Showing papers in "Journal of Applied Mechanics and Technical Physics in 1971"

Weak turbulence of capillary waves

Abstract: In recent years the theory of weak turbulence, i.e. the stochastic theory of nonlinear waves [I, 9], has been intensively developed. In the theory of weak turbulence nonlinearity of waves is assumed to be small; this enables us, using the hypothesis of the random nature of the phases of individual waves, to obtain the kinetic equation for the mean squares of the wave aplitudes.

Oscillations of a body filled with a viscous fluid

Abstract: The oscillations of a physical pendulum containing a spherical cavity filled with an incompressible viscous liquid were discussed in [1]. In this paper we consider the mote general problem of the motion of an axially symmetric solid with a spherical cavity filled with an incompressible viscous fluid and moving about a fixed point. It is assumed that the center of the cavity and the fixed point lie on the axis of symmetry of the body.

Development of perturbations in plane shock waves

Abstract: Investigation of the stability of plane shock waves as regards nonuniform perturbations was first performed by D'yakov [1]. He obtained criteria for stability, and showed that perturbations grow exponentially with time in the case of instability. Iordanskii [2] has shown that in the case of stability, the perturbations are attenuated according to a power law. However, the stability criteria of [2] do not agree with the results of [1], Kontorovich [3] has explained the cause of the apparent discrepancies, and asserts the correctness of the criteria of [2]. A power law for the attenuation of perturbations has also been obtained in [4,5] under a somewhat different formulation of the boundary conditions.

Inhomogeneous elastic medium with nonlocal interaction

Abstract: In [1] the author examined a macroscopically homogeneous elastic medium of simple structure with spatial dispersion. In that case the assumption of the existence of an elementary unit of length and long-range forces conditioned the nonlocalizability of the theory, and the macroscopic homogeneity was manifested in the invariance of the integral operators under shear (difference kernels).

Approximate statistical theory of a fluidized bed

Abstract: Under the conditions of developed fluidization there are intensive fluctuations both in the fluidizing medium and in the dispersed solid phase. These motions have a decisive effect on the rheologlcal properties of the fluidized bed, and on the chemical reactions and transport processes taking place in it [1], Thus, for example, in the experiments of Wicke and Fetting [2], who investigated the heat transfer between a fluidized bed and the walls of a heated container, the effective heat transfer coefficient was found to be higher by an order of magnitude than the corresponding result for a fluidized bed held down by a wire grid so that the random motion of the solid phase was reduced. It is clear that the initial stage of any study of the structure of the fluidized bed as a whole, and of the subsequent development of any model, must involve an investigation of local structural properties, including the above fluctuations. The time variation of the individual particle velocities is due to two different causes. First, there is the interaction between the particles both through direct collisions and through the medium of the liquid phase, and, secondly, there is the interaction with the viscous fluid. These two factors are not independent, so that the set of fluidized particles has certain features characteristic for both a dense gas, with a potential intramolecular interaction, and a set of particles executing Brownian motion in a continuous medium. Any detailed statistical theory of a system of fluidized particles must be based on a representation of the random particle motions in the medium by a stochastic process with some definite properties (see, for example, [3–4]). Ideally, this theory should lead to the formulation of a transport equation which, in view of the above properties of the system, should have some of the features of both the usual Boltzman transport equation and the Fokker-Planck equation. The solution of this final equation is, of course, more difficult than the solution of the Boltzman or Fokker-Planck equations. Moreover, there is also the problem of applying this equation to different special cases. An alternative approach is to develop an approximate, but still sufficiently effective, theory of the local properties of the fluidized bed, which would combine relative simplicity in application with sufficient rigor and generality. This kind of theory is put forward in the present paper. The conclusions to which it leads are in good qualitative agreement with experiment.

