Vol 24, No 2 (2023)

The system of Navier – Stokes differential equations describes gas flow near rocket nozzle. To find solution of this system in general case, scientists and engineers use numerical methods. Modern numerical methods do not allow engineers to model all features of gas flow. It happened because of sophisticated physical processes and limitations of computational hardware. So, at least where are two ways to improve it: to enlarge hardware or reduce computational complicacy. The global aim of many science investigations is to develop numerical approach with reduced computational complicacy and at the same time without loss of computational accuracy. In 1959, Aksel C. Wiin-Nielsen proposed a new and effective trajectories method for problem of numerical forecasting. In 1966, K. M. Magomedov developed similar approach (method of characteristics) for numerical modelling of space (three dimensional on space) gas flow. In 1982, O. Pironneau showed a new and effective approach for two dimensional approximation of the Navier – Stokes problem. It was based on method of characteristics also. Nowadays, these methods are called semi-Lagrangian or Eulerian – Lagrangian methods. They use Lagrangian nature of the transport process. To apply this advantage, scientists decompose each equation of Navier – Stokes system into three parts: convective part (hyperbolic type), elliptic part and part of right-hand side. Scientists use semi-Lagrangian approach to approximate the convective parts of equations. To develop and test modern algorithms from family of semi-Lagrangian methods, we use continuity equation from the system of Navier – Stokes equations. Conservative versions of semi-Lagrangian approach are based on Gauss – Ostrogradsky (divergence) theorem. It allows scientists to get conservation low (balance equation) for numerical solution in norm of L₁ space. Aim of our investigation is to use different time steps in different parts of computation domain. It enables us to obtain at the same time three advantages: convergence of numerical solution to exact solution, reduction of computational complicacy, implementation of conservation low (balance equation) without weight coefficients. For this purpose we decompose computational domain into two parts (subdomains) and use different time steps in them. Main complication is design algorithm in the boundaries of computational subdomains. We use one dimensional (on space) problem to demonstrate ability of developing numerical method with described advantages. Generalization of considered approach for two- or even three-dimensional cases allows engineers to model gas flow more accurately and without artificial viscosity. It is essentially important in the parts of computational domain with high level of solution gradient.

The relevance of this research work is dictated, among other things, by the need to ensure higher requirements for the accuracy characteristics of the navigation field created by spacecraft of the GLONASS navigation system in order to meet the high requirements for the accuracy characteristics of navigation determinations over long intervals of autonomous operation of spacecraft currently put forward by consumers. The presented concept of development uses the latest achievements of laser and radio engineering both to increase the throughput, noise immunity of transmitting information, as well as to reduce the mass and power consumption of onboard equipment, and to conduct inter-satellite range measurements and synchronization of onboard time scales of spacecraft navigation systems, including and for linking the system time scale of space navigation systems (or the group orbital time scale) to the time scale of the State standard of time and frequency. Ensuring the accurate operation of the laser guidance system in space is considered one of the critically important tasks, since its full-scale tests on Earth are almost impossible. Key experimental and also experimental works are analyzed according to the problems of constructing optical links of inter-satellite communication.

The question of the possibility of restoring information about a group by its lower layer, that is, by the set of its elements of prime orders, is considered. The question is classical for mathematical modeling: restoration of the missing information about the object from the part of the preserved data. A group is said to be recognizable from the bottom layer under additional conditions if it is uniquely reconstructed from the bottom layer under these conditions. A group G is said to be almost recognizable from the bottom layer under additional conditions if there exists a finite number of pairwise nonisomorphic groups satisfying these conditions, with the same bottom layer as the group G. A group G is called unrecognizable from the bottom layer under additional conditions if there is an infinite the number of pairwise non-isomorphic groups that satisfy these conditions and have the same bottom layer as the group G. Results are given on the recognition of groups by the bottom layer in various classes of groups. The concept of recognizability by the lower layer was introduced by analogy with the actively studied recognizability by spectrum, that is, by the set of orders of group elements. In this paper, we consider groups that, without a single element, coincide with their bottom layer. Examples of groups with these conditions in the classes of Abelian and non-Abelian groups are given. The properties of such groups are established. The results can be applied when encoding information in space communications.

In this paper, an analysis of existing domestic and foreign regulatory documents regulating the conduct of radiation tests of EEE-part to determine resistance to dose effects is carried out. Ionizing radiation from outer space is one of the most important operational factors affecting the performance of on-board equipment, as a result, determining the duration of the active existence. This largely determines the relevance of the topic of radiation effects in electronic equipment materials, radiation-induced degradation of semiconductor devices and integrated circuits, and determining the reliability and radiation resistance of on-board equipment under the influence of the ionizing radiation from outer space. Conducting radiation tests of EEE-part (total dose effects) is an integral part of the process of ensuring radiation resistance of on-board electronic equipment and the spacecraft as a whole. The paper identifies and shows the existing risks of the developer of the on-board equipment and the spacecraft as a whole while ensuring the radiation resistance of the equipment and the guaranteed fulfillment of the target task of the spacecraft during the entire period of active lifetime.

