Airflow behind strong shock front with account for nonequilibrium ionization and radiation

We consider the gas state behind a shock wave front in air with a velocity v10 km/sec. Nonequilibrium ionization and radiative transport are taken into account. We take into consideration the real air spectrum — the numerous lines, bands, and continuua. Account for the radiation leads to an integrodifferential system of equations for which a solution method is developed. As a result we obtain the gas parameter profiles behind the shock wave, which are affected by the relaxation processes and radiative cooling. The calculations were made for v=10–16 km/sec and a pressure p=10^–5–10^–2 atm ahead of the front.In order to obtain realistic results, we consider only the gas layer bounded by the shock and a surface parallel to it. It is assumed that the gas bounded by these planes is not irradiated from without. In this formulation still another defining parameter appears—the distancel between the planes. The calculations were made forl=1–100 cm.     

Radiative relaxation kinetics of shock-heated xenon

The kinetics of the ionization and radiation processes taking place in xenon heated in strong shock waves (Mach numbers on the interval 10–20) are numerically investigated. A fairly complete model of the medium and the processes is used. The influence of the radiation efficiency is taken into account on the assumption that the radiation layer is homogeneous and isotropic at every instant of time. The calculated distribution of plasma brightness temperature along the luminous layer is compared with that measured in shock-tube experiments. The experimental data are satisfactorily described by the modeling.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.6, pp. 157–163, November–December, 1992.     

Computation of the shock adiabats of argon and xenon

Results of computations of the shock adiabats of Ar and Xe taking account of ionization, electron excitation, and a nonideal plasma are represented. Energy losses by radiation are estimated.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 70–76, May–June, 1973.     

Calculation of high power relativistic beams with consideration of collision effects

Numerical calculation of relativistic charged particle beams moving in axisymmetric systems in which the presence of a residual neutral gas is possible is considered. In this content it is essential to consider phenomena related to collisions between charged particles and neutrals (for example, ionization and charge transfer). Algorithms are constructed for numerical modeling of ionization processes within the framework of the ERA program complex [1]. Solutions of model and practical problems are presented as examples. Such problems were studied previously in [2, 3] where ionization processes were considered by a more complex method requiring a greater volume of calculations but valid at lower pressures.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 3–8, January–February, 1986.The author expresses his sincere gratitude to P. I. Akimov and A. L. Komov for posing the problem of consideration of ionization processes.     

The distribution function of atomic level populations in a plasma

An analytic form is obtained for the population distribution function in an atomic plasma as a series in successive time derivatives of the population of the first level. The first approximation includes the well-known method of a stationary sink. The quasistationary distribution obtained for hydrogen agrees well with numerical calculations of recombination and ionization, and for lithium, helium, and argon the quasistationary distribution gives qualitative agreement with numerical calculations.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 18–26, July–August, 1972.We should like to thank B. F. Gordiets for a helpful discussion.     

Effect of precursor radiation on the flow structure and ionization behind the shock front in inert gases

The problem of the propagation of strong, intensely radiating shock waves in inert gases is considered. It is shown that the heating of the shock tube walls by the precursor radiation, accompanied by an increase in the temperature of the adjacent gas, leads to the transverse stratification of the medium and to the disturbance of the one-dimensionality of the flow of shock-heated gas behind the wave front. Ionization kinetics calculations which take this into account indicate an acceleration of ionization near the tube walls, which is consistent with experiment. On the basis of the gas heating values obtained it is possible to establish critical values of the gas pressures ahead of the front and the shock wave Mach numbers, transition through which is accompanied by a radical restructuring of the flow with the formation of a configuration.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 124–131, May–June, 1991.     

