M. B. Khadiev, I. V. Khamidullin, N. V. Sokolov, F. A. Kalimullin
Calculation of fluid pivot of tilting pad journal bearing
DOI: 10.25206/2588-0373-2025-9-3-5-13
The article presents a description of the design and the results of numerical studies of static features of a single pad of the fluid pivot tilting pad journal bearing. The authors describe a system of equations for the non-isothermal flow of lubricant in a hydrodynamic lubricant film; the conditions for the transition of the pad to an equilibrium mode; the flow of lubricating fluid in a hydrostatic recess. Moreover, the change in the pressure of the lubricant film along the length of the pads is illustrated depending on the magnitude of the relative eccentricity. Therefore, the features of the bearing operation mode are determined, in which a complete or unilateral “ascent” of the pad is observed. 

Keywords: journal bearing, pad, lubricant film, hydrostatic layer, temperature, pressure, preload coefficient.

S. Yu. Kaigorodov, N. E. Kuznetsov, V. L. Zabrovskiy
Development of a method for calculating the fluid inertia force in the mathematical model of a straight-line rotary pump
DOI: 10.25206/2588-0373-2025-9-3-14-21
The purpose of the article is to develop a methodology for studying the impact of liquid inertial forces on the operation of a direct rotary pump. The main focus is on creating an improved mathematical model that allows for the inertial effects of the fluid during the transition between suction and injection modes. The work proposes a new modeling approach that eliminates the limitations of traditional methods by considering the mass properties of the fluid and their influence on hydraulic resistances, changes in the working chamber geometry, and flow non-uniformity. The detailed description of model construction includes the physical formulation of the problem and the derivation of mathematical dependencies. The study resulted in the development of a method for calculating instantaneous flow that considering the liquid's angular acceleration, and the conditions for occurrence of the reverse flow. The developed methodology presents a practical value for the design and modernization of hydraulic machines in order to increase their reliability and efficiency during transition operations modes. 

Keywords: spur gear rotor pump, fluid inertia forces, mathematical modeling, calculation methodology, transient processes, angular acceleration.

A. G. Mikhailov, Yu. A. Anisimov
Developing a mathematical model to determine the optimal solar collector tilt angle: A case study of the temperate continental climate in the Omsk Region
DOI: 10.25206/2588-0373-2025-9-3-22-29
This paper investigates how the tilt angle of solar collectors affects the amount of solar radiation received under moderately continental climate conditions, with a focus on the Omsk region. A Python-based software package has been developed, which utilizes a mathematical model to convert total solar radiation on a horizontal surface into effective energy incident on an inclined plane. The effective energy values derived from the model are then applied to determine the optimal tilt angle that maximizes energy collection while taking into account regional climatic and geographical factors. The study provides a detailed assessment of the optimal tilt angle for the solar collector’s heat-absorbing surface in Omsk, analyzing conditions during both warm and cold periods. Furthermore, a comparative analysis is performed between the cumulative solar radiation obtained using the program-calculated optimal angles and the angles suggested by standard design guidelines. The findings from this research offer critical insights into the technical and economic feasibility of implementing new projects aimed at achieving higher energy efficiency. Overall, the paper presents a comprehensive methodological framework and practical data that could support future developments in solar energy harvesting and energy-efficient design. 

Keywords: tilt angle, solar collectors, insolation, mathematical modeling, Python, renewable energy sources.

