Longitudinal dispersion associated with the motion of an adsorbed mixture in a column filled with porous granules

The effect of the radial nonuniformity of the linear flow velocity on the radial nonuniformity of the adsorbate concentration distribution over the cross section of a column and on the longitudinal dispersion is estimated for the diffusion model, and the legitimacy (for relatively small adsorber radii) of using a one-dimensional diffusion model for describing the interphase mass transfer in cylindrical adsorbers is thereby determined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 93–101, July–August, 1987.     

Investigation of the hypersonic viscous shock layer around blunt bodies in a nonuniform flow

Unseparated viscous gas flow past a body is numerically investigated within the framework of the theory of a thin viscous shock layer [13–15]. The equations of the hypersonic viscous shock layer with generalized Rankine-Hugoniot conditions at the shock wave are solved by a finite-difference method [16] over a broad interval of Reynolds numbers and values of the temperature factor and nonuniformity parameters. Calculation results characterizing the effect of free-stream nonuniformity on the velocity and temperature profiles across the shock layer, the friction and heat transfer coefficients and the shock wave standoff distance are presented. The unseparated flow conditions are investigated and the critical values of the nonuniformity parameter a_k [10] at which reverse-circulatory zones develop on the front of the body are obtained as a function of the Reynolds number. The calculations are compared with the asymptotic solutions [10, 12].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 154–159, May–June, 1987.     

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.     

Supersonic ideal-gas flow of in the throat region of a nozzle

The problem of profiling a supersonic nozzle with uniform outlet flow is considered when the contour is constructed from a point on a given convergent section of the nozzle. It is shown that there are contours such that the flow in the throat is supersonic in choked regimes (as distinct from common notions of mixed or uniform sonic flow). The influence of flow nonuniformity in the throat region on the thrust of a supersonic nozzle is analyzed.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 132–139, May–June, 1996.     

Flow in a permeable tube surrounded by porous material. Application to the capillaries of the circulatory system

Unsteady problems are solved numerically for the system of one-dimensional quasilinear equations describing the flow in the capillaries of the circulatory system and the mass transfer between a capillary and the surrounding tissue. The effect of oscillations of the entrance pressure and the passage of a protein concentration jump on the characteristics of the system is investigated. The influence of the degree and nonuniformity of capillary wall permeability and lymphatic drainage factors is also examined. The sphere of applicability of the equations and the possibility of an analytical investigation of capillary flow are discussed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 14–20, July–August, 1986.     

Unsteady three-dimensional viscous shock layer in nonuniform gas flow in the neighborhood of a stagnation point

The combined influence of unsteady effects and free-stream nonuniformity on the variation of the flow structure near the stagnation line and the mechanical and thermal surface loads is investigated within the framework of the thin viscous shock layer model with reference to the example of the motion of blunt bodies at constant velocity through a plane temperature inhomogeneity. The dependence of the friction and heat transfer coefficients on the Reynolds number, the shape of the body and the parameters of the temperature inhomogeneity is analyzed. A number of properties of the flow are established on the basis of numerical solutions obtained over a broad range of variation of the governing parameters. By comparing the solutions obtained in the exact formulation with the calculations made in the quasisteady approximation the region of applicability of the latter is determined. In a number of cases of the motion of a body at supersonic speed in nonuniform media it is necessary to take into account the effect of the nonstationarity of the problem on the flow parameters. In particular, as the results of experiments [1] show, at Strouhal numbers of the order of unity the unsteady effects are important in the problem of the motion of a body through a temperature inhomogeneity. In a number of studies the nonstationary effect associated with supersonic motion in nonuniform media has already been investigated theoretically. In [2] the Euler equations were used, while in [3–5] the equations of a viscous shock layer were used; moreover, whereas in [3–4] the solution was limited to the neighborhood of the stagnation line, in [5] it was obtained for the entire forward surface of a sphere. The effect of free-stream nonuniformity on the structure of the viscous shock layer in steady flow past axisymmetric bodies was studied in [6, 7] and for certain particular cases of three-dimensional flow in [8–11].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 175–180, May–June, 1990.     

Supersonic flow over a cone with heat release in the neighborhood of the apex

Supersonic flow over a cone mounted in the wake of a spherical source of heat release is investigated. The free-stream nonuniformity generated by the source leads to effective drag reduction.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 110–114, March–April, 1993.     

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.     

Circulation flow at the front surface of a sphere in a supersonic wake

Several theoretical and experimental studies of supersonic flow past a blunt body located in the wake behind another body have been made [1–7]. It has been shown that a reverse-circulation flow can occur in the shock layer at the front surface. The possibility of such a flow forming depends on the nonuniformity of the freestream flow and the Reynolds number. This paper presents new results of the theoretical study of the structure of the shock wave at the front surface of such a sphere, obtained on the basis of numerical solution of Navier-Stokes equations. It is shown that for a fixed nonuniformity of the freestream flow, an increase in the Reynolds number and cooling of the surface of the body lead to the formation of a secondary vortex in the region where the contour of the body intersects the axis of symmetry. A study is made of the variations of the drag and heat transfer parameters over the front surface of a cooled and thermally insulated sphere. The possibility of numerical simulation of the flow on the basis of the Euler equations is discussed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 143–148, May–June, 1985.     

