Calculations for a cylindrical electric arc with allowance for energy transfer by radiation with the hydrogen at a pressure of 100 atm

An approximate method is described for the consideration of energy transfer by radiation during the utilization of real properties of a gas (in particular, the frequency-dependent absorption coefficient under conditions of local thermal equilibrium). With increasing pressure, it becomes necessary to take self-absorption into account over almost the entire frequency spectrum.Calculations are carried out for a wall-stabilized cylindrical electric arc in hydrogen as an example for a pressure of 100 atm and channel radii of 0.3, 1, and 3 cm at values of current strength up to the order of 10 A. The strong effect of radiation on the current-voltage characteristic of the arc, the gas temperature, and the nature of its distribution over the arc radius is demonstrated.The process of energy transfer by radiation plays a significant and sometimes predominant role in the thermal balance of electric arcs with high current strengths [1–9]. Calculations have been performed for cylindrical arcs in atmospheres of argon and hydrogen [5, 7] with allowance for energy transfer by radiation and for atmospheric pressure in which case the gas is essentially transparent to radiation. Approximate estimates were obtained for the self-absorbed portion of the radiation.The role played by radiation increases with increasing current strength, arc radius, and pressure, while self-absorption in this process extends over an increasingly large region of the spectrum. Hence, calculations must be carried out for the arc if conditions are such that the gas in the arc does not transmit radiation.In [10–13], an approximate method was developed for taking into account energy transfer by radiation in the presence of intense selfabsorption as applied to heat transfer problems under conditions of local thermal equilibrium with allowance for the variation of the absorption coefficient as a function of the frequency. The conditions for local thermal equilibrium in an arc passing through an argon or hydrogen atmosphere are fulfilled for pressures greater than atmospheric pressure and for current strengths greater than 10 A [14–16], The results of [10–12] were used as the foundation for calculations based on an electric arc in argon at atmospheric pressure, under which conditions, self-absorption affects only the transitions to the ground state. The part played by radiation in the heat transfer process is smaller than the part played in the energy transfer by conduction. Calculations confirmed the results of [5, 7].The role of energy transfer by radiation in the energy balance of the arc increases with increasing pressure, while in turn, the role of the continuous spectrum increases for the radiation. The results of calculations performed for a wall-stabilized arc burning in an atmosphere of hydrogen at a pressure of 100 atm are given in the present paper. In this case, almost the entire energy supply is lost by radiation. The approximate method of accounting for energy transfer by radiation is demonstrated by an example.Notation and T gas density and temperature, respectively - u velocity - c_p heat capacity of the gas at constant pressure - coefficient of thermal conductivity - coefficient of electrical conductivity - x and r cylindrical coordinates - r₀ channel radius - I current strength - E electric field strength - u ° equilibrium value of radiation energy density - u value of radiation energy density - radiation frequency - divergence of energy flux density transported by radiation - k absorption coefficient - c speed of light - _i emissivity of the i-th region of the spectrum     

Time studies of ionization processes

Summary Measurements of the temporal growth of ionization between parallel plane electrodes in hydrogen have been made. The results show that for low values ( 40 V/cm mm Hg) of the ratio of electric fieldE to gas pressurep the growth times can be short ( 1s for over-voltages V 1 %) while at values ofE/p 300 V/cm mm Hg the times are of the order of milli seconds withV 5%. Comparison of the experimental data with Davidson's mathematical analysis of current growth based upon the action of primary and secondary ionization processes shows that the relative significance of the possible secondary processes changes asE/p is altered. For the low values ofE/p, the predominant secondary process contributing to the growth was found to be photoelectric emission from the cathode, but with increasing values ofE/p the role of positive ion interaction with the cathode becomes increasingly important. No single secondary process was exclusively operating in any of the conditions examined.     

Hypersonic flow structure in a large-scale multi-diaphragm shock tube

The results of an experimental and theoretical study of the structure of the shock wave and the gas flow behind it are presented, together with data on the duration of the high-temperature working flows, the contact zones and the regions of uniform cold-flow parameters in the large (channel diameter 0.5 m, length 200 m, gas tank diameter 3 m, length 23 m) interchangeable-nozzle shock tube of the Central Scientific Research Institute of Mechanical Engineering.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 158–165, September–October, 1993.     

