Properties of the nonequilibrium high-velocity “Tails” of the molecular distribution function in plane couette flow of a compressible gas

The results of an analytic and numerical investigation of the properties of the high-velocity “tails” of the distribution function are given for the solution of the BGK model of the kinetic Boltzmann equation for plane Couette flow of a compressible gas. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 183–190, July–August, 1998. The work was carried out with financial support from the Russian Foundation for Basic Research (project No. 96-01-00573; grant in support of leading science schools No. 96-15-9603).     

Supersonic dusty-gas flows with Knudsen effect in interphase momentum exchange

On the basis of the two-continuum model of dilute gas-solid suspensions, the dynamic behavior of inertial particles in supersonic dusty-gas flows past a blunt body is studied for moderate Reynolds numbers, when the Knudsen effect in the interphase momentum exchange is significant. The limits of the inertial particle deposition regime in the space of governing parameters are found numerically under the assumption of the slip and free-molecule flow regimes around particles. As a model problem, the flow structure is obtained for a supersonic dusty-gas point-source flow colliding with a hypersonic flow of pure gas. The calculations performed using the full Lagrangian approach for the near-symmetry-axis region and the free-molecular flow regime around the particles reveal a multi-layer structure of the dispersed-phase density with a sharp accumulation of the particles in some thin regions between the bow and termination shock waves. The project supported by the National Natural Science Foundation of China (90205024), and the Russian Foundation for Basic Research (RFBR grant No. 02-01-00770 and joint RFBR-NSFC grant No. 03-01-39004)     

Properties of hypersonic separated flows at moderate reynolds numbers

The hypersonic rarefied flow past a flat plate with a transverse barrier and past a plate with a bend in the generator (a compression angle) is studied at Reynolds numbers Re≤10⁴. Direct statistical modeling (Monte Carlo method) is used to investigate the characteristics of the separated flow formed on the plate as a function of the Reynolds number, the surface temperature, the barrier dimensions, and the internal degrees of freedom of the molecules. The results obtained are compared with those for analogous high-Re flows. The possibility of using the similarity criteria derived for the continuum flow regime is considered. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 134–144, January–February, 2000. The study was carried out with the support of the Russian Foundation for Basic Research (project No. 97-01-00577) and the Program of State Support for Leading Scientific Schools (grant No. 96-15-9606).     

Calculation of the effect of a constant electric field on the gas dynamics and nitrogen oxide emission in a laminar diffusion flame

A laminar methane diffusion flame in a constant electric field whose direction is opposite to that of the velocity of the gas flow from the burner nozzle is considered. The mathematical model used includes the complete system of Navier-Stokes equations for the velocity and passive admixture concentration fields, the charge transport equation, together with the Poisson equation for the self-consistent electric field, and the chemical kinetic equations for a thin combustion zone. The calculations show that the flame shortens and its thickness increases in the root zone when an electric field is imposed. This effect is accompanied by a reduction in the nitrogen oxide emission, while is consistent with the experimental data. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 48–53, January–February, 2000. The work was supported by the Russian Foundation for Basic Research (project No. 96-01-014-50).     

Numerical simulation of shock wave propagation in microchannels using continuum and kinetic approaches

Numerical simulations of shock wave propagation in microchannels and microtubes (viscous shock tube problem) have been performed using three different approaches: the Navier–Stokes equations with the velocity slip and temperature jump boundary conditions, the statistical Direct Simulation Monte Carlo method for the Boltzmann equation, and the model kinetic Bhatnagar–Gross–Krook equation with the Shakhov equilibrium distribution function. Effects of flow rarefaction and dissipation are investigated and the results obtained with different approaches are compared. A parametric study of the problem for different Knudsen numbers and initial shock strengths is carried out using the Navier–Stokes computations.      

Numerical analysis of vortex cell efficiency in laminar and turbulent flows past a circular cylinder with embedded rotating bodies

The effect of flow intensification in small-sized vortex cells on the flow pattern in the near wake downstream of a cylinder and the cylinder drag in laminar and turbulent flows is analyzed on the basis of a numerical simulation of the two-dimensional steady-state flow past a circular cylinder with rotating cylindrical bodies built into the cylinder contour. St. Petersburg, Saratov. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 88–96, July–August, 2000. The study was carried out with the support of the Russian Foundation for Basic Research (projects Nos. 99-01-01115 and 99-01-00772).     

