Volume 21, Nº 3 (2020)

The plane problem for elasticity equations is well studied. It can be explained by its importance for applications and by the fact that the equations can be reduced to the Cauchy-Riemann system. In spite of this importance, exact solutions that would describe the stress-strain state of bodies of finite dimensions are not numerous. Conservation laws for differential equations have been appeared more than a hundred years ago, but, as a rule, they were not used to solve specific problems, but were of purely academic interest. The situation changed with the development of the technique of construction of conservation laws for arbitrary systems of differential equations, and then with the use of conservation laws to solve boundary value problems of the theory of plasticity and elastic-plasticity. In this article, new conservation laws are constructed for the equations of the plane theory of elasticity in the stationary case. These laws form an infinite series, which is closely related to the elasticity equations solving. This fact made possible to reduce solving of boundary value problems, in terms of displacements, to the calculation of contour integrals along the boundary of a domain bounded by the studying elastic body. As it follows from the proposed technique, the studied area can be multiply connected, and the considered boundary can be piecewise-smooth.

The most common indicator of the aluminium production process managing efficiency is the cost of the metal production, but this concept includes a lot of components. First, this is the cost of raw materials and electricity in this region, as well as the labour cost per ton of products, consumption coefficients of raw materials and energy, capital costs for construction and repairs, waste disposal cost, environmental payments, etc. At the same time, there is no single functional of the process quality, depending on technological parameters, that is, the problem of complete and relatively strict mathematical process optimization as a whole is currently not solvable, not only because of its volume, but because of the lack of a complete efficiency model. In this study, particular efficiency criteria are considered, the improvement of which is aimed at the optimization model of control actions developed by the authors, which are selected based on the possible levers of the current automated process control system (APCS) for aluminium electrolysis. All tests were carried out on Virtual cell software without transfer to a real control object.

The article is devoted to the automated information system modification to solve monitoring and forecasting problems of natural and man-made emergencies in order to increase the efficiency of its functioning, namely, to increase the execution speed of the main operations, to reduce the error probability. Monitoring and forecasting of emergencies are among the priorities in the field of population from emergencies protection, as the prevention and elimination of their consequences are carried out on the basis of these tasks. At the same time, the data collection speed, processing and analysis largely determine the efficiency of the obtained results. The existing system of monitoring and forecasting of natural and man-made emergencies, its functional model in IDEF0 notation, characteristic features, advantages and disadvantages are considered. The existing system can be improved by automating a number of tasks related to the processing, transmission and storage of large data amounts, including real time data, as well as the generation of consolidated reports on the results of monitoring and forecasting of various objects. The information architecture of the solution reviewed and the corresponding database model form the basis of the proposed solution. The IDEF0 model of emergency monitoring and forecasting has been introduced taking into account the proposed modification of the automated information system. The main operation execution time comparative analysis based on the initial and modified automated information system (AIS) using the existing hardware confirms the effectiveness of the proposed solution. Data exchange and generation automation of consolidated reports on multiple monitoring objects will simplify analysis of the obtained results and solutions development based on them aimed at prevention of natural and man-made emergencies, as well as elimination of their consequences.

The paper is devoted to the study and development of new algorithms for automatic grouping of objects. The algorithms can improve the accuracy and stability of the result of solving practical problems, such as the problems of identifying homogeneous batches of industrial products. The paper examines the application of the k-means algorithm with the Euclidean, Manhattan, Mahalanobis distance measures for the problem of automatic grouping of objects with a large number of parameters. A new model is presented for solving problems of automatic grouping of industrial products based on the k-means model with the Mahalanobis distance measure. The model uses a training procedure by calculating the averaged estimate of the covariance matrix for the training sample (sample with pre-labeled data). A new algorithm for automatic grouping of objects based on an optimization model of k-means with the Mahalanobis distance measure and a weighted average covariance matrix calculated from a training sample is proposed. The algorithm allows reducing the proportion of errors (increasing the Rand index) when identifying homogeneous production batches of products based on the results of tests. A new approach to the development of genetic algorithms for the k-means problem with the use of a single greedy agglomerative heuristic procedure as the crossover operator and the mutation operator is presented. The computational experiment has shown that the new mutation procedure is fast and efficient in comparison with the original mutation of the genetic algorithm. The high rate of convergence of the objective function is shown. The use of this algorithm allows a statistically significant increase both in the accuracy of the result (improving the achieved value of the objective function within the framework of the chosen mathematical model for solving the problem of automatic grouping), and in its stability, in a fixed time, in comparison with the known algorithms of automatic grouping. The results show that the idea of including a new mutation operator in the genetic algorithm significantly improves the results of the simplest genetic algorithm for the k-means problem.

The study of heat transfer from combustion products (CP) to the impeller and the casing of gas turbines of liquid rocket engines (LRE) is an urgent task.

