Parameters of streamer breakdown in xenon

It is known from experiments [1–3] that the velocity of streamers, induced in the center of the interelectrode gap and propagating to the electrodes under conditions when the streamer length is comparable with the distance between the electrodes, increases linearly as the streamer length increases. This relationship is in qualitative agreement with theory [4], Nevertheless, the velocity of streamers starting from the electrodes and propagating in a long interelectrode gap remains practically constant during the whole propagation process [5, 6], In the case of short gaps (2–5 cm), constancy of the velocity is observed during the stage of the process when the length of the streamer is much less (20%) than the length of the gap [7], Since the electric field at its end controls the streamer propagation, the constancy of the streamer velocity indicates that the controlling field is constant under these conditions. A number of theoretical models were proposed in [8–13] which describe uniformly moving anode- and cathode-directed streamers (henceforth called anode and cathode streamers). Comparison of experimental data with the corresponding theoretical model enables one to determine the streamer parameters: the electric field, the charged-particle density, the current density, the channel radius, etc. In the case of an anode streamer in Xe an attempt at such a comparison was made, in particular, in [6]. However, the lack of reliable data on the value of the drift velocity and the diffusion coefficient of electrons in Xe for E/p (10² – 10³) V/cm · mm Hg allowed only rough estimates to be made. In this paper a numerical calculation is made of the drift velocity, the diffusion coefficient of electrons in Xe, and the rate of excitation of Xe atoms in the resonance level in the range of values of E/p (10¹–10³) V cm · mm Hg, and the volt-ampere characteristic of the breakdown is measured under conditions described in [6] (p₀=300 mm Hg and E 10⁴–10⁵ V/cm). Using these results, the formulas for the velocity of anode [12] and cathode [13] streamers, and experimental data [6], the parameters of the streamers studied in [6] are determined.Translated from Zhurnal Prikladnoi Meknaniki i Tekhmcheskoi Fiziki, No. 3, pp. 6–11, May–June, 1976.The authors thank A. T. Rakhimov and A. N. Starostin for useful discussions, and A. V. Markov for help with the experiments.     

The flow structure near the windward side of V-shaped wings with an attached shock wave on the leading edges

The results of a numerical calculation of a symmetric flow of supersonic gas with the Mach number M=3 past the windward side of V-shaped wings with an opening angle =40° and apex angles =30, 45, and 90° are given. The possibility of the ascent of one or two Ferri points from the break point of the transverse contour of the wing is discovered and explained. It is shown that conical flow near wings of finite length need not exist in flow regimes corresponding to angles of attack at which a Ferri point ascends, while at angles of attack smaller and larger than a certain interval, conical flow will exist. The investigation is conducted by means of a numerical method of stabilization with an artificial viscosity. The longitudinal coordinate, relative to which the steady system of equations is hyperbolic, played the part of the time variable, usual for methods of stabilization. The numerical method constructed using the scheme of [1] is described in [2] and was successfully applied to the calculation of different regimes of supersonic flow past conical wings with supersonic leading edges [2–6]. In. the present investigation the calculation algorithm of [2] is modified and makes it possible to realize motion with respect to the parameter a, this being particularly important for the stabilization of the solution in the calculation of flow regimes for which regions with a total velocity Mach number close to unity arise in the flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 122–131, January–February, 1986.     

Numerical investigation of the growth of glowing discharges in two-dimensional geometry

It is known that a breakdown in gases can take place in two fundamental ways: by diffusion (the Townsend breakdown) or by forming a narrow current channel (the streamer breakdown). At present there are no reliable criteria for one or another of these mechanisms to occur. It is also an open question as far as the pressure region p < 10 mm Hg [I] is concerned. Even in the case of special preionization it is not always possible to avoid the streamer stage breakdown. It is obvious that the fundamental cause of a streamer breakdown is related to higher intensity of the electric field around the localized zone of higher conductivity [2]. In [3] the superiority was shown of using numerical methods in the analysis of an axisymmetric cathode directed streamer between two flat electrodes in nitrogen. In the present article the results are described of computations carried out to find out whether a mechanism is feasible for fusing the discharge at any early stage of ignition for the geometry of a flat electrode plane, which is the most favorable to an anode-oriented streamer. This effect was investigated within the framework of a nonstationary system of three equations in which the ionization processes, the recombinations in the balance of charged particles as well as the effect if space charge on the electric-field distribution have been taken into account [4], One has ignored the diffusion, which is also favorable to the streamer breakdown.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 49–54, September–October, 1978.The authors would like to express their thanks to A. A. Vedenov, A. P. Napartovich, and A. N. Starostin for their unceasing interest in this work and useful discussions.     

