Integral characteristics of MHD channel with nonconducting baffles

The electromagnetic characteristics of an MHD channel with insulated walls, two quite long electrodes, and nonconducting baffles are obtained for arbitrary magnetic field distribution law along the channel. Some specific cases of magnetic field and baffle location specification are examined in detail.Translated from Zhurnal Prikladnoi Mekhaniki Tekhnicheskoi Fiziki, Vol. 10, No. 6, pp. 30–39, November–December, 1969.     

磁流体动力学斜激波控制数值模拟分析

高超声速飞行器MHD(磁流体动力学)斜激波控制应用的关键在于理解等离子体斜激波流场与磁场的相互作用规律,这里发展了全MHD数值模拟方法对其进行研究,数值方法基于八波方程附加源项形式,进行有限体积离散,采用了Roe求解器、OC-TVD空间格式和LU-SGS方法,且采用投影方法降低磁场伪散度误差.考察外加均匀磁场的马赫10无粘导电拐角流动,压缩角为10°.结果中散度误差较低,并且通过激波参数验证了结果的准确性.流场显示,磁场使得激波角增大,部分情况下出现了快、慢激波结构,其中快激波变化更明显;壁面压强根据磁场的不同出现了不同程度的降低.最后采用群速度图方法进行了快慢激波形式分析,解释了磁场影响下流场形式变化机理.     

Calculation of the unsteady-state aerodynamic characteristics of three-dimensional bearing systems

At the present times effective numerical methods have been developed for solving both steady-state and unsteady-state linear problems on the determination of the aerodynamic characteristics of wings of complex form, in a plan view [1–3]. The transition to three-dimensional systems requires the development of new methods. There are a number of known investigations in this direction, for simple three-dimensional configurations [4–7]. The present article proposes a method for solving supersonic problems of the determination of the steady-state and unsteady-state three-dimensional bearing systems. It is a development of known methods for calculating wings of complex form in a plan view. The most effective route is one based on a solution of the problem for stepwise dependences on the time. After this, the transition to any other laws is effected using a packet integral.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 173–176, January–February, 1976.     

Investigation of the transitional process of the startup of a gas bearing

In this article we derive equations for transitional conditions of a gas lubricant under nonisothermal conditions. A numerical solution of the Reynolds equation is described for the problem of the pulsed startup of a radial bearing with a fixed geometry, and the results of this solution are given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 156–160, September–October, 1977.     

Influence of the hall effect on the characteristics of a MHD generator with two pairs of electrodes

The characteristics of segmented-electrode MHD generators with Hall currents are at present the object of considerable interest. Various types of electrode connections ate being examined: ordinary segmented-electrode generators, Hall generators, mixed-type generators, and Montardy generators. Research is being pushed in several directions. In some cases infinitely fine segmentation is assumed [1--4]. In these studies it is considered that the current density j in the duct is everywhere uniform; the net characteristics or the most favorable electrode connection angle are determined. In another group of studies periodic problems are solved, it being assumed that the processes taking place in a single elementary celi are repeated in the other ceils; fringe effects are not taken into account. In this case it is usually assumed that the lengths of the electrodes and insulators are finite, but small as compared with the duct height [5–7 ]. Finally, in a last group of studies nonperiodic problems are considered. In [3] Vatazhin solves the problem of the current distribution in a duct with a single pair of electrodes between infinitely long insulators. In [8] a general expression is found for the current density function in the case of an arbitrary number of electrode pairs and for any scheme of electrode connection at finite electrode and insulator dimensions. However, numerical calculations are made only for the periodic problem, whose solution is also obtained in [8]; the effect of segment pitch on the characteristics of a Montardy generator is studied.The present author has investigated the influence of the Hall effect on the characteristics of a MHD generator having two pairs of electrodes with symmetrical and crossed electrode connections. Although it is obvious that in practice only multisegment ducts will be employed, the examination of a generator with two pairs of electrodes makes possible the qualitative anatysis of the various effects observed in segmented-electrode ducts in which the electrodes are connected in different ways. Numerical calculations, based on formulas obtained by solving the corresponding problems, have been made on a M-20 computer. Integrated characteristics of the various generator systems have been obtained as a function of electrode and insulator length, external loads, and Hall parameter w.In conclusion, the author thanks A. B. Vatazhin and A. N. Kraiko for their helpful advice.     

