Flow of electrically charged aerosols past bodies

An experimental investigation was made of the flow of electrically charged aerosols with solid or liquid disperse phase past bodies. Air flows with solid particles (sand, iron) and water drops were produced by special apparatus. The regimes in which the disperse particles and the bodies were charged or neutral were studied. A system of dimensionless numbers and their values are indicated for the different gas-dynamic and electric flow regimes. The main features of the flows are explained and the integrated electric characteristics of the bodies determined. The possibility of controlling the flow of a disperse medium by means of electric fields is demonstrated. It is shown that the inductive charging of liquid films near sharp edges of a body has a strong influence on the electric characteristics of the body (when air with water drops flows past it).Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 71–79, July–August, 1982.     

Isothermal viscous incompressible flow in a hydrodynamic model of an electrophoresis chamber

A numerical solution and approximate analysis of the system of Navier-Stokes equations averaged over the transverse coordinate has made it possible to obtain the dependence of the length of the hydrodynamic flow stabilization interval in a thin cell of rectangular cross section on the Reynolds number, the relative thickness of the cell, and the relative size of the inlet opening. The principal and secondary flow regimes are calculated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 14–20, March–April, 1990.     

Development and instability of steady convective flows in a square cavity heated from below and a field of vertically directed vibrational forces

The present paper is devoted to numerical investigation of the spatial structure and stability of secondary vibrational convective flows resulting from instability of the equilibrium of a fluid heated from below. Vibrations parallel to the vector of the gravitational force (vertical vibrations) are considered. As in earlier work [7–9], a region of finite size is used — a square cavity heated from below. It is shown that enhancement of the vibrational disturbance of the natural convective flow may either stabilize or destabilize flows with different spatial structures; it may also stabilize certain solutions of the system of convection equations that are unstable in the absence of vibrational forces. In addition, increase of the vibrational Rayleigh number can lead to a change of the mechanisms responsible for equilibrium instability and oscillatory instability of the secondary steady flows.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 9–18, March–April, 1991.I thank G. Z. Gershuni for assistance and extremely fruitful discussions of the results of the paper.     

Occurrence of periodic regimes in steady supersonic mid flows due to loss of electrical conductivity of medium

A study is made of the features of supersonic magnetohydrodynamic (MHD) flows due to the vanishing of the electrical conductivity of the gas as a result of its cooling. The study is based on the example of the exhausting from an expanding nozzle of gas into which a magnetic field (Re_m 1) perpendicular to the plane of the flow is initially frozen. It is demonstrated analytically on the basis of a qualitative model [1] and by numerical experiment that besides the steady flow there is also a periodic regime in which a layer of heated gas of electric arc type periodically separates from the conducting region in the upper part of the nozzle. A gas-dynamic flow zone with homogeneous magnetic field different from that at the exit from the nozzle forms between this layer and the conducting gas in the initial section. After the layer has left the nozzle, the process is repeated. It is established that the occurrence of such layers is due to the development of overheating instability in the regions with low electrical conductivity, in which the temperature is approximately constant due to the competition of the processes of Joule heating and cooling as a result of expansion. The periodic regimes occur for magnetic fields at the exit from the nozzle both greater and smaller than the initial field when the above-mentioned Isothermal zones exist in the steady flow. The formation of periodic regimes in steady MHD flows in a Laval nozzle when the conductivity of the gas grows from a small quantity at the entrance due to Joule heating has been observed in numerical experiments [2, 3]. It appears that the oscillations which occur here are due to the boundary condition. The occurrence of narrow highly-conductive layers of plasma due to an initial perturbation of the temperature in the nonconducting gas has previously been observed in numerical studies of one-dimensional flows in a pulsed accelerator [4–6].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 138–149, July–August, 1985.     

