Shock wave diffraction by a square cavity filled with dusty gas

A simple two-dimensional square cavity model is used to study shock attenuating effects of dust suspension in air. The GRP scheme for compressible flows was extended to simulate the fluid dynamics of dilute dust suspensions, employing the conventional two-phase approximation. A planar shock of constant intensity propagated in pure air over flat ground and diffracted into a square cavity filled with a dusty quiescent suspension. Shock intensities were and , dust loading ratios were and , and particle diameters were and {\rm \mu}$m. It was found that the diffraction patterns in the cavity were decisively attenuated by the dust suspension, particularly for the higher loading ratio. The particle size has a pronounced effect on the flow and wave pattern developed inside the cavity. Wall pressure histories were recorded for each of the three cavity walls, showing a clear attenuating effect of the dust suspension. Received 15 November 1999 / Accepted 25 October 2000     

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.     

Shock wave structure for a fully ionized plasma

We study planar shock wave structure in a two-temperature model of a fully ionized plasma that includes electron heat conduction and energy exchange between electrons and ions. For steady flow in a reference frame moving with the shock, the model reduces to an autonomous system of ordinary differential equations which can be numerically integrated. A phase space analysis of the differential equations provides an additional insight into the structure of the solutions. For example, below a threshold Mach number, the model produces continuous solutions, while above another threshold Mach number, the solutions contain embedded hydrodynamic shocks. Between the threshold values, the appearance of embedded shocks depends on the electron diffusivity and the electron–ion coupling term. We also find that the ion temperature may achieve a maximum value between the upstream and downstream states and away from the embedded shock. We summarize the methodology for solving for two-temperature shocks and show results for several values of shock strength and plasma parameters in order to quantify the shock structure and explore the range of possible solutions. Such solutions may be used to verify hydrodynamic codes that use similar plasma physics models.     

Shock wave interaction with a cloud of particles

The present paper is devoted to experimental and theoretical investigation of the shock wave (SW) propagation in a mixture of gas and solid particles in the presence of explicit boundaries of the two-phase region (cloud of particles). The effect of the qualitative change in the supersonic flow behind the SW in a cloud of particles within the range of the volume concentration of the disperse phase 0.1-3% is experimentally shown and theoretically grounded. Received 15 April 1996 / Accepted 3 June 1996     

Interaction of a weak discontinuity wave with a characteristic shock in a dusty gas

In this paper, the evolution of a characteristic shock in a dusty gas is investigated and its interaction with a weak discontinuity wave is studied. The transport equation for the amplitude of the weak discontinuity wave, which is of Bernoulli type, is obtained. The amplitudes of the reflected and transmitted waves after interaction of the weak discontinuity with the characteristic shock are evaluated by using the results of the general theory of wave interaction.      

Shock waves in liquids containing gas bubbles

Results of theoretical and experimental studies on shock wave propagation in boiling and nonboiling liquids with gas bubbles are reviewed. The structure of shock waves, their reflection and attenuation in two-phase gas-liquid media are considered.     

Head on collision of a planar shock wave with a dusty gas layer

The head-on collision of a planar shock wave with a dust-air suspension is studied numerically. In this study the suspension is placed inside a conduit adjacent to its rigid end-wall. It is shown that as a result of this collision two different types of transmitted shock waves are possible, depending on the strength of the incident shock wave and the dust loading ratio in the suspension. One possibility is a partially dispersed shock wave, the other is a compression wave. The flow fields resulting in these two options are investigated. It is shown that in both cases, at late times after the head-on reflection of the transmitted shock wave from the conduit end-wall a negative flow (away from the end-wall) is evident. The observed flow behavior may suggest a kind of dust particle lifting mechanism that could shed new light on the complex phenomenon of dust entrainment behind sliding shock waves.      

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.     

Shock wave structure in a mixture of gas,vapour and droplets

The structure of the relaxation zone behind a shock wave of moderate strength in a mixture of gas, vapour and droplets is analysed. A model is presented for shock induced evaporation, which is based on wet-bulb equilibrium and on the absence of relative motion between droplets and gas. Experimental and numerical data on heterogeneous condensation induced by an unsteady rarefaction wave and on re-evaporation due to shock wave passage are reported for a mixture of water vapour, nitrogen gas and condensation nuclei. Pressure, temperature, saturation ratio and droplet size are experimentally obtained and are very well predicted by a numerical simulation based on the non-linear quasisteady wet-bulb model for phase transition, as well for the expansion wave as for the shock wave. During expansion, droplet number density decays much faster than predicted, which is not yet satisfactorily explained. Shock induced droplet evaporation is studied for post-shock saturation ratios ranging from 5×10^–3 to 0.2, corresponding to shock Mach numbers of 1.2 to 1.9. The evaporation times are well predicted by the theoretical model. No evidence is found for droplet break-up for Weber numbers up to 13, and droplet radii of the order of 1m.On leave at Institute of Fluid Science, Shock Wave Research Center, Tohoku University, Sendai 980, JapanThis article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Effect of dispersed impurities on the rise of a dusty thermal

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 69–77, September–October, 1990.     

Shock wave interaction with area changes in ducts

Whitham's approximation for handling shock wave propagation in area changes (reductions) in a duct was checked in comparison with a numerical solution. Also the Whitham approximation for shock wave propagation from a constant cross-sectional duct to a duct of a smaller cross-sectional area was studied and compared with a numerical solution. It was found that for modest incident shock Mach numbers and modest area reductions the Whitham approximation provided a fair solution for the shock Mach number and for the post-shock pressure. For higher shock Mach numbers and/or area reductions, large discrepancies exit between the approximate and exact solutions. A wider range of applicability of the Whitham approximation is found for the monotonical area reduction case; it is quite narrow for the passage of a shock wave from a wider to a narrower duct case. In addition, the effect of the extent of the area change region on the time required for reaching a quasi-steady flow was studied. It was shown that the longer the area change segment is, the longer it takes to reach a quasi-steady flow.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 structure in a diatomic gas based on a kinetic model

The structure of a normal (direct) shock in a gas for the parameters corresponding to nitrogen is investigated with allowance for the rotational degrees of freedom on the basis of a model kinetic equation. For various Mach numbers the structure is compared with both the known experimental results and the solutions of the Navier-Stokes approximation within the framework of two-temperature hydrodynamics. The possibility of assuming the constancy of the fraction of excited rotational degrees of freedom is studied.     

Natural convection of a dusty gas

The natural convection of a gas-particle suspension inside a two-dimensional square region is investigated within the framework of a two-velocity two-temperature model of the medium with allowance for phase relaxation and particle deposition. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 46–52, March–April, 1994.     

Wave propagation in a non-ideal dusty gas

In this paper we have studied the behavior of wave motion as propagating wavelets and their culmination into shock waves in a non-ideal gas with dust particles. In the absence of non-ideal effect the gas satisfies an equation of state of Mie–Gruneisen type. An expansion wave resulting from the action of receding piston is considered and the solutions to this problem showing effects of dust particles and non-idealness are obtained. The propagation of weak waves is considered and the flow variables in the region bounded by the piston and the characteristic wave front are found out. The expansive action of a receding piston undergoing an abrupt change in velocity is discussed. Cases of central expansion fan and shock fronts are studied and the solutions up to first order in the physical plane are obtained. The effects of non-idealness and dust particles are discussed in each case.