Investigation of the characteristics of an electrogasdynamic engine

This paper presents the results of a theoretical and experimental investigation of an electrogasdynamic (EGD) engine intended for developing thrust of aircraft. Calculated relations agreeing well with the experimental data are obtained. It is shown that the effectiveness of an EGD engine can be sufficiently high for practical use.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 167–170, November–December, 1971.     

Hall effects on MHD flow in a rotating system with heat transfer characteristics

Closed-form solutions are derived for the steady magnetohydrodynamic (MHD) viscous flow in a parallel plate channel system with perfectly conducting walls in a rotating frame of reference, in the presence of Hall currents, heat transfer and a transverse uniform magnetic field. A mathematical analysis is described to evaluate the velocity, induced magnetic field and mass flow rate distributions, for a wide range of the governing parameters. Asymptotic behavior of the solution is analyzed for large M ² (Hartmann number squared) and K ² (rotation parameter). The heat transfer aspect is considered also with Joule and viscous heating effects present. Boundary layers arise close to the channel walls for large K ², i.e. strong rotation of the channel. For slowly rotating systems (small K ²), Hall current parameter (m) reduces primary mass flow rate (Q _x /R ρ v). Heat transfer rate at the upper plate (d θ/d η) _η=1 decreases, while at the lower plate (d θ/d η) _η=−1 increases, with increase in either K ² or m. For constant values of the rotation parameter, K ², heat transfer rate at both plates exhibits an oscillatory pattern with an increase in Hall current parameter, m. The response of the primary and secondary velocity components and also the primary and secondary induced magnetic field components to the control parameters is also studied graphically. Applications of the study arise in rotating MHD induction machine energy generators, planetary and solar plasma fluid dynamics systems, magnetic field control of materials processing systems, hybrid magnetic propulsion systems for space travel etc.     

Well-Posedness of the Hydrostatic MHD Equations

The well-posedness of the equations of fluid mechanics in the hydrostatic limit is well known to be a difficult problem. Partial results, both positive and negative, will be reviewed below. In this paper, it is shown that, for ideal magnetohydrodynamics, a magnetic field parallel to the flow direction can ensure well-posedness. The only condition required is that the flow is subalfvenic. The result has some relevance to viscoelastic flows of the upper convected Maxwell fluid, which, in the infinite Weissenberg number limit, is related to ideal MHD.     

Investigation of the damage variable basic issues in continuum damage and healing mechanics

Consistent mathematics and mechanics are used here to properly interpret the damage variable within the confines of the concept of reduced area due to damage. In this work basic issues are investigated for the damage variable in conjunction with continuum damage and healing mechanics. First, the issue of the additive decomposition of the damage variable into damage due to voids and damage due to cracks in continuum damage mechanics is discussed. The accurate decomposition is shown to be non-additive and involves a term due to the interaction of cracks and voids. It is shown also that the additive decomposition can only be used for the special case of small damage. Furthermore, a new decomposition is derived for the evolution of the damage variable. The second issue to be discussed is the new concept of independent and dependent damage processes. For this purpose, exact expressions for the two types of damage processes are presented. The third issue addressed is the concept of healing processes occurring in series and in parallel. In this regard, systematically and consistently, the equations of healing processes occurring either consecutively or simultaneously are discussed. This is followed by introducing the new concept of small healing in damaged materials. Simplified equations that apply when healing effects are small are shown. Finally, some interesting and special damage processes using a systematic and original formulation are presented.     

