Detached flow over a step with the formation of a turbulent wake

A method of calculating the plane turbulent layer behind a step interacting with a free potential flow of incompressible fluid is developed. The method includes consideration of the initial boundary layer and injection (or suction) in the isobaric bottom region. Friction on the wall behind the step is neglected, which corresponds to symmetric quasisteady flow behind the straight edge of a plate. The inviscid flow is represented by the Keldysh-Sedov integral equations; the flow in the wake with a one-parameter velocity profile is represented by three first-order differential equations—the equations of momentum for the wake and motion along its axis and the equation of interaction (through the displacement thickness) of the viscous flow with the external potential flow. The turbulent friction in the wake is given, accurate to the single empirical constant, by the Prandtl equation. The different flow regions — on the plate behind the step, the isobaric bottom region, and the wake region — are joined with the aid of the quasi-one-dimensional momentum equation for viscous flow. The momentum equation for the flow as a whole serves as the closure condition. The obtained integrodifferential system of equations is approximated by a system of nonlinear finite-difference equations, whose solution is obtained on a computer by minimization of the sum of the squares of the discrepancies. The results of the calculations agree satisfactorily with experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 17–25, May–June, 1977.We are grateful to V. I. Kuptsov for consultation and help in programming and to Z. A. Donskova who assisted in the calculations and preparation of the paper.     

Non-isothermal polymer melt flow in sudden expansions

This paper presents numerical results for laminar, incompressible and non-isothermal polymer melt flow in sudden expansions. The mathematical model includes the mass, momentum and energy conservation laws within the framework of a generalized Newtonian formulation. Two constitutive relations are adopted to describe the non-Newtonian behavior of the flow, namely Cross and Modified Arrhenius Power-Law models. The governing equations are discretized using the finite difference method based on central, second-order accurate formulas for both convective and diffusive terms. The pressure–velocity coupling is treated by solving a Poisson equation for pressure. The results are presented for two commercial polymers and demonstrate that important flow parameters, such as pressure drop and viscosity distribution, are strongly affected by heat transfer features.     

Gas-dynamic calculation of pulsating flow in pipelines

A numerical solution is examined for a system of equations of one-dimensional isothermal flow of a perfect gas in a horizontal pipe with a periodically varying function of the flow rate at the boundary. The numerical solution is compared with the solution of the linearized problem. The results can be used to calculate the pulsating motion of gas in the pipeline systems of piston compressors [1].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 85–88, July–August, 1972.     

Motion of a spherical solid particle in a nonuniform flow of a viscous incompressible liquid

The effect of a particle on the basic flow is studied, and the equations of motion of the particle are formulated. The problem is solved in the Stokes approximation with an accuracy up to the cube of the ratio of the radius of the sphere to the distance from the center of the sphere to peculiarities in the basic flow. An analogous problem concerning the motion of a sphere in a nonuniform flow of an ideal liquid has been discussed in [1]. We note that the solution is known in the case of flow around two spheres by a uniform flow of a viscous incompressible liquid [2], and we also note the papers [3, 4] on the motion of a small particle in a cylindrical tube.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 71–74, July–August, 1976.     

Solution of a problem of flow in a porous medium with limiting gradient

For the law of flow in a porous medium with limiting gradient studied previously in [1], an exact solution is found for the problem formulated in [2] of the plane steady motion of an incompressible fluid in a channel with a rectangular step. Particular cases of the solution obtained are given; these represent the solutions of the problem of flow past a broken wall and of motion from a point source in a strip.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 76–78, January–February, 1985.     

Particle deposition on a channel wall in a turbulent disperse flow with gradient

Kinetic ideas about the motion of a set of particles (droplets) in a turbulent gas flow with gradient are used to derive a Fokker-Planck equation for the case of sufficiently large particles (more than few microns). This equation describes the process in which they are deposited on the wall of a channel. Satisfactory agreement has been obtained between the numerical solution to this equation for the deposition rate and the experimental data published in the literature. Under the assumption that the parameters of the carrier gaseous flow vary fairly slowly, a generalized equation is derived for particle diffusion in turbulent flow. This takes into account the intensity gradient of transverse pulsations in the velocity of the carrier gaseous flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 57–63, July–August, 1985.     

Wave flow of a liquid film in a horizontal separator

The calculation of the motion of separated moisture in a linear horizontal separator is made on the basis of the analysis of the development of the waves in a flow of a thin layer of liquid along a vertical surface without allowance for the transverse flow of mass [1].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 174–176, March–April, 1985.     

Gromeka-beltrami flow in a semiinfinite cylindrical pipe

The two-parameter homogeneous helical motion of an ideal incompressible fluid in a circular cylindrical pipe is investigated. It is shown that there may be various flow conditions defined by the value of the relative intensity of rotation of the flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 117–120, March–April 1971.     

Stability of the motion of a rigid body in an unsteady flow

The problem of rigid-body motion in an unsteady gas flow is considered using a flow model [1] in which the motion of the body is described by a system of integrodifferential equations. The case in which among the characteristic exponents of the fundamental system of solutions of the linearized equations there are not only negative but also one zero exponent is analyzed. The instability conditions established with respect to the second-order terms on the right sides of the equations are noted. The problem may be regarded as a generalization of the problem of the lateral instability of an airplane in the critical case solved by Chetaev [2], pp. 407–408.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 18–22, May–June, 1989.     

Investigation of gas-particle turbulent pipe flow with allowance for collisions with the wall and particle rotation

A model of gas-particle turbulent pipe flow which takes into account phase velocity slip, particle interaction with the wall and rotation of the particles is proposed. Allowance for the Magnus force makes it possible to describe the intense transverse skipping motion of the particles and to obtain good agreement between the calculation results and the experimental data over a broad range of flow conditions. The model is based on the use of the transport equations for the averaged flow parameters and the correlation moments describing the turbulent transfer of the momentum and angular momentum of the dispersed phase.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 56–64, January–February, 1990.     

