A self-consistent solution for nonlinear theory of the positive column in a magnetic field

Only the electron and ion gases were taken into account in all previous theories of the positive column of intermediately-low-pressure arc discharge with or without the longitudinal magnetic field, while the motion of neutral gas was neglected. In 1982, the authors^[1] presented a nonlinear theory of a positive column which indicated that the rotating velocities of neutral gas and ion gas were nearly equal, and the motion of neutral gas could not be ignored. They further discussed the problem of validity of Bohm's criterion. However, some of the parameters with which the computation was worked out in Ref. [1] were not correlated to the initial discharge parameters. In the present paper, two integral relations are supplemented, so that a complete mathematical formation of the problem is given. A convergent numerical solution is obtained by iteration and the solution of Ref. [1] turns out to be the first iteration approximation. It is shown that both functions and parameters obtained by self-consistent solution differ significantly from those obtained in the first iteration approximation. According to this paper the computation can be conducted when the initial discharge parameters are given, so this method could have certain practical applications.     

用格子Boltzmann方程模拟浅水波问题

提出了用格子Ｂｏｌｔｚｍａｎｎ方程（ＬＢＥ）模拟浅水波问题的方法．通过无粘气体运动方程与浅水波方程的比较，确定了ＬＢＥ方法中平衡态的形式，使宏观方程与浅水波方程一致．计算了二维浅水波的一个问题，数值结果与精确解做了比较．     

Interaction between slip and the high-frequency vibrations of a shaped surface in the working gap of a gas-lubricated bearing with inclined grooves

The article discusses a flat bearing with a gas lubricant, one of whose surfaces is shaped by inclined grooves and vibrates in accordance with a given harmonic law with a high frequency. The reaction of a thin layer of viscous compressible gas is formed as a result of interaction between the effects of slip and high-frequency vibrations. Asymptotic methods are used in the investigation of the reactions of the gaseous layer; the thermodynamic process in the lubricating layer is assumed to be isothermal, and in the equation of motion of the gas the effect of inertial and mass forces is not taken into consideration.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 43–50, March–April, 1976.     

Two-temperature model of a plasma under conditions of stationary blowing of a gas through a plasmotron

Results are given of a calculation conducted on the basis of a two-temperature plasma model for a cylindrical arc in a channel with the blowing through of a gas. It is shown that the gas venting leads to the appearance of a considerable separation between the electron and gas temperatures near the wall of the plasmotron and in the cathode zones. The possibilities of the two-temperature model are analyzed from the point of view of an approximate calculation of the electron temperature in arc and induction plasmotrons. It is shown that the electron temperature can be estimated from simple relationships with at least 10% accuracy for induction and 15–20% accuracy for arc plasmotrons.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 3–12, July–August, 1973.     

The stratified flow of gas and non-newtonian liquid in horizontal pipes

Predictions of pressure drop and holdup are presented for the stratified flow of gas and non-Newtonian liquid obeying the Ostwald-de Waele power law model. The model of Taitel & Dukler (1976) for gas/Newtonian liquid flow is extended to liquids possessing either shear-thinning or shear-thickening laminar flow behaviour and computed results are given for flow behaviour indices in the range $\text{0.1 ≤ n ≤ 2}$. In particular, conditions are defined for drag reduction of the liquid flow by the presence of the gas. It is concluded that drag reduction occurs over the largest ranges of liquid and gas flow rates at the lowest $\text{n}$ values, provided that liquid flow remains laminar, but that maximum drag reduction may be expected for shear-thickening liquids with $\text{n}$ values of 2 or greater. Ratios of the liquid flow rate in the presence of gas to that for liquid flow alone under a constant pressure gradient are also presented. These ratios frequently exceed unity and are greatest for highly shear-thinning liquids.Although the Taitel & Dukler approach is consistent with experiments on gas/Newtonian liquid flow, and, in addition, appears to be valid for immiscible Newtonian liquid-liquid systems, provided that the viscosity ratio of the two phases is at least five, experiments are required to confirm its applicability for gas/non-Newtonian systems.     

Calculation of supersonic gas flow over a ducted body in regimes with a detached shock wave

Calculations were made of the supersonic flow of an inviscid gas which does not conduct heat over two-dimensional and axisymmetric ducted bodies in regimes with a detached shock wave and completely subsonic gas velocity in the cylindrical duct. The investigated bodies have a pointed leading edge. The flow rate of the gas through the duct is assumed to be given. This corresponds to the presence in the exit section of the duct of a throttle or an impermeable barrier (in which case the flow rate is zero). The numerical algorithm used in the calculations is based on stabilization in time and Godunov's difference scheme [1] with separation of the shock wave. The integrated flow characteristics are given. The values of the wave resistance coefficient obtained in the calculations are compared with the values found using Taganov's approximate approach.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 160–163, May–June, 1981.I thank A. N. Kraiko for regular consultations, Yu. B. Lifshits for a helpful comment, and V. A. Vostretsov for assisting in the work.     