The results of the main theoretical calculations and some experiments on local heating of the supersonic flow of gases by an external inductor with low-temperature plasma during the ionization of gases in a ceramic, conical nozzle, carried out by means of a powerful, high-frequency, electromagnetic field, are given. Numerical calculations are based on the provisions of electromagnetic field theory based on the equations of Maxwell, Navier – Stokes for gas dynamics, Saha – Eggert for ions and electrons, which make it possible to calculate the basic parameters of the inductor and the necessary specific power for heating supersonic, multicomponent, gas flows with low-temperature plasma. A model of vortexless (laminar), supersonic, stationary gas flow was used and mathematical modeling of its movement in a conical nozzle was carried out with the aim of possibly using the effect of additional heating of the gas flow with low-temperature plasma to increase the efficiency of the liquid rocket engine.

It was found that in order to effectively heat the gas flow with low-temperature plasma in the design diameter, a conductivity of gases of at least σs ≥ 200 1/Ω·m is required for the initial temperature T_a = 2528 – 2674 ^оK and the frequency f = 27,12 MHz, which is not feasible even in the presence of a high concentration of impurities based on alkali metals. Therefore, a special device was developed – an ionizer for the combustion chamber. The use of an ionizer allows to achieve the specified conductivity for the pressure in the combustion chamber of 15 MPa (a link to the article is given in the list of references).

Calculations indicate the possibility of effective heating with low-temperature plasma of the supersonic flow of gases in the initial volume of the conical nozzle, which is adjacent to the critical cross-section of the liquid rocket engine. This will allow in the future to significantly increase its specific impulse and thrust at the start, due to an increase in the flow rate of gases in the design section. It has also been determined that the parietal region of a conical nozzle has a significant temperature gradient in the radial direction, whereas along the symmetry axis of the conical nozzle, the temperature increase has a linear relationship.

The results of numerical simulations are qualitatively consistent with the experiments conducted in a quartz reactor cooled by water, which made it possible to use a variety of gas and gas-liquid mixtures to select fuel with the optimal composition of components. Preliminary data obtained on a working stand with a thermal power of a quartz reactor not exceeding 4 kW are given.

Mirror antenna subsystems (AS) with the deployable reflectors are important integral parts of the telecommunication spacecraft payloads and provide reception and transmission of the information in a given service area [1–4]. The reflector design shall provide strength and stiffness, specified radiofrequency (RF) characteristics and antenna pattern boresight error of the AS. Performance compliance shall be approved in the frame of ground experimental testing, and thermo-elastic distortion (TED) testing to assess their effect on the antenna pattern boresight error is the part of the ground testing.

This testing is hard to carry out because of the following aspects resulting in lack of the guaranteed achieved criteria to assess the test results:

– considerable difference of thermal and physics behavior between carbon-fiber-reinforced polymer (CFRP) filler and epoxide component and the steep CFRP anisotropy result in increased variation of the layer strain-stress state and internal stresses which make the design behavior undefined under thermal environment;

– it is almost impossible in the frame of the testing to implement and maintain the real map of the thermal fields of specified accuracy on the large-sized object due to the fact that the temperature in a giant thermal chamber is extremely varying;

– in the frame of testing it is possible to carry out few optical measurements for the deformed reflector surface points which are not enough to provide the required level of confidence for geometric parameters ‘variation;

– the test lasts 50 days and requires cost-intensive chamber exploitation, huge power consumption & operating fluid rate (liquid nitrogen), expensive equipment providing thermal modes.

Development and implementation of the cutting-edge “digital twin” technology is the effective method to address TED testing issue. The main idea of the technology is to substitute real object to be tested with digital model verified based their parameter compliance using convergence criteria. The paper presents technology block diagram, convergence criteria and correlation technique of the predicted and measured TED cases. Evaluation data of the deformed reflector effects on AS RF performances are given and demonstrate that performances comply with the specified requirements and qualify successfully the “digital twin” technology under real testing. The “digital twin” was successfully implemented in 2019 year in JSC “RESHETNEV” in the frame of reflector TED testing for RF antenna subsystem with shaped antenna pattern for “Express-AMU7” spacecraft, which was launched and accepted for the flight operation in 2021.

