# Vol 24, No 2 (2023)

## Section 1. Computer Science, Computer Engineering and Management

### Conservative semi-Lagrangian method for continuity equation with various time steps in different parts of computational domain

#### Abstract

*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 L _{1} 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. *

**Siberian Aerospace Journal**. 2023;24(2):218-233

### Algorithm for calculation of wave numbers in a chiral metamaterial based on composite spiral elements

#### Abstract

*Materials** with various exotic electromagnetic characteristics have been extensively studied in recent decades to satisfy the growing interest in various fields, including visualization, telecommunications, energy use, and so on. As a particularly promising candidate, electromagnetic metamaterials exhibit electromagnetic properties that are inaccessible to natural materials. Due to the fact that the chiral medium (metamaterial) is a set of uniformly distributed conductive mirror-asymmetric (chiral) elements in an isotropic dielectric medium. In addition to the material from which the chiral element is made, its shape also plays an important role. That is why it is so important to study new types of chiral elements, as well as to determine the electrodynamic properties of chiral metamaterials based on them. The paper considers the solution of the problem of determining the reflection and transmission coefficients when a plane electromagnetic wave falls on a planar layer of a chiral metamaterial based on multi-pass conducting elements of the spiral type, taking into account the structural parameters of the metamaterial, which is a matrix of thin-wire ideally conducting elements in the form of N mutually orthogonal spirals. To determine the parameters of a chiral metamaterial based on composite spiral elements, the construction of a particular mathematical model of a composite element based on an arbitrary number of spiral elements in a spatial configuration, as well as a metamaterial based on a matrix of such elements, is considered. An algorithm for calculating the propagation constants of waves with circular polarizations in the specified metamaterial is proposed. From the calculations presented, it can be noted that the metastructure under study at one frequency can act as a frequency-selective protective shield that is not transparent to radiation near the main resonant frequency.*

**Siberian Aerospace Journal**. 2023;24(2):234-246

### Development concept of inter-satellite laser communication

#### Abstract

*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.*

**Siberian Aerospace Journal**. 2023;24(2):247-259

### Space integrated network: architectural and technical solutions justifica-tion of the ReshUCube-2 space mission

#### Abstract

*Space** missions using small CubeSat-type spacecraft have become widespread. In this regard, integrated space networks are a promising direction for the development of this industry. In this paper, the architecture of such a network is proposed. It is planned that the first node of this network will be the ReshUCube-2 device.*

*Functional** requirements and technical limitations of the described architecture were determined. Based on the requirements, a review and comparative analysis of network protocols and technologies of different levels: physical, channel, network, transport and application. As a result, a network stack is proposed that meets these requirements. The key protocols in the stack were chosen: LoRa, 802.15.4, IPv6, 6LoWPAN, RTL, TCP, UDP and CoAP. Methods of software and hardware implementation of network nodes are proposed. A test bench based on specially developed unified devices is demonstrated, on which it is proposed to work out the functions of network interaction. A test payload board for small spacecraft – nodes of the space segment is also shown.*

*The** results obtained will be used in the development of future space missions of the Reshetnev Siberian State University. In addition, the results can be useful in the design of the Internet of Things, the Internet of vehicles and similar networks. The results of the work can also serve as a basis for future research in the field of network technologies, digital signal processing, inter-satellite interaction and space information systems.*

**Siberian Aerospace Journal**. 2023;24(2):260-272

### On the bottom layer in groups

#### Abstract

*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. *

**Siberian Aerospace Journal**. 2023;24(2):273-278

## Section 2. Aviation and Space Technology

### Problematic issues of application of methods of accelerated radiation testing of ECB

#### Abstract

*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.*

**Siberian Aerospace Journal**. 2023;24(2):280-290

### Algorithm for simulation of vibration effects during track tests of aircraft and missile technology

#### Abstract

*Track** high-speed ground tests of products of aviation and rocket technology make it possible to experimentally confirm the aerodynamic and strength characteristics of new aircraft or their components. Experimental installation “Rocket rail track 3500”, located on the territory of the Federal State Enterprise “Scientific Test Range of Aviation Systems named after L. K. Safronov” (FKP “GkNIPAS” named after L.K. Safronov), is a complex hydro-gas-dynamic engineering structure. The main part of this installation is a rail track placed on a special concrete base, which is based on piles to eliminate the influence of viscoelastic ground vibrations. Between the rails, taking into account the profile of the track, a hydrodynamic multi-level tray is made, designed for hydraulic braking of the stored track sled. The movable rocket track sled rests on slip shoes covering the top rail head. On the track sleigh, solid propellant rocket engines and the object of study are placed. The article describes the approach to the calculation of determining the dynamic loads acting on the elastic structure of the track sled with the test object. The design is represented by a schematic spatial model of elastic beams in the form of rods, plates, pipes with equivalent mass and stiffness, interconnected by elastic links. A model of non-stationary aerodynamic forces is formulated taking into account viscosity for numerical calculations of the flow around the sled structure. Programs have been developed and modeling of the aerodynamic interaction in the case of a supersonic air flow around the structure of a rocket sled has been carried out. The results of vibrational accelerations of elements, components of the sled and the test object, depending on the speed of movement, were obtained by calculation. The forms and frequencies of natural free vibrations of the sled structure are determined, and the densities of the vibration acceleration spectra are calculated.*

