Effect of the accommodation coefficient on transfer processes in a supersonic rarefied gas flow around a transversely aligned cylinder

A supersonic flow around a cylinder is studied by the direct statistical Monte Carlo method in a wide range of rarefaction: from regimes close to continuum to free-molecular flow. The effect of the accommodation coefficient on the flow near the cylinder and on heat transfer between the gas and the cylinder is examined. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 64–72, May–June, 2008.     

Stability of nonisothermal couette flow

A study is made of the loss of stability of the stationary flow of a viscous fluid between two heated rotating cylinders. The linearized stability problem is studied in the Boussinesq approximation. The perturbations are assumed to be periodic in the time, and also in the axial and azimuthal directions. The neutral curves are calculated numerically. The ranges of variation of the parameters of the problem are found, and in them the most dangerous perturbations (in the class of spatially periodic perturbations) are those without rotational symmetry.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 167–170, January–February, 1980.I thank V. I. Yudovich for constant interest in the work.     

Asymptotic investigation of two-phase couette flow

We consider plane and cylindrical Couette flow for a two-phase medium. The motion of the medium is described by the equations obtained in [1]. Collisions between the particles are disregarded, and their motion, in addition to the inertial forces, is determined by the pressure gradient of the carrying phase and the forces of viscous interaction between the carrying phase and the particles. We obtain simple asymptotic solutions of the indicated problems for small and large values of the dimensionless determining parameters. In a number of cases the solution has the nature of a boundary layer on solid walls.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 67–73, July–August, 1978.     

Numerical analysis of the stability of nonisothermal couette flow

The stability of convective motion of a liquid between two rotating heated cylinders is investigated in the absence of external forces. The mathematical model for describing the convection is obtained from the general equations [1, 2] on the assumption that the density of the liquid, the thermal conductivity, the specific heat and the viscosity coefficients depend only on temperature, and that the work done by the pressure forces and the viscous dissipation are negligibly small. The thermal expansion coefficient of the liquid is not assumed to be small, which distinguishes the models in question from the classical Oberbeck-Boussinesq model [1, 3, 4]. Rostov-on-Don. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 70–76, September–October, 1988.     

Characteristics of a viscoplastic material in the couette flow

A model governing a steady flow of a viscoplastic material between coaxial cylinders is proposed. Nonlinear velocity sensitivity typical of superplastic materials is taken into account. An algorithm of calculating the characteristics of the material is developed. The algorithm is based on the experimental data on moments and angular velocities of the rotating coaxial cylinders. The stability of the algorithm to errors in the initial data is estimated.     

Investigation of the accommodation coefficient using the thermomagnetic effect

On the basis of a theoretical consideration of the problem of heat transfer in a free molecular gas in parallel constant and variable fields, a new method is proposed for investigating the accommodation coefficients of molecules interacting with the surface of a solid, and the setting-up of an appropriate experiment is discussed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 198–200, March–April, 1976.     

Stability of the inviscid plane couette flow in bubbly fluids

The aim of this article is to study the stability of shear flows in bubbly fluids. A mathematical model of bubbly fluids is presented. The stability of shear flows is studied by two methods: by using a spectral approach and by solving the initial-value problem. It is proved that the linear velocity profile is stable in the long wave approximation. Communicated by R. Grimshaw     

Experimental comparison of methods of determining the thermal accommodation coefficient

An experimental comparison of two widely employed methods of determining accommodation coefficients is presented; these are the method of free molecular flow and the method of the temperature jump. The values of the coefficients which have to be introduced into the computing relationships of the temperature-jump method in order to obtain the true values of the accommodation coefficient are determined, this method being theoretically the less rigorous. Correction factors are determined for both monatomic and polyatomic gases.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 173–176, July–August, 1972.     

Unsteady-state development of plane couette flow for viscoelastic fluids

Unsteady-state development of plane Couette flow for viscoelastic fluids is analyzed using a constitutive equation that can be obtained from molecular theory, in which the molecules are regarded as finitely extensible dumbbells. Typical features of the flow situation are as follows: (i) For a fluid with moderate elasticity, not only stress overshoot but also velocity overshoot are predicted. (ii) For suitable combinations of elasticity and gap width, and for some time intervals stress propagation and reflection phenomena are predicted. (iii) After a sufficient time has elapsed, the stress state behaves similarly to that corresponding to the start-up of a steady simple shear flow.     

