Sound and weak shock wave propagation in gas-liquid foams

Propagation of sound and weak shock waves in gas-liquid foams is investigated theoretically and experimentally. An original physical model is developed to describe the evolution of small perturbations in a foam of polyhedral structure. The model developed takes into account both peculiarities of interface heat transfer in foam and liquid motion through the system of Plateau-Gibbs borders which results in the appearance of an additional hydrodynamic dissipative force. The Rayleigh equation analog, which takes into account the latter phenomenon, is obtained. Structure and dynamics of weak shock waves are investigated. A vertical shock tube was constructed and used to measure the parameters of weak shock wave propagation in gas-liquid foams of polyhedral structure. Spectral analysis of the data obtained shows that there are weak dispersion and strong dissipation of the initial signal. Comparison of the evolution of experimental and theoretical profiles permits to conclude that the suggested model allows to describe the peculiarities of acoustical perturbations in gas-liquid foam more precisely than it follows from the standard models. Received 15 September 1993 / Accepted 27 December 1993     

Instability theory of shock wave in a shock tube

The instability theory of shock wave in a shock tube including the effects of tube wall and contact surface is studied. The experimental data of unstable shock wave coincide with one of instability criteria derived in the present paper.     

The formation of a secondary shock wave behind a shock wave diffracting at a convex corner

This paper deals with the formation of a secondary shock wave behind the shock wave diffracting at a two-dimensional convex corner for incident shock Mach numbers ranging from 1.03 to 1.74 in air. Experiments were carried out using a 60 mm 150 mm shock tube equipped with holographic interferometry. The threshold incident shock wave Mach number () at which a secondary shock wave appeared was found to be = 1.32 at an 81° corner and = 1.33 at a 120° corner. These secondary shock waves are formed due to the existence of a locally supersonic flow behind the diffracting shock wave. Behind the diffracting shock wave, the subsonic flow is accelerated and eventually becomes locally supersonic. A simple unsteady flow analysis revealed that for gases with specific heats ratio the threshold shock wave Mach number was = 1.346. When the value of is less than this, the vortex is formed at the corner without any discontinuous waves accompanying above the slip line. The viscosity was found to be less effective on the threshold of the secondary shock wave, although it attenuated the pressure jump at the secondary shock wave. This is well understood by the consideration of the effect of the wall friction in one-dimensional duct flows. In order to interpret the experimental results a numerical simulation using a shock adaptive unstructured grid Eulerian solver was also carried out. Received 1 May 1996 / Accepted 12 September 1996     

Ion-acoustic turbulence in a collisionless shock wave

The structure of a collisionless shock wave at the front of which ion-acoustic turbulence is excited is investigated. On the basis of the theory of anomalous resistance, equations are obtained for the oscillational spectrum and the particle distribution function in the plasma which, when known, make it possible to determine the magnetic field profile, density, and other macroscopic characteristics of the shock wave. The possibility of comparing theoretical predictions with experimental results from light scattering at the shock front is discussed.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 38–43, May–June, 1974.The author thanks R. Z. Sagdeev and D. D. Ryutov for discussions of the work.     

Three-dimensional diffraction of a shock wave

The diffraction of a shock wave (M₀=4.7) at an angle close to 180 has been experimentally investigated for the three-dimensional case. Interferograms of the flow and the pressure distribution on the back wall in the course of its interaction with the diffracted wave were obtained. Rotation of the flow structure behind the shock wave relative to the axis of symmetry was observed as the flow pattern develops in time and space.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 200–201 March–April, 1993.     

Neck propagation as a shock wave

Neck propagation in the stretching of elastic solid filaments having a yield point was analyzed using the space one-dimensional thin filament governing equations developed previously by the authors and other researchers. Constitutive model for the filament was assumed to be expressible as engineering tensile stress(X) (tensile force) given as a function of elongational strain with the(X) curve having a yield point maxima followed by a minima and a breaking point greater than the yield point maxima. Also incorporated into the model is the hysteresis of irreversible plastic deformation. When inertia is taken into consideration, the thin filament equations were found to reduce to the nonlinear wave equation ² (X)/ ² =C ₁ ² X/ ² where is Lagrangean space coordinate, is time, andC ₁ is inertia coefficient. The above nonlinear wave equation yields a solutionX(, ) having a stepwise discontinuity inX which propagates along the axis. The zero speed limit of the step wave solution was found to describe the above neck propagation occurring in solid filaments. Furthermore, it was recognized that the nonlinear wave equation was known for many years to also govern the plastic shock wave which propagates axially within a metal rod subjected to a very strong impact on its end. The one-dimensional atmospheric shock wave also was known to be governed by the nonlinear wave equation upon making certain simplifying assumptions. The above and other evidences lead to the conclusion that neck propagation occurring in the extension of solid filament obeying the above(X) function can be formally described as a shock wave.     

