Stability of two-dimensional curvilinear flows of an ideal barotropic fluid

It was established by Arnol'd [1] that the conservation laws for the energy and vorticity can be used to establish sufficient conditions of stability of two-dimensional curvilinear flows of an ideal incompressible fluid in the exact nonlinear formulation. It is shown below that one can obtain similarly conditions of stability of two-dimensional curvilinear steady flows of an ideal barotropic fluid in the linear approximation. One of the conditions has a significance similar to Rayleigh's criterion and its generalization by Arnol'd [1]; the other is the condition of subsonic flow. In addition, a variational principle is established and an expression found for the second variation of the corresponding functional; these can be used to prove the stability of these flows in the exact nonlinear formulation.Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 5, pp. 19–25, September–October, 1981.I am sincerely grateful to V. L. Berdichevskii and A. G. Kulikovskii for constructive advice.     

Methods of calculation and numerical analysis of conducting-gas flow in high-current electric arcs

The mechanism of conducting-gas acceleration in an electric arc by intrinsic magnetic field was first investigated in [1]. Further theoretical study of this question was associated with the numerical calculation of arcs [2–7]. A more general approach to the solution of the problem was realized in [4], where the finite-difference method was used. Integral calculational models were developed in [5–7]. The present work proposes a modified version of the difference method [4] and a series of integral methods for the calculation of the conducting-gas flow in a high-current electric arc. The development of integral methods is of interest in that they are usually associated with adequate accuracy in determining integral values and values averaged over the cross section by a relatively simple calculation, and also allow the solution of the problem to be obtained in a number of situations when the realization of a difference method is complicated. The results of different calculation methods are compared. The effect of conditions in the initial cross section of the calculation region of the arc on its characteristics is investigated and a numerical analysis of the heating and acceleration of conducting gas is carried out.Translated from Izvestiya Akademiya Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 103–110, September–October, 1978.     

Experimental investigation of return currents in electrogasdynamic flows

An investigation is made of return electric currents in electrogasdynamic flows for laboratory sources of unipolar charged particles. These currents play an important role in the process of airplane electrification as a result of the work of jet engines. Models have been built, making it possible to study the behavior of return currents outside and inside an axisymmetric electrogasdynamic flow, in the absence (single-contour source) and the presence (double contour source) of an external annular neutral jet. It is shown that a rise in the return current J^– outside an electrogasdynamic jet is accompanied by a decrease in the take-off current J °. A decrease in the relative distance L from the source to an external grounded surface and an increase in the ratiov of the velocity of the external neutral jet to the velocity of the electrogasdynamic flow lowers J^– in both grounded and insulated models; in the latter case, where J ° J°0, there is an appreciable return current outside the jet. With an increase in the potential of the source from =0 to the floating potential, the current J^– rises, attaining a maximum, and then decreases. This effect is observed also when J^–=0 in both grounded and insulated models. For the case L–1,v=1, the theoretical and experimental dependences of J^– on the potential of the source , retarding the charged particles of the flow under transitional conditions, are in satisfactory agreement.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 127–134, January–February, 1978.In conclusion, the authors thank A. B. Vatazhin for his interest in the work, and A. P. Strekal and V. F. Kudryashov for their participation in the experiments.     

