Motion of a suspension in the laminar boundary layer on a flat plate

The boundary layer motion of a weak suspension is investigated with allowance for the effect on the particles not only of the Stokes force but also of the additional transverse force resulting from the transverse nonuniformity of the flow over the individual particle. As distinct from studies [1–3], in which the limiting values of the transverse force (Saffman force) were used [4], the velocity and density of the dispersed phase have been determined with allowance for the dependence of the Saffman force on the ratio of the Reynolds numbers calculated from the velocity of the flow over the individual particle and the transverse velocity gradient of the undisturbed flow, respectively [5, 6].Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 66–73, January–February, 1992.In conclusion the authors wishes to thank M. N. Kogan, N. K. Makashev, and A. Yu. Boris for useful discussions of the results.     

Dispersed phase motion in laminar boundary layer flow over a wedge

The motion of a dispersed phase in the laminar boundary layer on a wedge is considered with allowance for the effect of not only the Stokes force, which coincides in direction with the flow velocity, but also the transverse force (Saffman force) resulting from the transverse nonuniforrnity of the flow over the individual particle [1–3].Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.6, pp. 34–42, November–December, 1993.In conclusion, the authors wishes to thank S. V. Manuilovich for assisting with the numerical calculations.     

Particle motion in a laminar boundary layer on the transverse velocity relaxation length

The properties of the equation of quasi-equiiibrium particle motion in the boundary layer on a flat plate are investigated. In particular, it is shown that in general it has a nonunique solution and that, depending on its initial velocity, the particle may approach the surface of the plate or move in the opposite direction.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.1, pp. 86–93, January–February, 1993.     

Lift force exerted on a spherical particle in a laminar boundary layer

A spherical particle moving in an unbounded viscous shear flow is acted upon by a lift force [1, 2] which results from taking the inertial terms into account in the equations of motion. When the particle moves at the bottom of a laminar boundary layer the magnitude of the force differs from that obtained in [1, 2], The problem of determining the lift force exerted on the particle as a function of its distance from the wall has been solved by matched asymptotic expansions. The magnitude of the force is expressed in terms of a multiple integral which can be evaluated numerically.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 66–71, September–October, 1989.In conclusion, the author wishes to thank M. N. Kogan, N. K. Makashev, and A. Yu. Boris for useful discussions.     

Motion of a dusty gas at the entrance to a flat channel and a circular pipe

It is shown that at large Reynolds numbers, calculated from the entrance velocity and the half-width of the channel, four characteristic flow regions are formed in the entrance section. The equations describing the motion of the mixture in each of these regions are constructed by the method of matched expansions. An expression relating the particle concentration distribution at points remote from the entrance section to the particle concentration distribution in the boundary layer on a flat plate at points remote from the beginning of the plate is obtained. The dependence of the dispersed-phase concentration profile formed on the governing parameters is studied on the basis of a numerical solution. It is shown that as the contribution of the Saffman force to the interphase momentum transfer increases, the rise in particle concentration in the direction of the wall is replaced by a fall. A qualitative correspondence between the calculated particle concentration profiles and certain known experimental data is noted.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 80–87, November–December, 1988.     

Energy spectra of velocity pulsations in a turbulent boundary layer on a penetrable plate

Results of measurements of the pulsation characteristics of a turbulent boundary layer on a flat penetrable plate, in a range of variation of the parameters of in-blow from 0 to 20, are presented. It is shown that for supercritical in-blows close to the surface there exists a zone in which the energy spectra of velocity pulsations do not vary as the distance from the surface increases, and they differ from the spectra in the core of the boundary layer.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 115–119, May–June, 1973.     

Diffraction of acoustic waves on the leading edge of a flat plate in a supersonic flow

A scheme is proposed for calculating the intensity of the acoustic wave field generated by diffraction of a beam of acoustic waves on a sharp leading edge of a flat plate in a supersonic flow. This wave field is shown to be a functional of the mass-flow amplitude distribution in the acoustic field at the level of the plate surface upstream of the latter. This distribution can be found on the basis of measurements. The discontinuity of the normal-to-plate component of the velocity perturbation on the plate edge plays an important role in determining mass-flow fluctuations along the plate. At large distances from the leading edge of the plate, where the diffraction wave on the boundary-layer edge degenerates into longitudinal acoustic waves, the amplitude of mass-flow fluctuations decreases with increasing distance from the leading edge and depends on wave orientation.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 2, pp. 64–70, March–April, 2005.     