Parameters of a stationary radially symmetrical jet of vapors heated by laser radiation

The solution [1] of the problem of the stationary radially symmetrical movement of vapors heated by monochromatic radiation is generalized for the case of an arbitrary (tabular) dependence of the coefficient of absorption and the adiabatic index on the temperature and density. The calculations of thermodynamical and optical properties of vapors of a number of elements carried out in a wide range of densities and temperatures and the solution referred to made it possible to determine the parameters of a stationary jet of vapors in a wide range of radiation flux densities and characteristic dimension. Some results of the calculations for carbon and aluminum are presented. It turns out that a characteristic property of the distribution pattern of parameters in a jet of vapors is the presence on the surface of a zone of cold vapors and a zone of their heating — the heating wave front. However, for large radiation flux densities the extent of the zone of cold vapors is not large. A rough estimate of the intensity of reradiation of the heated vapors is derived. It is shown that for characteristic dimensions of the vapor layer on the order of 0.3–1 cm the intensity of reradiation can be high enough that the pattern of movement found without considering reradiation can change somewhat. It is shown that the solution examined can be generalized also to the case where the transfer of energy by radiation of the continuous spectrum is taken into account.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 58–75, September–October, 1972.The authors are grateful to V. V. Novikova for great assistance in conducting the calculations for the stationary state problem and analyzing their results and to L. P. Markelova and V. A. Onishchuk for help in conducting the calculations of the thermodynamic and optical properties of the vapors.     

Calculation of axially symmetrical free expansion of a no ne quilibrium hydrogen plasma

A scheme and the results of a calculation by the method of characteristics are presented for free expansion of a nonviscous, thermally nonconducting, nonequilibrium, optically thick hydrogen plasma from a round supersonic nozzle. The elementary process determined is considered to be collision-radiative recombination. A strong disturbance in the thermal and ionization equilibrium are observed in the flow field. The effect of relaxation processes on the geometry of flow and the field of gas-dynamic parameters is examined. The results of the calculations are compared with analogous data for an ideal perfect gas.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 27–30, July–August, 1972.     

Momentum produced by intense radiation falling on a surface

The transient flow produced in a stationary gas when an intense beam of radiation falls on a plane surface is studied. A flow pattern is proposed and approximate relations are derived for finding the momentum produced by sufficiently long irradiation of the body. The calculations are compared with available experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2. pp. 196–199. March–April, 1977.     

Calculating scheme and switching-on of the load of plane explosive-driven magnetic generators

A scheme is described for calculating explosive-driven magnetic generators, and analytical and numerical calculations are made of the problem of switching a generator on to a constant ohmic and induction load, to a load whose resistance rises linearly with the temperature, and to a plasma load with equilibrium radiation. In the latter case, a calculation is made of a variant involving switching on the load through a matched transformer.Translated from Zhurnal Prikladnoi Mekhanika i Tekhnicheskoi Fiziki, No. 2, pp. 37–41, March–April, 1973.     

Calculation of the thermally nonequilibrium near-electrode region in an alkali-metal-seeded plasma

Distribution of parameters in the region of disturbance of a plasma near the surface of an electrode is considered based on diffusion equations. Thermoelectronic and thermionic emission from the electrode surface, the Schottky effect, and volume ionization and recombination are borne in mind. Two regions are assumed in the solution, namely, the region of ambipolar diffusion and the region of the space charge. A comparatively simple geometry for the discharge gap, given in the form of two infinite plane-parallel electrodes, is considered. A comparison is carried out with calculations for a thermally balanced region of a plasma disturbance.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 13–17, January–February, 1976.     

Distribution of radiant thermal flux over the surface of a sphere for hypersonic flow of a nonviscous radiating gas past the sphere