This is the first time in the Russian space industry tests using the “digital twin” technology of a domestic reflector for RF space AS with parameters at the imported analogues level have been successfully qualified. The qualification of this technology will ensure the competition of domestic high-tech developments and will solve the problems of import substitution and increase the share of the Russian component in the global space telecommunications market.

In the program documents, which describe the national development goals of the Russian Federation until 2030 with a forecast until 2025, it is stated that one of the main state goals is to expand public access to safe and high-quality transport services, increase spatial connectivity and transport accessibility of territories and mobility of the population, etc. To solve the state tasks, it is proposed to use new aviation equipment generations based on cylindrical wing propellers. The article discusses the results of research and development work on several dimensions of cylindrical wing propellers. The results obtained allow us to lay the foundation for the theory and practice of operation of cylindrical wing propellers. The understanding of the role of the geometric relations of the rotor elements and the number of blades is laid. The limits of regulation of the angles of attack and deflection of the thrust vector are determined. Strength requirements have been formed for the design and rigidity of the parts of the cylindrical-shaped impeller. The solution of kinematic mechanisms for controlling the angles of attack of the blades and flaps, and the thrust vector in general, etc. was formed. A conceptual image of a two-seat aircraft using cylindrical wing propellers is proposed. Based on the conducted bench tests of a cylindrical-type winged propulsor, tactical and technical requirements for a two-seat local aircraft using these propellers were formed. Conclusions were drawn about the need for additional research and development work to study the influence of several working aircraft rotors on each other. It is stated that it is necessary to optimize the overall dimensions of the cylindrical rotors themselves, etc. It is proposed to conduct further research to determine structural solutions for promising aircraft of greater payload and capacity.

Magnetic semiconductors are widely used in microelectronics, which is used to control spacecraft. The transport and electrical properties depend on the magnetic structure, which can be changed by the action of the magnetic field and controlled by the current. The magnetic structure of semiconductors with a strong spin-lattice interaction, which is reduced to a four-spin exchange interaction, is investigated. The magnetic characteristics are calculated in a classical Heisenberg model constructed from equivalent magnetic atoms forming a simple cubic and square lattice. The Hamiltonian of the system contains the exchange interaction between the nearest neighbors, the four-spin exchange, and the one-ion anisotropy of the “light axis” type. The Monte Carlo method calculates the thermodynamic characteristics: the sublattice magnetization, the quadrupole parameter, the pairwise spin-spin correlation functions, the spontaneous moment at the node directed along the “light axis” and in the basis plane, the internal energy, and the magnetic susceptibility. The magnetic order type was found to change from a collinear antiferromagnet (AFM) to a noncollinear (NAF) as the four-spin exchange constant increases. The dependence of the spin correlation functions on the distance has a weakly damped oscillatory character. In the AFM-NAP transition region, the near antiferromagnetic order is replaced by the ferromagnetic one, while the far antiferromagnetic order is preserved. A phase diagram of the antiferromagnetic (AFM) and non-collinear (NAF) on square and cubic lattices is constructed on the four-spin exchange-single-axis anisotropy plane. The longitudinal and transverse susceptibility of the NAF from temperature for different parameters of the four-spin exchange is calculated. The region of anisotropy and quadrupole exchange parameters in noncollinear NAF with a first-order phase transition, the sublattice magnetization jump, and the quadrupole parameter from temperature are determined. The anisotropy and four-spin exchange constants in a classical antiferromagnet with spontaneous momentum and far- and near-order parameters were found.

The problem of providing increased accuracy without sacrificing productivity is encountered in almost all machine-building enterprises. cutting fluids affect the entire process of blade processing: they remove heat from the surface of the cutting tool, form an additional surface between the surfaces of the cutting tool and the workpiece, and affect the juvenile surfaces of the workpiece by means of a wedging action. The positive effect of cutting fluids is achieved only if they are rationally chosen. Currently, the choice of technological environments is based on some legislative standards of the enterprise. The market for cutting fluid has a large number of brands, which makes the decision more difficult. Сutting fluids give only a qualitative assessment of their brands based on their functional actions. A similar problem of choosing a rational brand of cutting fluids was also encountered in the manufacture of the innovative «Fregat» and «Fregat-SB» accelerating units. During the processing of the structural materials previously mentioned, the impact of cutting fluids was evaluated using an experimental method. The equipment for the experiment was machining center. The methodology for the experiment included external turning at different cutting speeds and feeds of the cutting tool. Free-falling jet irrigation was chosen as the method of supplying the cutting fluids. The cutting forces were measured under the action of various cutting fluids. On the basis of the experiment, regression dependences of the physicochemical properties of cutting fluids on cutting conditions were compiled. Subsequently, according to the regression dependencies, it is possible to select the optimal brand of the cutting fluids, taking into account the cutting forces in various cutting modes.