Propagation of two-dimensional plastic waves in a thick plate

A study is made of the propagation and interaction of two-dimensional waves of high amplitude in a thick plate. A monotonically decreasing pressure is applied to the surface of the plate. Deformations are assumed to be large; the problem is formulated and solved in Lagrangian variables. An approximate method for constructing the fronts of the shock waves is proposed. The pressure and particle velocity at an arbitrary point and at an arbitrary instant of time are determined by the method of characteristics. A numerical example is given.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 100–106, January–Febraury, 1971.     

Parameters of nonuniform shocks in aluminum

A method of recording the pressure profile and mass velocity behind the front of a two-dimensional shock excited in a flat plate by a load moving over its surface is described. Results obtained for the case of detonation of a layer of explosive on the surface of an aluminum plate are presented.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 147–152, July–August, 1971.In conclusion, the authors are grateful to E. I. Silkin, A. N. Tkachenko, and N. I. Shishkin for interest manifested in the research.     

Vortex motion of a disperse mixture

A study is made of the motion of fine spherical particles in a given steady vortex flow of an incompressible fluid. The results are given of an investigation into the Lyapunov stability of a particle trajectory coincident with the vortex axis, and of trajectories from which the distance to the vortex axis is determined by the condition of equality of the radial components of the force of the phase interaction and of the centrifugal force which acts on the particle.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 167–169, November–December, 1984.     

Measuring the momentum flux of molecules reflected from a surface of given roughness in free molecule flow

The magnitude of the force transferred to a solid surface by reflected molecules in free molecule flow depends firstly on the mechanism of the interaction of the molecules and the element of the surface, or, more precisely, is determined by the velocity distribution function of the reflected molecules, and secondly on the collisions of the molecules with the irregularities of the surface, the number of which depends on the angles of inclination of the sides of these irregularities [1]. Thus, if the microrelief of a plate placed in a molecular flow is known, then certain information about the character of the interaction of the molecules and the surface element can be extracted from measurements of the force acting on it. The aim of this paper is the experimental study of the transfer of momentum by molecules reflected from a plate, depending on the degree of roughness of the surface. Most experimental studies of the transfer of momentum and energy between a flow of rarefied gas and a surface have been made with the aim of revealing the qualitative features of the influence of roughness on the interaction [2–5]. Quantitative estimates of the angles of inclination of the irregularities on test models have been given in very few papers [6–8]. An integral measure is proposed in [6] for estimating the roughness. This is the measure used in the present study.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 158–162, July–August, 1985.     

Supersonic gas flow over a semi-infinite plate with small harmonic spanwise disturbances

The method of matched asymptotic expansions is used to investigate the problem of supersonic perfect-gas flow over a semi-infinite surface with longitudinal ribbing formed by imposing small transverse harmonic perturbations on a flat plate. The ratio of the maximum amplitude of the surface perturbations to the thickness of the boundary layer is of the order of Re^–1/4. The problem is solved with allowance for four terms of the expansion.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.1, pp. 146–156, January–February, 1993.     

Thermocapillary Vortices Induced by a Light Beam near a Bubble Surface in a Hele-Shaw Cell

This paper studies thermocapillary vortices induced by local heating of a bubble surface in a Hele-Shaw cell by a light beam. It is found that the vortex rotation frequency and its depth depend on the distance from the light-beam projection onto the layer to the bubble boundary. The surface velocity of the thermocapillary flow is calculated using the balance of the near-surface and return flows of the thermocapillary vortex and the equality of capillary and dynamic pressures. It is shown that a decrease in the surface velocity and the vortex rotation frequency with increase in the distance from the light beam to the bubble surface is due to a decrease in the temperature gradient between the illuminated and cold poles of the bubble.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 5, pp. 93–99, September–October, 2005.     