Breakdown voltage calculation for air in uniform fields

Summary Expressions are derived for the determination of the space-charge field in front of an avalanche, for the widening of the avalanche's head due to electrostatic repulsion and for the minimum breakdown voltage of uniform gaps. In principle, this last condition is based on a modification of the criterion for streamer advance developed by Raether, Meek et. al. An attempt is made to consider the avalanche as an electric dipole oriented in a direction parallel to the applied field and use is made of the radial instead of the axial field of the avalanche's head.     

Estimate of the amplitudes of the fields created by an unsteady gamma source

It is known [1–4] that an unsteady gamma source gives rise to an electromagnetic field in the surrounding space. Most of the studies of the characteristics of such fields have been performed in the approximation which is linear in the field [1–3]. An exception is [4] in which the slowing down of Compton electrons by the electric field is taken into account. It follows from [1, 2] that the characteristic scale of the fields created close to the source is of the order of 3 · 10⁴ V/m. Although this value is appreciably lower than the value of breakdown fields in air, electric discharges are observed [5] in the vicinity of a gamma source, indicating the presence of substantially larger fields. One effect not taken into account in the latter approximation which could lead to an increase in the field is the increase in electron termperature due to the electric field [6]. On the one hand, this decreases the electron mobility and consequently also the conductivity of the system, On the other hand, it is known that the electron attachment coefficient for electronegative molecules strongly affects the characteristics of electric fields and depends on the electron energy. Therefore, the electron balance equation must take account of the dependence of on the electric field through the electron energy, and this leads to a further change in conductivity. We take account of these effects on the shaping of electric fields in air in the vicinity of the source. It is assumed that electron lifetimes are determined solely by their attachment to molecules. This is a good approximation for air pressures near normal [1–3].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 163–170, July–August, 1976.     

Steady flow around a plane cascade by an ideal gas

The steady separation-free flow around a flat cascade by an ideal gas is discussed. Most of the attention is devoted to blocking regimes with a supersonic velocity in the entire flow and its subsonic component normal to the front of the cascade. A directing action of the cascade (the direction of the velocity and the Mach number of the advancing flow turn out to be related) is exhibited in these regimes which is a consequence of an independence of the flow in front of the cascade of the conditions behind it [1–5]. The most widespread method of their calculation [3, 4, 6] is based on the method of characteristics with establishment of the flow outside the cascade in a timelike coordinate. Although the integrated conservation laws also permit finding the parameters at infinity, the numerical construction of as long-range fields as desired with periodic sequences of attenuating discontinuities is practically impossible. The approximation of nonlinear acoustics (ANA) [7, 8] is justified here, as it is very effective in such problems [8–12]. A combination of ANA, the integrated conservation laws, and establishment in a calculation according to [13, 14] with isolation of the discontinuities has been realized in [5] for the construction of a solution on the entrance section of a cascade and everywhere in front of it. Below the method of [5] is extended to the entire flow and simplified even more. The flow on the entrance section of the cascade is, just as in [3], found in the approximation of a simple wave, in the rest of it and in a finite strip behind it-the flow is found with the help of the straight-through version of the scheme of [13, 14], and in the long-range field-in the ANA. A simpler version is proposed. In it ANA is applied outside the cascade and the linear theory is applied inside the cascade. Examples of the calculations are given. Similarity laws are formulated for all the regimes of streamline flow.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 35–43, November–December, 1984.     