The solution of the flow problem, taking into account heat transfer, in rotational flows, in the flowing parts of the turbopump units (TPU) of the rocket engine, is carried out by the following methods: numerical methods; analytical approach, when solving the equations of dynamic and temperature boundary layers; as well as using empirical dependencies. The temperature parameter of the gaseous combustion products and, as a consequence, the heat exchange between the combustion products and the structural elements of the flow part, significantly affects the working and energy characteristics of the TPU LRE.

When designing gas turbines of LRE, it is necessary to take into account the presence of heat exchange processes, the working fluid temperature distribution and the structural element temperatures in the cavities of the TPU LRE (since energy losses and viscosity depend on the temperatures of the working fluid, and also determine the flow parameters). The temperature distribution in the structural elements determines the performance and reliability of the unit.

In the case of the use of cryogenic fuel components in the TPU LRE units the heating of the component leads to the implementation of cavitation modes and a drop in operating and energy characteristics. On the other hand, a lowered temperature of the working fluid leads to an increased viscosity of the components and, as a consequence, a decrease in the efficiency of the unit (especially when using gel-like components).

When studying heat transfer in the field of centrifugal forces for elements of rocket engine gas turbines it is necessary to obtain a joint solution of the equations of dynamic and temperature boundary layers in the boundary conditions of the flow parts.

This article offers a model of the distribution of dynamic and temperature boundary layers taking into account the convective component (for the case of a gaseous working fluid, i. e. Pr < 1), which is necessary for the analytical solution and determination of the heat transfer coefficient in the boundary conditions of the flow cavities of the LRE turbine. The energy equation has been analytically obtained for the boundary conditions of the temperature boundary layer, which allows integration over the surface of any shape, which is necessary in determining the thickness of the energy loss. Taking into account the integral relation, the heat transfer law of the turbulent boundary layer for the rotation cavities is written. The equations for determining the heat transfer coefficient in the form of the Stanton criterion for rectilinear uniform and rotational flows for cases of turbulent flow regimes were obtained analytically. The obtained equations for heat transfer coefficients are in good agreement with experimental data and dependences of other authors.

To clarify the trajectory of the spacecraft in a given orbit, the parameter of unmodeled acceleration is taken into account. Today, in the design and manufacture of a spacecraft to meet the requirements of the technical specifications for the maximum allowable values of unmodeled accelerations during the operation of on-board equipment, it is necessary to take into account the effects of asymmetric heat fluxes from the panels of the spacecraft on the deviation of its center of mass from a given orbit. This article discusses the problem of the influence of asymmetric heat fluxes from the surfaces of the spacecraft emanating from the panels ± Z, + Y (deterministic and non-deterministic component) on the level of unmodeled accelerations, which significantly affects the trajectory of the spacecraft.

In order to meet the requirements for the temperature control system in terms of ensuring efficient heat removal from the on-board equipment devices and its distribution over the surface of the instrument installation panel, it is necessary to significantly improve the technical characteristics of heat transfer and heat conduction processes in the spacecraft. The analysis of the current thermal control system in modern satellites is carried out and its shortcomings are revealed. A constructive option is proposed for creating an energy-intensive thermal panel, which allows more efficient heat removal from devices and distribution over the panel. The designed thermal panel is a flat sealed panel of a single complex design of aluminum alloy, made by the additive technology method. The dimensions of the thermal panel are limited by the structural dimensions of the working area of 3D printers. At the moment, the main dimensions reach 600-800 mm. An increase in the working area in the future will enable the installation of large-sized electronic equipment.

A two-dimensional mathematical model for calculating heat transfer processes in the designed thermal panel is presented. For the calculation, specific average values are introduced that characterize the effective cross sections for the vapor channels and the wick in the longitudinal and transverse directions, physical parameters (porosity of the wick and its degree of liquid saturation).

The aim of this paper is to describe an energy saving automatized simulation test complex used for spacecraft power supplies full-scale electrical ground-based tests.  The complex allows you to simulate the operation of solar array, lithium-ion-battery and spacecraft payload. The distinctive features of the test complex are a continuous and impulse control methods combination with  an improved dynamic accuracy, and recuperation of consumed energy into its internal DC network for the better energy efficiency. Test complex operational time from uninterruptible power supply accumulator batteries is significantly increased due to the recuperation of excess power into the test complex internal DC network. The results are experimentally proved.

The authors of the paper analyzed dynamic accuracy improvement and energy saving during ground-based spacecraft power system electrical tests. The process of ground-based spacecraft electrical testing includs the following tasks:

• the accurate simulation of static and dynamic characteristics of spacecraft power system energy sources and loads;
• the utilization of energy produced by power system under load and during spacecraft battery charge simulation.

The paper deals with the description of energy saving automatized simulation test complex (ESAST) including complex subsystems structure and experimental study of the test complex characteristics.

Commercially available simulation test complexes usually use continuous or impulse control methods. The continuous control methods decrease energy efficiency, as the most part of energy is dissipated on the regulator, which
requires massive heat sink, increasing weight and size. It makes difficult to produce high-power test complexes. The impulse control methods provide better energy efficiency, but limit dynamics and real devices fast response reproduction accuracy. The paper describes the combination of continuous and impulse control methods with the aim of taking the advantages of both.