Viscous flow in a cylindrical vessel in the presence of a rotating disk

Viscous flows in the cylinder-disk system have been investigated theoretically and experimentally, over a broad range of Reynolds numbers Re, H/R_T, and R_k/R_T in order to explore the characteristics of the flow, which is a function of time, the depth of the liquid, the Reynolds number, the radii of the disk and the cylinder, and their geometry (flat, convex or concave disk). The results of comparing the data of numerical and laboratory simulations are presented. The appearance of secondary eddies in the axial region at large Reynolds numbers has been detected and diagrams of flows of different spatial configuration constructed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 33–40, September–October, 1985.     

Calculation of the flow in ejector nozzles

A method is proposed for calculating the two-dimensional nonviscous flows in ejector nozzles of arbitrary shape, for two operating cycles: the subsonic flow cycle of a secondary stream and a cycle when the secondary stream attains critical velocity, i.e., it is cut off. In the second case, the possibility is allowed for the appearance of a direct compression shock in the supersonic part of the secondary stream.Translated from Mekhanika Zhidkosti i Gaza, No. 1, pp. 111–118, January–February, 1974.The authors thank A. N. Kraiko and M. Ya. Ivanov for useful discussions and assistance, V. V. Polyakov for interest in the project and L. P. Frolova for assistance in drawing up the task.     

Quasihomogeneous model of cavitation flows in diffuser channels

Starting with the experiments carried out by Reynolds in 1894, the flow in Venturi tubes has traditionally been used to study and demonstrate various forms of cavitation. Numerous authors have carried out experimental research on the various flow regimes in diffuser channels [1–7] or have investigated theoretical models of such flows [6, 8]. The occurrence and development of cavitation is closely associated with the phenomenon of turbulent separation complicated by the presence of two-phase flow in the dissipation zone. For a long time these effects were considered separately, until Gogish and Stepanov [9] proposed a single model of cavitation and separation based on the theory of intense interaction of an incompressible potential flow and a turbulent cavitation layer of variable density and embracing the various stages of cavitation. The object of this study is to demonstrate the possibilities of this model with reference to the simple example of flows accompanied by cavitation and separation in plane and axisymmetric diffuser channels of the Venturi tube type with straight and curved walls. The dissipative flow near the walls is described by a quasihomogeneous model of turbulent two-phase flow, in which the presence of two phases is taken into account only by varying the mean density. The potential core of the flow is considered in the one-dimensional formulation. The displacement thickness serves as the flow interaction parameter. The conditions of ocurrence and development of circulatory flows are determined. Examples of symmetrical and nonsymmetrical flows are presented.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 47–54, September–October, 1986.     

Liquid flow in the cylindrical vessel filling process

The axisymmetric flow of a highly viscous incompressible liquid as it fills the space between semi-infinite vertical coaxial cylinders is investigated. The liquid flows into the vessel at a constant rate along the surface of the inner cylinder. The flow is characterized by the presence of a free surface. The problem is formulated in the creep flow approximation and is solved numerically. The numerical solution leads to an investigation of the hydrodynamics of the filling process, including the stage in which the liquid spreads over the horizontal surface and the filling stage which follows the arrival of the free surface front at the wall of the outer cylinder.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 65–70, January–February, 1990.     

Direct numerical simulation of turbulent Taylor–Couette flow

The direct numerical simulation (DNS) of the Taylor–Couette flow in the fully turbulent regime is described. The numerical method extends the work by Quadrio and Luchini [M. Quadrio, P. Luchini, Eur. J. Mech. B/Fluids 21 (2002) 413–427], and is based on a parallel computer code which uses mixed spatial discretization (spectral schemes in the homogeneous directions, and fourth-order, compact explicit finite-difference schemes in the radial direction). A DNS is carried out to simulate for the first time the turbulent Taylor–Couette flow in the turbulent regime. Statistical quantities are computed to complement the existing experimental information, with a view to compare it to planar, pressure-driven turbulent flow at the same value of the Reynolds number. The main source for differences in flow statistics between plane and curved-wall flows is attributed to the presence of large-scale rotating structures generated by curvature effects.     