M. A. Sutyaginskiy, Yu. A. Potapov, A. Yu. Gromov, P. V. Ushakov, S. S. Busarov, V. L. Yusha
Predictive analysis of temperature and energy features of medium-pressure process hydrogen compressors based on long-stroke piston stages
DOI: 10.25206/2588-0373-2025-9-3-30-37
The article considers the issues related to the prospects for implementing promising hydrogen compression technologies at large chemical, oil and gas processing plants using single- or multi-stage compressors based on low-speed long-stroke piston stages. The development and implementation of new technologies is one of the most urgent areas of development of the domestic compressor industry, ensuring the technological safety of a number of industries, including those related to the processing of natural resources. In developing the technical design of the proposed hydrogen compressor and analyzing its features, the need to ensure a safe temperature regime is considered as the dominant prerequisite. The calculations use a repeatedly tested mathematical model of the working processes of the compressor stage with a combined schematization — a quasi-stationary model of working processes with concentrated parameters in the flow part and a non-stationary model of the heat transfer through the walls of the working chamber with boundary conditions of the third type. The authors demonstrate the high efficiency of using low-speed piston stages in hydrogen compressor units, also including booster stages. 

Keywords: compressor, hydrogen, low-speed long-stroke stage, working processes, mathematical modeling, discharge temperature.

R. R. Khotsky, A. V. Burakov, L. G. Kuznetsov
Development of a mathematical model for technical diagnostics of reciprocating compressors for the rocket and space complex
DOI: 10.25206/2588-0373-2025-9-3-38-46
The article examines a piston compressor as the object of diagnostics, which is a part of the compressor equipment complex for the production, storage, and distribution of gases at launch sites providing launch vehicles. A diagnostic model for the piston compressor as for the primary device for producing compressed air has been selected, based on the processes of changes in air parameters such as pressure, volume, and temperature over one full cycle. The use of the Hilbert–Huang transforming is proposed for processing diagnostic parameters obtained from the analysis of indicator diagrams of the piston compressor stages. By applying a correlation-type function similar to the Hausdorff metric, the method compares signals from a technically faulty piston compressor with a reference (a properly functioning piston compressor) to identify characteristic malfunctions. 

Keywords: reciprocating compressor, indicator diagram, Hilbert–Huang transforming, diagnostic model, diagnostic parameters, technical diagnostics.

O. V. Vdovin, E. N. Slobodina, A. G. Mikhailov
Modeling of heat and mass transfer processes in nanofluids on the example of a parabolic solar collector
DOI: 10.25206/2588-0373-2025-9-3-47-56
The article presents the main mathematical models for numerical simulation of heat transfer processes occurring in a nanofluid — single-phase and two-phase models. A description of the device and the principle of operation of a concentrating parabolic solar collector are demonstrated. The authors perform computational studies of heat transfer processes using the single-phase method with laminar and turbulent flow of heat transfer fluids in a smooth absorbing tube and a tube with a spiral turbulator wire. Pure water and a water-based nanofluid with Al2 O3 nanoparticles with a volume concentration of 1 % are used as the heat transfer fluid. The size of Al2 O3 nanoparticles is 50 nm. The research analyses the effect of using a spiral wire turbulator in a solar collector in combination with a nanofluid as a heat transfer fluid on the temperature distribution in the absorption tube. 

Keywords: nanofluid; concentrating, parabolic, solar collector; single-phase model; two-phase model; turbulator.

K. E. Denisov, A. K. Liamasov.
Methodology for calculating the actuation mechanism of a movable blade system in low-specific-speed centrifugal pumps
DOI: 10.25206/2588-0373-2025-9-3-57-63
The paper outlines the principal stages of a calculation methodology for the blade-rotation mechanism of a low-specific-speed centrifugal pump impeller. The primary objective of the proposed approach is to enhance the energy efficiency of the pumping unit. The study focuses on an impeller of the CMG M 12.5/80 pump (head H = 80 m, design flow Qопт = 12.5 m³/h). In the first stage, the optimized geometry of the impeller’s flow passages is computed for nominal, increased and reduced flow rates. CFD results revealed that, as flow increases, the blade wrap angle must  decrease while the exit angle must increase, with the leading edge remaining fixed. Based on this insight, an adaptive control strategy is adopted, prescribing a rotation angle for each blade that maximizes hydraulic efficiency at each operating point. A numerical experiment was conducted, varying the blade rotation angle at flows of 0.7 Qопт and 1.3 Qопт to derive the correlation between the blade position and the flow rate. In the second stage, analytical expressions are derived considering the blade rotation angle to impeller outer diameter and blade exit angle, enabling construction of theoretical head curves for both fixed and adaptive blade configurations. Theoretical investigations corroborate the numerical findings. The calculation methodology has been developed for a spring-based blade actuation mechanism, for calculating the blade rotation mechanism, which is based on a spring element, and the force of which is determined by calculating the total hydraulic force acting on the blade from the working medium. 