Stress Distribution in a Slip Trace of Deformed Ni3Ge Single Crystals

The shearstress distribution produced by distortion of Ni₃Ge single crystals under compression is studied. The evolution of the dislocation structure during deformation of Ni₃Ge single crystals of various orientations ([2¯34], [1¯11]$, [1¯39], and [001]) at T = 77, 293, 523, 673, and 873 K is analyzed. It was found that, up to failure strains, the dislocation structure is characterized by a uniform dislocation distribution. Regardless of the strainaxis orientation, the linear relation = f(^0.5) is valid for all the test temperatures except for T = 77 K. The deviation from the linear relation at T = 77 K is due to the suppressed thermally activated slip of dislocations in nonuniformstrain fragments at the specimen edges. In these fragments, the shear stresses are substantially reduced, and hence, the stresses produced by the dislocation cluster retard the development of slip in this trace.     

Application of the integral diffusion equations to the investigation of turbulent transport

In recent years there have appeared several experimental studies [1–5] which have shown that there are cases of turbulent flow with an asymmetric distribution of the flow velocity and in which at the point where the velocity derivative is zero the turbulent shear stress is not zero. This raises the question of the connection of the Reynolds stress tensor with the characteristics of the average flow. The relationships used in the usual mixing length theory connect the shear stress with the local value of the flow velocity derivative and are not consistent with the experimental results mentioned above. These relationships are based on the assumption that the mixing length is small in comparison with the characteristic length of the flow. Experiment shows that this assumption is not justified [6].Thus, turbulent diffusion refers to the case of diffusion with a large mean free path. In addition to the concept of gradient diffusion, there is also the concept of bulk convection or integral diffusion [10], which means a transfer mechanism in which the shear stress is not expressed in terms of the velocity gradient. The generalization of mixing length theory proposed in [11–14] is based on the very simple kinetic equation which was used for the examination of turbulent transfer problems in [8] and which is encountered in the treatment of transport problems in gases, neutron diffusion, and radiative energy transfer.The proposed generalization of mixing length theory employs an analogy with the indicated processes and permits the derivation of formulas which are valid for large mean free paths. In the case of small mean free paths the obtained relationships lead to the relationships for diffusion in a continuous medium and, in particular, to the relationships of the Prandtl mixing length theory. The integral diffusion model is a phenomenological semiempirical theory in which empirical constants and several hypotheses common in mixing length theory are used. A very general analysis of the expression for the shear stress leads to the conclusion that if the flow is asymmetric over a distance comparable with the mixing length the points at which the velocity derivative and the turbulent shear stress are zero do not coincide [12]. Hence, it is to be hoped that the integral diffusion model will allow treatment of the above questions, which cause difficulty in the case of ordinary mixing length theory. Incompressible turbulent flow is considered.     

On the theory of stationary velocity of propagation of an exothermic reaction front in a condensed medium

It has been demonstrated experimentally that in the combustion of many explosives and powders in the condensed phase (k-phase) an exothermic chemical reaction occurs. Although the heat release in the k-phase is usually small in comparison with the calorific value, it may play an important role in the multistage reaction in the combustion zone.Analysis of the heat balance of the k-phase reveals that in a number of cases heating of the substance before gasification is primarily due to self-heating. According to the thermocouple measurements made by A. A. Zenin, the heat release in the k-phase during combustion of nitroglycerine N powder is more than 80% of the total quantity of heat in the heated layer of the k-phase (pressure 50 atm). This makes it possible to speak of the propagation of the exothermic reaction front in a condensed medium as the first stage in the combustion of condensed systems. Cases are also known where the propagation of the reaction front is maintained only by self-heating (flameless combustion [1]), and there are cases when such propagation is not accompanied by gasification (combustion of thermites, sometimes the polymerization process). Theoretical investigations of stationary propagation of a reaction front in a condensed medium were made in [2–6]. We note that this problem is also of interest in relation to the study of various nonstationary phenomena associated with the combustion of powders [7–9]. One of the principal theoretical problems is the derivation of a formula for the velocity of propagation of the reaction front in the k-phase. The Zel'dovich-Frank-Kamenetskii method [10] was used in [2–5] in the solution of this problem.This paper is an investigation of the applicability of the Zel'dovich-Frank-Kamenetskii method to the case of propagation of a zero-order reaction front in the k phase. A method is proposed for deriving a formula for the propagation velocity of the front leading in the case of a zero-order reaction to a formula identical to that obtained using the Zel'dovich-Frank-Kamenetskii method, and this method is then used to derive a formula for the propagation velocity of a first-order reaction front in the k-phase. The upper and lower limits of the velocity given by this formula are investigated.     