Invariant submodels of the model of thermal motion of gas in a rarefied space

A model describing the thermal motion of a gas in a rarefied space is investigated. This model can be used in the study of the motion of gas in outer space, and the processes occurring inside the tornado, and the state of the medium behind the shock front of the wave after a very intense explosion. For a given initial pressure distribution, a special choice of mass Lagrange variables leads to a reduced system of differential equations describing this motion, in which the number of independent variables is one less than the original system. This means that there is a stratification of a highly rarefied gas with respect to pressure. Namely, in a strongly rarefied space for each given initial pressure distribution, at each instant of time all gas particles are localized on a two-dimensional surface moving in this space. At each point of this surface, the acceleration vector is collinear with its normal vector. The resulting system admits an infinite Lie transformation group. All significantly various submodels that are invariant with respect to the subgroups of its eight-parameter subgroup generated by the transfer, extension, rotation, and hyperbolic rotation operators (the Lorentz operator) are found. For invariant submodels of rank 1, the basic mechanical characteristics of the gas flow described by them are obtained. Conditions for the existence of these submodels are given. For invariant submodels of rank 2, integral equations describing these submodels are obtained. For some submodels, the problem of describing the gas flow from the initial location of its particles and the distribution of their velocities has been investigated.     

Similarity motions of a gas in the case of local supply of mass and energy in a fuel mixture

One-dimensional nonstationary similarity motions of a gas with exothermic reactions behind shock waves are analyzed. The thickness of the region of chemical reactions is ignored. New solutions are obtained for the problems of flows of a chemically active gas with the formation of shock and detonation waves. In particular, it is shown that in the framework of the adopted schemes of the combustion process a solution with five strong-discontinuity surfaces can be constructed. The results are given of numerical solutions for supercompression detonation and Chapman-Jouguet detonation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 70–77, July–August, 1979.     

关于水气界面处的气体传输

水气界面处的气体传输问题由于其对于地球大气中温室效应气体收支的重要意义,近年来受到广泛的关注．综述国际上在水气界面处传质研究的新进展,在简评各种基本的传质模型基础上,着重介绍在剪切水气界面附近湍流相干结构及其与气体传输的关系方面的一些新发现、新观点．对于实际海气界面气体传输的若干机制进行了评述．为实际估算海气界面处气体传输速度的目的,建议了一种综合考虑剪切与波破碎两种机制的气体传输复合计算方法,得到与实测较满意的符合．      

The turbulent boundary layer of dissociated gas in the initial section of a tube

Many theoretical and experimental papers [1–4] have been devoted to investigating the turbulent boundary layer in the initial section of a channel. For the most part, however, the flow of an incompressible fluid with constant parameters is considered. There are many practical cases in which it is of interest to treat the development of the turbulent boundary layer of gas in the initial section of a pipe when conditions are strongly nonisothermal. A solution of a problem of this type, based on the theory of limit laws, is given in paper [1]. The present article extends this solution to the case of the flow of a high-enthalpy gas when the effect of gas dissociation on the turbulent boundary layer characteristics must be taken into account. We shall consider the flow of a mixture of i gases which is in a frozen state inside the boundary layer, and in an equilibrium state on its boundaries. Formulas are derived for the laws of friction and heat exchange, and a solution is given for the turbulent boundary layer equations in the initial section of the pipe when the wall temperature is constant and the gas flows at a subsonic velocity.Finally the authors are grateful to S. S. Kutateladze for discussing the paper.     

Microwave gas discharge breakdown

Summary A brief survey of microwave gas discharge breakdown is given. The conditions for breakdown in electron attaching and non-attaching gases is discussed. Results for air show both electron attachment and diffusion are operating. Hydrogen is taken as an example of a gas in which electron attachment is absent. For this case, data in the low pressure region, in the diffusion controlled region, and in the mobility controlled region are discussed and the results of the many studies in these regions are shown to be consistent with each other.This work was supported in part by the Signal Corps; the Office of Scientific Research, Air Research and Development Command; and the Office of Naval Research; of the United States of America.     

恒稳推进的煤与瓦斯突出

本文建立理想的一维运动模型,对煤与瓦斯突出的机理进行了探讨,指出煤的破碎起动与瓦斯渗流的耦合是煤与瓦斯突出的内在因素,大型突出相应于恒稳推进的情况,通过分析给出了讨论煤与瓦斯突出的重要的无量纲参数以及突出判据的近似形式。     

Not fully established flow around bodies under the conditions of the law of localness

A solution is given to the problem of determining the aerodynamic characteristics of bodies under not fully established conditions of flight, where the law of localness can be used (the modified Newton theory, free molecular flow of the gas, flow of a rarefied gas under intermediate conditions, etc.) It is shown that it is relatively easy to calculate the coefficients of the rotational derivatives of the first order. Numerical examples of the calculation are given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 168–173, May–June, 1977.In conclusion, the author thanks A. I. Bunimovich for his interest in the work and M. A. Vorotyntsev for his useful observations.     

