Effect of humidity on the flow characteristics of a two-phase medium in a diffuser

The effect of the initial humidity of a two-phase flow on the aerodynamic characteristics of a diffuser is considered. A series of calculations is carried out which permit the pressure distribution in the diffuser to be investigated in the case of change of the initial flow velocity, coefficient of slip of the phases, and the initial humidity of the flow. It is shown that, with increase of the initial humidity in the diffuser, there appears a sharply expressed region which has a negative pressure gradient, where the steam velocity can reach the critical value. The numerical solution is compared with the experimental results.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 44–49, November–December, 1973.     

Separation control in a conical diffuser with an annular inlet: center body wake separation

In many practical applications of conical diffusers, the flow is fed by an annular flow passage formed by a center body. Flow separation, which occurs if the center body ends abruptly, is undesirable because it degrades the diffuser performance. The present experiment utilizes magnetic resonance velocimetry to acquire three-component mean velocity measurements for a set of conical diffusers with an annular inlet. The results show strong coupling between the diffuser wall boundary layer development and the wake of the center body. Coanda blowing is used to mitigate the center body wake separation. The diffuser wall boundary layer is thick in the absence of the central separation bubble and separates when Coanda blowing is too strong.     

Investigation of diffuser characteristics in an aerodynamic shock tube

An investigation has been made in an aerodynamic shock tube, with M=8, of the diffuser starting with variable Reynolds numbers, and its throttle characteristics have been recorded. The results obtained enable conclusions to be made regarding the possibility of investigating diffusers in such types of tubes. In [1] the possibility of, in principle, determining the throat starting of a diffuser in an aerodynamic shock tube, and the time to establish flow in the diffuser channel, which was 300 sec, was measured. This paper is devoted to the further investigation of diffuser operation with variable Reynolds numbers, and to determining the throttle characteristics, in particular, the total pressure reduction coefficient.Moscow. Translated from Izvestiya Akademii Nauk SSSR, mekhanika Zhidkosti i Gaza, No. 1, pp. 156–161, January–February, 1972.     

Effect of the form of the electrodes on the current distribution in a magnetogasdynamic channel

A solution is given to the plane problem of the flow of a conducting gas across a homogeneous magnetic field in a magnetogasdynamic channel taking account of the Hall effect at small magnetic Reynolds numbers. The channel is formed by two long electrodes, and the cross section of the channel varies slightly and periodically along the gas flow. It is assumed that the electromagnetic forces are small. It is shown that the current distribution in the channel is nonuniform to a consider able degree and that inverse currents can form at the electrodes, with both subsonic and supersonic flows of the conducting gas. Transverse motion of the gas, due to a change in the cross section of the channel, leads to an increase of Joule energy losses. In [1] the current distribution was obtained in a flat channel formed by infinite dielectric walls, with the flow of a steady-state stream of plasma through the channel across a homogeneous magnetic field. With interaction between the flow and the magnetic field, closed current loops develop in the channel.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 26–33, November–December, 1970.     

Mechanism of turbulent boundary layer separation from a smooth wall

The mechanism of turbulent boundary layer separation under the influence of a positive pressure gradient is analyzed. The process of turbulent separation from a smooth wall in a plane diffuser channel has been experimentally investigated. It is shown that separation is determined by the nature of the flow in a certain inner part of the boundary layer, where the friction effect is unimportant. This region of the boundary layer is most exposed to the action of the positive pressure gradient and it is there that the stagnant zone primarily appears.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 69–77, November–December, 1990.     

Short round diffuser with a high area ratio and a permeable partition

The parameters of a short round diffuser whose channel diameter increases threefold along a length equal to about half the inlet diameter, are experimentally investigated. The absence of flow separation in this diffuser is ensured by specially selecting the channel profile and mounting a hydraulic resistance in the form of a permeable partition at the diffuser outlet. The experiments were carried out at the inlet flow Mach numbers up to 0.2. When the flow at the diffuser entry is steady, an axisymmetric flow is formed immediately downstream of the entry. The static pressure in the flow that has passed through the diffuser increases by 20% of the ram pressure at the entry. There is a possibility of optimizing the diffuser parameters.     