Blowing into a supersonic stream through a permeable surface

Distributed blowing of gas into a supersonic stream from flat surfaces using an inviscid flow model was studied in [1–9]. A characteristic feature of flows of this type is the influence of the conditions specified on the trailing edge of the body on the complete upstream flow field [3–5]. This occurs because the pressure gradient that arises on the flat surface is induced by a blowing layer whose thickness in turn depends on the pressure distribution on the surface. The assumption of a thin blowing layer makes it possible to ignore the transverse pressure gradient in the layer and describe the flow of the blown gas by the approximate thin-layer equations [1–5]. In addition, at moderate Mach numbers of the exterior stream the flow in the blowing layer can be assumed to be incompressible [3]. In [7, 8] a solution was found to the problem of strong blowing of gas into a supersonic stream from the surface of a flat plate when the blowing velocity is constant along the length of the plate. In the present paper, a different blowing law is considered, in accordance with which the flow rate of the blown gas depends on the difference between the pressures on the surface over which the flow occurs and in the reservoir from which the gas is supplied. As in [8, 9], the solution is obtained analytically in the form of universal formulas applicable for any pressure specified on the trailing edge of the plate.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 108–114, September–October, 1980.I thank V. A. Levin for suggesting the problem and assistance in the work.     

Diffraction of a sound wave by a nonmoving plate

The problem of determining the velocity field excited by a sound wave impinging on a plate at rest is analyzed as an initial- and boundary-value problem with a movable boundary for the two-dimensional wave equation. The latter problem is solved by the formulation and inversion of integral equations of the Volterra type. The solution is obtained in closed form for any angle of inclination of the incident wave relative to the plate surface and is represented by recursion relations allowing for the influence of any number of diffracted waves generated in succession at the plate boundary.Moscow. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 123–130, March–April, 1972.     

Blood flow in a muscle capillary cell. Two-dimensional effects

The two-dimensional motion of the blood in a capillary cell is considered, i.e., the calculations take into account not only the main capillaries running along the muscle fibers but also the transverse interconnections [1, 3, 4, 6] for the purpose of estimating their effect on the nonuniformity of the velocity distribution within the cell and on its total hydrodynamic resistance.N. S. Utushkin and V. A. Egorov also participated in this research.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 94–100, September–October, 1989.     

Influence of a floating elastic plate on the surfaceeffects of internal waves generated by motion of a source in a non-homogeneous liquid

Perturbations of the surface of an exponentially stratified liquid of finite depth, free or covered by an elastic plate, are studied on the assumption that the perturbations are caused by internal waves generated by the steady motion of a constant -intensity source. The dependence of the spatial distribution of perturbations on the plate properties, velocity and the submersion depth of the source is considered.Sevastopol. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 118–125, March–April, 1995.     

Effect of the Conductance and Thickness of a Conducting Plate on the Signal from a Material–Velocity Inductive Transducer

The perturbation problem of the magnetic field of a constant–current turn located above a conducting plate set into motion by a plane shock wave with a rectangular profile is considered. It is shown that not only the velocity of the plate but also its dynamic conductivity can be determined on the basis of the electromotive force of induction recorded by means of the turn. For the case where the conductance of the plate is known for both the conducting half–space and for a plate whose thickness is comparable with the skin–layer thickness, approximatecalculated dependences for the velocity of the plate are obtained. A comparison with experimental data and the clarification of the calculated dependences allows one to conclude that the approaches proposed can be used for determining the conductance of metals in shock–wave processes.     

Flow around the afterbody of a plate in a longitudinal gas stream with transverse injection from the lateral surface

The flow around the afterbody of a plate of finite thickness in a supersonic gas stream is investigated on the basis of a numerical solution of the time-dependent Navier-Stokes equations for a compressible viscous heat-conducting gas. The change in the flow pattern with the onset of transverse slot injection from the body surface in the vicinity of the base section is studied. For constant supersonic injection, both steady and unsteady flow regimes could be obtained depending on the values of certain relevant parameters.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 157–163, March–April, 1996.     

Effect of moving wall on the three-dimensional separation of an incompressible fluid in front of an obstacle

The problem of the laminar boundary layer formed on the surface of a semiinfinite plate with a perpendicular semi-infinite circular cylinder in a uniform steady incompressible flow normal to the leading edge is considered. Near its sharp edge the plate has a stationary part and, located at a finite distance further downstream, a part of the surface moving downstream at a constant velocity. The first-order boundary layer equations are solved numerically by an implicit finite-difference method. The effect of the moving wall on the variation of the dimensions of the separation zone ahead of the obstacle over a broad range of the governing parameters and flow characteristics is investigated. The flow in the laminar boundary layer on the surface of a plate ahead of such an obstacle was calculated in [1, 2] without motion of the wall. Data on the structure of the separated flow are given in [3].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 49–53, November–December, 1990.