Propagation of an ion jet near a dielectric surface

Difficulties in determining experimentally the local electrical parameters of unipolar-charged jets are arousing interest in the theoretical investigation of electrogasdynamic (EGD) flows. Free EGD jets were examined, for example, in [1–3]. In order to control the charge on the dielectric parts of aircraft surfaces, which results from their static electrification and may have certain negative consequences [4], and, moreover, to influence the flow in the boundary layer use is being made of unipolar-charged jets propagating near the dielectric [5, 6]. In [6] the case of an ion jet near a dielectric surface possessing surface conductivity was investigated. In these circumstances it is possible to neglect charge diffusion, which considerably simplifies the problem. Space charge diffusion was taken into account in [7], but subject to certain very important simplifications. The author has calculated the electrical parameters of a unipolar-charged jet propagating in a viscous incompressible gas near an ideal dielectric plate, with allowance for surface and polarization charges and, moreover, the diffusion processes near the surface. An asymptotic solution is obtained for the equations of the ionic diffusion layer as the ratio of the thickness of the diffusion layer to the thickness of the hydrodynamic boundary layer tends to zero.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 174–180, September–October, 1984.The author is grateful to V. V. Mikhailov and A. V. Kazakov for valuable advice and comments.     

Inhomogeneous inverse problem in finite elasticity

For a class of materials for which the principal strain directions always coincide with the principal stress directions one can determine the stress field in an inhomogeneously deformed body from given boundary conditions and a known strain field without knowing the constitutive equations. Each point of the inhomogeneously deformed body contains information such as that derived from an individual homogeneous identification test. The practically important two-dimensional case leads to a problem of solving a linear hyperbolic system where two differential equations describe the principal stress components. The problem can be reduced to that of integration along characteristics.Under a certain globality condition the existence, uniqueness, and correctness of the solution are guaranteed in the whole test piece. It is shown that the globality condition is closely related to whether or not the test piece is isotropic and elastic. The influence of experimental error on the correctness of problem formulation is discussed.

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Abstrakte Für die Klasse der Materialen, für welche die Grundspannungsrichtungen und die Grundverformungsrichtungen gleich sind, kann man das Spannungsfeld in einem inhomogen deformierten Körper für gegebene Randbedingungen und einem bekannten Verformungsfeld ohne Kenntnis der detailierten Form der Dehnungs-Spannungsgleichung bestimmen. Jeder Punkt des inhomogen deformierten Körpers liefert dieselbe Information wie ein individueller homogener Test. Der praktisch wichtige zweidimensionale Fall führt zu einem Problem der Lösung eines linear hyperbolischen Systems von zwei Differentialgleichungen für die Grundspannungskomponenten. Das Problem kann auf die Integration entlang der Charakteristik des Systems reduziert werden.Unter einer Bedingung der Globalität das die Existent, Eindeutigkeit und Richtigkeit der Lösung in der ganzen Testprobe gewährleistet sind. Es wird gezeigt, dass diese Globalitätsbedingung damit zusammenhängt eng, ob die Testprobe isotrop und elastisch ist. Der Einfluss der experimentellen Fehler auf die Richtigkeit der Formulation des Problems wird auch analysiert.

     

Rheological determination of polymer-filler affinity

An experimental method to quantify the affinity of polymers for certain fillers is presented. In this method, the relative viscosity of filled and unfilled polymer systems as determined by capillary rheometry is taken as a measure of the thickness of the adsorbed layer of polymeric material on the filler surface and hence of the affinity of the polymer for the filler. A styrene-butadienestyrene block copolymer is thus found to have a higher affinity for talc than do polypropylene and an ethylene-propylene-diene terpolymer.     

Vibrations and stability of cylindrical panels with elliptical cross section

Summary The free vibrations of cylindrical panels with elliptical cross section subjected to an initial stress state are investigated. The buckling problem of the panel under the stress state considered is studied as special case of the free vibration problem.

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Übersicht Es wird die freie Schwingung offener Zylinderschalen mit elliptischem Querschnitt behandelt, die sich in einem Anfangspannungszustand befinden. Das Schalenbeulproblem wird als Spezialfall der freien Schwingung untersucht.

     

Single-phase heat transfer characteristics of concentric-tube thermosyphon

An experimental study has been conducted to evaluate the influence of the presence of inner tube and the Rayleigh number on free convective heat transfer in an open thermosyphon. Water and fluorocarbon R-11 refrigerant as the working fluids were utilized. Heat transfer results using the concentric geometry were given for modified Rayleigh number from 3.6×10² to 4.1 × 10⁷ which encompasses the regions of similarity, impeded and boundary layer flow conditions. It was found that the presence of the inner tube markedly increases the overall heat transfer coefficient of open thermosyphon by a factor as large as 2 to 10 in the turbulent impeded and boundary layer regimes.