Propagation of small disturbances in a relaxing and radiating diatomic gas in vibrational nonequilibrium

In radiation gasdynamical problems, where the primary object of investigation is a moving gas, the influence of radiation on the parameters of the gas flow is usually neglected to avoid overcomplication of the problem. The growth and behavior of initial disturbances in a scattering, radiating, absorbing, viscous, heat-conducting gas characterized by local thermodynamic equilibrium has been investigated previously [1]. However, for low pressures (p10^–4 to 10^–3 technical atm) and fairly high temperatures of the active molecular degrees of freedom (T10³ to 3·10³K) the distribution of the molecules among the vibrational levels can differ markedly from the equilibrium distribution due to the or der-of-magnitude closeness of the vibrational relaxation time _c associated with collisions and the radiative deactivation time * of excited molecules [2, 3]. We now analyze normal modes in a vibrationally nonequilibrium medium with allowance for radiation scattering in the vibrational-rotational band. We formulate a dispersion relation and discuss some limiting cases.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 168–171, September–October, 1976.The author is grateful to V. I. Kruglov, Yu. V. Khodyko, and M. A. El'yashevich for their interest and discussions.     

On the electrical discharge in d.c. and high frequency fields simultaneously

Summary When a d.c. and a h.f. field are perpendicularly superposed in a electrical discharge (p 10–10^–4 mm Hg), three types of discharge can exist, classified from the standpoint of d.c. conduction: (1) d.c. glow type, d.c.-dominant discharge with additional ionization by h.f. field; (2) space chargelimited type, the same as the conduction in the floating double probe in a plasma produced by h.f. field; (3) an intermediate stage between the first and second types, herein referred to as transition type. According to our analysis of the transition type at low pressure, the value of in high electric fields can be deduced from the measurement.     

MHD-Effects Due to the Hypersonic Motion of a Cylindrical Body in the Magnetosphere of a Planet for Mutually Perpendicular Orientations of the Generatrix and Magnetic Field

MHD-effects associated with the movement of a weakly conducting cylindrical body in a planetary atmosphere are analyzed numerically. The longitudinal axis of the body is perpendicular to the direction of motion and the field lines of the planetary magnetic field. In the calculations we used data similar to those for the collision of the Shoemaker-Levy 9 comet with Jupiter. The simulation is developed for two atmospheric levels: H100 km (magnetic pressure number R _H1) and H280 km (R _H1). It is shown that the maximum strength of the induced magnetic field is 2–3 orders of magnitude greater than the planetary magnetic field. For small R _H, analytical expressions giving a fairly reliable estimate for the field strength in the shock-compressed space ahead of the body are obtained.     

The near field behavior of turbulent gas jets in a long confinement

The present investigation reports on the near field behavior of gas jets in a long confinement and points out the differences between this type of jet flow and those of free jets and jets in a short confinement.The jet, with a diameter of 8.73 mm, is aligned concentrically with a tube of 125 mm diameter; thus giving a confinement area ratio of 205. The arrangement forms part of the test section of an open-jet wind tunnel and this gives a confinement length-to-jet diameter ratio of 1,700. Experiments are carried out with carbon dioxide, air and helium/air jets at different jet velocities. Mean velocity and turbulence measurements are made of the jet near field using a one-color, one-component laser doppler velocimeter operating in the forward scatter mode. In addition, the turbulent shear field of an air jet is examined in more detail using hot-wire anemometers.In view of the long confinement, the presence of the jet is not being felt immediately at the tunnel exit. Consequently, the air column inside the tunnel is first compressed by the jet and then slowly pushed out of the tunnel. This behavior causes the jet to spread rapidly and to decay quickly. As a result, an equilibrium turbulence field is established in the first two diameters of the jet. This equilibrium field bears striking similarity to that found in self-preserving, turbulent free jets and jets in short confinement and is independent of jet fluid densities and velocities. In terms of these characteristics, the near field of jets in a long confinement is very different from that found in free jets and jets in short confinements.     

Nonmagnetic containment of a dense plasma

A study is made of the possibility of confining a thermonuclear plasma with temperature T 10⁴ eV and density n 10¹⁸ cm^-3, not by magnetic field pressure, but by hard walls of a chamber (nonmagnetic containment). This method of plasma containment has some specific features: the occurrence of plasma flow, formation of a dense layer at the wall, increased importance of radiative losses from the plasma, and more. A numerical solution of the plasma-transport equations is used to investigate the influence of these features on the energy lifetime of the plasma. The results indicate that the additional energy losses by the plasma are not catastrophically large, and, in principle, nonmagnetic containment of a dense plasma is possible.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 3–13, November–December, 1974.     