**Siberian Aerospace Journal**. 2023;24(2):291-308

### Numerical simulation of supersonic gas flow in a conical nozzlewith local plasma heating and experimental results

#### Abstract

*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* *σ**s** ≥ 200 1/**Ω·**m* *is* *required* *for* *the* *initial* *temperature* *T _{a}*

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*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.*

**Siberian Aerospace Journal**. 2023;24(2):309-324

### To the method of calculation of the main characteristics of promising booster electric pump units of liquid processor engines

#### Abstract

*The* *increase* *in* *the* *capacity* *of* *electric* *power* *sources**, **the* *use* *of* *electric* *motors* *in* *the* *systems* *for* *supplying* *rocket* *fuel* *components* *from* *foreign* *companies**, **the* *limitations* *on* *the* *power* *of* *classical* *fuel* *supply* *systems** – **all* *these* *conditions* *set* *a* *trend* *for* *studying* *the* *possibility* *of* *introducing* *electric* *drives* *for* *rocket* *engine* *power* *systems**.*

*The* *study* *is* *devoted* *to* *the* *analysis* *of* *the* *possibility* *of* *using* *electric* *motors* *as* *a* *drive* *for* *the* *main* *and* *auxiliary* *pumps* *of* *liquid* *rocket* *engines**. **Promising* *developments* *in* *the* *field* *of* *rechargeable* *batteries* *give* *grounds* *for* *a* *mathematical* *justification* *for* *the* *use* *of* *this* *technical* *solution* *in* *order* *to* *modernize* *power* *systems**, **both* *existing* *rocket* *engines* *and* *samples* *under* *development**.*

*The* *article* *presents* *a* *selection* *of* *patents* *for* *modern* *technologies* *for* *creating* *high**-**capacity* *batteries**, **an* *analysis* *of* *the* *use* *of* *technology* *for* *the* *use* *of* *electric* *motors* *in* *the* *international* *market* *for* *delivering* *payloads* *to* *orbits**, **and* *a* *rationale* *for* *the* *prospects* *of* *this* *direction* *in* *the* *development* *of* *rocket* *engines**. **The* *statistics* *of* *the* *causes* *of* *failures* *of* *upper* *stages* *and* *their* *correlation* *with* *units**, **which* *can* *be* *replaced* *by* *more* *reliable* *systems* *using* *electric* *motors**, **have* *been* *studied**. **The* *advantages* *and* *disadvantages* *of* *power* *supply* *systems* *with* *the* *use* *of* *electric* *drives* *are* *determined**.*

*This* *study* *allows* *us* *to* *conclude* *that* *the* *use* *of* *electric* *motors* *in* *rocket* *engine* *power* *systems* *is* *a* *promising* *solution* *that* *improves* *the* *efficiency* *of* *the* *propulsion* *system**, **performance* *and* *reliability**.*

**Siberian Aerospace Journal**. 2023;24(2):325-334

### Implementation of “digital twin” technology within the thermo-elastic distortion testing of a precision carbon fiber reflector for the spacecraft antenna subsystem

#### Abstract

*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**-**AMU**7” **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**.*

