Ideal gas flow behind a finite-amplitude shock wave

The equations of one-dimensional (with a plane of symmetry) adiabatic motion of an ideal gas are transformed to a form convenient for studying flows between a moving piston and a shock wave of variable intensity. The solution is found for the equations of a motion containing a shock wave which propagates through a quiescent gas with variable initial density and constant pressure. This solution contains four arbitrary constants and, in a particular case, gives an example of adiabatic shockless compression by a piston of a gas initially at rest.     

Transonic transition behind a shock wave traveling through a dust-gas mixture

The results of investigating shock-wave interaction with a particle cloud on the range of transonic relative velocities are presented. Transition of the two-phase flow from the supersonic to the subsonic regime during phase velocity relaxation under conditions of well-expressed gas-phase nonstationarity was observed. The effect of gas acceleration in the subsonic phase interaction region, previously predicted by the authors on the basis of the accelerating screen model, is confirmed experimentally. The presence of a substantial chaotic component of the particle longitudinal velocity, which indicates close internal phase interactions of the collision type, is demonstrated. Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 165–173, July–August, 2000. The work received financial support from the Russian Foundation for Basic Research (project N98-01-00722) and INTAS (project N97-2027).     

Nonequilibrium vibration-dissociation phenomena behind a propagating shock wave: Vibrational population calculation

An analysis of nonequilibrium phenomena behind a plane shock is presented concerning the vibrational relaxation and the dissociation of a pure diatomic gas. In the first part, the temperature range is 600 K–2500 K and the dissociation processes are neglected. The population of each vibrational level is computed by solving relaxation and conservation equations. The relaxation process is described by the master equations of each vibrational level. The vibrational transition probabilities appearing in the relaxation equations are calculated analytically and take into account the anharmonicity of molecular vibration and the potential angular dependence. The populations obtained are compared to those calculated using a Treanor model and to those calculated with a nonequilibrium Boltzmann distribution. For moderately high levels significant differences may be observed. The importance of the V-V process is found to be weak for the transitions involving the lowest levels. In the second part, the temperature range is 2500 K–5500K and the dissociation process is taken into account as well as the gas dynamic behavior which did not appear in several recent works. The kinetic equations are transformed to obtain a first order differential system and the resolution of such a system coupled with the conservation equations leads to the population of each vibrational level. The vibrational transition probabilities associated with the atom-molecule interaction are deduced from the cross section calculation used in the first part. The bound-free transition probabilities are obtained, following Marrone and Treanor, assuming that dissociation must occur preferentially from the higher vibrational states: the Marrone and Treanor probability model is extended and employed with an anharmonic oscillator. In the present investigation, behind the shock wave, the evolution of the population distribution expressed as a function of the distance is not monotonous: a lag time appears as shown experimentally in previous works for the macroscopic parameters. For moderately high levels the influence of the anharmonicity and those of the V-V processes appear significant and strongly related. In a general way, in both temperature ranges investigated, the V-V processes reduce the effects of the T-V transfer. Finally the influence of thecharacteristic probability temperature U of Marrone and Treanor is analyzed and a method of determination of local varying U is proposed.     

Flow behind magnetogasdynamic exponential shock wave in self-gravitating gas

The propagation of a cylindrical (or spherical) shock wave driven out by a piston moving with time according to an exponential law, in a self-gravitating ideal gas with azimuthal magnetic field is investigated. The initial magnetic field is assumed to be varying according to an exponential law. Solutions are obtained for both the cases of isothermal and adiabatic flows. The effects of variation of ambient magnetic field, gravitational parameter and adiabatic exponent are worked out in detail. It is manifested that the increase in strength of ambient magnetic field has decaying effect on the shock wave however increase in the value of gravitational parameter has reverse effect on the shock strength. The compressibility of the medium is increased in the presence of gravitational field. Also, a comparison between the solutions obtained in the case of isothermal and adiabatic flows is done. Density, pressure, velocity and magnetic field increases, however mass decreases as we move inward from the shock front towards the piston.     

Shock wave ignition in N2O-CO(N2)-He mixtures

The behavior of the pressure behind shock waves in N₂O-CO-He mixtures is investigated. The pressure can be relatively easily measured and, at the same time, reflects the general influence of the experimental conditions on flow formation in the shock tube. Shock-wave mixture ignition effects and, moreover, hydrogen combustion in the contact zone are analyzed from the standpoint of their influence on the stagnation parameters and the optical properties of the flow in the shock tube nozzle. The correctness of modeling the conditions behind the reflected wave by means of mixtures similar in composition to the equilibrium products of the N₂O-CO reaction [1] is discussed in the same context.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 164–170, September–October, 1989.The authors wish to thank G. D. Smekhov for calculating the equilibrium compositions of the mixtures behind the shock waves and A. P. Zuev for stimulating discussions.     

