Head-on collision of normal shock waves in dusty gases

The head-on collision of normal shock waves in dusty gases has been investigated numerically, using the modified random-choice method. The results concerning the various flow field properties as well as the waves configuration were compared with those of a pure gas case.     

A parametric study of the head-on collision of normal shock waves in dusty gases

The effect of the various flow parameters, namely: the diameter of the solid particles, the material density of the solid particles, and the loading ratio of the solid particles on the flow field which is obtained when two normal shock waves collide head-on in a two phase dust-gas suspension has been investigated numerically, using the modified random choice method (RCM). The results were compared with those appropriate to the dust physical parameters used recently by Elperin, Ben-Dor and Igra in their study of the head-on collision of normal shock waves in dusty gases.     

Rarefaction waves in nonequilibrium-boiling fluid flows

The depressurization of a high-pressure vessel initially filled with water heated to below the saturation point is investigated. After depressurization, the pressure in the vessel drops and the boiling fluid flows out into the atmosphere. The experiments [1–3] showed that, when the first rarefaction wave passes through the fluid and the pressure falls below the saturation point, a two-phase mixture with a small steam volume fraction (below 20%) is formed in the vessel. Intense boiling starts only after the arrival of a rarefaction wave traveling at a speed ∼ 10 m/s called the "boiling shock" in [4]. To explain the specific features of this process we developed a mathematical model which takes the difference in the phase velocities into account. Although in bubbly flows this difference is only ∼ 1 m/s, it is enough to cause bubble fragmentation. The calculation showed that the fragmentation proceeds like a chain reaction, i. e. one fragmentation event creates the conditions for the succeeding events. The avalanche-like bubble number growth leads to sharp boiling intensification and the rapid transition of the non-equilibrium mixture to the equilibrium state. This process occurs in a narrow region, namely, in a slow boiling wave which, in the numerical calculations, looks like a shock. The model developed has made it possible to obtain numerical solutions which agree well with the experimental data, to study the wave structure, and to explain the wave mechanism. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 20–33, July–August, 2000. The work received financial support in part from the Russian Foundation for Basic Research (project 99-03-32042) and from INTAS (grant OPEN 97-2027).     

Chapman-Jouguet waves in a dusty gas

An analytic solution is obtained of the problem of flow of a two-phase medium, representing a mixture of gas and solid or liquid particles behind plane, cylindrical, and spherical Chapman-Jouguet detonation waves. It is assumed that all the particles are the same, are chemically inert, have a true density much greater than the density of the gas, and that their volume concentration a is low. The interaction of the particles and the influence of Brownian motion on them are disregarded. The gas is assumed to be perfect. On the detonation wave, the particle parameters are assumed to be continuous, and the usual gas-dynamical relations on the detonation wave have been applied for the gas parameters because is low. Behind the detonation front, the phases interact through interphase forces and heat transfer. It has been found that the dust content of the combustible gas qualitatively changes the character of flows with Chapman-Jouguet (C-J) waves. It is shown that a plane C-J wave is an envelope of one of the acoustic families of characteristics, and not a characteristic, as occurs in a pure gas [1]. In view of this, only two solutions of the problem of flow behind a plane C-J wave are possible: one solution corresponds to a rarefaction flow and the other to a compression flow. In a pure gas such a problem has a nondenumerable set of solutions: an arbitrary Riemann rarefaction wave can adjoin the plane C-J wave. It is found that in a dusty gas there are converging cylindrical and spherical C-J waves. In a pure gas, there are no converging C-J waves [2, 3]. An expression is found for the distance r_* from the axis (center) of symmetry on which the converging cylindrical (spherical) C-J wave changes into a supercompressed detonation wave. It has been found that r_* d/₀, = 1, 2 for the cylindrical and spherical waves, respectively, d is the particle diameter, ₀ is their initial volume concentration, and the proportionality factor decreases together with d. For the detonating mixture 2H₂ + O₂ the calculations of r_* are given in a number of cases.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 111–118, July–August, 1985.The author wishes to thank V. A. Levin for his interest in the work and his useful discussion of the results.     

