's model and solved the problem for the general case of steady flow in a channel of arbitrary section. Many papers have been published in the meanwhile devoted to particular applications of this theory (for example, [3–5]). Various dispersion models have been constructed [6–8] that make the Taylor—Aris model more accurate at small times and agree with it at large times. The acceleration of the mixing of the solute considered in these models in the presence of the simultaneous influence of molecular diffusion and convective transport also operates in unsteady flows. In particular, the presence of velocity pulsations influences the growth of the dispersion even if the mean flow velocity is equal to zero at every point of the flow. In the present paper, the Taylor—Aris theory is extended to the case of laminar flows with periodically varying flow velocity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 24–30, September–October, 1982.     

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.     

Gas flow from a finite volume through a laval nozzle

Self-similar nonsteady flow in a Laval nozzle is considered; the flow is established when an ideal gas issues from a volume into a space at a sufficiently small pressure. The flow in the nozzle is assumed to be one-dimensional. Qualitative conclusions are formed on the effect of the nonsteady flow conditions on the distribution of M. For the case when the nonsteady properties have little effect, an asymptotic solution is obtained in quadratures and an example of a calculation is given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 71–76, March–April, 1978.     

Primary pressure wave in a fluid after actuation of a pipeline valve

This paper considers the variation in the velocity, density, and pressure of an inviscid compressible fluid due to flow acceleration or deceleration after a change in the flow area of a valve installed on the pipeline with rigid walls. Expressions are given for the amplitude of the primary compression or rarefaction wave resulting form the change in flow area of the valve.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 1, pp. 78–84, January–February, 2005     

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.     

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.     

Calculation of a Heat Flow from a Spherical Particle in a Diatomic Gas

The problem of heat flow from a uniformly heated spherical particle in a diatomic gas is considered. The paper reports results of numerical calculations for an analog of the Bhatnagar–Gross–Krook model of the collision integral under for purely diffuse reflection of the gas molecules from the surface.     

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.     

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.     

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.