Keywords: centrifugal pump, impeller, vane grate, regulation of the centrifugal pump, energy efficiency, hydrodynamics, numerical modeling, optimization of the flow rate.

A. S. Zolotukhin, L. N. Marenina, A. A. Drozdov, A. M. Yablokov, A. G. Nikiforov
Modern approaches of the axial compressors optimization
DOI: 10.25206/2588-0373-2025-9-3-64-74
The research reviews current and modern approaches to optimizing axial-type compressors. According to open sources, the authors present a classification of optimization approaches depending on the dimension phenomena: 1D/quasi-2D, 2D and 3D. Moreover, the authors describe purposes in the general compressor design cycle for each group of optimization tasks, as well as specific examples. The main and relevant optimization algorithms of axial compressors are considered. As a result, a universal block diagram of the optimization problem has been compiled. The objective functions and optimization parameters are also analyzed. The authors review comments and recommendations on each of the points by setting the appropriate tasks. 

Keywords: axial compressor, optimization problems, multi-objective optimization, optimization algorithms, target functions, IOSO, genetic algorithms.

A. A. Staseyev, A. A. Zharkovskiy
Development of a module of direct optimization methods for a two-dimensional automated design system of a centrifugal pump stage
DOI: 10.25206/2588-0373-2025-9-3-75-82
The paper describes the architecture of software designed to optimize the flow paths of centrifugal pump stages. The principle of selecting geometric parameters that affect the values of the head and efficiency of the stage is described. The number of points in the design of experiments is selected and a formula for the rating of the optimization calculation is proposed. Described functionality is used to perform optimization of the flow path of a stage of console centrifugal pump stage with a speed coefficient equal to 93 Based on the obtained geometric parameters, automated modeling of 3D models of the flow path is performed, which is used to perform CFD calculations in the Ansys CFX package. 

Keywords: direct optimization, CAD, correlation, latin hypercube, automation, Python, centrifugal pump, spiral outlet.

V. I. Trushlyakov, A. A. Petruk
Comparative analysis of induction, microwave and two-stage pyrolysis methods for various polymers
DOI: 10.25206/2588-0373-2025-9-3-83-91
The article presents a comparative analysis of existing methods based on pyrolysis using electromagnetic currents: induction, ultra-high frequency and two-stage combination (induction and ultra-high frequency). The authors consider the possibility of creating energy independence of the pyrolysis process for each method. Moreover, the effectiveness of each method is evaluated based on the introduced efficiency criteria: a temperature regime, reaction time, the output of liquid, combined-cycle and solid fractions, energy consumption, the complexity of control, versatility and productivity. All criteria are reduced to a dimensionless form. The corresponding criteria of induction heating are considered as the basic one. 

Keywords: pyrolysis, induction, ultra-high frequency, two-stage, criteria, energy independence.

I. S. Vavilov, K. I. Zharikov, P. S. Yachmenev, I. A. Kuzmenko, I. V. Volod’kov
Studies of the power of high-frequency losses in the toroidal resonator of a prototype of the high-frequency ion thruster
DOI: 10.25206/2588-0373-2025-9-3-92-100
The authors present a prototype of an accelerator micro thruster for a small spacecraft with a maximum power consumption of 5 W. The design is demonstrated and the main structural elements are described. Moreover, the paper also presents vacuum calorimetric studies of the power of high-frequency losses in the volume of a toroidal resonator for various working fields: air, helium, carbon dioxide, nitrogen, argon and water vapor. Due to the joint measurement of the main frequencies of the oscillator with calorimetric studies, the electrical capacitances of the oscillating circuit are obtained. With prototype 4–4.8 power consumption the calculated values of accelerating alternating voltages are 199.65–287.9 V for various gases. The measured power of high-frequency losses is 0.088–0.183 W, which is no more than 4 % of the total power consumption. 