**Siberian Aerospace Journal**. 2023;24(2):335-347

### Features of defining the damping function in spacecraft finite-element models

#### Abstract

*Dynamic* *analysis* *of* *spacecraft* *structures* *is* *a* *key* *item* *in* *the* *process* *of* *structure* *design**. **For* *example**, **a* *launch* *vehicle* *generates* *the* *highest* *loads**, **including* *dynamic* *ones**, **for* *most* *spacecraft* *structures**. **Determining* *of* *damping* *parameters* *is* *an* *important* *component* *in* *the* *analysis* *of* *the* *structure* *response* *to* *mechanical* *loads**. **It* *is* *therefore* *very* *important* *to* *be* *aware* *of* *the* *damping* *properties* *of* *the* *structure**. **The* *characterization* *of* *damping* *is* *important* *in* *making* *accurate* *predictions* *of* *the* *frequency* *response* *of* *any* *loaded* *structure**. **The* *article* *presents* *some* *excerpts* *from* *sources* *devoted* *to* *the* *space* *technique* *design**, **and* *containing* *information* *about* *damping* *in* *structures**. **The* *aim* *of* *the* *work* *was* *to* *improve* *the* *accuracy* *of* *calculations* *using* *finite* *element* *models**. **The* *paper* *demonstrates* *the* *results* *of* *the* *search* *for* *a* *method** (**form**) **of* *setting* *the* *damping* *function* *in* *the* *Femap* *software* *that* *would* *provide* *the* *correct* *levels* *of* *the* *frequency* *response* *of* *the* *structure* *to* *the* *loads* *applied**. **A* *finite* *element* *model* *of* *a* *cantilever* *beam* *was* *an* *object* *of* *the* *computational* *experiment* *carried* *out**. **A* *frequency* *table* *obtained* *at* *the* *modal* *analysis* *stage* *prove* *to* *be* *useful* *for* *frequency* *response* *analysis**. **The* *only* *one* *natural* *frequency* *in* *spectrum* *is* *enough* *to* *implement* *current* *study**. **Further**, **damping* *function* *was* *set* *in* *several* *ways* *in* *order* *to* *identify* *the* *one* *that* *provided* *the* *most* *correct* *response* *for* *the* *natural* *frequency* *under* *study**.*

**Siberian Aerospace Journal**. 2023;24(2):348-354

### The use of cylindrical wing propellers in aviation technology

#### Abstract

*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.*

**Siberian Aerospace Journal**. 2023;24(2):355-363

## Section 3. Technological Processes and Materials

### Thermodynamic properties of anisotropic antiferromagnets with four-spin exchange

#### Abstract

*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**.*

**Siberian Aerospace Journal**. 2023;24(2):366-374

### Production of blanks for flexible waveguide sections of the spacecraft by laser weld-ing

#### Abstract

*Currently**, **JSC** “**ISS**” **named* *after* *Academician* *M**. **F**. **Reshetnev* *is* *working* *on* *the* *development* *of* *the* *production* *of* *billets* *of* *flexible* *waveguide* *sections** (**DHW**) **with* *sections* *from** 20**´**10 **to** 70**´**30, **with* *a* *wall* *thickness* *of** 0.1 **mm* *made* *of* *BrB**2 **copper* *alloy**. **The* *maximum* *deviation* *of* *the* *size* *of* *the* *inner* *channel* *is* *not* *more* *than** 0.1 **mm**. **Such* *methods* *of* *manufacturing* *DHW* *blanks* *by* *pressure**, **such* *as* *rolling* *and* *drawing**, **take* *up* *to** 20 **working* *shifts* *and* *include* *a* *large* *number* *of* *cycles** (**from** 6 **to** 8), **require* *heat* *treatment* *and* *etching* *of* *parts* *after* *each* *cycle**. **In* *this* *regard**, **the* *task* *was* *set* *to* *reduce* *the* *complexity* *of* *the* *production* *of* *DHW* *blanks**. **The* *solution* *to* *the* *problem* *can* *be* *welding* *of* *shells* *from* *sheet* *blanks* *on* *a* *forming* *device**, **followed* *by* *the* *execution* *of* *a* *longitudinal* *seam**. **As* *part* *of* *the* *solution* *of* *the* *task**, **the* *calculation* *of* *the* *amount* *of* *energy* *required* *to* *melt* *the* *edges* *of* *the* *part* *was* *carried* *out**, **the* *analysis* *of* *the* *possibility* *of* *assembly* *by* *various* *welding* *methods* *for* *welding* *thin**-**walled* *shells* *with* *exact* *dimensions* *was* *carried* *out**.*

*The* *analysis* *of* *the* *material* *showed* *that* *welding* *should* *be* *carried* *out* *in* *inert* *media**. **The* *following* *methods* *were* *chosen* *for* *welding* *the* *samples**: **arc* *welding* *in* *the* *environment* *of* *argon* *protective* *gas* *with* *a* *non**-**melting* *electrode**, **microplasma* *and* *laser* *welding**. **In* *the* *course* *of* *the* *work**, 30 **samples* *of** 100**´**200 **were* *welded**, **showing* *that** 70 % **of* *the* *samples* *are* *defective* *during* *arc* *welding* *and* *microplasma* *welding**, **while* *only** 5 % **are* *formed* *during* *laser* *welding**. **The* *following* *conclusions* *are* *obtained**: **with* *arc* *welding* *methods* *of* *small* *thicknesses**, **unacceptable* *defects* *occur* *due* *to* *the* *instability* *of* *the* *arc**, **whereas* *when* *using* *laser* *welding**, **uniform* *formation* *of* *the* *weld* *is* *observed**. **Metallographic* *studies* *and* *tensile* *tests* *were* *carried* *out* *on* *samples* *welded* *by* *laser* *welding**, **showing* *the* *specific* *strength* *of* *the* *weld* *metal* *at* *least** 90 % **of* *the* *strength* *of* *the* *base* *metal* *and* *the* *absence* *of* *defects* *in* *the* *cross* *section* *of* *the* *weld* *metal**.*