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Wärmeübergang in einem Thermosyphon aus konzentrischem Rohr bei einphasiger Strömung

Zusammenfassung Es wurde experimentell untersucht, wie der Einbau eines Innenrohres und wie die Rayleigh-Zahl auf die freie Konvektion in einem offenen Thermosyphon, gefüllt mit Wasser oder dem Kältemittel R 11, einwirkt. Der untersuchte Bereich bei konzentrischer Geometrie lag bei modifizierten Rayleigh-Zahlen von 3,6 · 10² bis 4,1 · 10⁷ und umfaßte damit die Regionen der Grenzschichtströmung. Es ergab sich, daß der Einbau eines Innenrohres den Gesamtwärmeübergang eines offenen Thermosyphons im Bereich der behinderten turbulenten Strömungen und Grenzschichtströmungen um den Faktor 2 bis 10 steigert.

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Nomenclature a inner radius of heated tube, D/2 - A_in sectional space area of inner tube, d _i ² /4 - A_an sectional space area of annulus, (D^2-d ₀ ² )/4 - C_p specific heat - d_i inner diameter of inner tube - d₀ outer diameter of inner tube - D inner diameter of heated tube - g gravitational acceleration - L tube length of thermosyphon - Nu_a Nusselt number based on inner radius of heated tube - Nu_r Nusselt number based on equivalent heattransfer radius - Nu_x Nusselt number, defined in equation (1) - Pr Prandtl number, defined in equation (3) - q heat flux from heated tube - r equivalent heat-transfer radius, defined in equation (4) - Ra_a modified Rayleigh number based on inner radius of heated tube - Ra_r modified Rayleigh number based on equivalent heat-transfer radius - Ra_x modified Rayleigh number, defined in equation (2) - T_e temperature of entrance-fluid - T_w temperature of heated surface - T temperature difference between heated wall and entrance-fluid, T_w-T_e Greek Symbols coefficient of volumetric expansion - thermal diffusivity - thermal conductivity - viscosity - kinematic viscosity     

Effects of the interaction between radiation and a disintegrating vitreous material

This article considers the disintegration of a vitreous semitransparent material at the critical point in a stream of radiating gas. A study is made of the effect on the rate of disintegration of the indeterminacy of the effect of interaction between the radiation and the gaseous disintegration products and of the spectral distribution of the density of the radiation flux of the gas with respect to the semitransparancy of the material. An analysis of the error of the gray approximation with calculation of the disintegration of materials with a semitransparency window is also given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 133–137, September–October, 1978.     

Differentiation along arbitrary orientations

A prevalent problem of mechanics is the differentiation of experimental information with respect to various directions, including the determination of cross derivatives. Simple methods for evaluating such derivatives along straight and curved directions are described. The concepts are demoinstrated at boundary and internal locations of in-plane and transversely loaded plates.     

Stability of the combustion process in elastic combustion chambers

High-frequency instability phenomena in rigid combustion chambers have been studied theoretically in [1–3]. This phenomenon is attributed to the interaction between the combustion processes and combustion-product fluctuations in the chamber. One of the possible mechanisms of formation of high-frequency instability is examined in [3], where the combustion rate is represented in the form of a retarded pressure functional. In this case, the problem is reduced to studying the stability of a certain distributed self-oscillating time-lag system.If the oscillation frequencies of the combustion products are comparable to the natural vibrations of the shell which forms the combustion chamber, then it is natural to expect that the elasticity of the chamber walls will affect the combustion process. Coupled effects of acoustoelastic instability can arise, in whose development the vibrations of the chamber wall play a substantial role. These effects are particularly undesirable from the point of view of the vibrational stability of combustion chambers.In this paper, a theory of high-frequency instability of stationary combustion is developed with allowance for elastic deformations of the combustion chamber walls. The theory is based on the mechanism of vibrational combustion [1–3], according to which the combustion front is assumed to the concentrated, while the velocity jump at the front is expressed through a retarded pressure functional. It is assumed that the combustion product flow is one-dimensional and isentropic and that the chamber is cylindrical. The deformations of the chamber are described via the moment theory of shells. The existence is revealed of additional instability regions produced by the interaction between the elastic vibrations of the chamber walls and the acoustic oscillations of the combustion products. The influence of the relation between the elastic and acoustic frequencies and of the structural damping factor in the combustion chamber walls on the stability of the stationary combustion process is examined. The problem discussed is treated as a mathematical model for more complex asymmetric problems in which the elastic and acoustic frequencies can be of the same order.