Theory of electrostatic focusing of intense beams of charged particles

Abstract: The mathematical formulation of the problem of determining the electrodes for the formation of intense beams of charged particles reduces to the solution of the Cauchy problem for the Laplace equation. One can proceed either by separating the variables [1] or on the basis of the theory of analytic continuation [2–5], This approach can be used for plane or axisymmetric flows. An algorithm for the construction of the analytic solution, which can also be used in the threedimensional case, is given below. It is assumed that the beam boundary coincides with the coordinate surface x1=0 of an orthogonal system xi (i=1,2,3). The solution is put in the form of a series in x1 with coefficients dependent on x2 and x3, determined from recurrence relations. The case of emission limited by space charge and temperature generally gives rise to difficulties due to the divergence of the series which makes it impossible to calculate the zero equipotential by the indicated method.

Allowance for bulk relaxation by the method of internal friction

Abstract: There is presently no reliable experimental evidence for the relaxation spectra of solids due to purely bulk deformations, because direct measurement of basic relaxation characteristics (frequency and modulus defect) involves major difficulties. For this reason, even the existence of bulk relaxation is not entirely clear, in spite of many statements [1-3] that there is a second, or bulk, viscosity. The internal-friction method is valuable in the study of relaxation processes, and for shear deformation (torsion Pendulum) it allows one to compare each relaxation process with a theological model and a physical mechanism [4]. It is difficult to isolate bulk relaxation in pure form, so it is of interest to take into account its effects on shear relaxation with reference to the longitudinal oscillations of a specimen. The relaxation spectrum can sometimes he described in the theory of elasticity by means of Rabomov's fractional exponentials [5]. Then the stress tensor Oik of a homogeneous isotropic solid (neglecting thermal relaxation) is t

Nonstationary burning of propellants with variable surface temperature

Abstract: The author examines nonstationary processes (combustion at varying pressure, quenching, and ignition) for a model propellant whose burning rate u and surface temperature t1 depend on pressure p and initial temperature T0. All the processes in the surface reaction zone and the gas phase are assumed inertialess. It is shown that a theory of nonstationary combustion for such a model can be constructed by analogy with the Zel'dovich theory [1, 2], in which the surface temperature of the powder is assumed fixed. The variation of burning rate with time has been investigated for small sudden pressure changes. It is shown how a sufficiently large and steep pressure drop may cause quenching of the propellant. The process of propellant ignition is subjected to a qualitative analysis.

Stochastic instability of nonlinear oscillations

Abstract: Consider a dynamic system whose behavior is described by (0.1) $$x'' + \omega ^2 _0 (1 + \alpha x^2 )x + F(t)x = 0$$ in which the external force F(t) is very nearly periodic, with frequency Ω ≪ ω0. It is known [1,2] that such a system retains its periodic motion if the nonlinearlty parameter α is sufficiently small, and such motion will be called stable. Let us examine the conditions under which system (0.1) is a dynamic system with mixing in the sense of [3,4], i.e., what are the conditions under which system (0.1) may be described approximately by means of statistical laws (the stochastic criterion, SC). The solution to (0.1) may be represented as quasi-periodic motion with a substantially varying phase. The criterion is deduced from the condition that the time correlations of the. phase decrease exponentially. Roughly speaking, we must be able to state the moment at which the time sequence of the phases can be considered approximately as a sequence of random numbers. It is clear that in that case we speak of stochastic motion, not in the whole of phase space, but in a region where there is ergodic motion with respect to phase. There are major difficulties in defining a criterion for stochastic behavior; this criterion has recently [5–8] * been derived for some very simple physical systems. The titles of these papers show the importance of the topic. An equation of the type (0.1) has also been used in examining the stability of magnetic field lines in systems of closed type. Here we give an asymptotic method of defining the SC for motion of the type (0.1), which allows extension to somewhat more complicated systems. The method cannot be said to be mathematically rigorous; certain points need a more rigorous basis, although they are entirely reasonable from the physical viewpoint.

The dynamic equations of motion for a two-component system

Abstract: The motion of solid particles in a fluid flow is represented as a random process with independent increments. The resulting kinetic equation for the particle distribution has the form previously proposed [1]. The solution to this equation provides a system of equations for the hydrodynamics of the assembly of solid particles. These equations differ from ones previously proposed [2, 3] in having additional terms related to relative motion of the components, whose presence is due to anisotropy in the distribution of the normal stresses in the pseudogas.