Measurement of parameters of a gas suspension behind a shock wave in foam

A study has been made of the propagation of a shock wave in dry polyhedral foam with cell diameter 1 cm. The experiments were made in a shock tube in the range of Mach numbers M < 1.4 of the shock wave. The interaction of the shock wave with the foam was photographed. This established that the destruction of the foam by the shock wave leads to the formation of a gas-droplet flow behind the shock front. To determine the parameters of the suspension, the flow was probed by He-Ne lasers with different radiation wavelengths. The spectral-transparency method was used to find the modal diameter of the droplets of the gas suspension and the volume concentration of the droplets in the flow. The modal diameter of the droplets was 2m, and the volume concentration of the droplets decreased downstream.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 134–141, May–June, 1993.     

Self-similar solution of cylindrical shock wave propagation in a rotational axisymmetric mixture of a non-ideal gas and small solid particles

Similarity solutions are obtained for one- dimensional isothermal and adiabatic unsteady flow behind a strong cylindrical shock wave propagating in a rotational axisymmetric dusty gas, which has a variable azimuthal fluid velocity together with a variable axial fluid velocity. The shock is assumed to be driven out by a moving piston and the dusty gas to be a mixture of non-ideal (or perfect) gas and small solid particles, in which solid particles are continuously distributed. It is assumed that the equilibrium flow-condition is maintained and variable energy input is continuously supplied by the piston. The shock Mach number is not infinite, but has a finite value. The azimuthal and axial component of the fluid velocity in the ambient medium are assumed to be vary and obey power laws, and the density of the ambient medium is taken to be constant. In order to obtain the similarity solutions the angular velocity of the ambient medium is assumed to be decreasing as the distance from the axis increases. Effects of the variation of the parameter of non-idealness of the gas in the mixture, the mass concentration of solid particles and the ratio of the density of solid particles to the initial density of the gas are investigated.     

Experimental and numerical studies of rotational relaxation behind a strong shock wave in air

This paper describes the experimental and numerical investigations of unknown characteristics of the rotational nonequilibrium phenomena behind a strong shock wave in air. Experiments were carried out using a piston-driven shock tube with helium as driving gas and air as driven (test) gas, operated as a two-stage shock tube. In the experiments, emission spectra of NO were measured to evaluate the rotational temperature behind a strong shock wave. The numerical calculations use the computational code for the thermal and chemical nonequilibrium flow behind a strong shock wave developed by the present author's group, where 11 chemical species (N, O, NO, N, O, N, O, NO, N, O, e) and 48 chemical reactions of high-temperature air are considered. The thermal nonequilibrium is expressed by introducing an 8 temperature model composed of translational temperature, rotational and vibrational temperatures for N, O, NO, and electron temperature. The coupling of a rotation, vibration and dissociation (CRVD) model was incorporated to take sufficiently into account the rotational nonequilibrium. The calculations were conducted for the same conditions as the experimental ones. From the calculated flow properties, emission spectra were re-constructed using the code for computing spectra of high temperature air “SPRADIAN”. Furthermore, rotational and vibrational temperatures of NO (0,1) were determined from a curve fitting method and compared with the computed results. Received 12 September 2001 / Accepted 18 February 2002     

Formation of inversion in jet of CO2-H2O-N2 gas mixture expanding through a slot

A calculation is made of the kinetics of vibrational relaxation of CO₂ molecules in a CO₂ -H₂O-N₂ mixture escaping into a vacuum from a slot. The examination of vibrational relaxation led to a solution of the kinetic equations corresponding to the most important channels of energy exchange in vibration-vibration and vibration-translation processes. It proved possible to consider the dynamics of a nonequilibrium gas in an approximation of the adiabatic motion of a medium with an effective adiabatic index corresponding to a certain degree of freezing in of the vibrational component of the heat capacity of the gas. The calculated values of the gain index agree well with experimental data. The gain index was calculated with allowance for Doppler and Lorentz mechanisms of line broadening. The results of the calculation were analyzed.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 25–31, November–December, 1973.The authors thank A. S. Biryukov and N. N. Sobolev for advice and comments and É. A. Ashratov and G. K. Bunin for conducting the gasdynamical calculation on an electronic computer.     

Processes of hydrate formation and dissolution behind a shock wave in a liquid containing gas bubbles (mixture of nitrogen and carbon dioxide)

The processes of dissolution and hydrate formation behind a moderate-amplitude shock wave in water containing gas bubbles (mixture of nitrogen and carbon dioxide) are studied in experiments with different initial static pressures in the medium and concentrations of carbon dioxide in bubbles. An increase in static pressure in the gas-liquid medium is demonstrated to enhance the influence of the non-reacting gas (nitrogen) on the processes of dissolution and hydrate formation. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 2, pp. 178–187, March–April, 2009.