Energy analysis of the stability of MHD flows

The analog of Orr's problem is formulated for MHD flows. Arbitrary three-dimensional disturbances satisfying the continuity equations are considered. It is established that direct interaction of the disturbances of the magnetic field and the velocity field cannot increase the energy estimate of the critical Reynolds number. Numerical calculations for Hartmann flow and modified Couette flows are made for the particular case of small magnetic Reynolds numbers, The minimum value of R is attained for disturbances with a wave vector perpendicular to the velocity vector of the main flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 3–9, July–August, 1971.The authors thank M. A. Gol'dshtik for his interest in their work.     

MHD Asymmetric flow in the presence of diffusion

The present work is made to study the MHD flow in the presence of diffusion, for asymmetric flow past a semi-infinite unmoving plate. We consider the flow of an incompressible, viscous and electrically conducting fluid under the influence of a transversely applied magnetic field.

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Asymmetrische MHD-Strömung in Gegenwart von Diffusion

Zusammenfassung Diese Arbeit ist ein Versuch, MHD-Strömungen in Gegenwart von Diffusion zu untersuchen. Dabei wurde für die asymmetrische Strömung hinter einer halbunendlichen festen Platte ein inkompressibles, viskoses und elektrisch leitendes Fluid angenommen. Senkrecht zur Platte wirkt ein magnetisches Feld, das Einfluß auf die Strömung nimmt.

     

Effects of axial preload of ball bearing on the nonlinear dynamic characteristics of a rotor-bearing system

This research studies the effects of axial preload on nonlinear dynamic characteristics of a flexible rotor supported by angular contact ball bearings. A dynamic model of ball bearings is improved for modeling a five-degree-of-freedom rotor bearing system. The predicted results are in good agreement with prior experimental data, thus validating the proposed model. With or without considering unbalanced forces, the Floquet theory is employed to investigate the bifurcation and stability of system periodic solution. With the aid of Poincarè maps and frequency response, the unstable motion of system is analyzed in detail. Results show that the effects of axial preload applied to ball bearings on system dynamic characteristics are significant. The unstable periodic solution of a balanced rotor bearing system can be avoided when the applied axial preload is sufficient. The bifurcation margins of an unbalanced rotor bearing system enhance markedly as the axial preload increases and relates to system resonance speed.     

Experimental determination of the basic characteristics of heat and mass transfer upon thermoerosion fracture of materials

Using an original technique, heat and mass transfer in the interaction between a high-temperature heterogeneous jet with a high concentration of particles and the surface of structural materials was studied for the first time. The characteristics of heat and mass transfer were obtained under conditions of intense destruction of the materials under the action of a heterogeneous jet whose axis is perpendicular to the heating surface. Based on the results of experimental studies, some signs of high-temperature fracture of steel and cement grout under the action of a heterogeneous jet were revealed. Deceased. Tomsk State University, Tomsk 634050. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 2, pp. 138–143, March–April, 2000.     

Exact analytical solution of the MHD Jeffery-Hamel flow problem

This article shows that the well known nonlinear boundary value problem namely MHD Jeffery-Hamel flow problem, investigated in recent years by many numerical and semi-analytical approximative methods, is exactly solvable and furthermore, gives analytical exact solution in the implicit form for further physical interpretation.     

Some Steady MHD Flows of the Second Order Fluid

The exact analytic solutions of two problems of a second order fluid in presence of a uniform transverse magnetic field are investigated. The governing equation is of fourth order ordinary differential equation and is solved using perturbation method. In the first problem we discuss the flow of a second order fluid due to non-coaxial rotations of a porous disk and a fluid at infinity. In second problem the flow of a second order conducting fluid between two infinite plates rotating about the same axis is investigated, with suction or blowing along the axial direction. For second order conducting fluid it is observed that asymptotic solution exists for the velocity both in the case of suction and blowing.