In the present study using the Newtonian approximation [1] we obtain an analytical solution to the problem of flow of a steady, uniform, hypersonic, nonviscous, radiating gas past a sphere. The three-dimensional radiative-loss approximation is used. A distribution is found for the gasdynamic parameters in the shock layer, the withdrawal of the shock wave and the radiant thermal flux to the surface of the sphere. The Newtonian approximation was used earlier in [2, 3] to analyze a gas flow with radiation near the critical line. In [2] the radiation field was considered in the differential approximation, with the optical absorption coefficient being assumed constant. In [3] the integrodifferential energy equation with account of radiation was solved numerically for a gray gas. In [4–7] the problem of the flow of a nonviscous, nonheat-conducting gas behind a shock wave with account of radiation was solved numerically. To calculate the radiation field in [4, 7] the three-dimensional radiative-loss approximation was used; in [5, 6] the self-absorption of the gas was taken into account. A comparison of the equations obtained in the present study for radiant flow from radiating air to a sphere with the numerical calculations [4–7] shows them to have satisfactory accuracy.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 44–49, November–December, 1972.In conclusion the author thanks G. A. Tirskii and É. A. Gershbein for discussion and valuable remarks.     

Investigation of an Electromagnetic Pulse Generated by a System on a Standard Spacecraft

Results on generation of an electromagnetic pulse on a spacecraft under the action of X-ray and gamma radiation are described. The computational technology used is based on a hierarchical system of mathematical models constructed on a system of the Maxwell-Vlasov equations and spacecraft models that rather accurately describe all physical processes typical of origination of secondary electromagnetic fields and the object geometry. It is shown that polarization components of the electric field, which are directed normal to irradiated surfaces, depend weakly on geometric factors and are mainly determined by the photon radiation flux density. Formation of the magnetic field is determined by the dynamics of variation of the first derivative of the dipole moment of the electron layer formed owing to emission of particles under the action of ionization radiation and depends on the object shape, characteristic size of the irradiated surface, and spacecraft attitude.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 5, pp. 3–13, September–October, 2005.     

A method of calculating the radiation flux and its divergence in regions with stepped temperature and chemical composition distribution

An approximate method is proposed which makes it possible to compute the radiation flux and its divergence when the absorption cross section depends in a complex manner on the wavelength. Radiation scattering is ignored. The method is described for the case when the region occupied by the radiating and absorbing gas can be divided into finite number of subregions in which the temperature and the chemical composition are constant. Examples are given of the numerical calculations of the radiation flux.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 54–62, March–April, 1971.The author wishes to express his gratitude to É. Filippova for help in the computations.     

Investigation of flow past blunt bodies with allowance for radiation by the large-particle method

Much recent work has been done on developing methods of solving gas-dynamic problems in which radiation plays a part (see, for example, [1–7]). This is because the temperature in the shock layer associated with flight in the atmosphere at hypersonic velocities can reach values exceeding 10⁴ °K. In such a case, heat transfer by radiation can make an important contribution to the total heat transfer. With increasing flight velocities, the importance of radiation in heat transfer increases and then becomes predominant. In the present paper, the large-particle method as developed by Belotserkovskii and Davydov [8] is developed to calculate flows with radiation around blunt bodies, including the case when there is distributed blowing from the surface of the bodies into the shock layer, which simulates ablation of a heat-shielding covering under the influence of strong heating by radiation. The results are given of systematic calculations of flow past blunt bodies of various shapes by a stream of radiating air, and the results are compared with the data of other methods.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 106–112, July–August, 1982.     

Effect of surface and volume ionization on the electrode potential drop

We consider the change in the potential of the electric field in the free fall layer at the electrodes as a function of the characteristics of the surface and the volume ionization. Systematic calculations are made of the electrode potential drop for a tungsten cathode and anode in a lithium and cesium plasma. The potential of the electric field is obtained as a function of the plasma pressure, the degree of volume ionization, the electron temperature, the electrode temperature, and the current density.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 137–139, July–August, 1970.     

