Ground track tests of modern ballistic-type aircraft products make it possible to simulate aerodynamic loads in conditions with a maximum medium density and having a significantly lower cost compared to flight tests. During track testing of products at supersonic speeds, intense vibrations of the structural elements of the movable track equipment and the product under test occur. The article deals with the processes of air flow around a rail installation moving with a high acceleration. Basic models are applied that describe the motion of a homogeneous medium at various velocities, accounting the effects of compressibility, turbulence, and heat transfer. Depending on the conditions, various flow turbulence models are used. An algorithm for numerical implementation on a rectangular grid with local adaptation and subgrid resolution of complex geometry is developed. The methodology for the numerical solution of the equations of dynamics describing the flow of a compressible gas around a curved surface is based on the integration of fluid motion and the transfer of scalar quantities in partial derivatives with respect to the volumes of computational cells-polyhedrons.

Using the FlowVision software package, the simulation of the supersonic air flow around products of various shapes was performed in relation to track tests. This made it possible to determine previously unknown dependences of the coefficients of aerodynamic drag, lift force and lateral force on the speed of motion, as well as the moments of aerodynamic forces for estimating the contribution of airflow processes to the total vibration field acting on the track carriage with the product.

Keywords: rail track, rocket carriage, numerical simulation, supersonic flow, turbulence, mesh adaptation algorithms.

Sergey A. Astakhov (Beloozersky, Russian Federation) – CSc in Technical Sciences, Director, State Research and Testing Ground for Aviation Systems named after L.K. Safronov (140250, Voskresensk district, Beloozersky, e-mail: info@gknipas.ru).

Vasily I. Biryukov (Moscow, Russian Federation) – Doctor of Technical Sciences, Professor, Moscow Aviation Institute (National Research University) (4, Volokolamskoe Highway, 125993, Moscow, e-mail:
aviatex@mail.ru).

Sergey F. Timushev (Moscow, Russian Federation) – Doctor of Technical Sciences, Professor, Moscow Aviation Institute (National Research University) (4, Volokolamskoe Highway, 125993, Moscow, e-mail:
irico.harmony@gmail.com).

Andrey V. Kataev (Moscow, Russian Federation) – Leading Engineer, State Research and Testing Ground for Aviation Systems named after L.K. Safronov (140250, Voskresensk district, Beloozersky); post-graduate student, Moscow Aviation Institute (National Research University) (4, Volokolamskoe Highway, 125993, Moscow, e-mail: a-kataev@mail.ru).

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The use of thermal non-destructive testing of products made of polymer composite materials for impact damage is one of the promising directions. The paper presents a mobile monitoring approach that provides damage detection at low impact values. A feature of the developed method of impact damage detection is a comprehensive consideration of the presence of a coating on the surface of composite material, the type of a source of thermal loading, the technical excellence of the thermal imager and the capabilities of the temperature imaging software. In the post-processing of thermal imaging data, the method used monoframe-processing technology, which included a set of operations: visualization of imaging data in a monotone palette, contrast enhancement of the thermal image and sub-framing – narrowing the area of analysis of the original thermal image, with a scanning search.

Keywords: automatic gain control, paint coating, impact energy, localization.

Gleb A. Kornilov (Zhukovsky, Russian Federation) – Head of the Research Laboratory, Central Aerohydrodynamic Institute named after N.Е. Zhukovsky (1, Zhukovsky str., 140180, Zhukovsky, e-mail: Gleb.Kornilov@TsAGI.ru).

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Connection between pilot fuel flow and pressure pulsations in dry low emission combustor is established on base of experimental data. Determining quantitative criteria of homogeneous or diffusion flame is formulated. The criteria give chance to evaluate quality of mixing fuel and air and combustion without emission measuring. The root-mean-square deviation of the dependence of the distribution of the air-fuel mixture concentration field over the combustion chamber cross section on the correlation coefficient between the pilot fuel ratio and the double amplitude of pressure pulsations in the flame tubes for a homogeneous (technically mixed air-fuel mixture) circuit was approximated based on the data obtained. The results obtained make it possible to significantly improve the quality of emission prediction by refining the semi-empirical mathematical model of the nitrogen oxides' generation, built on the basis of the Zeldovich thermal mechanism for low-emission operating modes of dry low emission combustor of the gas turbine engines. The account of heterogeneity of the process in the flame tubes makes it possible to move from the assumption of the geometric and gas-dynamic identity of the flame tubes to their actual heterogeneity. This conclusion allows refining the model. The developed mathematical model can be used as a virtual emission sensor in advanced tracking control systems of gas turbine engines.