A collisionless thermal wave in a plasma

Experiments are described on the collisionless propagation of heat in a plasma along the magnetic field. Thermal waves can be propagated in a medium whose thermal conductivity is a power function of the temperature. In a collisionless plasma, where the mean free path of particles is much greater than all typical lengths, in particular the length of the equipment, the heat must be propagated by a different method. Experiments to study this phenomenon showed that heat is propagated along the magnetic field with velocity exceeding that of ion-acoustic velocity (I. A. Velocity), and that the spatial width of the thermal disturbance is much less than the mean free path. Heat is propagated because hot electrons are replaced by cold [1]. Noise was observed experimentally in the vicinity of the ion plasma frequency and an estimate of its intensity was obtained. Theoretical discussion showed that the I. A. Velocity instability which develops at the wave front leads to collective friction of the cold electrons with the ions and makes it possible to find the effective collision frequency. It was also shown theoretically that, in accordance with experiment, noise is localized near _pi, and the level agrees with that obtained experimentally. The phenomenon can be pictured as follows: hot electrons expanding into the region occupied by cold electrons and ions create an electric field. Cold electrons, accelerating in this field, oscillate the I. A. Velocity. This instability leads to heating of the electrons and the appearance of collective friction which forms the heat front.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 51–59, January–February, 1971.     

Nonexpansive Periodic Operators in l1 with Application to Superhigh-Frequency Oscillations in a Discontinuous Dynamical System with Time Delay

We prove that the iterates of certain periodic nonexpansive operators in l₁ uniformly converge to zero in l norm. As a by-product we show that, for any solution x(t) of the equation x(t)= –sign(x(t-1))f(x()), t0, x|_[–1,0]C[–1,0] where f:(–1, 1) is locally Lipschitz, the number of zeros of x(t) on any unit interval becomes finite after a period of time, with the single exception of the case f(0)=0 and x(t)0.     

Computer solution of a kinetic equation for electrons

Physical and mathematical approaches are presented for the behavior of a weakly ionized plasma in a thermoelectronic converter. Numerical solutions are obtained by computer methods. The distribution function for the electrons is examined in series form for a Boltzmann kinetic equation subject to boundary conditions; the coefficients of the series are deduced via moment equations. The electric field is incorporated in the quasineutrality approximation. An exampIe envisaging only electron-atom collisions is presented. Consider two unbounded planar electrodes (cathode and anode) heated to different temperatures, between which lies a weakly ionized plasma subject to a potential difference. From the electrodes flow ion and electron fluxes into the plasma, where ionization and recombination can occur. The quantities to be determined are the current, the potential distribution, the temperature, and the charge density. This problem occurs for a cesium converter in the arc mode. If the volume ionization can be neglected, the processes are ctosely described by the diffusion theory [1], but it is desirable to have more detailed information about the distribution function for the electrons when ionization, excitation, and recombination become important. The diffusion theory is then replaced by a Boltzmann kinetic equation, but this greatly increases the computational difficulties. The present approach envisages the use of computers.The method of solution is basically as follows. The electron-distribution function in the kinetic equation is replaced by a series in some complete set of functions of the velocity coordinates. There is a second system of independent functions; these are mukiplied by the two parts of the kinetic equation, whereupon integration over velocity space gives differential equations of first order in the spatial coordinates for the parameters of the series for the distribution function. These are balance equations or equations for the moments with respect to the above system of independent functions (usuaIly these are polynomials in the velocity coordinates).We select from this system a subsystem of functions, which we multiply by the boundary conditions for the kinetic equation and integrate over the region where they are given (i.e., with respect to the velocity of the electrons leaving the electrode). This gives the boundary conditions for the differential equations for the moments. Varieties of this method are to be seen in Grad's [2] and Weitzsch's [3] methods in gas dynamics, or the method of spherical harmonics [4, 8] in neutron physics; see [6] for review. The method of expansion used here differs from Grad's method in that I use functions of the energy and spherical angles in velocity space, whereas Grad used functions of the cartesian coordinates of the velocity. Moreover, the zero-th-approximation function is taken as the isotropic exp(--mu a/2kT) instead of Grad's anisotropic exp[--m(v-v0)/2kT] (m is electron mass, T is temperature, k is Boltzmann's constant, v is particle velocity, and v0 is the mean particle velocity). These differences are introduced for the following reasons. The electrons in a weakly ionized plasma collide frequently with neutral atoms, so there is more rapid relaxation in momentum than in energy [7], and the distribution function differs little from isotropic. On the other hand, a principal purpose here is to examine the inelastic processes of ionization and excitation, and the major feature is the energy distribution of the electrons without reference to the orientation of the momentum vector. Hence we need take only the first two terms in the expansion with respect to the spherical coordinate ~=vx/U (the Pt approximation in the method of spherical harmonics).We also take account of the electric field set up by the space charge.Let d be the distance between cathode and anode, V be the potential differences, r the Oebye radius, n+ and n. the concentrations of ions and electrons, and q the charge on an electron. As in [1], we consider the case where the main change in the electrical potential U occurs near the electrodes in regions of scale r, while the rest of the region obeys the quasineutrality condition n₊ - n_ n₊ (Fig. 1). The size of the space-charge regions is less than the mean free path for any of the bulk processes, so no scattering occurs in these regions, while their presence is allowed for by the additional potential barriers U t (cathode) and U 2-V (anode), Both physical conditions are obeyed for r sufficiently small.We also assume that the potential changes monotonically in the space-charge regions, as in Fig. 1, where 1 is the cathode, 2 is the anode, a are the space-charge regions, and 4 is the quasineutral plasma.I am indebted to G. E. Pikus for direction and assistance, and to L. A. Oganesyan for assistance in programming the problem for the computer,     