Diffusional interaction of drops in a liquid

The method of combining asymptotic expansions (with respect to a large Peclet number) is used to investigate the three-dimensional problem of steady-state convective diffusion to the surface of drops, around which flows a laminar stream of a viscous incompressible liquid whose velocity field is assumed to be known from the solution of the corresponding hydrodynamic problem. It is shown that for large Peclet numbers the heat and mass transfer between drops is completely determined by the mutual arrangement of special (starting or ending at the surface of a drop) lines of flow; under these circumstances, in the flow there are chains of drops which have no mutual diffusional effect on one another, and the total diffusional flow to a drop is determined by diffusion to particles located upstream in the same chain. For the case where the distance between the drops in the chain is much leas than P^1/2 (P is the Peclet number), formulas for the distribution of the concentration and the total diffusional flow to the surface of each drop are obtained. It is shown that the total diffusional flow to the surface of a drop approaches zero in inverse proportion to its order number in a chain, which generalizes [1], in which the axisymmetric case is considered. A solution of the diffusional case is obtained for the case where there are critical lines at the surface of the drop. The problem is solved to the end if the singular flow lines are not closed and depart to infinity. With the presence of a region of closed circulation behind the drops, the problem is reduced to an integral equation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika, Zhidkosti i Gaza, No. 2, pp. 44–56, March–April, 1978.The author thanks Yu. P. Gupalo and Yu. S. Ryazantsev for their interest in the work.     

Numerisch einfache Beziehungen zwischen Verlust- und Speicherkomponente des dynamischen Schermoduls und der dynamischen Nachgiebigkeit

Zusammenfassung Es werden Formeln hergeleitet, die analog den Kramers-Kronig-Beziehungen Verlust- und Speicherkomponente des komplexen dynamischen Schermoduls bzw. der komplexen dynamischen Nachgiebigkeit miteinander in Verbindung bringen, die aber den Vorteil haben, daß kein Integral mehr auftritt und daß sich der Einfluß der jeweiligen Kurvenausläufer für 0 und in Form einer einfach gebauten Summe aus Stützstellenwerten darstellen läßt, wobei als Stützstellen die Punkte 2 ^j ₀ mitj= ±1, ±2, benützt werden.Die Formeln enthalten zusätzlich die logarithmische Ableitung einer der jeweiligen Meßgrößen an der Stelle ₀. Es ist jedoch möglich, Näherungsformeln aufzustellen, welche die Ableitung nicht mehr enthalten. Der relative Fehler, der dabei in Kauf zu nehmen ist, beträgt weniger als 0,5%.Durch Linearkombination der Gleichungen für entsprechende Stützstellen kann der Anteil der unendlichen Summen eliminiert werden, so daß man Beziehungen erhält, welche zur Kontrolle einer Messung beider Komponenten des Moduls beziehungsweise der Nachgiebigkeit dienen können. Um den Preis einer geringeren Genauigkeit, wobei die maximale Abweichung relativ zur Verlustkomponente angegeben wird, können solche Kontrollbeziehungen schon für wenige, mindestens aber drei Stützstellen aufgestellt werden.Darüber hinaus sind aufgrund der Formeln einseitige Schranken für die GrenzwerteG , usw. aus den Meßwerten berechenbar. Die Schranken sind um so schärfer, je größer der gemessene Bereich ist. Bis zu einem gewissen Grade kann auch der Verlauf der Funktionen über die Grenzen des Meßbereichs hinaus abgeschätzt werden.

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Summary Formulae are derived, which relate the loss modulus to the storage modulus and the loss compliance to the storage compliance as the Kramers-Kronig equations do. The advantage of the formulae given is, that they involve simple sums of functional values instead of integrals. Additionally the logarithmic derivative of for example the storage modulus at ₀ must be known to calculate loss modulus at ₀. But there are also given approximation formulae, which do not involve any derivative. The relative error of all approximations is smaller than 0.5%.By combining the equations at different values of the influence of unaccessible parts of one of the components can be eliminated. In this way relations are obtained, which are very useful for checking measurements. The error of each of these approximate relations can be given relative to the loss component. As a further application, formulae are discussed, which allow the calculation of an upper limit forG and a lower limit for the viscosity, when both components of dynamic modulus or of compliance are measured. The lower or upper limits are the sharper the greater the-range where measurements are available.