Three-dimensional instability of an elliptic Kirchhoff vortex

The instability of a Kirchhoff vortex [1–3] with respect to three-dimensional perturbations is considered in the linear approximation. The method of successive approximations is applied in the form described in [4–6]. The eccentricity of the core is used as a small parameter. The analysis is restricted to the calculation of the first two approximations. It is shown that exponentially increasing perturbations of the same type as previously predicted and observed in rotating flows in vessels of elliptic cross section [4–9] appear even in the first approximation. As distinct from the case of plane perturbations [1-3], where there is a critical value of the core eccentricity separating the stable and unstable flow regimes, instability is predicted for arbitrarily small eccentricity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 40–45, May–June, 1988.     

Motion of a free axisymmetric viscous liquid film

Axisymmetric free-film flows are encountered in connection with the atomization of liquids and the collision of jets [1, 2]. In [3] steady motion with transverse symmetry is examined and its inviscid instability is studied. Here, steady flow with an arbitrary velocity profile is investigated numerically by the collocation method. The study of the stability of the steady flow under the assumption of local plane-parallelism leads to the formulation of a sixth-order eigenvalue problem which is solved numerically. The existence of unstable disturbances of two types is demonstrated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 23–29, July–August, 1990.     

Slow flow of gas around a strongly heated or cooled sphere

Problems similar to those considered in [1, 2] are studied, namely, slow flow over a uniformly heated (or cooled) spherical particle and flow past a weakly nonuniformly heated sphere in the absence of external body forces and with allowance for thermal stresses in the gas. The use of an improved method of numerical solution [3] has made it possible to advance into the region of large temperature differences. A new effect is found: allowance for the thermal stresses in the case of flow around a strongly heated sphere leads to the appearance of a suction force instead of a drag. In the case of flow around a nonuniformly heated sphere the influence of thermal stresses is unimportant. The problems are considered for two temperature dependences of the transport coefficients.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 170–175, October–December, 1981.     

Electrosolenoidal flows in a cylindrical cavity

The main difficulties in investigating three-dimensional magnetohydrodynamic (MHD) flows with vorticity arise, first, because it is necessary to solve an independent boundary-value problem in order to find the field of the electromagnetic forces and, second, because the regimes of these flows are strongly nonlinear for the majority of high-power technological MHD processes and a number of natural phenomena. Particular importance attaches to MHD flows generated by the interaction of an electric current applied to the fluid with the magnetic self-field. This class of MHD flows has become known as electrosolenoidal flows [1]. The presence of a definite symmetry in the distribution of the electromagnetic forces and the geometry of the region of the liquid conductor makes it possible to find a solution in self-similar form. The present paper is devoted to exact solutions of the nonlinear equations for axisymmetric electrosolenoidal flows of a conducting incompressible fluid in infinite cylindrical cavities.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 48–53, May–June, 1991.     

Viscous sublayer in the neighborhood of a corner point in supersonic flow past a cooled body

The behavior of the flow functions at the upper edge of the viscous sublayer is subjected to an asymptotic analysis. The results obtained permit a more accurate formulation of the boundary-value problem and an improvement in the quality of numerical calculation of the flow in the viscous sublayer. The heat flux and friction distributions on the surface of the body are obtained for precritical and postcritical interaction regimes; for expansion flows the calculated results are presented in the form of the dependence of the maximum values of the friction and heat flux on the temperature factor and the angle of deflection of the flap; approximate expressions suitable for practical use are proposed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 142–147, November–December, 1989.     

Numerical investigation of viscous gas secondary flows in a rotating cylinder with sources and sinks

A source-sink model of secondary flow excitation in a rotating cylinder, which describes the interaction between a circulator and a rotating gas, is proposed for a nonlinear system of Navier-Stokes equations, and the results of a numerical calculation of the resulting circulating flows are presented. The modified Newton's method employed in the numerical solution makes use of regularizing perturbations to ensure its stability and convergence at low Ekman numbers and high rates of rotation of the cylinder. The combined effect of mechanical and thermal means of flow excitation and the influence of viscous energy dissipation are considered.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 39–44, July–August, 1989.     

