Flow of a dual-temperature plasma in the channel of a disk-magnetohydrodynamic generator,taking account of nonequilibrium ionization and recombination reactions

The establishment of a supersonic one-dimensional flow of a dual-temperature, partially ionized plasma is investigated in the channel of a disk-MHD generator, taking account of nonequilibrium ionization and recombination reactions. A detailed formulation of the problem is given in [1]; flows are considered in the absence of ionization and recombination reactions and in the case of equilibrium reactions.Moscow. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 6, pp. 135–142, November–December, 1972.     

Stationary supersonic nonequilibrium-plasma source

Electron recombination associated with the expulsion of a monatomic-gas plasma into a vacuum was examined in [1]. It was assumed that recombination by collision and radiation constitutes the basic elementary process. Under certain conditions, dispersion that involves residual ionization of the gas at infinity proved to be possible.In this paper, we examine the stationary flow in a supersonic spherical source of a nonequilibrium monatomic-gas plasma, which consists of electrons, singly charged ions, and atoms. Among the important practical applications of such flows are the motion of a gas in a nozzle and stationary expulsion into a vacuum.     

Ionization and Recombination Kinetics in a Plasma Accelerator Channel

A number of theoretical approaches to the investigation of ionizing gas flows are analyzed and compared with reference to a plasma accelerator channel. The transition from a weakly ionized gas to a plasma is considered within the framework of the complete system of equations. The ionizing gas flow model is based on the magnetogasdynamic equations of a continuum and the equation of ionization and recombination kinetics. The corresponding coefficients are determined both within the framework of the standard theory and within a modified diffusion approximation, including possible variations. In addition, for comparison purposes some results of numerical experiments on the ionization process under conditions of local thermodynamic equilibrium are given.     

Investigation of the wake of a hypersonic sphere in air by means of an open microwave resonator

The use of an open microwave resonator with plane-parallel mirrors for plasma diagnostics was first proposed in [1]. A resonator with spherical mirrors, which provides better spatial resolution in addition to high sensitivity, was used later [2, 3] to investigate the wake flow of models moving through air at hypersonic velocities. The presence of free electrons in the flow field is caused by ionization processes behind the bow shock and in the model boundary layer in this case. However, only the results of measurements of the density of electrons are presented in [2, 3], and no information is given on another important plasma parameter: the effective collision frequency of electrons with heavy particles. In the present study we use a microwave (8-mm range) resonator for an experimental study of the flow of gas in the wake of a polymer (Kaprolon) sphere traveling through air at hypersonic velocity. The flow is visualized by the schlieren technique. The electron densities and effective collision frequency of electrons with heavy particles are determined as a function of the distance behind the sphere.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 156–160, July–August, 1978.     

Kinetics of electron recombination in a molecular gas expanding into a cavity

The kinetics of recombination in a diatomic or polyatomic gas dispersing into a cavity is investigated in a model gas with one ionization potential and one electron affinity. In addition to the recombination reaction in triple collisions, which play the most important role in the case of a monatomic gas [1], dissociative recombination, ion-atom charge transfer, and reactions involving negative ions are considered. The qualitative differences in the kinetics of recombination of a molecular gas (in comparison with a monatomic gas) are due to the smallness of the relative electron concentrations at the instant of disturbance of ionization equilibrium and to the important contribution of dissociative recombination reactions and the kinetics of formation and recombination of negative ions.In addition, owing to the greater specific heat of a polyatomic gas and the corresponding lower rate of cooling on dispersion, recombination due to collision of three charged particles is not, as distinct from the case of a monatomic gas, decisive for the asymptotic values of the adiabatic exponent and residual ionization. For this reason the values of the adiabatic exponent can be assigned irrespective of a in the solution of the equations of the kinetics of recombination of diatomic and polyatomic gases. Expressions for the instant of failure of the equilibrium relationship between electrons and, respectively, positive and negative ions are obtained.The relationship between the charged-particle concentration in a gas in ionization nonequilibrium and the time for known values of the reaction rate constants is expressed by quadratures. The values of the rate constants of some ionization processes are known only in order of magnitude. However, available data on rate constants indicate that for practically any initial data for dispersion of the products of explosion or combustion of chemical compounds ionization equilibrium is upset at a time when there is still an equilibrium ratio of concentrations of electrons and negative ions.     