Generalization of the blunt-body problem in nonuniform supersonic flowfields

The properties of the steady-state gas flow in the shock layer associated with a blunt body immersed in a supersonic stream with an arbitrary shear-like nonuniformity are studied.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 164–170, March–April, 1996.     

Numerical investigation of the process of displacement of oil by steam

A calculation model of the process of displacement of oil by steam, based on the equations of three-phase nonisothermal flow with allowance for phase transitions in the water-steam system, is proposed. This model is used for the numerical investigation of the recovery of oil from wateroil zones by means of steam injection. The extraction of oil from wateroil zones is one of the difficult problems of the theory of exploitation of petroleum deposits. The presence of two zones with sharply different fluid resistances leads to considerable nonuniformity in production rates. It is shown that injecting steam significantly reduces this nonuniformity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 78–84, July–August, 1987.     

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.     

On nonisothermal electroconvection

The flow from the tip of a needle electrode is caused by the Coulomb force acting on the space charge [1–3]. This charge is formed because of the dependence of the conductivity on the temperature, nonuniformity of which is due to Joule heating [1] and the electric field intensity [2] or processes near the electrode [3–5]. The present paper considers the stability of a dielectric liquid between spherical electrodes in order to elucidate the possibility of a thermoelectrohydrodynainic flow due to Joule heating. In the presence of external heating, the possibility of such a flow has been demonstrated both experimentally and theoretically [6–8].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 133–137, March–April, 1980.     

The flow of a dielectric liquid

The nature of the forces acting on a dielectric liquid in an electric field in the presence of a temperature gradient is investigated. It is shown that the electrical forces produced by nonuniformity in the electrical conductivity of the medium can give rise to a hydrodynamic flow.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 136–137, November–December, 1973.     

Numerical modeling of the process of oil displacement from reservoirs with zonal nonuniformity

In extracting oil from nonuniform reservoirs a considerable fraction remains unrecovered from the zones of lesser permeability. The mechanism of displacement of oil from reservoirs with zonal nonuniformity is investigated within the framework of the two-dimensional Muskat-Meres model of combined oil, water and gas flow [1]. A wholly conservative difference scheme implicit in the saturations and pressure is used for the calculations. Various reservoir exploitation regimes are considered with the object of seeking means of improving the characteristics of the process.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 177–180, September–October, 1987.     

Formation and decay of a quasisteady detonation complex in a nonuniformly heated combustible gas

This work is a continuation of the study of explosive reaction regimes associated with an initial nonuniformity of the reaction induction period. Relations determining the time and place of formation and decay of a quasisteady detonation complex are obtained for a linear nonuniformity. These are compared with the results of numerical calculations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 161–168, March–April, 1991.     

Numerical simulation of the nonuniform breakup of capillary jets

The problem of the evolution of the surface of a jet up to the stage at which it breaks up into droplets is solved numerically for two initial wave disturbances. The wave number of one of these coincides with the wave number of the disturbance that grows most strongly according to the linear theory, while the wave number of the other is varied. The effect of the wave numbers and the amplitude ratio of the initial disturbances on the breakup time and the appearance of nonuniformity is investigated.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 12–17, March–April, 1993.     

Analysis of Displacement Variances in Stochastic Nonuniform Flows by Means of a First Order Analytical Model and Comparison with Monte-Carlo Simulations

Flow, particle displacement and particle arrival time statistics in 2D nonuniform flows, without microdispersion, are studied both theoretically, in the framework of stochastic modelling, and numerically by means of Monte-Carlo simulations.Turning, radial convergent and dipolar flow fields are considered. These three types of flow are numerically investigated in heterogeneous media with different levels of heterogeneity. Monte-Carlo simulations show (1) that the scale separation hypothesis, frequently used in fluid mechanics, is justified for one-point flow statistics; and (2) how displacement variances, and consequently the dispersivities defined as their spatial derivatives, depend on the type and the amplitude of flow nonuniformity: in none of the investigated cases does the assumption of scale separation hold for displacement, except in the turning flow when the spatial scale associated to the nonuniformity is much greater than the correlation scale of transmissivity.The theoretical approach of displacement and arrival time statistics relies on the analysis of particle trajectory. Displacement variances expressions are derived by the perturbation method for each type of flow and for different approximation orders. The proposed expressions of displacement variances are, on the whole, in good agreement with the numerical results. On the other hand, the uniform flow approximation – commonly used for the interpretation of tracer experiments – chosen such as to satisfy the mean arrival time to the pumping well, gives the best prediction of the breakthrough curves.     

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.     

Dynamics of a spherical particle in a laminar boundary layer

The problem of the motion of an individual spherical particle in a laminar boundary layer is considered for small Reynolds numbers determined from the relative velocity and the transverse velocity gradient of the flow undisturbed by the particle. The dependence of the transverse force acting on the particle, which results from the nonuniformity of the free stream, on the distance of the particle from the surface of a flat plate is calculated. It is shown that the direction of the transverse force changes with the distance of the particle from the plate: near the surface the force is positive, i.e., directed away from the plate, and at greater distances negative.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 91–96, November–December, 1990.The author wishes to thank M. N. Kogan and N. K. Makashev for useful discussions.