Stability of steady plane-parallel convective motion of a chemically active medium

A study is made of a vertical plane layer of reacting fluid whose boundaries are maintained at constant equal temperatures. As a result of heating due to a chemical reaction of zeroth order taking place in the fluid a steady plane-parallel convective flow develops in the layer, and if the internal heat release is sufficiently intense this can become unstable. The linear stability of this motion has hitherto been considered only in the hydro-dynamic formulation [1], in which one can ignore the thermal perturbations and their influence on the development of the hydrodynamic perturbations (the region of small Prandtl numbers). In the present paper, the stability boundary is determined for arbitrary values of the Prandtl number and the Frank-Kamenetskii parameter FK characterizing the steady plane-parallel regime. An important difference between this flow and the types of convective motion hitherto studied [2] is that the basic planeparallel flow of the reacting medium is possible only in a definite range of the parameter FK: At values of the parameter exceeding a critical value, there is a thermal explosion — abrupt strong heating of the fluid. This is due to the essentially nonlinear dependence of the heat release of a chemical reaction on the temperature.     

Aerodynamics of an asymmetrically deformed body in nonstationary supersonic motion

A method for making numerical calculations of the stationary and nonstationary aerodynamic characteristics of bodies of variable shape is considered. The results of calculations of the aerodynamic coefficents are given [1]. The results of numerical calculations are compared with the results of Newton's theory.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 162–167, March–April, 1980.     

Motion of a rarefied gas between infinite plane-parallel emitting and absorbing surfaces

The problem of the motion of a rarefied gas between infinite plane-parallel emitting and absorbing surfaces is solved numerically on the basis of the Boltzmann kinetic equation.Moscow. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 176–178, March–April, 1972.     

Plane nonstationary gas flow with a strong discontinuity

The problem of plane, nonstationary gas motion under the effect of a piston in the shape of a dihedral angle moving at constant velocity in the gas is considered. In contrast to one-dimensional motion under the effect of a flat piston, a curvilinear shockwave originates here, and the flow becomes nonisentropic and vortical. This problem is examined herein in a linear formulation when the angle of the piston breakpoint is assumed small. The linear problem reduces to an inhomogeneous Riemann—Hilbert problem whose solution is found explicitly. The problem under consideration adjoins a circle of problems associated with shockwave diffraction and reflection studied by Lighthill [1], Smyrl [2], Ter-Minassiants [3], etc.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 45–50, May–June, 1971.The author is grateful to L. V. Ovsyannikov for interest in the research and useful comments.     

Linear and nonlinear stability of combined plane-parallel flow of a film of liquid and gas

The problem of the linear stability of a layer of liquid entrained by a gas has been investigated for some special cases in [1–7]. In [8], the linear problem was solved numerically and the solution compared with some analytic solutions for special cases of the flow. In the present paper, the results of linear analysis are presented more comprehensively; the problem of finite-amplitude stability of the film is posed and solved numerically; the results of the linear and nonlinear analysis are compared with data of an experiment performed by the authors and by other experimentalists.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 36–42, January–February, 1979.We are grateful to V. Ya. Shkadov for supervising the work, to all the participants of G. I. Petrov's seminar for helpful discussion, and also to E. L. Kokon for assistance in evaluating the experimental data.     

Vortex perturbations of the nonstationary motion of a liquid with a free boundary

The first studies on the stability of nonstationary motions of a liquid with a free boundary were published relatively recently [1–4]. Investigations were conducted concerning the stability of flow in a spherical cavity [1, 2], a spherical shell [3], a strip, and an annulus of an ideal liquid. In these studies both the fundamental motion and the perturbed motion were assumed to be potential flow. Changing to Lagrangian coordinates considerably simplified the solution of the problem. Ovsyannikov [5], using Lagrangian coordinates, obtained equations for small potential perturbations of an arbitrary potential flow. The resulting equations were used for solving typical examples which showed the degree of difficulty involved in the investigation of the stability of nonstationary motions [5–8]. In all of these studies the stability was characterized by the deviation of the free boundary from its unperturbed state, i.e., by the normal component of the perturbation vector. In the present study we obtain general equations for small perturbations of the nonstationary flow of a liquid with a free boundary in Lagrangian coordinates. We find a simple expression for the normal component of the perturbation vector. In the case of potential mass forces the resulting system reduces to a single equation for some scalar function with an evolutionary condition on the free boundary. We prove an existence and uniqueness theorem for the solution, and, in particular, we answer the question of whether the linear problem concerning small potential perturbations which was formulated in [5] is correct. We investigate two examples for stability: a) the stretching of a strip and b) the compression of a circular cylinder with the condition that the initial perturbation is not of potential type.     