**Siberian Aerospace Journal**. 2023;24(2):375-384

### Influence of physical and chemical properties of cutting fluids on the cutting force of the cutting process

#### Abstract

*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**. **С**utting* *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**.*

**Siberian Aerospace Journal**. 2023;24(2):385-395

### Simulation model of the system for ensuring the intraclimatic characteristics of clean industrial premises of space industry enterprises

#### Abstract

*The* *creation* *of* *modern* *products* *of* *rocket* *and* *space* *technology* *is* *provided* *at* *the* *enterprises* *of* *the* *space* *industry* *by* *a* *large**-**scale* *production* *and* *technological* *complex* *that* *unites* *the* *main* *production* *and* *auxiliary* *units**, **engineering**, **technological* *and* *operational* *services* *that* *perform* *complex* *tasks* *to* *improve* *the* *quality* *and* *reliability* *of* *products**.*

*The* *most* *important* *operations* *of* *the* *technological* *processes* *of* *assembly* *and* *testing* *of* *spacecraft* *are* *carried* *out* *in* *the* *so**-**called** “**clean* *rooms**” (**PE**), **in* *which* *the* *concentration* *of* *aerosol* *dust* *particles* *is* *regulated* *by* *the* *regulatory* *industry* *documentation**, **as* *well* *as* *the* *parameters* *of* *the* *temperature* *and* *humidity* *regime* *are* *set**. **In* *order* *to* *control* *the* *internal* *climatic* *condition* *of* *clean* *rooms* *and* *control* *the* *operation* *of* *heat* *and* *power* *equipment* *for* *the* *appropriate* *purpose**, **it* *is* *proposed* *to* *develop* *a* *digital* *twin* *of* *a* *production* *clean* *room* *and* *a* *system* *for* *maintaining* *the* *stability* *of* *the* *internal* *climatic* *characteristics* *of* *this* *room**, **taking* *into* *account* *the* *ongoing* *technological* *processes* *and* *individual* *operations* *with* *a* *large* *amount* *of* *functionality**.*

*As* *an* *initial* *model* *of* *this* *system**, **a* *simulation* *model* *of* *the* *object* *of* *study* *is* *considered**, **which* *is* *a* *clean* *room* *located* *in* *a* *typical* *industrial* *building**. **The* *boundary* *conditions* *of* *the* *model* *are* *established**, **the* *main* *factors* *of* *the* *heat* *and* *humidity* *state* *of* *the* *internal* *volume* *are* *determined**, **a* *method* *for* *calculating* *heat* *flows* *from* *various* *heat* *sources* *is* *developed**.*

*Taking* *into* *account* *the* *aerodynamic* *characteristics* *of* *the* *ventilation* *equipment**, **recommendations* *are* *presented* *for* *the* *mathematical* *determination* *of* *the* *parameters* *of* *air* *flows** (**inflow* *and* *removal* *of* *air* *masses* *during* *the* *operation* *of* *ventilation* *equipment**).*

*As* *a* *result* *of* *the* *development* *of* *computational* *methods**, **a* *closed* *system* *of* *implicit* *nonlinear* *equations* *is* *obtained**, **which* *is* *solved* *by* *numerical* *bisection* *methods* *with* *a* *given* *accuracy**.*

*The* *simulation* *model* *of* *the* *state* *of* *emergency* *is* *the* *basic* *basis* *for* *constructing* *a* *digital* *twin* *of* *an* *object**, **the* *concept* *of* *which* *assumes* *that* *the* *object* *can* *be* *represented* *as* *a* *physical* *and* *virtual* *system**. **At* *the* *same* *time**, **the* *display* *and* *interaction* *of* *real* *and* *virtual** (**digital**) **objects* *makes* *it* *possible* *to* *form* *specific* *recommendations* *for* *maintaining* *the* *required* *parameters** (**temperature**, **humidity**, **flow* *rate**), **optimizing* *the* *operating* *modes* *and* *maintenance* *of* *a* *real* *clean* *production* *room* *for* *the* *assembly* *and* *testing* *of* *modern* *competitive* *spacecraft**.*

**Siberian Aerospace Journal**. 2023;24(2):396-410