Turbulent flow in a circular separationless diffuser at Reynolds numbers smaller than 2000

The results of experimental and numerical investigation of flow in a circular conical diffuser with a small conicity angle ensuring separationless flow are presented. The measurements are carried out in an air flow with the Reynolds number Re₂ in the diffuser exit section ranging from 600 to 3000. A considerable effect of the channel expansion on the flow pattern is found to exist. It is shown that, as distinct from a tube, in which only laminar flow can be realized as steady for Re < 2000, in the exit section of a diffuser with the generator slope of 0.3° and a length equal to 70 entry diameters a developed turbulent flow is formed for Re₂ > 1000. For Re₂ > 1300 this flow is steady, that is, almost independent of the turbulence level at the entry, and is determined by the Reynolds number Re₂ in the exit section. For Re₂ ≈ 1000 the turbulent flow continuously goes over into a laminar flow. The flow parameters measured at the diffuser exit correspond to calculations in accordance with the threeequation turbulence model.     

Rotational inviscid flow with circulation zones in a channel of variable cross section

The development of the theory of rotational motion of inviscid fluids for the purposes of describing channel flow encounters certain difficulties in connection with the appearance of viscosity effects near the walls. In the potential-rotational model [1], in which the vorticity is nonzero only in a closed circulation zone surrounded by potential flow, it is assumed that the separation and attachment points are known in advance. For example, for flow around a cavity these points coincide with the extreme corner points of the contour. The problem of determining the vorticity in a closed zone for the potential-rotational model has been investigated in a number of studies [2, 3], etc. In the case of an incompressible fluid the vorticity in the circulation zone is constant for two-dimensional flow and proportional to the distance from the axis for axisymmetric flow. The value of the constant is found from the steady-state condition for the adjoining viscous layers. If the channel walls have a smooth profile without corner points, then for determining the boundaries of the circulation zones additional conditions must be used. This study employs another scheme, in which the vorticity is formed outside the region of flow and in a particular problem is specified in the form of a boundary condition. An analytic solution describing the rotational flow of an inviscid fluid in a channel with a slightly varying cross section is obtained. Three types of entrance flow nonuniformity are considered: 1) uniform shear flow, 2) wake-type flow, and 3) potential flow with a narrow wall boundary layer. Streamline patterns with circulation zones are constructed for flows in diffuser channels with the above-mentioned types of entrance nonuniformity. A model of flow separation in a channel with a turbulent boundary layer on the walls is discussed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 31–37, March–April, 1985.In conclusion the author wishes to thank E. Yu. Shal'man, A. N. Kraiko, and A. B. Vatazhin for useful discussions and advice.     

Nonisothermal flow of a viscous incompressible fluid in a two-dimensional diffuser

The velocity and temperature distributions in a viscous incompressible fluid flow in a two-dimensional diffuser are analyzed. Fully developed flow is considered, i.e., the influence of the entrant section is disregarded. It is assumed that the diffuser walls are maintained at a temperature depending on the polar radius. The dynamic viscosity is considered to be an exponential function of the temperature. The problem is reduced to the solution of a system of ordinary differential equations, which is solved by the method of successive approximations. The convergence of the iterative scheme is proved.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 40–48, July–August, 1973.The author is indebted to L.A. Galin and N. N. Gvozdkov for assistance with the study.     

Theoretical and experimental investigations of the flow of a viscous fluid near the line of intersection of a cylindrical surface and a flat surface

Flow along a corner was investigated at large Reynolds numbers in, for example, [1–3]. The present author [4] considered flow in the neighborhood of a corner formed by the intersection of a plane and a concave cylindrical surface, the main attention being devoted to the formation of the three-dimensional boundary layer on the plane near the corner. It was shown that the curvature of one of the intersecting surfaces changes the flow pattern qualitatively. In the present paper, we report an investigation of the formation of the flow on a concave cylindrical surface near such a corner and consider how the flow is rearranged in the neighborhood of a corner in, for example, a channel of rectangular cross section that has an initial straight section and then a bend with a discontinuity of the curvature of the line of intersection of the concave and flat sides of the channel. The results are given of some experimental investigations of flow near the line of intersection of a flat wall and a curved (concave and convex) wall at a bend in a rectangular channel.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 64–68, January–February, 1983.I thank G. M. Bam-Zelikovich for constant interest in the work and A. I. Ruban for a number of extremely helpful comments.     

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.     