Solution of the temperature jump (Knudsen layer flow) and linear heat-transfer problems for two parallel plates in a rarefied gas

The Monte Carlo method [1, 2] is used to solve the linearized Boltzmann equation for the problem of heat transfer between parallel plates with a wall temperature jump (Knudsen layer flow). The linear Couette problem can be separated into two problems: the problem of pure shear and the problem of heat transfer between two parallel plates. The Knudsen layer problem is also linear [3] and, like the Couette problem, can be separated into the velocity slip and temperature jump problems. The problems of pure shear and velocity slip have been examined in [2].The temperature jump problem was examined in [4] for a model Boltzmann equation. For the linearized Boltzmann equation the problems noted above have been solved either by expanding the distribution function in orthogonal polynomials [5–7], which yields satisfactory results for small Knudsen numbers, or by the method of moments, with an approximation for the distribution function selected from physical considerations in the form of polynomials [8–10]. The solution presented below does not require any assumptions on the form of the distribution function.The concrete calculations were made for a molecular model that we call the Maxwell sphere model. It is assumed that the molecules collide like hard elastic spheres whose sections are inversely proportional to the relative velocity of the colliding molecules. A gas of these molecules is close to Maxwellian or to a gas consisting of pseudo-Maxwell molecules [3].     

Exponential Decay for Soft Potentials near Maxwellian

We consider both soft potentials with angular cutoff and Landau collision kernels in the Boltzmann theory inside a periodic box. We prove that any smooth perturbation near a given Maxwellian approaches zero at the rate of for some λ > 0 and 0 < p < 1. Our method is based on an unified energy estimate with appropriate exponential velocity weight. Our results extend the classical result Caflisch of [2] to the case of very soft potential and Coulomb interactions, and also improve the recent “almost exponential” decay results by [5, 14].     

Mutual relationship of adsorption processes on the surface of a cathode and the processes taking place in the parts of a heavy-current plasma discharge close to the electrodes

The effect of alkali metal vapor on the work function of the cathode material in various MHD installations has as yet been little studied [1]. Nor has the mutual influence of adsorption processes on the cathode surface and processes taking place in the parts of a plasma discharge close to the electrodes, although this information is extremely vital in order to make a correct determination of the emission characteristics of cathodes in plasma. The manner in which the electrode becomes coated with the plasma material determines the work function of the electrode and thus the discharge current density and cathode potential drop _s. On the other hand, the degree of coverage of the cathode with the adsorbed particles depends substantially on the value of _s. In this paper we shall propose a method of calculating the emission characteristics of cathodes during a heavy-current plasma discharge allowing for the mutual influence of the processes in question. The problem is solved in a one-dimensional setting for an automatic thermionic-emission discharge (discharge of the spotless type).Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 29–32, September–October, 1972.     