Effect of a Dispersed Admixture on the Flow Pattern and Heat Transfer in a Supersonic Dusty-Gas Flow Around a Cylinder

A mathematical model of two-phase (gas-solid particle) flow which takes into account particle-particle collisions and the feedback effect of the admixture on the gas parameters is proposed. The dispersed phase is described by a kinetic equation of the Boltzmann type and the carrier gas by modified Navier-Stokes equations. Using this model, a supersonic uniform dusty-gas flow past a cylinder is calculated. The fields of the macroparameters of the admixture and the carrier medium are obtained. The dependence of the heat transfer at the stagnation point on the relative particle size and the free-stream admixture concentration is studied in detail. The ranges of these parameters on which particle collisions and the feedback effect of the admixture on the carrier-gas flow are important are found.     

Separationless flow past a body of revolution with simultaneous suction and ejection of fluid

The problem of the axisymmetric potential flow past a body of revolution with a channel along the axis in the presence of a recirculation flow zone near the body, first proposed by G. Yu. Stepanov, is solved. Kazan’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 14–21, January–February, 2000. The study was carried out with the support of the Russian Foundation for Basic Research (project No. 96-01-00123).     

Subsonic compressible cavitation flow past a plate at small cavitation numbers

A solution of the problem of symmetric inviscid compressible cavitation flow past a plate at small cavitation numbers is presented. Kazan’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 94–104, July–August, 1998. This research was carried out with financial support from the Russian Foundation for Basic Research (project No. 96-01-00111).     

Gas injection from the surface of a triangular plate in a hypersonic flow

The flow formed as a result of gas injection through the permeable surface of a triangular plate is investigated in the regime of strong viscous-inviscid interaction between the hypersonic flow and the laminar boundary layer. The features of the flow past strongly cooled surfaces with the formation of supercritical and subcritical flow regions in the boundary layer are studied. The injected gas distribution ensuring the existence of self-similar solutions in the supercritical flow regions is obtained. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 125–133, January–February, 2000. The study was carried out with the support of the Russian Foundation for Basic Research (project No. 96-01-01391).     

Numerical analysis of supersonic viscous gas flow past axisymmetric nonpointed bodies

Supersonic viscous homogeneous gas flow past axisymmetric smooth nonpointed bodies is analyzed numerically for widely varying Mach and Reynolds numbers and flow geometry. The initial equations of a viscous shock layer are solved by the stabilization method. The effect of the determining parameters on the flow character and the heat transfer distribution along the surface is analyzed. The accuracy and domain of applicability of several approximate approaches to the solution of the problem are estimated. Tomsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 107–117, January–February, 1999. This research was carried out with financial support from the Russian Foundation for Basic Research (project No. 98-01-00298).     

Modeling the dynamics of colliding particles in a turbulent shear flow

A kinetic model for the probability density function (PDF) of the particle velocity in a turbulent flow with account for particle collisions is presented. The model is tested by comparison with the results of a numerical experiment for a nonstationary homogeneous shear layer. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 105–112, July–August, 1998. The study received financial support from the International Science Foundation INTAS (project No. 94-4348) and the Russian Foundation for Basic Research (project No. 97-01-00398).     

Three-dimensional supersonic turbulent flows past conical bodies

The results of the numerical simulation of supersonic three-dimensional flow past sharp-nosed cones with circular and elliptic cross-sections in the turbulent shock-layer flow regime are presented. The calculations are performed in the local conical approximation using the system of Reynolds equations and the differential one-equation turbulence model. The numerical solutions are obtained by means of an implicit constant-direction finite-difference scheme. The emphasis is placed on the investigation of the transverse flow separation and the flow features associated with the turbulent flow regime. St.Petersburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 99–105, January–February, 2000. The study was carried out with the support of the Russian Foundation for Basic Research (project No. 99-01-00735).     

Using the perturbation method to solve the problem of separated incompressible flow past thin airfoils

A model for separated incompressible flow past thin airfoils in the neighborhood of the “shockless entrance” condition is constructed based on the averaging of the vortex shedding flow past the airfoil edges. By approximation of the vortex shedding by two vortex curves, determination of the average hydrodynamic parameters is reduced to a twofold solution of an integral singular equation equivalent to the equation describing steady-state nonseparated airfoil flow. In this case, the calculation time is two orders of magnitude smaller than the time required for the solution of the corresponding evolution problem. The results of a test calculation using the proposed method are in fair agreement with available results of calculations and experiments. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 49–63, May–June, 2006.     

