Rarefied gas motion in a short planar channel over the entire knudsen number range

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 48–53, September–October, 1989.     

Evaporation and condensation growth of a droplet in a vapor-gas medium for arbitrary knudsen numbers

In this paper, a study is made of the weak isothermal and nonisothermal evaporation of a particle, taking account of thermodiffusion, for arbitrary Kn numbers, evaporation-condensation coefficient , vapor concentration c, and arbitrary potential of intermolecular interaction.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 131–137, July–August, 1985.     

A method for solving boundary-value problems of transfer at arbitrary knudsen numbers

A new method is proposed, called the method of the smoothed distribution function, which makes possible a considerable simplification in the procedure for calculating moments of the collision integral, and enables us to obtain a solution to the system of Maxvell-Boltzmann moment equations. The approximating distribution function used in the collision integral in the Boltzmann form ensures a limiting process towards continuous expressions for the flux of molecular characteristics. For the example of the solution to the classical problem of heat transfer between two parallel plates with arbitrary Knudsen numbers, a comparison was made of the theoretical results with the results of other analyses, and also with experiment.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Shidkosti i Gaza, No. 3, pp. 182–185, May–June, 1986.     

Transport phenomena in a knudsen molecular gas in a magnetic field

We consider the behavior of a strongly rarefied (Knudsen) polyatomic gas between two surfaces that have different temperatures in a magnetic field. We show that in the magnetic field H there can arise a flux of gas and a heat flux along the surfaces (odd functions in H), and also normal and tangential forces on the walls.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 124–130, January–February, 1979.     

Strong recondensation in a one-component and a two-component rarefied gas for an arbitrary value of Knudsen number

As is known, surface phenomena such as evaporation, absorption, and reflection of molecules from the surface of a body depend strongly on its temperature [1–5]. This leads to the establishment of a flow of a substance between two surfaces maintained at different temperatures (recondensation). The phenomenon of recondensation was studied in kinetic theory comparatively long ago. However, up to the present, only the case of small mass flows in a onecomponent gas has been investigated completely [3,4]. Meanwhile it is clear that by the creation of appropriate conditions we can obtain considerable flows of the recondensing substance, so that the mass-transfer rate will be of the order of the molecular thermal velocity. Such a numerical solution of the problem with strong mass flows along the normal to the surface for small Knudsen numbers for a model Boltzmann kinetic equation was obtained in [7]. In this study we numerically solve the problem of strong recondensation between two infinite parallel plates over a wide range of Knudsen numbers for a one-component and a two-component gas, on the basis of the model Boltzmann kinetic equation [6] for a one-component gas and the model Boltzmann kinetic equation for a binary mixture in the form assumed by Hamel [8], for a ratio of the plate temperatures equal to ten. We also investigate the effect of the relative plate motion on the recondensation flow.Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 130–138, September–October, 1972.     

Laminar boundary layer in an equilibrium dissociated gas for arbitrary external velocity distribution

The development of machine computing technology permits calculating the boundary layer by direct numerical integration of the corresponding system of partial differential equations [1, 2]. In order to derive general conclusions concerning the boundary layer with a pressure gradient we must perform the integration for each concrete form of velocity specification at the outer edge of the boundary layer. The method of calculating the boundary layer used in the present study [3], based on the solution of a universal (independent of the specification of the velocity at the outer edge of the boundary layer) system of equations, permits the clarification of several general relationships.     

Two-dimensional free boundary layer in a stratified medium

Expressions for the fluctuation characteristics of shear flow in a stratified medium are obtained on the basis of the equations for the single-point second-order moments of the velocity and temperature fields and then closure of those equations by means of semiempirical hypotheses. The Prandtl equation, with the influence or Archimedean forces taken into account, is used to analyze plane jet flows and wake flows of a body, Numerical computations are carried out for a plane wake, and the results are compared with the experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 71–79, July–August, 1977.     