Criteria for excitation of a shock wave and its intensity during an explosion in a rarefied gas

The effect of the initial pressure of the surrounding gas on the intensity of the shock wave (SW) formed during the dispersion of material vaporized by a powerful laser pulse is examined. The initial stage of expansion of the plasma generated through the focusing of powerful laser radiation on the surface of a solid material in air was studied experimentally in [1, 2]. The times of formation and the initial radii of the SW were recorded on the photo-scans of the SW front radiation presented in these reports. It is found that at an air pressure below 0.1 mm Hg the recordings of the intrinsic radiation of a flare do not differ from the corresponding recordings in a vacuum. For instance, in [2] a bright shock front was observed at a pressure of 0.18 mm Hg, while at a pressure of 0.1 mm Hg SW radiation was not detected. In [2] the hypothesis was made that at an air pressure below 0.1 mm Hg a SW is not formed and the interaction of the vaporized material with the surrounding gas has a diffusion nature. However, in [1] SW were detected by the Schlieren method at a considerably lower pressure, about 2 · 10^–2 mm Hg. It will be shown below that the sharp decrease observed in the brightness of the radiation of SW fronts generated during laser heating of a solid material in a rarefied gas is explained by the rapid decrease in the maximum SW velocity at a pressure below 0.1 mm Hg. The expansion of the vaporized material at a pressure of the surrounding gas much less than 0.1 mm Hg is also examined.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 48–51, September–October, 1973.     

Electrical conductivity of a partially ionized gas mixture in a magnetic field

A considerable number of papers [1–5] has been devoted to determining the electrical conductivity of a partially ionized gas on the basis of kinetic theory. In so doing, a three-component plasma model (electrons, ions, neutrals) is generally employed. The general expressions for the electrical conductivity of a many-component system are fairly complicated [1], and the calculation of their determinants is most laborious.The case of a N-component gas mixture in which one of the components is partially ionized (N+2-component plasma) is considered below. A series of simplifications in the solution of the initial system of equations allows one to represent the expressions for the electrical conductivity of such a mixture in the same form as for the three-component plasma case, but with certain effective parameter values. The results obtained correspond to the second approximation of Cowling [1.6].     

On the method of indirectly measuring gas and particulate phase velocities in shock induced dusty-gas flows

A method of indirectly measuring the temporally varying velocities of the gas and particulate phases in the nonequilibrium region of a shock wave moving at constant speed in a dusty-gas flow is described, and this method is assessed by using experimental data from shock-induced air flows containing 40-m-diameter glass beads in a dusty-gas shock-tube facility featuring a large horizontal channel (19.7-cm by 7.6-cm in cross-section). Simultaneous measurements of the shock-front speed with time-of-arrival gauges, particle concentration by light extinctiometry and gas-particle mixture density by beta-ray absorption are used in conjunction with two mass conservation laws to obtain the indirect velocity measurements of both phases. A second indirect measurement of the gas-phase velocity is obtained when the gas pressure is simultaneously recorded along with the particle concentration and shock-front speed when used in conjunction with the conservation of mixture momentum. Direct measurements of the particulate-phase velocity by laser-Doppler velocimetry are also presented, as a means of assessing the indirect velocity measurement method.List of symbols a _f frozen speed of sound - D particle diameter - d _f LDV interference fringe spacing - d _m LDV probe-volume diameter - l _m LDV probe-volume length - M _sf frozen shock Mach number - M _se equilibrium shock Mach number - Ñ(D) probability density distribution by number - p pressure - R gas constant - t time - T temperature - S LDV-signal amplitude - v _g gas velocity in laboratory frame of reference - v _p particle velocity in laboratory frame of reference - V _s shock-front velocity - ratio of specific heats of particles and gas - ratio of specific heats of gas - equilibrium specific heats ratio - particle-to-air loading ratio - half-angle between incident laser beams - laser light wavelength - _g gas density - _p particle material density - _g gas concentration - _m mixture concentration - _m ^app apparent mixture concentration - _p particle concentration - particle volume fraction - (D) probability density distribution by volume     