Systems of nonlinear differential equations with bounded solutions

We establish sufficient conditions for the existence of solutions bounded on ℝ for the equation {fx168-01}, in a finite-dimensional Banach space {ie168-01}. __________ Translated from Neliniini Kolyvannya, Vol. 11, No. 2, pp. 160–167, April–June, 2008.     

Averaged model with capillary nonequilibrium effects for two-phase flow through a highly heterogeneous porous medium

Two-phase flow through a medium with two porosities in which the absolute permeabilities and the capillary pressure functions of the components differ by an order of magnitude is investigated. A classification and diagram of the elementary flows are proposed at the single cell level. An averaged model is developed for a single class of systems in which source-type capillary-dispersion flow predominates in the blocks. This model contains a nonlinear kinetic relation between the average values of the capillary pressure functions. An expansion of the effective phase permeability tensor allowing it to be calculated efficiently is proposed. The capillary relaxation time is explicitly determined. Examples of calculations of the averaged phase permeability tensor and the capillary relaxation time are given. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 93–103, May–June, 1998. The work was carried out with the support from the Russian Foundation for Basic Research (project No. 95-01-01179a).     

Laminar boundary layer in a flow past an aerofoil with a circular cavity

The paper describes a numerical study of a method of preventing the separation of a laminar boundary layer from the forward section of a symmetric aerofoil, the flow past which does not separate at zero angle of incidence. In order to increase the maximum angle of incidence at which the flow has still not separated, a circular cavity (vortex cell) located almost completely inside the aerofoil is introduced on the segment vulnerable to separation. The asymptotics of the corresponding flow at high Reynolds number are described using the Prandtl-Batchelor model. Krasnodar. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 52–57, March–April, 1998. The work was financially supported by the International Science Foundation (grants M4K000 and M4K300) and by the Russian Foundation for Fundamental Research (project No. 96-01-01290).     

Effect of random longitudinal vibrations on the Poiseuille flow of a complex liquid

In this work, the rectilinear Poiseuille flow of a complex liquid flowing in a vibrating pipe is analyzed. The pipe wall performs oscillations of small amplitude that can be adequately represented by a weakly stochastic process, for which a quasi-static perturbation solution scheme is suggested. The flow is analyzed using the Bautista–Manero–Puig constitutive equation, consisting on the upper-convected Maxwell equation coupled to a kinetic equation to account for the breakdown and reformation of the fluid structure. A drastic enhancement of the volumetric flow is predicted in the region where the fluid experiences pronounced shear-thinning. Finally, flow enhancement is predicted using experimental data reported elsewhere for wormlike micellar solutions of cetyl trimethyl ammonium tosilate.     

Particle deposition from a turbulent flow

The diffusion equations and boundary condition for particle deposition from a turbulent flow are obtained on the basis of the kinetic equation for the probability density of the particle distribution. This approach makes it possible to calculate the deposition fairly simply without introducing additional empirical information relating to the particles (empirical constants are needed only for calculating the characteristics of the turbulent carrier flow). Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 96–104, September–October, 1988.     

Investigation of the variability of the structure of a stratified wake behind a horizontal cylinder using optical and acoustic methods

The shadow flow pattern behind a horizontal cylinder uniformly towed in a stratified fluid with constant buoyancy frequency (in the imbedded vortex and turbulent wake regime) is recorded synchronously with acoustic echo sounding (basic frequency equal to 1 MHz) in a laboratory tank. Using computer processing, the illumination profiles in the schlieren pattern are constructed on scales comparable with the sounding acoustic ray width. Although the optical and acoustic profiles are not similar, nevertheless they enable the basic structural elements of the wake, including its high-gradient core to be identified, and their time variability traced. The features of the integral acoustic scattering characteristic, in particular, the volume scattering strength, allow this characteristic to be used, together with optical images of the flow pattern, to distinguish the flow regime identification criteria. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 5–17, May–June, 1998. The work was partly financed by the Russian Foundation for Basic Research (projects Nos. 96-05-64004 and 97-01-01013) and by INTAS Grant No. 93-1584.