Conditions of pulsed starting of supersonic diffusers of wind tunnels

In the framework of an ideal gas and quasi-one-dimensional approach, a study is made of the unsteady processes associated with the starting of supersonic unregulated diffusers of pulsed wind tunnels. Application of Chisnell's hypothesis to the reversed shock wave propagating through the inhomogeneous flow, allowance for the interaction of this wave with the perturbations reflected from the diffuser, and also the assumption of quasistationarity of the flow in the concluding stage make it possible to obtain finite relations for the optimal conditions of pulsed starting of the diffuser. The starting limit found in this manner agrees well with numerical calculations based on a more complete model when the relative length of the convergent part of the diffuser is short. The obtaining of the starting conditions for other cases requires the introduction into the proposed model of a correction for the extent of the region of interaction of the reversed shock wave with the perturbations reflected from the diffuser. This correction was found on the basis of some numerical calculations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 133–141, January–February, 1982.I thank A. N. Kraiko and V. T. Grin' for constant interest in the work and helpful advice.     

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.     

Developing mixed convection in vertical eccentric annuli

This paper deals with the problem of combined (forced–free) convection in vertical eccentric annuli with simultaneously developing hydrodynamic and thermal boundary layers. A bipolar model has been developed and a numerical algorithm for solving this model is outlined. Results, not available in the literature, are presented for the developing velocity profiles, axial variation of pressure, full development length, and heat transfer parameters under thermal boundary conditions of having one of the annulus boundaries at a constant temperature while the other boundary is insulated. Both aiding and opposing free convection have been considered and possibilities of flow reversal occurrence have also been checked. After a distance from the channel entrance and provided that the value of Gr/Re is sufficiently large, aiding free convection can develop to overcome the fluid friction and the eccentric annular channel eventually works as a diffuser. The value of Gr/Re for which a vertical eccentric annular channel can work as a diffuser decreases as the eccentricity increases. The axial distance from the entrance at which the channel starts to work as a diffuser decreases as Gr/Re increases.     

Effect of an inhomogeneous magnetic field on the structure of an ionized gas flow

Results of an experimental study of the flow of an ionized gas produced by a shock wave through an inhomogeneous magnetic field are presented. Braking of the gas flow produced by the end currents is determined at two fixed sections of the magnetogasdynamic channel from the value of the isolated shock wave formed in the vicinity of the hemispherical model over which the flow passes. Maximum recorded reduction in Mach number was 30%, and with a magnetogasdynamic interaction parameter greater than 1.5, a transition of supersonic flow to infrasonic at the exit of the magnetic zone was observed. Experimental results were compared with a solution of a model problem which assumed one-dimensional flow in the flow core. The gas used was argon, with a maximum magnetic field induction of 1.5 T.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 174–178, September–October, 1976.     

Analysis of flow in an annular duct with large injection at the walls

Viscous heat-conducting compressible fluid flow in an annular duct formed by two coaxial cylinders with large injection at the walls is investigated. An asymptotic solution exhibiting the influence of the axial symmetry of the duct is obtained in the vicinity of the y axis and is compared with the results of exact numerical calculations. Asymptotic solutions of the Navier-Stokes equations have been obtained earlier for flows in a plane channel with various rates of wall injection in the case of an incompressible gas [1, 2] and a compressible gas [3].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 135–139, May–June, 1976.     

Interaction and separation in internal flows with low skin friction

High-Reynolds-number plane steady flow of a viscous incompressible fluid past small distortions on straight-line walls intersecting at a point source is considered. The flow regimes are investigated in detail for a near-critical diffuser opening half-angle, when the skin friction is small. Solutions with local separation zones are obtained. The dependence of the skin friction on the Reynolds number is determined for transition to streams with a large region of reversed flow.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 98–111, September–October, 1996.     

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.     

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.     

Similarity solutions of the equations of a boundary layer in a nonuniform external flow

Similarity solutions of the equations of a laminar incompressible boundary layer, formed in a rotational external flow, are investigated. Such problems arise in the analysis of the flow in a boundary layer when there is an abrupt change in the boundary conditions (for example, in the case of a discrete inflation of the boundary layer, in hypersonic flow about blunt bodies, etc.). Various approaches to their solution have been proposed earlier in [1–4]. Solved below is the so-called inverse problem of boundary layer theory (see [3], p. 200), where the contour of the body that causes a given flow outside the boundary layer is unknown beforehand and is found during the course of solution of the problem in connection with the coupling of the longitudinal and transverse velocity components. The cases of a parabolic (u_e ~ y²) and a linear (u_e=a(x)+b(x)y) variation in the velocity of the external flow with distance along the transverse direction are considered in detail. The latter includes an investigation of the flow in the neighborhood of the critical point of a blunt body, taking account of the vorticity of the flow in the shock layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 78–83, March–April, 1971.