Structure of a steady-state ionization front in the plasma accelerator channel

A theoretical approach to studying ionizable gas flows with the formation of an ionization front in the plasma accelerator channel is proposed. The study is based on the MHD equations supplemented with the ionization and recombination kinetics equation. As a result, the structure of an ionization front is investigated.     

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.     

Gas-Dynamic Processes in Two-Phase Flows in MHD Generators

A plane problem of a two-phase monodisperse flow of combustion products of plasma-forming composite solid propellants in the duct of a Faraday's MHD generator with continuous electrodes, including an accelerating nozzle, MHD channel, and diffuser, is considered. An algorithm based on the pseudo-transient method is developed to solve the system of equations describing the two-phase flow. Gas-dynamic processes in the channels of the Pamir-1 setup are numerically studied. It is shown that shock-free deceleration of a supersonic flow to velocities close to the equilibrium velocity of sound in a two-phase mixture and significantly lower than the velocity of sound in the gas is possible in two-phase flows.     

Motion of a two-temperature plasma in the channel of a disc-type magnetohydrodynamic generator

A study was made of the fully developed homogeneous flow of a two-temperature partially ionized plasma in the channel of a disc-type Hall generator. Experiments with a disc-type generator are described in [1, 2]. In a simplified statement, the problem is analogous to that considered in [3]. The present article takes the chemical reactions of ionization and recombination into account. The energy equation for an electron gas is brought down to a differential form which permits clarification of the question of the applicability of the Kerrebrock [4] formula for the difference in the temperatures of the electrons and the heavy particles.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 18–25, November–December, 1970.In conclusion, the author thanks V. V. Gogosov for his interest in the work and for his valuable observations.     

Recombination of electrons in a plasma expanding into a vacuum

As noted in a paper by one of the authors [1], when a hot ionized gas expands into a vacuum, at a certain moment ionization equilibrium must necessarily break down. Shortly after this point, which may be found by the method indicated in [1], ionizing events become very rare and only recombination occurs in the gas. In [1] photorecombination and triple collisions with the capture of an electro to the ground level of the atom were considered. Here the recombination did not proceed to the end: on expanding to infinity and cooling to zero the gas remained partially ionized.Papers have recently appeared [2–7] in which the significant role of triple collisions with the capture of electrons to upper atomic levels is noted. The recombination process has a cascade character at low temperatures and densities which are not excessively small. At first, the electron is captured by one of the upper atomic levels in a triple collision with an ion and another electron. Subsequently, as a result of electron collisions of the second kind, and later also as a result of radiative transitions, the bound electron descends through the energy levels to the atomic ground state. The recombination coefficient for such a process depends much more strongly on the electron temperature T than for a triple collision with capture directly by the ground level (as T^–9/2 as opposed to T^–1), and at low temperatures cascade recombination proceeds much more quickly than capture to the ground level. Since this casts doubt upon the conclusions of [1] regarding the residual ionization when a plasma expands into a vacuum, we were led to re-examine the question, which, as will be clear from what follows, is not considerably more complicated.     

Effect of the form of the electrodes on the current distribution in a magnetogasdynamic channel

A solution is given to the plane problem of the flow of a conducting gas across a homogeneous magnetic field in a magnetogasdynamic channel taking account of the Hall effect at small magnetic Reynolds numbers. The channel is formed by two long electrodes, and the cross section of the channel varies slightly and periodically along the gas flow. It is assumed that the electromagnetic forces are small. It is shown that the current distribution in the channel is nonuniform to a consider able degree and that inverse currents can form at the electrodes, with both subsonic and supersonic flows of the conducting gas. Transverse motion of the gas, due to a change in the cross section of the channel, leads to an increase of Joule energy losses. In [1] the current distribution was obtained in a flat channel formed by infinite dielectric walls, with the flow of a steady-state stream of plasma through the channel across a homogeneous magnetic field. With interaction between the flow and the magnetic field, closed current loops develop in the channel.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 26–33, November–December, 1970.     