Key words: gas turbine engine, dry low emission combustor, flame tube, pressure pulsations, homogeneous flame, diffusion flame, pilot fuel ratio, emission, correlation coefficient, mathematical model.

Valery G. Avgustinovich (Perm, Russian Federation) – Doctor of Technical Sciences, Professor,
Department of Aircraft Engines, Perm National Research Polytechnic University (29, Komsomolsky av., 614990, Perm, e-mail: august.valery@yandex.ru).

Tatyana A. Kuznetsova (Perm, Russian Federation) – CSc in Technical Sciences, Associate Professor, Department of Design and Technologies in Electronics, Perm National Research Polytechnic University (29, Komsomolsky av., 614990, Perm, e-mail: tatianaakuznetsova@gmail.com).

Almir I. Fatykov (Perm, Russian Federation) – Postgraduate student, Department of Aircraft Engines, Perm National Research Polytechnic University (29, Komsomolsky av., 614990, Perm, e-mail: fatykov-ai@avid.ru).

Vladimir O. Fofanov (Perm, Russian Federation) – Head, IT Department, Professional Development Center "European" (54a, Gagarin boulevard, 614077, Perm, e-mail: vovafofanov@gmail.com).

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The problem of constructing general solutions to the problems of terminal control of nonlinear systems is considered. It is proved that: 1) the optimal trajectory is the envelope of a parametric family of surfaces and, accordingly, a parametric family of singular curves defined on them, 2) optimal control can be found on this family. A constructive method for constructing singular curves is given. The "free" parameters of singular curves are found from the condition of minimization of the terminal functional. Such an approach in some cases avoids the explicit solution of the boundary value problem for a class of nonlinear dynamical systems, and simplifies computational algorithms.

Keywords: nonlinear discrete systems, optimal control, envelopes, parametric family, singular curves.

Vladimir P. Ivanov (St. Petersburg, Russian Federation) – CSc in Technical Sciences, Senior
Researcher, Associate Professor, St. Petersburg Federal Research Center of Russian Academy of Sciences (39, line 14, 199178, St. Petersburg, e-mail: vpivanov.spb.su@gmail.com).

1. Aleksandrov A.G. Optimaln·yye i adaptivn·yye sistemy [Optimal and adaptive systems]. Moscow, Vysshaya shkola, 1989, 263 p.

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9. Ivanov V.P. Optimizatsiya upravleniya dinamicheskimi sistemami na granitse dopustimogo mnozhestva upravleniy metodom ogibayushchikh [Optimization of the control of dynamic systems on the boundary of the admissible set of controls by the envelope method]. SPIIRAS Proceedings, no. 4, SPb, Nauka, 2007, pp. 270-276.

10. Anodina-Andrievskaja E.M., Ivanov V.P. New Methods of Synthesis and Calculation of Optimal Terminal Control. 2021 Wave Electronics and its Application in Information and Telecommunication Systems (WECONF), 2021. URL: http://dx.doi.org/10.1109/weconf51603.2021.9470551 (Date of access: 15.01.2023).

11. Ivanov V.P. Informatsionnyy dualizm zadachi optimalnogo terminalnogo upravleniya dinamicheskim obyektom [Information dualism of the problem of optimal terminal control of a dynamic object]. Informatizatsiya i svyaz, no. 2, 2021, pp. 85-90.

12. Ivanov V.P. Informatsionnyy dualizm v nelineynoy differentsialnoy igre «presledovaniye-ukloneniye» [Information dualism in the non-linear differential game "pursuit-evasion"]. Informatizatsiya i svyaz, 2021, no. 5, pp. 111-116.