The study of a supersonic jet of rarefied argon plasma

Abstract: We have carried out an experimental study of a supersonic jet of argon plasma flowing in a rarefied medium. We have measured the distribution of total thrust along the axis of the jet at various temperatures in the arc chamber of the plasmatron. Using spectroscopic methods, we obtained the axial and radial distributions of the electron concentration and temperature and of the concentration of excited atoms. With the help of a probe we measured the electron temperature and concentration at large distances from the nozzle tip.

Film cooling by injection into a turbulent boundary layer

Abstract: Most papers on film cooling concern injection of a homogeneous gas. Stollery et al. [1] examined the case of tangential injection of gas into a boundary layer, the specific heat63-01 differing little from that of the main flow,63-02.

Motion of a polydisperse material in a. vertical gas flow

Abstract: The method of solution previously presented [1] for a two-phase flow is based on replacing the actual interaction between groups of particles by some continuously acting force. Here a more rigorous method of solution is presented via an analysis of the laws of collision between numerous particle groups. Only steady-state flows under isothermal conditions are considered, to simplify the problem.

Experimental study of the effect of relative viscosities on the rate of counter-current capillary impregnation of porous media

Abstract: Laboratory experiments are described on mechanics of simultaneous movement in opposite directions of water and petroleum through a porous medium. This countercurrent impregnation is important on a field scale in recovering isolated oil pockets surrounded by water. Glass cylinders filled with oil-saturated glass powder were impregnated from one end by an advancing waterfront. The rate of advance of the waterfront was shown to be proportional to the square root of elapsed time. Impregnation rates decreased as the ratio of oil viscosity to water viscosity increased although total oil recovery was constant at about 70% for all oil viscosities. Waterfront did not advance at a uniform rate over whole cross section of cylinders. Fingers of water tended to bypass and leave untouched small pockets of oil.

Optimum shape of radiation-cooled ring fins

Abstract: Figure 6 shows that V decreases as x0 increases, as is to be expected, since the heat flux per unit length of root at a fixed Q0 then decreases.

Stress relaxation, creep, and uniaxial strain: General and special features

Abstract: Papers devoted to the development of methods of describing the behavior of materials during creep and stress relaxation in terms of uniaxial strain data are usually based on the idea of the existence of a mechanical equation of state, i.e., an equation relating deformation or rate of deformation, temperature, stress, and time for such processes. The idea of a mechanical equation of state was first put forward by Nadai [1] and Zener and Holloman [2]. Holloman [3] has reported some experimental evidence for the existence of such an equation of state. However, Orowan [4], Dorn et al. [5], and Johnson et al. [6] have obtained data which are not in agreement with this idea. Freudenthal [7] has considered the physical basis of these processes and their mathematical description, and has not rejected the basic possibility of conversion of the data of one type of test into another. He ascribes the various difficulties in this area to insufficient knowledge about the nature of these processes. Guiu and Pratt [8] have come to the same conclusion and have noted the complexity of the processes taking place in the material under test.

Steady states of a continuous-flow adiabatic chemical reactor

Abstract: Flow reactors are widely used in the chemical industry for purposes of catalytic reactions [1,2]. Calculation of reactors of this type, even in one-dimemional approximation, is complicated and possible only with the use of numerical methods [1, 3]. Such calculations make it possible to find the steady-state distribution of temperature and concentration in the chemical reactor if one exists; in general, however, there may be other steady-state regimes which may be preferable from the standpoint of obtaining a different degree of conversion of the starting product, operating stability, etc.

Effects of vibrations on mass transfer from a sphere at high prandtl numbers

Abstract: Sonic vibrations are used to intensify diffusion in chemical technology [1]. We have previously [2–4] examined the effects of such waves on transport in gaseous media (Prandtl's number P≤1). Here we extend the results to heterogeneous mass transfer in liquids (P large). Mass transfer in this case occurs via internal secondary flows, not external ones. The main calculated results have been tested by experiment.