A Numerical Study of the Critical Gas Saturation in a Porous Medium

We use porenetwork simulations to study the dependence of the critical gas saturation in solutiongas drive processes on the geometric parameters of the porous medium. We show that for a variety of growth regimes (including global and local percolation, instantaneous and sequential nucleation, and masstransfer driven processes), the critical gas saturation, Sgc, follows a powerlaw scaling with the final nucleation fraction (fraction of sites activated), fq. For 3D processes, this relation reads Sgcfq0.16, indicating a sensitive dependence of Sgc to fq at very small values of fq.     

Cone in a supersonic flow near a surface with a turbulent boundary layer

The published information about the interaction of incident shocks and a turbulent boundary layer relate to cases of a thin boundary layer ( 1–3 mm) on a flat surface. The present study relates to supersonic flow with Mach number M = 3 and stagnation pressure p₀=1.2 MPa past cones near a surface with a thick boundary layer formed on a plate abutting the lower edge of a plane nozzle.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 177–180, July–August, 1991.     

Calculation of transverse flow of a stream of rarefied gas past a plate

We give the results of a calculation by the Monte Carlo method of the coefficient of resistance and the field of flow past a plate placed perpendicular to a stream of rarefied gas at Mach numbers M = 2–20 and Reynolds numbers Re₀27. The calculations were carried out for two forms of the law governing the variation of the coefficient of viscosity as a function of temperature (T, T). The results are compared with available calculated and experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 106–112, July–August, 1976.     

On the Viscous Drag of a Plate with Spherical Recesses

The drag of flat plates with spherical recesses was measured using the direct balance method. The experiments were run in a low-turbulence wind tunnel with a cross-section measuring 1000 × 1000 mm and a length of 400 mm. Three surfaces with recesses 7.0, 3.9, and 1.3 mm in diameter and 0.5, 0.3, and 0.2 mm deep, respectively, were tested. It is shown that on the Reynolds and Mach number ranges Re= (3–9)· 10⁶ and M 0.3 the spherical recesses add to the drag of a flat plate in turbulent flow. The recesses have almost no effect on the location of laminar-turbulent transition, which occurs at Re_t 3· 10⁶.     

The motion of explosion products behind the front of a detonation wave

The velocity of the explosion products behind the detonation wavefront in a 50/50 TNT-hexogen explosive was measured by an electromagnetic method.The experimental data on the mass velocity profile behind the wavefront in charges of different lengths, and the results of measurements of the motion of the backward rarefaction waves can be well described if in the mass velocity-time curves one isolates a stationary zone of 0.1 sec and regards the rest of the motion as self-similar.The experimentally observed sharp drop of mass velocity behind the wavefront indicates that the isentropic exponent of the explosion products increases upon expansion.The observed data on the distribution of mass velocities were used to calculate the isentrope of the explosion products in the pressure range 100–250 000 atm.     

Gas flow in cylindrical capillaries under intermediate conditions

At present, there are sufficient solutions of the problem of free-molecular gas flow through a short cylindrical channel, for example, [1–3]. In intermediate flow conditions, for Knudsen number Kn 1, solutions have been obtained for the limiting cases: an infinitely long channel [4] and a channel of zero length (an aperture) [5]. However, no solution is known for short channels for Kn 1. The present work reports a calculation by the Monte Carlo method of the macroscopic characteristics of the gas flow through a short cylindrical channel (for various length—radius ratios), taking into account intermolecular collisions.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 187–190, January–February, 1977.     

Reduction of gas breakdown voltage with pulsed ionizing radiation

An algorithm is described for computer calculation of the dynamic breakdown voltage of a gas gap affected by a spatially uniform pulse of ionizing radiation. The algorithm is based on numerical integration of a system of nonlinear equations with integral boundary conditions. The program is used to calculate the breakdown voltage of an air gap affected by a bell-shaped ionizing pulse. It is shown that the relative reduction in breakdown voltage can amount to tens of percent for a radiation exposure dose rate P₀ 10⁸ R/sec.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 52–60, November–December, 1973.     

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.     