The analytical solution for Helmholtz boundary problem in non-horizontally stratified domains

There are N domains D_j(j=0,1,...,N-1) of different physical parameters in the whole space and their interfaces S_j,i+1 are non-horizontally smooth curved surfaces. The following boundary problem is called Hclinholiz boundary problem:V²H⁽¹⁾+K_jH⁽¹⁾=0 (j=0,1,…,N-1)(H⁽⁰⁾-H⁽¹⁾)=δ(S) (δ(S):generalized function)(H¹-Hⁱ⁺¹)=0 (j=0,1,…,N-2)The analytical solution of the above problem is given in this paper.     

Characteristics of an unstably localized disturbance in a compressed boundary layer

Experiments have demonstrated [1] that the transition of streamline-type flow into turbulent flow in a boundary layer occurs as a result of the formation and development of turbulent spots apparently arising from small natural disturbances. A study of the nonlinear evolution and interaction of localized disturbances requires knowledge of their characteristics to a linear approximation [2]. In the current work, results are presented of calculations of such characteristics for the first two unstable modes in a supersonic boundary layer on a two-dimensional plate (M = 4.5, T_w = 4.44).Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 50–53, January–February, 1976.     

Traveling disturbance appearing in boundary layer transition in a Yawed cylinder

Boundary layers that develop over a body in fluid flow are in most cases three-dimensional owing to the spin, yaw, or surface curvature of the body. Therefore, the study of three-dimensional (3D) boundary-layer transition is essential to work in practical aerodynamics. The present investigation is concerned with the problem of 3D boundary layers over a yawed body. A yawed cylinder model that represents the leading edge portion of a swept wing and the mechanism of crossflow instability are investigated in detail using hot-wire velocimetry and a flow visualization technique. As a result, traveling disturbances having frequencies f₁ and f₂, which differ by about one order of magnitude, are detected in the transition region. The phase velocities and directions of travel of those disturbances are measured. Results for the low-frequency disturbance f₁ show qualitative coincidence with results numerically predicted for a crossflow unsteady disturbance. Nameley, F₁ travels nearly spanwise to the yawed cylinder and very close to the cylinder wall. The results for the high-frequency disturbance f₂ good agreement with the existing experimental results. The ₂ disturbance is found to be the high-frequency inflectional secondary instability that appears in 3D boundary layer transition in general. A two-stage transition process, where stationary crossflow vortices appear as the primary instability and a traveling inflectional disturbance is generated as a secondary instability, was observed. Secondary instability seems to play a major role in turbulent transition.     

Stability of a compressible boundary layer relative to a localized disturbance

The problem of stability of an incompressible boundary layer relative to a localized disturbance is considered in a linear approximation. It is shown that the stability analysis reduces to the study of a discrete spectrum of eigenvalues of the corresponding boundary value problem. By means of numerical integration, analysis of the character of the emerging instability is carried out for an unstable mode for the Mach number M = 4.5.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, pp. 107–114, May–June, 1973.The author is grateful to V. V. Struminskii for his interest in this work; he is grateful to L. B. Aizin for useful discussion of the subjects broached, and to A. A. Maslov for the great help in carrying out the numerical calculations.     

Conditions of stability and instability for a pair of arbitrarily stratified compressible fluids in an arbitrary non-uniform gravity field

The work continues and develops authors’ previous investigation of stability in the small for a two-layer system of inhomogeneous compressible fluids in the uniform gravity field. Here we present a solution of a similar problem in the case of arbitrary non-uniform potential gravity field. The equilibrium stratification of both density and elastic properties of the fluids is supposed arbitrary, as well as the shape of open on top reservoir filled by the fluids. The problem of stability of equilibrium is analyzed as the corresponding problem for the non-linearly elastic bodies, basing on the static energy criterion with regard for the boundary conditions at all parts of the boundary. The crucial element of the analysis is conversion of the quadratic functional of second variation of total potential energy of the system into a “canonical” form that enables to determine its sign. Making use of this canonical form, we obtain almost coinciding with each other necessary and sufficient conditions for stability (those being valid also for an arbitrary number of layers).