Solution of the direct problem of the flow of a two-phase mixture of a gas and foreign solid or liquid particles in a laval nozzle

Within the framework of a two-liquid (two-velocity and two-temperature) model of a continuous medium, the article considers the flow of a mixture of a gas and foreign particles in the subsonic, transonic, and supersonic parts of a Laval nozzle. In the case of a thin layer of pure gas near the wall, the problem is solved in two stages. First, the method of establishment is used to calculate the core of the flow, where the gas with the particles is flowing; under these circumstances, the parameters in the layer of pure gas are determined approximately; then simplified equations (of the type of the equations of the boundary layer) are used to find the distribution of the parameters in the zone of pure gas, and the flow in the core of the stream is refined. Examples of the calculation are given. Use of the method developed permitted establishing some of the special characteristics of the flow of a mixture of gas with particles in a Laval nozzle in the case of Stokes flow around the foreign particles.     

一种非火药驱动气体炮内弹道模型及发射诸元协调

介绍一种新型非火药驱动的气体炮,它有五个气室控制气体炮的整个发射过程。给出了该气体炮的结构原理和内弹道数学模型,并通过计算机模拟,分析了这种气体炮的发射参数的协调和优化关系,指出了影响弹丸最大加速度的主要因素。     

Simulation of supersonic and hypersonic flows

A simple convection algorithm for simulation of time-dependent supersonic and hypersonic flows of a perfect but viscous gas is described. The algorithm is based on conservation and convection of mass, momentum and energy in a grid of rectangular cells. Examples are given for starting flow in a shock tube and oblique shocks generated by a wedge at Mach numbers up to 30·4. Good comparisons are achieved with well-known perfect gas flows.     

Some effects of strong blowing of gas into a supersonic flow

The intense evaporation of bodies moving in the atmospheres of planets at high supersonic velocities has been partly simulated both theoretically [1–5] (numerical calculations of strong blowing in the framework of the Navier-Stokes equations were also made at the Scientific-Research Institute of Mechanics at the Moscow State University by É. A. Gershbein and A. F. Kolesnikov [6]) as well as experimentally [7–9]. Below, the results are given of investigations of strong blowing of gas from the flat end of a cylinder into a supersonic flow at Reynolds numbers such that the mixing layer separating the blown and the oncoming gas is fairly thin. In this case, the mixing layer can be regarded as a contact surface, so that the problem of blowing can be solved in the framework of Euler's equations. The results of a numerical solution are compared with the results of experiments on the separation and profile of the shock wave, the thickness of the blowing layer on the axis, and also on the pressure distribution on the end of the cylinder. It was established experimentally, and then confirmed numerically that there is a downwash of the blown gas on the periphery of a porous end. It is shown that for the same blowing parameter K, which is equal to the ratio of the dynamic head of the blown gas to the dynamic head of the oncoming gas, and for a given distribution of K over the surface of the body the contact surface tends to a certain limiting position with increasing Mach number of the oncoming flow, i.e., the profile of the contact surface is stabilized. The influence of the adiabatic exponent on the thickness of the blowing layer is estimated. The present investigations continue earlier experimental studies, the main results of which have been presented in [9].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 91–98, January–February, 1980.     

Slip boundary conditions on a catalytic surface in a multicomponent gas flow

The boundary conditions for the velocity slip and temperature and concentration jumps on the surface of a body in a rarefied multicomponent gas flow are obtained. The mathematical treatment is given in detail because of the need to examine critically some previous results which disagree with each other in spite of the fact that the initial premises and the methods of solution were the same. The results of this study, which are given in a convenient form, represent the boundary conditions for both the simplified and the complete Navier-Stokes equations in problems of hypersonic rarefied gas flow past bodies with a catalytically active surface.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 159–168, January–February, 1996.     

Self-similar solution to a problem of axisymmetric motion of gas through a porous medium in the case of a quadratic law of resistance

The results of solution of the self-similar problem of planar flow of gas through a porous medium in the case of a quadratic law of resistance [1] are generalized to the case of axisymmetric motion. The equation in similarity variables for the velocity of isothermal gas flow is reduced to an equation having cylindrical functions as solution. Analytic dependences of the pressure and the gas velocity on the coordinate and time are obtained for a given flow rate of the gas at the coordinate origin and for zero Initial gas pressure in the porous medium.Translated from Izvestlya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza., No. 4, pp. 168–171, July–August, 1982.