Experimental study of strong shock propagation in a channel

The widespread use of shock tubes in laboratory practice is well known. However, despite existing information [1] about shock-wave velocities of 100 km/sec, experimental data on the size of the shock-heated region behind the shock front are confined to the Mach numbers M = 10 [2]. Theoretical data do not go beyond the limit of this range except for air where calculations were performed up to M = 20 [3, 4]. Behind strong shocks, the effects resulting from viscosity, thermal conductivity, and radiation of the medium should lead to serious deviation of the actual flow from the idealized pattern for uniform motion of a piston in a channel filled with anonviscous, thermally nonconducting, and nonradiating medium. It is therefore practical to make an experimental study of the behavior of density and of the size of the shock-heated region behind a shock front propagating down the channel of a shock tube that is capable of producing velocities up to 8 km/sec.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 23–28, July–August, 1976.     

Relaxation of overdriven detonation waves with finite reaction rate

A numerical study is made of the interaction of a detonation wave having finite reaction velocity with a rarefaction wave of different intensity which approaches it from the rear, for the Zeldovich-Neumann-Doring (ZND) model with a single irreversible reaction A B. It is found that, for a fixed value of the parameter characterizing the initial supercompression (depending on the activation energy and the heating value of the mixture), the considered interaction leads either to a gradual relaxation of the detonation wave and its transition to the Chapman-Jouguet (CJ) regime, or to the development of undamped oscillations.Interest in the problems of detonation and supersonic combustion has increased in recent years. This is associated with the appearance and development of new experimental and theoretical techniques; it is also associated with the further development of air-breathing reaction engines, and other practical requirements. The present state of detonation theory is reflected in the survey [1].It has been established [2] that the detonation wave in gases nearly always has a complex nonuniform structure. Transverse disturbances are observed under a wide range of conditions and differ both in amplitude and wavelength. At the same time, behind the detonation leading front there is a region of uncompletely burned gas corresponding to the effective ignition induction period [3]. In spinning detonation the induction period is significantly longer than the heat release period and transverse detonation waves traveling in the induction zone of the head wave appear [3, 4]. Such a secondary detonation wave is free of transverse disturbances. The same is true of the detonation waves observed in the wake behind a body moving at high speed in a combustible medium [5] or in a gas which has been preheated by a shock wave [6].Although it is possible, under favorable conditions, to study in detail the system of discontinuities accompanying detonation, information on the extensive zones in which heat release takes place is scarce, the mechanism of detonation wave autonomy (in particular, the role of the rarefaction zone behind the wave) is not entirely clear, and the fact that, in spite of the complex structure, an autonomous detonation propagates with the CJ velocity calculated on the basis of one-dimensional theory has not yet been explained.In studying the nonlinear phenomena associated with the finite reaction rate it is quite acceptable to investigate only the simple one-dimensional detonation model, with which it is convenient to restrict ourselves to a single effective chemical reaction. This model is particularly reasonable since, in certain cases, the real detonation is virtually one-dimensional.The question of the stability of the one-dimensional detonation wave to disturbances of its structure has been examined by several authors [7–13]. The use of computers makes possible the direct computation of flows with heat release and the study of their properties. This method has been used in [11–13] to study the stability problem for a detonation wave with respect to finite disturbances.In the present paper we present a numerical study of the interaction of a detonation wave having finite chemical reaction rate with a rarefaction wave of different intensity approaching it from the rear for the ZND model with a single irreversible reaction A B. It is found that for a fixed value of the parameter characterizing the difference between detonation and the CJ waves, depending on the activation energy E and the mixture heating value Q_m, the interaction in question leads either to a gradual relaxation of the detonation wave and its transition to the CJ regime (this relaxation may be accompanied by decaying oscillations) or to the appearance of undamped oscillations (the unstable regime). The parameters E and Q_m affect the wave stability differently: with increase of Q_m, the wave is stabilized; with increase of E, it is destabilized. The boundary between the stable and unstable detonation wave propagation regimes is found. This boundary has a weak dependence on the rarefaction wave intensity. Estimates and calculated examples show that the amplitude of the unstable wave oscillations is finite and that the average detonation propagation velocity is close to the CJ velocity computed for the given heating value Qm.The author wishes to thank G. G. Chernyi for his guidance and L. A. Chudov for advice on computational questions.