Algorithm for transient growth of perturbations in channel Poiseuille flow

This study develops a direct optimal growth algorithm for three-dimensional transient growth analysis of perturbations in channel flows which are globally stable but locally unstable. Different from traditional non-modal methods based on the OrrSommerfeld and Squire(OSS) equations that assume simple base flows, this algorithm can be applied to arbitrarily complex base flows. In the proposed algorithm, a reorthogonalization Arnoldi method is used to improve orthogonality of the orthogonal basis of the Krylov subspace generated by solving the linearized forward and adjoint Navier-Stokes(N-S) equations. The linearized adjoint N-S equations with the specific boundary conditions for the channel are derived, and a new convergence criterion is proposed. The algorithm is then applied to a one-dimensional base flow(the plane Poiseuille flow) and a two-dimensional base flow(the plane Poiseuille flow with a low-speed streak)in a channel. For one-dimensional cases, the effects of the spanwise width of the channel and the Reynolds number on the transient growth of perturbations are studied. For two-dimensional cases, the effect of strength of initial low-speed streak is discussed. The presence of the streak in the plane Poiseuille flow leads to a larger and quicker growth of the perturbations than that in the one-dimensional case. For both cases, the results show that an optimal flow field leading to the largest growth of perturbations is characterized by high-and low-speed streaks and the corresponding streamwise vortical structures.The lift-up mechanism that induces the transient growth of perturbations is discussed.The performance of the re-orthogonalization Arnoldi technique in the algorithm for both one-and two-dimensional base flows is demonstrated, and the algorithm is validated by comparing the results with those obtained from the OSS equations method and the crosscheck method.     

Stability of transonic two-phase flow

The nature of a singular point in the stability of one-dimensional transonic flow of a vapor-drop mixture in a channel of variable cross section is considered within the framework of a two-lquid hydrodynamical model. It is shown that the singular point in the case of any lags of the drops preserves the nature of a saddle inherent to homogeneous gas flow, shifting only towards the divergent part of the channel if the content of condensed phase is not too high. Here the transition of subsonic two-phase flow into supersonic flow is stable and the predominance of drop agglomeration over fragmentation and the positive curvature of the channel profile are stabilizing factors. The saddle nature of the singularity is possible only if the lag of the drops is not too high in the case of flows with a higher content of condensed phase. In the opposite case, the point at which the speed of sound is attained loses the nature of a saddle point.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 163–171, January–February, 1976.     

Voltage-current characteristics of the electrode boundary layer in a thermally nonequilibrium dense plasma

The contact between a thermally nonequilibrium dense plasma and the emitter electrode in a subsonic MHD generator channel is considered. Only the three-particle recombination reaction is treated, in the absence of any magnetic field. The electrode layer is divided into two regions — quasineutral and space-charge areas. The equations which describe the electrophysical processes in these regions are solved numerically on a BÉSM-6 computer. The results are presented in the form of voltage-current curves for the electrode boundary layer at various temperature values for the wall, main flow, and electrons.     

Calculation of nonequilibrium flows in nozzles

This paper studies in the one-dimensional formulation the flow of a reacting gas with account for the nonequilibrium behavior of the chemical reactions; the pressure distribution along the stream filament is given. Viscosity, heat conduction, diffusion, and ionization are not taken into account. It is assumed that there is equilibrium excitation of the translational, rotational, and vibrational degrees of freedom.Several studies have already been made of nonequilibrium flows in nozzles [1–5]. It is known that in the calculation of nonequilibrium flows considerable difficulty arises in selecting the integration step in those regions where the flow is nearly equilibrium. It is found that with the use for numerical integration of the explicit difference schemes of the type of the Euler, Runge-Kutta, etc., methods the integration step for carrying out a stable calculation must be so small that the calculation becomes practically impossible. The present study proposes a method for calculating nonequilibrium flows using a single implicit difference scheme to calculate with a high degree of accuracy and a quite large step (exceeding the step in the explicit schemes by several orders) both those flow regions which are close to equilibrium and those regions where the flow deviates markedly from equilibrium. A program was compiled using this method for the M-20 electronic digital computer which permitted calculating in the one-dimensional approximation flows in nozzles with account for the nonequilibrium behavior of the chemical reactions for mixtures containing H, O, C, and N atoms.Some qualitative peculiarities of the nonequilibrium flows are demonstrated using as an example nonequilibrium air discharge. A comparison is made with experimental and theoretical results of other authors.The authors wish to thank L. F. Kuz'mina for her assistance in carrying out the present study.     