Numerical study of shock diffraction in dusty gases

ＮＵＭＥＲＩＣＡＬＳＴＵＤＹＯＦＳＨＯＣＫＤＩＦＦＲＡＣＴＩＯＮＩＮＤＵＳＴＹＧＡＳＥＳＷｕＱｉｎｇ－ｓｏｎ（吴清松）ＺｈｕＨｏｎｇ（朱红）ＸｕＹａｎ－ｈｏｕ（徐燕侯）（ＵｎｉｖｅｒｓｉｔｙｏｆＳｃｉｅｎｃｅａｎｄＴｅｃｈｎｏｌｏｇｙｏｆＣｈｉｎａ,...     

Dust acoustic shock waves in coupled dusty plasmas with nonthermal ions

Dust acoustic shock waves of the Korteweg-de Vries–Burgers (KdV–Burgers) equation and the modified Korteweg-de Vries–Burgers (MKdV–Burgers) equation are studied in strongly coupled dusty plasmas containing nonthermal ions and Boltzmann-distributed electrons. The effects of important parameters, such as nonthermal parameter, relative temperature, relative density and dust particles viscosity, on the properties of shock waves are discussed.     

Translational nonequilibrium effects in shock waves in gases

An attempt is made to find real systems in which translational non-equilibrium effects can be experimentally detected.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 134–140, May–June, 1990.     

Parameters of shock waves with emission in gases

Parameters of emitting shock waves in gases are investigated in the limiting case when there is no screening of emission from the shock front by the precursory layer. The one-dimensional quasi-steady-state formulation of the problem with deceleration of high-speed gas flow against a plane fixed obstacle under conditions of strong emission is given. The case of the shock waves of large optical thickness is analytically considered over a wide range of variation of the obstacle reflectivity. The parameters of emitting shock waves generated in experiments in shock tubes in the inert argon gas are estimated using the methods developed and compared with the measurement results. The shock “adiabats” of optically thick shock waves are considered with allowance for the radiation energy losses. The calculations are carried out for aluminium plasma.     

Propagation of shock and detonation waves in dust-laden gases

This article examines the flows of a two-phase mixture of a gas with solid particles arising as a result of the propagation of shock waves or detonation waves through a homogeneous medium at rest. It is assumed that the basic assumptions of the mechanics of mutually penetrating continua hold [1], whereby it is possible to describe the flow of each phase of the mixture within the framework of the mechanics of a continuous medium. We assume that the solid phase consists of identical, incompressible, and nondeformable particles of spherical shape. It is assumed that the temperature inside the particles is homogeneous. Collisions between particles and their Brownian motion are ignored. It is assumed that the carrier phase is an ideal gas (the viscosity is only allowed for in the interaction forces between phases). The contribution of the volume of the particles is not considered. On the basis of these assumptions, the following problems are considered: the propagation of a detonation wave in a mixture of a detonating gas and chemically inert particles and the motion of a dust-gas mixture in a shock tube in the presence of combustion of the particles.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6. pp. 93–99, November–December, 1984.     