The energy consumed by the test complex can be utilized either by the heat dissipation in the environment or by the recuperation into industrial AC grid. The heat dissipation reduces the energy efficiency, increases the testing room temperature (in case of high-power spacecraft power system) and an air conditioning system.  The recuperation into AC grid is free of specified disadvantages, but it requires the recuperated excess energy parameters matching with AC grid requirements through the network of grid-tied inverters, which leads to the increase of weight and size of the test complex. Moreover, the recuperation into AC grid is difficult during grid emergency shutdown, which can result in long test failure. The paper describes the method of excess energy recuperation into the complex internal DC network. The method significantly reduced test complex energy consumption, which in case of powering test complex from uninterruptible power supply (UPS) notably increase operating time from UPS accumulator batteries during AC grid emergency shutdown.

In conclusion the main advantages of ESAST are given:

• more than twice wattage reduction of test complex main power supply;
• the ability to work during AC grid emergency shutdown with increased operating time from UPS;
• the significant reducing of ESAST main parts weight and size.

Currently, design and manufacture of liquid-propellant rocket engines (LRE) are imposed with ever greater reliability requirements. Accordingly, the standards for the design and manufacture of rocket engine units are raising. One of these units is a turbopump unit (TNA), which provides continuous supply of liquid components from combustion reaction to the combustion chamber of a rocket engine to create traction or other engine units. TNA is also the main source of pressure increase for these liquid components in front of the LRE combustion chamber. Important requirements are imposed on a turbopump unit (TNA): ensuring work performance and basic parameters for a given resource with the necessary possible pauses of a specified duration; providing all engine operating modes, supplying the fuel components of the required flow rate and pressure, guarantying a high degree of reliability with acceptable entire unit efficiency; providing high anti-cavitation characteristics of the pump in all modes. In the article, the authors summarize the latest results of the study on cavitation in turbopump units of liquid propellant rocket engines alongside with the relevant research in the field of hydraulics. The problems of cavitation in cryogenic liquids, simulation of stall characteristics, and usability of various models to simulate cavitation flow are observed. A solution to the problems of flow modeling was considered with respect to applicability to the following structural elements of LRE units: interscapular space of the screw centrifugal main and booster pumps, axial pre-pump. Particular attention is paid to the implementation of various numerical methods based on the use of various cavitation models, computational fluid dynamics in various CFD packages, and also comparison of results with the model. In summary, the authors draw conclusions about the possibility of applying these methods to solve the problems of the cavitation phenomenon research in LRE.

The topological point defects in nematic liquid crystal materials have been studied. The method of oblique light incidence has been proposed to determine an azimuthal director angle of an achiral nematic as well as a chiral nematic (cholesteric). The idea of the method is based on the dependence of the optical phase difference between ordinary and extraordinary light beams on the azimuthal director angle at the layer center at oblique incidence of light on a structure in which the polar director angle of a nematic liquid crystal is not equal to 0° or 90° (conical boundary conditions). It has been shown that the phase difference reaches a maximum at a zero azimuthal angle at the center of the layer regardless of the total twist angle of the director. The developed method has been used to analyze topological defects formed in the nematic and cholesteric layers under conical boundary conditions at the interface. The director field distributions of nematic and cholesteric near the surface point defects (boojums) with topological charges m = +1 and m = –1 have been drawn based on the experimental data. The proposed method of oblique light incidence can be used to analyze a wide class of the achiral and chiral liquid crystal media of various types: smectics, nematics, and cholesterics with tilted or hybrid boundary conditions.

Holmium-manganese sulfide with giant magnetoresistance refers to new magnetic sulfide compounds of holmium and manganese that have the effect of giant magnetoresistance (i. e., with special magnetoelectric properties), which can be used as components of sensor technology, magnetic memory, and spintronics. The technology of manufacturing polycrystals Ho_XMn_1-XS grown by crystallization from the melt of the obtained powdered sulfides with a purity not lower than 99,9 %, in glass-carbon crucibles and a quartz reactor in an argon atmosphere is presented. According to the results of x-ray diffraction analysis, Ho_XMn_1-XS holmium-manganese sulfides have a HCC structure of the NaCl type. As the degree of cationic substitution increases, the unit cell parameter increases linearly with the concentration. No concomitant impurity phases are detected in the synthesized samples. To determine the state of the spin glass, magnetic moment measurements are conducted at several frequencies ω = 1 kHz, 10 kHz and 100 kHz. The dependence of magnetic characteristics on the frequency of measurements is found. The damping of the magnetic moment and its increase with a decrease in temperature is reviled, which is connected with the formation of metastable States. Measurements of electrical resistance without a field and in a magnetic field are conducted. Anomalies in the temperature dependence of the conductivity are found. A change in the magnetoresistance sign is detected with the increase of temperature below and above room temperature.