A qualitative investigation of the equations of quasi-one-dimensional magnetohydrodynamic channel flow

A qualitative investigation of the system of differential equations describing the quasi-one-dimensional flow of an electrically conducting medium at small magnetic Reynolds numbers gives an idea of the different possible flow patterns occuring when the electromagnetic field and channel shape are given in different ways. Such a treatment is essential for the calculation of one-dimensional flows, and also for the solution of variational problems [1].In the literature devoted to this question studies have been made of flow in a one-dimensional electromagnetic field and a channel of constant cross section [2], as well as of the flow when the magnetic field is described by specially given functions of the flow velocity [3]. These cases reduce to the analysis of integral curves in a plane.In the present paper the investigation is carried out for an arbitrary distribution of the electric and magnetic fields and channel shape, which leads to a consideration of the behavior of integral curves in three-dimensional space. The qualitative results are illustrated by examples.     

Classical molecular dynamics model for coupled two component plasmas

This work is an improved continuation of a previous attempt to use classical molecular dynamics (MD) as a tool for the investigation of hot and dense “real” plasmas. “Real” in this context refers to ions and electrons interacting through Coulomb forces and undergoing ionization/recombination. The objective of designing such a non standard approach to plasma equilibrium is to explore a new way to discuss warm and dense matter with a method able to deal with the whole complexity of a N-body system of ions and electrons. Plasma relaxation times can be investigated up to a picosecond. The resulting equilibrium ion populations, built self consistently, are comparable to those found in literature and, potentially validate access to all the statistical data usually derived from MD simulations.     

On reactive heat conduction for multiple ionized two-temperature argon plasma

Two models to computer equilibrium composition of a two temperature plasma with degree of ionization larger than one have been evaluated, and the range of validity of each model is discussed. These are then applied further for the calculation of the ambi-polar diffusion coefficient and the reactive heat conduction coefficient for the electrons and the heavy particles. Numerical results for multiple-ionized two-temperature argon plasma atp=1 bar are presented.     

Averaging of magnetohydrodynamic streams and applicability of the hydraulic approximation to the calculation of MHD flows in channels

At the present time the hydraulic approximation equations are used widely for calculating MHD flows in channels. Several years ago these solutions were considered as a method of expanding our ideas of the qualitative effect of various factors on the MHD flow in the channel of a MHD device. Today, however, the hydraulic analysis methods are beginning to be used for calculations on specific systems. In this case the selection of a particular design solution frequently is based on an analysis of the over-all characteristics (efficiency, power delivered to the external load, etc.) obtained from the hydraulic calculation, where a few percent rather than tens of percent are taken into account.On the other hand, it is known [1] that in gas dynamics the results of the hydraulic calculation for the same specific nonuniform stream may differ by an order of magnitude of tens of percent depending on the averaging method used, since the magnitude of this difference depends on the degree of nonuniformity of the actual stream.We may expect that the nonuniformity of the MHD streams will be far greater than for the gas dynamic flows as a result of the nonuniformities of the force and the thermal effect of the currents flowing in the stream. These nonuniformities may be associated, for example, with the nonuniform distribution of the currents in the channel cross section because of the nonuniform electrical conductivity, which may be significant in spite of the weak nonuniformity of the temperature distribution, or with the presence in the cross section of forces associated with the induced longitudinal component of the magnetic field, the presence of anisotropy of the electrical conductivity, etc.Moreover, in contrast with gas dynamics, in the design of various MHD devices several characteristics (power delivered to the external load, various efficiencies, etc.) which may be calculated in terms of the average value of the gas dynamic parameters are of great importance. Thus, it seems probable that the question of the applicability of the hydraulic approximation to the calculation of MHD flows in channels, the rational selection of the means for averaging the actual flows, the comparison of the results of the hydraulic calculations with the experimental data, and so on, may be far more significant than was the case for the study of gas dynamic flows.     

Monte Carlo analysis of dissociation and recombination behind strong shock waves in nitrogen

Computations are presented for the relaxation zone behind strong, one-dimensional shock waves in nitrogen. The analysis is performed with the direct simulation Monte Carlo method (DSMC). The DSMC code is vectorized for efficient use on a supercomputer. The code simulates translational, rotational and vibrational energy exchange and dissociative and recombinative chemical reactions. A new model is proposed for the treatment of three body recombination collisions in the DSMC technique which usually simulates binary collision events. The new model represents improvement over previous models in that it can be employed with a large range of chemical rate data, does not introduce into the flow field troublesome pairs of atoms which may recombine upon further collision (pseudo-particles) and is compatible with the vectorized code. The computational results are compared with existing experimental data. It is shown that the derivation of chemical rate coefficients must account for the degree of vibrational nonequilibrium in the flow. A nonequilibrium chemistry model is employed together with equilibrium rate data to compute successfully the flow in several different nitrogen shock waves.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1990.