Keywords: power of high-frequency losses, plasma, small spacecraft, nitrogen, argon, accelerating voltage, thermocouple, electrical capacity.

A. B. Yakovlev
Investigation of the effect of the working fluid flow parameters on the fineness of cleaning the centrifugal filter of the hydraulic system of a power plant
DOI: 10.25206/2588-0373-2025-9-3-101-106
The article considers the influence of the parameters of the working fluid flow (flow rate, pressure, velocity) on the fineness of cleaning the centrifugal filter of the hydraulic system of a power plant. Based on the compiled mathematical model, the author develops a calculation method and obtains the dependences characterizing the purification process, namely, the limiting size of the pollutant particles deposited in the cleaner from the pressure at the filter inlet, the flow rate of the working fluid, the tangential and radial components of the fluid velocity. 

Keywords: vortex chamber, pollutant particles, filtration fineness, tangential nozzle, tangential velocity component, radial velocity component.

A. V. Baklanov
Experimental determination of the excess air coefficient at the outlet of the burners of a two-zone combustion chamber
DOI: 10.25206/2588-0373-2025-9-3-107-113
The paper presents the results of computational and experimental determination of the excess air coefficient at the outlet of the burners of the experimental two-zone combustion chamber of the NK-16ST engine. The design features of the combustion chamber are described. The author demonstrates the bench equipment on which the burners and the combustion chamber are tested. The methodology of testing burners and combustion chambers to determine their throughput are described. Moreover, the author forms an algorithm for the sequence of computational and experimental work. As a result, the measurements of environmental characteristics during fuel consumption control in the combustion chamber zones are presented. 

Keywords: two-zone combustion chamber, gas turbine engine, burner, test, concentrations of harmful substances emissions, nitrogen oxides, carbon monoxide, excess air coefficient.

D. A. Negrov, V. Yu. Putintsev, S. V. Shil’ko, E. V. Knyazev, A. I. Glotov, D. A. Veber
Influence of the modulated ultrasound on the structure, mechanical and tribotechnical properties of polytetrafluoroethylene composite and multi-layered carbon nanotubes
DOI: 10.25206/2588-0373-2025-9-3-114-122
The article presents a comprehensive study of the structure, mechanical, and tribotechnical properties of polymer composite materials based on polytetrafluoroethylene (fluoroplastic-4) filled with multi-walled carbon nanotubes. The mechanical and tribotechnical properties are tested, and the supramolecular structure are investigated. The authors establish the patterns of changes in the complex of functional characteristics of polymer composite materials, depending on the filler concentration and the manufacturing process. A method of cold pressing with ultrasonic exposure and low-frequency amplitude modulation is proposed and implemented. The method provides intensification of the filler particles deaggregation, increasing the homogeneity of their distribution and strengthening the interfacial interaction. Moreover, the method leads to more efficient transfer of the contact load between the polymer composite material components and increase the durability of the tribosystem as a result of reducing the abrasive wear. In particular, the use of ultrasonic pressing, studied by polymer composite material at a content of 1.5 wt. % of nanotubes, the use of ultrasonic pressing provides an increase in the tensile strength by 10 %, the modulus of elasticity by 16 % and a decrease in the mass wear rate by 15 % compared to the traditional pressing technology. The results indicate the correlation of the pressing mode parameters, structure and mechanical- tribotechnical properties, which allow obtaining antifriction composites with increased strength and wear resistance. 

Keywords: polytetrafluoroethylene, multiwalled carbon nanotubes, friction surface, abrasive wear, dry friction, ultrasound, modulation.