Bouncing and Coalescence of Bubble Pairs Rising at High Reynolds Number in Pure Water or Aqueous Surfactant Solutions

The encounter of bubble pairs of O(1 mm) in both pure water and aqueous surfactant solutions was studied experimentally. In pure water, two equally sized bubbles were found to coalesce if the Weber number, W = V² R/, based on the velocity of approach, V, was below a critical value, W_cr = 0.18, where and are the density and surface tension of the liquid respectively and R the equivalent radius of the bubbles. After coalescence bubbles perform volume and shape oscillations.When W_cr is exceeded, bubbles bounce. After bouncing, bubbles can either coalesce or separate without coalescing. This was found to depend on the Weber number, based on the rise velocity U, We = U² R/. If this number was below a critical value, bubbles coalesced after bouncing. The relative motion of the bubbles was found to be damped out by acoustic damping due to surface oscillations rather then by viscosity.If We was above a critical value, which was close to that for path instability of a single bubble (We = 3.3), the bubbles separated after bouncing. This is probably caused by shedding of vortices which dominate the relative motion of the bubbles. This mechanism may cause bubbles in bubbly flows not aggregating in horizontal planes, as was found in calculations based on potential flow theory. For modelling bubbly flows it will therefore be essential to incorporate the influence of vorticity.When surfactants are added to the water it was found that bubbles are prevented to coalesce above a critical concentration, which is nearly identical to that of single rising bubbles. Above this critical concentration, bubbles behave as rigid spheres and trajectories cannot be predicted by potential flow theory.     

Jet characteristics in confined swirling flow

Jets in confined swirling flow are investigated in a facility where the swirling flow in the tube is produced by a vane-type swirler. The jet is located centrally in the swirler, and the diameter ratio of the tube to the jet is 14. Both the jet and the swirling flow are fully turbulent. Results show that the confined jet is highly dissipative in nature. Consequently, the flow in the tube does not resemble a free jet with axial pressure gradient. The presence of swirl increases the rate of dissipation and the jet decays even faster. A fairly isotropic turbulence field is observed in the confined swirling flow. However, the introduction of the jet does not significantly affect this behavior and near isotropy of the turbulence field is again observed at 30 jet diameters downstream.     

Channel flow of an anisotropically conducting medium in a zone of entry into a magnetic field

A considerable number of papers are devoted to the problem of the deformation of a plane flow of a conducting liquid moving through a channel |x| < , 0 y h=const in a zone of entry into a magnetic field B=(0, 0, B. (x)), where (x) is the Heaviside unit function((x)=0 for x < 0 and (x)=i for x < 0). Apparently the first paper in this direction was that of Shercliff [1, 2] in which the asymptotic (for x .o- )profile of a perturbed velocity was. determined for a flow of an isotropic conducting liquid in a channel with nonconducting walls. The flow considered by Shemliff takes place in magnetohydrodynarnic flowmeters. Complete calculation of the perturbed flow of an isotropie conducting liquid in the channel of a magnetohydrodynamic generator is carried out in [3]. Asymptotic velocity profiles in the channel of a magnetohydrodynamic generator, with ideally segmented electrodes and the flow of an anisotropically conducting medium along them, were found in [4]. General formulas for the calculation of the asymptotic velocity profile, from the known distribution of the perturbing forces along the channel, are presented in [5]. In [6, 7] the Green function is proposed for the solution of the equation for the stream function of the perturbed flow. Finally, in [8], the solution for the perturbed flow of an anisotropically conducting liquid in a channel with continuous electrodes is described by means of the Green function, and the asymptotic profiles of the velocity are calculated.In this paper the flow of anauisotropically conducting liquid is determined in a channel with ideally segmented electrodes. The solution is set up with the aid of the Fourier method. The resulting series, in which the slowly converging part can be related to the asymptotic profile [4] calculated from the solution of an ordinary differential equation, make it possible to determine the velocity field rapidly. A detailed deformation pattern of the velocity profile is set up. Certain general properties of the flow in a zone of entry into a magnetic field are noted; with the aid of these it is possible to discover the error in the calculations [8].     

On scattering of a gas behind deflagration waves propelled by powerful radiation fluxes

Two self-similar problems about plane nonstationary gas scattering in a vacuum behind a deflagration wave for which the conservation laws are satisfied are considered. The energy flux density is considered to vary according to a power law. In the first problem the gas is transparent and scattered adiabatically. The solution is found analytically. It is shown that the Jouguet condition is conserved for a flux growing with time, while such a condition is not satisfied for a decreasing flux, and the parameters on the wave depend on the flow behind it. In the second problem, the gas absorbs radiation, where the absorption coefficient varies from infinitely large to infinitely small at some transparency temperature. The motion is isothermal. A definite fraction of the incident energy, corresponding to the effective optical thickness 0.25, is extracted in the gas.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 41–48, May–June, 1973.The author is grateful to V. I. Bergel'son for the mentioned assistance, and to A. A. Nikol'skii and Yu. P. Raizer for interest in the research.