Optimal disturbances of a dusty-gas plane-channel flow with a nonuniform distribution of particles

The classical stability theory for multiphase flows, based on an analysis of one (most unstable) mode, is generalized. A method for studying an algebraic (non-modal) instability of a disperse medium, which consists in examining the energy of linear combinations of three-dimensional modes with given wave vectors, is proposed. An algebraic instability of a dusty-gas flow in a plane channel with a nonuniform particle distribution in the form of two layers arranged symmetrically with respect to the flow axis is investigated. For all possible values of governing parameters, the optimal disturbances of the disperse flow have zero wavenumber in the flow direction, which indicates their banded structure (“streaks”). The presence of dispersed particles in the flow increases the algebraic instability, since the energy of optimal disturbances in the disperse medium exceeds that for the pure-fluid flow. It is found that for a homogeneous particle distribution the increase in the energy of optimal perturbations is proportional to the square of the sum of unity and the particle mass concentration and is almost independent of particle inertia. For a non-uniform distribution of the dispersed phase, the largest increase in the initial energy of disturbances is achieved in the case when the dust layers are located in the middle between the center line of the flow and the walls.     

Heat transfer in rarefied couette flow on the basis of discrete ordinate method

The method of discrete ordinates, in conjunction with the modified “half-range” quadrature, is applied to the study of heat transfer in rarefied gas flows. Analytic expressions for the reduced distribution function, the macroscopic temperature profile and the heat flux are obtained in the general n-th approximation. The results for temperature profile and heat flux are in sufficiently good accord both with the results of the previous investigators and with the experimental data.     

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).     

Spherical couette flow: Transitions and onset of chaos

The results are given of an experimental investigation of the transition to chaos and of the properties of the chaotic regimes in a wide range of Reynolds numbers: 460 Re 3200 7Re₀. Estimates of the probability dimension of the attractors and Lyapunov exponents and the exponential damping of the highest-frequency part of the spectrum indicate a deterministic nature of the chaos in the considered range of Re. It is noted that in one and the same range of Re values the route to chaos is not unique and can depend on the prehistory of the flow development; the simultaneous existence of chaotic and regular regimes for fixed values of the parameters is also noted.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 10–18, January–February, 1991.     

Influence of the atomic weight of the target on the magnitude of the energy accommodation coefficient of ions of a partially ionized gas flow

One of the most essential parameters in the investigation of singularities in molecule interaction with the surface of a solid is the energy accommodation coefficient. Data on the positive ion accommodation coefficients in the energy range 1–100 eV are scarce [1], hence the value of _i is often taken close to one, although this condition is not satisfied in practice for the majority of working gases. In this paper we discuss the resultant measurements of the value of _i in a high-speed flow of rarified plasma.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 83–87, May–June, 1979.     

Oscillatory rotationally symmetric loss of stability of nonisothermal couette flow

A study is made of the stability of nonisothermal Couette flow — steady flow of a viscous heat conducting fluid between two rotating concentric cylinders heated to different temperatures. The methods of perturbation theory are used to establish conditions sufficient for bifurcation of a neutral curve of oscillatory instability from the neutral curve of monotonic instability. Computer calculations show that for certain values of the parameters of the problem these conditions are realized and there is an oscillatory loss of stability of the nonisothermal Couette flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 76–80, January–February, 1984.I thank V. I. Yudovich for constant interest in the work.     

On the spiral form of instability of couette flow of a viscous fluid

Summary The instability of Couette flow caused by vortices with spiral symmetry is studied; the equations of motion in a suitable spiral metric turn out to be analogous with those describing vortices with axial symmetry. The approximate solution is obtained by discretization of the differential equations. Special numerical techniques reduce drastically the dimensions of the matrices involved in the calculations. The Taylor number for transition is computed; comparisons with known results are established. The results are shown in a number of graphs.

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Sommario Si studia la forma di instabilità del moto alla Couette per vortici con simmetria a spirale. In una opportuna metrica a spirale le equazioni risultano analoghe a quelle che descrivono i vortici a simmetria assiale. La soluzione approssimata delle equazioni è ottenuta per discretizzazione mediante differenze finite, usando opportuni accorgimenti per ridurre notevolmente le dimensioni delle matrici su cui si eseguono i calcoli. Viene fatto il calcolo del numero critico di Taylor per le equazioni linearizzate in funzione dei parametri significativi e si stabiliscono confronti con risultati noti. Alcuni grafici mostrano i risultati ottenuti.

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