The effects of ionization on the compression of a gas by a converging shell

One of the effective methods of obtaining a dense high-temperature plasma is compression of the gas by converging shells, which can be accelerated to high velocities by the products of an explosion either as a result of ablation caused by laser radiation, or by an electron beam [1–3]. In order to interpret the results of such experiments, it is very important to construct satisfactory physical models which enable us to obtain plausible estimates for the parameters of the plasma which are realized as a result of the compression. In a number of cases the process of compression may be described with sufficient accuracy by a system of simple hydro-dynamic equations which have particular analytical solutions (see, for example, [4–7]); however, as a rule, for more realistic estimates it is necessary to take into account the complex of physical phenomena accompanying the process, and in such cases the most effective method is numerical simulation of the process, which enables a fuller study to be made of the effect of various factors [7–9]. Compression regimes corresponding to velocities of projection of the shells of some tens of kilometers a second (attainable in experiments with laser compression of shells of a width of some microns) have at present been considered in detail in studies devoted to a pulse thermonuclear synthesis (for example, [8–10]), from which it follows that the process corresponds with sufficient accuracy to the compression of a gas which is completely ionized at the initial moment. In experiments with more massive shells (of the order of 100 m and more), the velocities attained in practice do not exceed 5–20 km/sec [1]. At such velocities, the energy densities contained in the shock wave detaching from the shell may turn out to be insufficient for complete ionization of the gas which has been compressed, and this must have an effect on its further compression and heating. The present study considers precisely these regimes of compression of gas-filled targets. The studies were carried out by the numerical method. For comparison, the studies were made in a number of cases both with allowance for ionization of the gas which was being compressed, and also on the assumption that the gas was already completely ionized at the initial moment.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 155–160, January–February, 1935.In conclusion the author expresses his appreciation to S. I. Anisimov for his constant attention to this study, and to M. F. Ivanov for his help in carrying out the calculations.     

Effect of leading radiation on the stability of strong shock waves in gases with an arbitrary equation of state

The effect of leading radiation on the stability of a strong shock wave in an ideal gas with an arbitrary equation of state is investigated. The ionization ahead of and behind the shock front and the radiation are assumed to be in equilibrium. The investigation is carried out in the linear approximation with respect to amplitude for disturbances with a wavelength much greater than the width of the relaxation zones ahead of and behind the shock. The conditions under which the leading radiation has a destabilizing effect on the shock wave are established. It is shown, in particular, that neutrally stable shock waves become unstable. The conditions under which the onset of instability is of the threshold type with respect to the radiation intensity are determined. It is found that the radiation also has a destabilizing effect on stable shock waves, including shock waves in a perfect gas. However, in this case instability can develop only when the disturbances have a wavelength comparable with the width of the relaxation zone. A simple physical mechanism of the onset of instability under the influence of leading radiation is proposed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 125–133, May–June, 1990.The authors are grateful to A. G. Kulikovskii and A. A. Barmin for their constant interest and useful discussions.     

Ionization and nonequilibrium radiation of air behind strong shock waves

It is shown that at high velocities of shock waves (V 9.5 km/sec) an important factor influencing the rate of ionization is the depletion of the number of excited states of the atoms through de-excitation. In the case of low pressures (p 1 torr) and for a bounded and optically transparent region of gas heated by the shock wave (for example, for the motion of gas in a shock tube or in a shock layer near a blunt body), the effective ionization rate k_f depends on the pressure [1], which leads to violation of the law of binary similarity which holds under these conditions without allowance for de-excitation. On leaving the relaxation zone, the gas arrives at a stationary state with constant parameters differing from those in thermodynamic equilibrium. The electron concentration and also the radiation intensity in the continuum and the lines are lower than the values for thermodynamic equilibrium. These considerations explain the results of known experiments and some new experiments on ionization and radiation of air behind a travelling shock wave.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 105–112, January–February, 1980.     

Low-frequency oscillations of the plasma of a circular discharge in crossed electric and magnetic fields

Low-frequency oscillations in a circular discharge plasma are studied experimentally. Values of the magnetic field corresponding to the generation and collapse of ionization oscillations are determined. An analysis of plasma stability in the absence of ionization equilibrium is conducted. Agreement is noted between the theoretical and experimental results.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 171–173, May–June, 1972.