Rarefaction shock waves in porous media that accumulate CO2, CH4, N2

In this paper, a porous medium whose core is built from a solid substance is considered. Such a medium can accumulate liquid and gaseous substances absorbing on the surface of the solid body and diffusing within its molecular lattice. The medium forms a so-called solid solution. A change in the values of the thermodynamic parameters of this medium leads to phase transitions in these substances. Besides, some other associated phenomena may occur. There are given the results of laboratory analyses concerning the relation between the specific volumeV of the solid solution formed by the coal with CO₂, CH₄, N₂ dissolved in it and its confining pressurep. This relation indicates the possibility of the propagation of a rarefaction shock waves in such a medium.A mathematical model of the generation of such waves and its specific applications to describe the initial boundary conditions affected during the experiments presented. The results of these experiments have confirmed the adopted model, particularly those aspects that are concerned with the specific sliced structures of the coal medium with the accumulated CO₂ and N₂, through which a rarefaction shock wave has passed (Figs. 10a, 10b, 11a, and 11b). The presented model explains the phenomena of sudden massive rock-and-gas outbursts, occurring in nature, e.g. as a result of disturbing the primary equilibrium of the rocks in the Earth crust which form a solid solution, by underground mining exploitation.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Shock wave interaction in a dusty gas and the appearance of fully dispersed waves

A problem of regular (symmetric and asymmetric) interaction of plane shock waves in a steady-state dusty-gas flow is considered. The possibility of the formation of wave structures is revealed, in which either all or some of the incident or reflected waves degenerate into fully dispersed waves, i.e. zones in which the parameters of both phases vary continuously. Using the Rankine-Hugoniot relations for a one-velocity “effective-gas” model, the ranges of nondimensional governing parameters (the Mach number, the angles between the incident waves and the free stream, the phase specific-heat ratio, and the particle mass concentration) are found, which correspond to different wave configurations. In the framework of a two-fluid dusty-gas model, the flow structure in the region of symmetric interaction of the shocks is calculated numerically for typical configurations containing fully dispersed waves. The flow in the region of a normal fully dispersed wave is also calculated. Good agreement between the calculated wave structure and the data known in the literature is obtained. A range of governing parameters in which the carrier-phase temperature has a local maximum inside the wave structure is found.     

Boundary layer flows behind constant speed shock waves moving into a dusty gas

Laminar boundary layer flows behind constant speed shock waves moving into a dusty gas are analyzed numerically. The basic equations of two-phase flows are derived in shock fixed coordinates and solved by an implicit finite-difference method for the side wall boundary layer in a dusty gas shock tube. The development of the boundary layer and resulting velocity and temperature profiles, respectively, for the gas and particles are given from the shock front to far downstream. The effects of diaphragm pressure ratio, mass loading ratio of particles and particle size upon the flow properties are discussed in detail.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1990.     

Thermo-acceleration waves and shock formation in Extended Thermodynamics of gravitational gases

The possibility of shock formation as degeneration of acceleration waves in a thermoviscous gravitational ideal gas is studied by exploiting the hyperbolic system of Extended Thermodynamics. The mathematical aspects of this problem are discussed by considering the different contributions of gravity and dissipative effects. In particular, we evaluate the critical time (i.e. the instant in which a shock wave starts) proving that it exists, in the usual physical situations, only for a sufficiently large critical initial amplitude of the acceleration jump. We show that an acceleration wave can never degenerate into a shock wave except in some limiting cases and so, since gravity force is overcome by dissipative effects, our results do not differ, qualitatively, from the case without gravity: this result implies the asymptotic stability (in the sense of [1]) of the static isothermal solutions.     

Hyperbolicity singularities in Rarefaction Waves

For mixed-type systems of conservation laws, rarefaction waves may contain states at the boundary of the elliptic region, where two characteristic speeds coincide, and the Lax family of the wave changes. Such contiguous rarefaction waves form a single fan with a continuous profile. Different pairs of families may appear in such rarefactions, giving rise to novel Riemann solution structures. We study the structure of such rarefaction waves near regular and exceptional points of the elliptic boundary and describe their effect on Riemann solutions.     

Evolution of pressure waves in a liquid with bubbles of two dissimilar gases

The structure and dissipation of moderateamplitude pressure waves in a liquid with bubbles of two dissimilar gases (freon and helium) are experimentally studied. It is shown that introduction of a small (by volume) quantity of helium bubbles with a high thermal conductivity into a liquid with poorly heatconducting freon bubbles, sharply increases the rate of damping of solitary pressure waves.