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Mit 5 Abbildungen und 6 Tabellen     

Comparison of low-cycle fatigue results with axial and diametral extensometers

Low-cycle fatigue tests at room temperature have been carried out on a stainless steel and an aluminum alloy utilizing an axial extensometer with cylindrical specimens and a diametral extensometer with hour-glass specimens. In all cases, the axial strain was the controlled parameter. The results obtained with both extensometers are compared. For the materials studied, it is found that the data obtained with a diametral extensometer correspond to a somewhat longer life (by a factor of the order of 1.6 for the parameters used). Furthermore, two tests have been carried out on cylindrical specimens with both extensometers where the axial-strain computed through the diametral strain was controlled throughout the material life and the measured axial strain was simultaneously recorded. Results indicate that geometry of specimen is the predominant factor influencing fatigue life.     

Towards the solution of finite plane-strain problems for compressible elastic solids

A new approach to the solution of finite plane-strain problems for compressible Isotropie elastic solids is considered. The general problem is formulated in terms of a pair of deformation invariants different from those normally used, enabling the components of (nominal) stress to be expressed in terms of four functions, two of which are rotations associated with the deformation. Moreover, the inverse constitutive law can be written in a simple form involving the same two rotations, and this allows the problem to be formulated in a dual fashion.For particular choices of strain-energy function of the elastic material solutions are found in which the governing differential equations partially decouple, and the theory is then illustrated by simple examples. It is also shown how this part of the analysis is related to the work of F. John on harmonic materials.Detailed consideration is given to the problem of a circular cylindrical annulus whose inner surface is fixed and whose outer surface is subjected to a circular shear stress. We note, in particular, that material circles concentric with the annulus and near its surface decrease in radius whatever the form of constitutive law within the given class. Whether the volume of the material constituting the annulus increases or decreases depends on the form of law and the magnitude of the applied shear stress.     

Effect of external radiation on the distortion of a vitreous body in a flow of gas

The semitransparency of a material, which determines the penetration of external radiation into the inside layers, affects significantly the temperature profile in the body [1, 2]. Since the viscosity of a melt of viscous materials depends strongly on the temperature, deformation of the temperature profile close to the surface leads to considerable change of the rate of spread of the liquid film, which has a significant effect on the rate of distortion of the body. In the present paper, the problem of distortion is formulated taking into account the transfer of radiation inside the body. The dependence of the distortion parameters and the degree of blackness of the body on the fraction of radiation in the external thermal flux and the mean free path of the radiation inside the material is determined. A sufficient condition is also obtained for the presence of a temperature maximum inside the body in a more general case than in [3].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 127–134, July–August, 1976.The author thanks G. A. Tirskii for a discussion of the posing of the problem.     

Experimental investigation of flow in a trench

An experimental investigation was made of the flow of a viscous incompressible liquid in a trench of square transverse cross section, using a laser Doppler velocimeter. The investigation was made with two values of the Reynolds number Re, corresponding to laminar and turbulent flow conditions in the channel. The experimental data show that a core with a constant vorticity is formed in the trench, that a jet propagates near the walls of the trench, and that there are secondary eddies in the corners of the trench. The motion of a viscous liquid in a trench of rectangular cross section is part of a broad class of breakaway flows. Experimental data on the investigation of flow in trenches are extremely few. A majority of the existing information is limited to visual observations [1–4]. In [2, 5, 6] the question of the unstable character of flow in trenches was discussed. Quantitative measurements of stable eddy flows in trenches were made in [7–9] using a thermoanemometer, and in [7] measurements were made of the pressure at the bottom and walls of trenches; there are data on the distribution of the velocity in the middle sections of trenches. In [8] the mean velocity, the intensity of the turbulence, and the stress of the turbulent flow were obtained in several sections parallel to the side walls of the trench, In [9] a measurement was made of the velocities also in two cross sections of a trench in which one component of the velocity prevails. A brief analysis of the existing experimental results shows that these data are insufficient to form a detailed representation of the character of flow in a trench.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 76–86, March–April, 1976.     

Probe diagnosis of a flow of particles desorbed from the surface of a solid by a low-density plasma jet

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 5, pp. 144–150, September–October, 1993.