Calculation by the Krylov-Bogolyubov method of the velocity profile and fluxes in the nonisothermal flow of a rarefied gas in a cylindrical capillary

The Krylov-Bogolyubov numerical method is used to solve integral transfer equations obtained from the kinetic equation with the BHC (Bhatnagar—Cross—Krook) model of the collision operator. The velocity profiles and the thermal-creep flows and Poiseuille flow are calculated in different modes of flow under conditions of incomplete accommodation of the tangential momentum of molecules at the wall.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 143–150, November–December, 1978.     

Draft of a nozzle with the circulating outflow of a vortical flow of gas

The presence of circulation in an outflowing gas leads to a change in the working parameters of a nozzle. The question of the mass flow rate and the draft of a nozzle without a diffusor (a point) for twisted flows has been studied theoretically and experimentally [1–6]. The use of nozzles with a supersonic part introduces a considerable degree of complication into the method for the analytical calculation of the draft characteristics and the program for their experimental investigation. In [2, 7], a theory of a nozzle is formulated for a model of a potential circulating flow of gas; in [5, 8], an electronic computer was used to solve the complete system of the equations of gasdynamics for the motion of a rotating flow along a nozzle; in [7, 9], an investigation was made of a variational problem of the shaping of a diffusor for a circulation flow. The calculation of the draft, carried out in the above-mentioned communications (with the exception of [2], in which a study was made of a partial model of an eddyless rotational motion), is bound up with labor-consuming computer calculations. In the present article, in a development of [3, 6], a quasi-one-dimensional theory of a supersonic nozzle for a vortical flow of gas is formulated and verified experimentally.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 145–149, September–October, 1975.     

Resistance matrix for a particle in a nonuniform gas flow

The slow (relative to the medium) motion of a heat-conducting particle in a gas flow described by the Navier-Stokes equations is examined. The particle is small as compared with the macroscopic scale of the flow and the Local perturbation it creates is therefore described by a Linear Boltzmann equation. A system of thermodynamic fluxes corresponding to the thermodynamic forces is established, and the transport coefficients forming the resistance matrix are shown to be symmetric.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 101–108, January–February, 1988.     

Calculation of the flow of a two-phase mixture in a Laval nozzle,allowing for the turbulent diffusion of the particles

The flow of a mixture of gas and condensed particles in an axisymmetric Laval nozzle is considered. The motion of the particles is calculated in a specified field of gas flow, with due allowance for their turbulent diffusion. The results of calculations indicating the necessity of allowing for this phenomenon when considering the motion of particles toward the wall of a profiled nozzle are presented.Translated from Izvestiya Akademii Nauk SSSR, No. 2, pp. 161–165, March–April, 1973.     

Influence of particles on the drag of bodies in a disperse flow

A study is made of the motion of a disperse medium with a low volume but high mass concentration of very inert particles. It is shown that in the framework of linearization of the equations the motion of such a medium will be irrotational if the oncoming flow is undisturbed at infinity. Simple expressions are proposed for estimating the influence of the particles on the drag of a body of arbitrary shape moving in the medium and also for the determination of the flow velocity by means of a Pitot-Prandtl tube.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 164–167, May–June, 1982.     

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.     

Some peculiarities of two-phase flow in nozzles

Calculations are conducted for unidimensional two-phase flow in nozzles for a wide range of particle concentrations and dimensions. It is established that there exists a maximum in loss of specific momentum due to a lag in particle velocity and temperature relative to the gas. The results obtained are compared with calculations using linearized theory as well as with experimental data. The agreement between calculation and experiment is noted. Equilibrium flow of a two-phase mixture with solidification of liquid particles is considered. The presence of an anomalous flow region is established, where in the model of an ideal unidimensional equilibrium flow in a nozzle with discharge into a vacuum the presence of two successively located minimum sections is necessary.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 50–57, May–June, 1973.     

Specific momentum of a flow in the minimal cross section of a laval nozzle and in the outlet cross section of a contracting nozzle

The article discusses the question of the effect of nonuniformity of the parameters, brought about by the two-dimensional character of the flow on the value of the specific momentum of the flow under supercritical conditions. It is shown, that, in the approximation of an ideal (nonviscous and non-heat-conducting) gas, the corresponding value with a continuous flow always exceeds the value calculated in accordance with the one-dimensional theory for the same nozzle and the same stagnation parameters of the gas.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 186–188, January–February, 1976.     

Linear stability in the flow of a liquid film concurrent with a gas flow

The two-phase flow of liquid films are often encountered in practice, but the number of theoretical papers devoted to this problem is limited. The problem of the linear stability of a viscous liquid film subjected to a gas flow has been formulated in [1] and, in somewhat different form, in [2]. The linear stability of plane-parallel motion in films has been studied analytically in [1–8] for some limiting cases. The range of validity of the analytic approaches remains an open question. Therefore, an exact numerical analysis of flow stability over a fairly broad range is required. In the present paper a separate solution of the problem for the gas and the liquid is shown to be possible. The Orr-Sommerfeld equation has been integrated numerically, and the results are compared to the results of analytic calculations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 143–146, January–February, 1976.The author is grateful to É. É. Markovich for directing the work and to V. Ya. Shkadov for his interest in the work and many useful comments.     

Supersonic flow past a body with transverse jets

The results of an experimental study of the flow past a body with transverse jets are presented. The gas jets flowed out simultaneously from several nozzles arranged on the body's lateral surface. Various flow regimes were considered to such parameters as the relative jet momentum, the angle of incidence, etc. The experimental results were generalized on the basis of an approximate similarity law.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 75–80, July–August, 1995.