An Embedding Method for Bluff Body Flows: Interactions of Two Side-by-Side Cylinder Wakes

We introduce a simple method for the numerical simulation of bluff body flows where the solid object is represented by a distributed body force in the Navier–Stokes equations. The body force density is found at every time step to reduce the velocity within the computational cells occupied by the rigid body to a prescribed value. The method combines certain ideas from the immersed boundary method which was developed to treat biofluid mechanical flows and the volume-of-fluid method for simulating flows with fluid–fluid interfaces. The main advantage of this embedding method is that the computations can be effected on a regular Cartesian grid, without the need to fit the grid to the bluff body surfaces. Thus, flow past several complex bodies can be treated as easily as flow past a single body. The method is validated by reproducing well-established results for vortex shedding from a stationary cylinder. The flow past two side-by-side cylinders is then investigated. When the distance between the cylinders is small, they are seen to shed vortices in-phase, whereas for larger distances, the shedding occurs in anti-phase. For intermediate distances, various shedding patterns are observed, including quasi-periodic, asymmetric and chaotic regimes. Mean values and phase portraits associated with the cylinder lift and drag coefficients, as well as spectral analysis of the same data, are used to describe the flow. A transition diagram that can be compared with experiments or models outlines the various dynamical regimes as a function of the distance between the cylinders and the Reynolds number.     

Numerical simulation of shock wave intersections

A large number of papers, generalized and classified in [1, 2], have been devoted to unsteady gas flows arising in shock wave interaction. Experimental results [3–5] and theoretical analysis [6–9] indicate that the most interesting and least studied types of interaction arise in cases when there are several shock waves. At the same time, nonlinear effects, which depend largely on the nature of the shock wave intersections, become appreciable. Regions of existence of different types, of plane shock wave intersections have been analyzed in [10–13]. It has been shown that in a number of cases the simultaneous existence of different types of intersections is possible. The aim of the present paper is to study unsteady shock wave intersections in the framework of a numerical solution of the axisymmetric boundary-value problem that arises in the diffraction of a plane shock wave on a cone in a supersonic gas flow. Flow regimes that augment the experimental data of [3–5] and the theoretical analysis of [9] are considered.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 134–140, September–October, 1986.     

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.     

Inviscid gas flow in a nozzle with a bend in the contour ahead of the throat

Two possible regimes of inviscid gas flow in a nozzle with a convex angle-type contour ahead of the throat are described, namely, the regimes with the choking in a cross-section passing through the angle vertex and in the throat, respectively. The conclusions are supported by numerical results obtained using a time-dependent method based on the Godunov-Kolgan finite-difference scheme.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 130–136, January–February, 1995.     

General arrangement of regimes for spatial local flows

Different local features at the surface of a body are breaks or sharp changes in boundary conditions, separation or joining of a flow, irregularities, etc., and they may have a marked effect on local and global characteristics of flow over it [1]. This situation stimulates continued interest towards to flow in local regions, which apart from considerable practical importance, often exhibit considerable theoretical novelty (see, e.g., [2–6], where a systematic study was carried out of planar local regions of flow). However, the majority of local regions are spatial, and whereas in studying flat regions considerable success have been achieved, for spatial regions only individual solutions have been obtained, often using considerable simplifications [7–19]. In addition, due to the absence of systematic studies it is difficult to determine the boundaries for existence of different flow regimes in local spatial regions, and limiting transitions which make it possible to changeover from one flow regime to another. In this work systematic studies are carried out for flow regimes in local spatial regions for each of the boundary problems formulated, the main properties of their solution are studied, and a general classification for the arrangement of flow regimes is built up.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 80–91, November–December, 1986.