Variational problem of optimum side wall design for a narrow three-dimensional nozzle

The optimum design of the side walls of the supersonic section of a three-dimensional nozzle with two planes of symmetry is considered in the narrow channel model approximation, which reduces three-dimensional to two-dimensional flow. This nozzle realizes maximum thrust for given sonic or supersonic inlet flow, upper and lower walls, maximum permissible length and pressure outside the nozzle. In general, an approximate solution of the variational problem can be obtained by the indeterminate control contour method [1]. For nozzles with nonexpanding end sections of the upper and lower walls this is a rigorous solution. Numerical algorithms, based on the method of characteristics, for constructing the optimum, side walls and calculating the flow in narrow channels are developed in the formulation adopted using the optimality conditions found, which generalize the wellknown conditions for plane and axisymmetric configurations [1]. In addition, the three-dimensional supersonic flow in the nozzles thus designed has been calculated in accordance with a shock-capturing marching scheme [2], which for the uniform grids employed in the calculations gives a second-order approximation. A rather complex relation is established between the thrust of the optimum configurations constructed and the shape of their inlet cross sections.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 102–112, March–April, 1992.The authors are grateful to L. E. Sternin for drawing their attention to the problem and to V. A. Vostretsova for assisting with the work.     

Some unique features of supersonic unsteady gas flow around bodies

We consider unsteady supersonic gas flow about bodies for small Strouhal numbers. The amplitude of the angles of attack is assumed arbitrary under the condition that the bow shock remains attached, and the flow behind the shock is supersonic. A criterion is formulated which permits the comparison of the damping characteristic for small and large amplitudes of the disturbed motion. A comparison is made, using the wedge as an example, of the damping characteristics calculated by various theories, and the hypersonic similarity law is verified. Simple asymptotic equations are presented for the rotary derivatives of the thin wedge in a hypersonic gas stream.     

Electrification of weakly conducting liquids in the neighborhood of a wall

The problem of the generation of an uncompensated electric space charge in weakly conducting viscous fluid channel flows in which the medium interacts electrochemically with an interface is investigated for an arbitrary relation between the mobilities of the charged particles of different kinds. New models of the electrochemical surface processes are considered. The effect of the parameters of these processes on the electrification current and on the time taken by the electric parameters of the medium is studied to reach saturation. The possibility of the generation of strong induced electric fields on the interface is justified theoretically, two basic parameters affecting the strength of these fields are determined, and an explanation of the discharge process observed in the experiments in the form of local fluid glow zones is proposed.     

Features of the scattering of protons and relativistic electrons intersecting a thin planar target at a small angle to its surface

The processes of scattering of protons and relativistic electrons incident on a planar target at a small angle to its surface have been simulated by the Monte Carlo method. The spatial and energy distributions of the beams of particles both passed through the target and reflected from it have been calculated. The dependence of the characteristics of beams on the initial energy and direction of injection of particles, as well as on the material and thickness of the target, has been considered. The transmission, reflection, and absorption coefficients for electrons in the target have been calculated. The initial energy in the calculations is varied in the range of 7–100 MeV and the angle between the trajectory of particles and the surface of the target is in the range of 1°–45°. The thickness of the target varies from 0.2 to 3 mm. Aluminum, iron, and copper targets have been considered. It has been shown that the intersection of targets at small angles not only increases the transverse dimensions of a beam, but also changes the direction of its motion. The results of the reported calculations of the scattering of relativistic electrons intersecting a foil at small angles to its surface are in qualitative agreement with experimental data.     

Temperature hysteretic effect and its influence on colossal magnetoresistance of La0.33Nd0.33Ca0.33MnO3

Electrical resistance (R) measurements of a bulk La_0.33Nd_0.33Ca_0.33MnO₃ perovskite in magnetic fields up to 40 kOe have revealed anomalous temperature hysteretic effects both in 0 Oe and 20 kOe magnetic fields. The sharp peak observed in the R vs. T plot indicates the occurrence of metal-to-insulator (M-I) transition at a temperature of T _MI=110 K and 140 K, for cooling and warming paths, respectively. An applied magnetic field of 20 kOe reduces the resistance and shifts T _MI to 160 K and 185 K for cooling and warming, respectively. We have observed a much higher resistance in the cooling path than in the warming path leading to the hysteretic resistance ratio (R _cool/R _warm) of 200 at 110 K and 1.8 at 160 K for 0 Oe and 20 kOe, respectively. Record values of colossal magnetoresistance (CMR) have been achieved. The CMR value reaches nearly 99% in the temperature ranges of 90 K to 140 K and 90 K to 170 K for 20 kOe and 40 kOe magnetic fields in the cooling mode, respectively. The observed unusual behavior is attributed to the co-existence of La-rich and Nd-rich domains assumed to be distributed randomly in the compound.     

Peak effect studies in single crystals CeRu2 and 2H-NbS2

We have studied the peak effect (PE) phenomenon in single crystals of weakly pinned superconductors CeRu₂ and 2H-NbS₂. 2H-NbS₂ is iso-structural and iso-electronic to 2H-NbSe₂, whose similarity with CeRu₂ as regards the PE representing the order-to-disorder transformation of the flux line lattice was claimed some time ago. We report on the step change in equilibrium magnetization across the peak effect in CeRu₂. We also present the vortex phase diagram of 2H-NbS₂ obtained from the magnetization data, and compare the PE phenomenon in 2H-NbS₂ and 2H-NbSe₂.     

Qualitative Identification of Milk Fat from Chromatographic Data

The data on the amount of fatty acids in milk, animal, vegetable, and mixed fats were obtained by capillary gas–liquid chromatography. Statistical data on the concentrations of myristic, palmitic, stearic, oleic, linoleic, and linolenic acids in milk fat were considered as criteria of its natural origin. Concepts were formulated for the detection of a multicomponent adulterating additive of variable composition in a product containing variable amounts of the same components. A graphical interpretation of the results of the analysis was proposed based on the identification zone.     

Interaction of a blown gas jet with a supersonic oncoming stream without formation of a three-dimensional region of boundary layer separation

A study is made of the flow resulting from the interaction of a supersonic stream with a transverse sonic or supersonic jet blown at right angles to the direction of the main stream through a nozzle whose exit section is situated on a flat wall.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 137–139, May–June, 1981.     

Theory of cooled electric probes in a dense plasma. Influence of thermal diffusion

The problem of an electric probe in the shape of a sphere in a weakly ionized three-component plasma at rest is studied. It is assumed that the probe diameter is appreciably larger than the mean free path of the charged particles and that the temperature of the probe surface differs from the temperature of the undisturbed plasma. The contribution of thermal-diffusion mass transport is taken into account in the expressions for the densities of the electric currents of the components. A new numerical method is developed to obtain a solution of the problem in a wide range of the determining parameters. The current-voltage characteristics are constructed. The influence of the probe temperature, the transport coefficients, and other parameters on the current-voltage characteristics is analyzed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 103–112, March–April, 1979.