Acceleration of a conducting gas in a strong nonstationary electromagnetic field

The problem of nonstationary acceleration of a conducting gas in a channel is solved, together with the problem of a discharge in an electric-circuit. As distinct from other papers, in which the typical solution assumed a thin cluster subject to acceleration, we examine the case in which the gas flow fills the entire channel. The motion of the gas in the channel is examined in one-dimensional formulation, under the assumption that the particle transit time in the channel is small compared to the discharge time and that the electromagnetic force is large compared to the pressure gradient.For impulsive acceleration of the conducting gas, use is made of a discharge with a certain capacitance. Since the (time-variable) resistance of the channel and, consequently, the behavior of the discharge depend upon the channel flow of the conducting gas, the correct solution of the problem of gas acceleration in the induced electromagnetic field can be obtained only by analyzing simultaneously the magnetogasdynamic channel flow and the discharge process in the entire electric circuit. On the other hand, the acceleration of the gas itself is a function of the instantaneous potential difference at the electrodes. Hitherto, such simultaneous solutions were obtained by many investigators under the assumption, proposed in [1], that a channel gas flow may be treated as the motion of a unique narrow cluster, whose length is negligible as compared to the channel length. Experiments and theoretical estimates show, however, that in many cases the conducting gas fills the entire channel length during the acceleration process, so that the assumption of a narrow cluster is not even approximately fulfilled [4, 5].     

Plane nonstationary self-similar gas flow with energy liberation in shock waves

Two plane nonstationary, self-similar problems occurring with energy supply in shock waves are examined in a linear formulation; the pressure distributions in the perturbed flow domains are obtained. Results and methods used extensively in the theory of diffraction of shock waves [1–3] are employed in this paper.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 164–167, July–August, 1978.In conclusion, the author is grateful to M. N. Kogan for supervising the research, and also to A. I. Golubinskii and V. P. Kolgan for useful comments and valuable discussion.     

Instability of a moving plane-parallel layer

A study is made of infinitely small perturbations of a moving plane-parallel layer. It is shown that, in distinction from an isolated tangential discontinuity, a layer is unstable with any given values of the projection of the velocity of the layer on the wave vector of the perturbation. The instability of an isolated tangential discontinuity has been repeatedly investigated in detail (see, for example, [1–4]). The instability of a moving layer has remained almost unanalyzed. It is of importance to make such an analysis, the more so since the results for a layer differ qualitatively from the results for an isolated tangential discontinuity.Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 11–14, May–June, 1972.     

Influence of a longitudinally compressed elastic plate on the nonstationary wave motion of a homogeneous liquid

In a linear formulation, a study is made of the influence of a longitudinally compressed elastic isotropic plate on the nonstationary wave motion of a stream of homogeneous liquid of finite depth on which the plate floats. The waves are generated by periodic (in time) normal stresses applied to a restricted region of the plate surface and beginning at a certain initial time.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 68–75, September–October, 1980.     

Effect of broken ice on the wave resistance of an amphibian air-cushion vehicle in nonstationary motion

The uniformly accelerated motion of an amphibian air-cushion vehicle on the surface of a basin covered by finely small ice floes is considered. Institute of Machine Science and Metallurgy, Far-Eastern Division, Russian Academy of Sciences, Komsomol'sk-on-Amur 681005. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 6, pp. 48–53, November–December, 1999.