Behavior of sonic lines in a shock layer behind a detached shock wave

A numerical investigation is made into the formation of local supersonic zones in the subsonic flow region between a detached shock wave and the surface of the body in the case of supersonic three-dimensional flow over conical bodies with opening angle _k = 120 ° of the cone in the range of Mach numbers M = 2.5–15.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No.4 pp. 143–145, July–August, 1979.We thank G. I. Petrov for suggesting the problem and for helpful advice and O. M. Belotserkovskii for constant interest in the work.     

Equation of a shock wave front

Second-order differential equations of the hyperbolic type are derived for describing the local law of shock wave propagation. The shock waves are assumed to be two-dimensional unsteady in a stationary gas flow and three-dimensional steady in a supersonic flow. The behavior of the characteristics of these equations is investigated as a function of the governing flow parameters and their relative position with respect to the typical bicharacteristics of the characteristic cone behind the shock is analyzed. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 159–165, May–June, 2000.     

Role of the absorption of radiation ahead of a shock wave with hypersonic flow around a blunt body

A study was made of conditions at the front of a strong shock wave taking account of the absorption of leading radiation. Emphasis is laid on the role of the dimensionless parameters which arise under these circumstances, and an evaluation is made of the values of these parameters for a number of practically important cases involving the entry of blunt bodies into dense layers of the Earth's atmosphere. Calculations are carried out to determine the composition and the parameters of the flow of molecular nitrogen entering into the shock wave, and conclusions are drawn with respect to the general problem of hypersonic flow around a blunt body, taking radiation into account. In an investigation of the flow of a hypersonic stream of air around a blunt body, taking account of radiation, it is necessary to have some idea of how the radiation leaving the zone of the shock wave reacts with the oncoming flow of cold air. The importance of taking this reaction into account is indicated by the results of observation of the reentry of spacecraft into dense layers of the atmosphere [1], and by existing experimental data on strong shock waves [2]. This reaction is bound up with the fact that the absorption of intense short-wave radiation from the shock wave in cold air leads to photodissociation and photoionization of the molecules of air, i.e., to an actual increase in the enthalpy of the air. Some of the general questions of the structure of a very strong direct shock wave, taking account of the absorption of radiation leading the wave front, have been investigated in [3],Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 40–47, November–December, 1970.     

Nonlinear wave processes in a hypersonic shock layer

Nonlinear disturbance development in a hypersonic flat-plate shock layer (M_∞ = 21, Re _L = 1.44×10⁵) exposed to external-flow slow-mode acoustic perturbations at one or several frequencies is studied on the basis of the numerical solution of the Navier-Stokes equations. The mean flow distortion by disturbances and the nonlinear self-interaction between spectral modes is investigated by varying the initial amplitudes of the acoustic waves introduced. The appearance of combination frequencies, both summarized and subtracted, and their interaction with each other is shown to exist.     

Instability theory of shock wave in a channel

The instability theory of shock wave was extended from the case with an infinitefront to the case of a channel with a rectangular cross section.First,themathematical formulation of the problem was given which included a system ofdisturbed equations and three kinds of boundary conditions.Then,the general solutionsof the equations upstream and downstream were given and each contained fiveconstants to be determined.Thirdly,under one boundary condition and oneassumption,it was proved that all of the disturbances in front of the shock front andone of the two acoustic disturbances behind the shock front should be zero.Theboundary condition was that all of the disturbed physical quantities should approach tozero at infinity.The assumption was that only the unstable shock wave was concernedhere.So it was reasonable to assumeω=iγ,γwas the instability growth rate andwas a positive real number.Another kind of boundary conditions was that the normaldisturbed velocities should be zero at the solid wall of the cha     

Model of a viscous nonequilibrium shock layer with a thin shock wave

It is shown that the concept of a viscous shock layer with boundary conditions specified in a thin shock wave is unsuitable for analyzing the flow of a chemically reacting gas, even in the case of high Reynolds numbers; it may produce a finite error when determining the parameters of the shock layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 175–178, September–October, 1973.     

Nonequilibrium radiation of a strong shock wave

We examine the nonequilibrium radiation from the first negative band of the molecular nitrogen ion N ₂ ⁺ . The various N ₂ ⁺ ion excitation mechanisms are discussed. It is shown that for a shock wave velocity in air 8 km/sec the primary excitation mechanism is electronic impact.In conclusion the authors wish to thank V. K. Vertushkin and A. A. Gladkov for supplying the calculations on the structure of the normal compression shock and L. I. Ponomarev for helpful discussions.