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The dynamics of transient in-chamber processes of booster (overclocking) multi-hop of solid rocket motor is investigated. The research method is the formulation of a computational experiment. The conjugate formulation of the problem is considered, which includes:

– the ignition device is triggered (the combustion rate of the igniting composition is described on the basis of an experimental and theoretical approach that takes into account the burning of combustion products behind the body of the igniting device);

– heating, ignition and subsequent unsteady and turbulent combustion of a charge of a mixed solid fuel (a quasi-homogeneous combustion model is used, formulated on the basis of the equations of thermal conductivity and chemical kinetics recorded for the condensed phase (solid fuel), taking into account the influence of the gas phase (flare) on the combustion process in the condensed phase; the method of solving the problem is the finite difference method);

– unsteady three-dimensional homogeneous-heterogeneous three-phase flow of nitrogen (pre-pressurization gas of the combustion chamber) and combustion products of the igniting composition and mixed solid fuel in the combustion chamber, multi-core block and behind the multi-core block of the rocket engine (approaches of mechanics of continuous multiphase media are used; the basic system of equations is a system of vortex differential equations of gas dynamics; the solution method is multiparametric a class of difference splitting schemes by physical processes of the Davydov method);

– depressurization of the combustion chamber and the departure of the plugs of the multi-nozzle block of solid rocket motor (the equation of motion of the nozzle block plug is Newton's second law; the method of solving the problem is the Euler method).

Each of the subtasks is considered in relation and resolved simultaneously – at one-time step. To solve the formulated problem, a set of application programs has been developed using (for the main calculation module) the OpenCL multithreading information processing standard. The operability of the software product was checked.

Keywords: numerical study, multi-nozzle solid rocket motors, burning of solid propellant, gas dynamics, calculation method.

Mikhail Yu. Egorov (Perm, Russian Federation) – Doctor of Physical and Mathematical Sciences, Professor, Department of Higher Mathematics, Perm National Research Polytechnic University (29, Komsomolsky av., 614990, Perm, e-mail: egorov-m-j@yandex.ru).

Dmitry M. Egorov (Perm, Russian Federation) – CSc in Technical Sciences, General Director, Scientific-Research Institute of Polymeric Materials (16, Chistopolskaya str., 614113, Perm, e-mail: egorovdimitriy@mail.ru).

Sergey M. Egorov (Perm, Russian Federation) – CSc in Physical and Mathematical Sciences, Head of the Calculation Department, Scientific-Research Institute of Polymeric Materials (16, Chistopolskaya str., 614113, Perm, e-mail: know_nothing@bk.ru).

Vasily I. Belov (Perm, Russian Federation) – Senior Researcher, Department of the Calculation, Research Institute of Polymer Materials (16, Chistopolskaya str., 614113, Perm, e-mail: vasili.belov.1995@gmail.com).

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Achieving the speed limits by ballistic aircraft is a priority, relevant and new technical challenge for the present. Track tests of such products are one of the final stages, confirming their practical performance and efficiency. Testing of products of aviation and rocket technology at the "Rocket Rail Track 3500" FKP "GkNIPAS" named after L.K. Safronov allow to accurately simulate the real conditions in which they are operated. The experimental setup includes a two-rail track, made on a special base, which excludes the unacceptable deflection of the R65 rail, with its fixing every 0.5 m by a special embedment design. The rail track has an acceleration section with an angle of attack of 2º and a length of 2500 m and a deceleration section. The test object is placed on the missile track carriage in such a way as to exclude the impact on it of shock waves reflected from the elements of the carriage and relief. Solid propellant rocket engines are installed on the carriage, which provide the necessary thrust. The sliding bearings of the rocket carriage cover the head of the rails. The thrust of the starting rocket engines provides the necessary acceleration to achieve the maximum values of the required test speed. Track high-speed tests of special equipment objects are accompanied by intense vibration and shock loading of the structure. As the speed of products increases above 600 m/s, as tests have shown, the amplitude of elastic oscillations of the structure can reach the maximum values permissible from the strength conditions. Experimental and theoretical study of vibration and shock effects on the structure of a track carriage with test objects under the conditions of an existing rail track is an urgent task for practice.

Keywords: ground tests, rail track, rocket carriage, vibration, power spectrum density, correlation, transfer functions.

Sergey A. Astakhov (Beloozersky, Russian Federation) – CSc in Technical Sciences, Director, State Research and Testing Ground for Aviation Systems named after L.K. Safronov (140250, Voskresensk district, Beloozersky, e-mail: info@gknipas.ru).

Vasily I. Biryukov (Moscow, Russian Federation) – Doctor of Technical Sciences, Professor, Moscow Aviation Institute (National Research University) (4, Volokolamskoe highway, 125993, Moscow, e-mail: aviatex@mail.ru).

Andrey V. Kataev (Moscow, Russian Federation) – Leading Engineer, State Research and Testing Ground for Aviation Systems named after L.K. Safronov (140250, Voskresensk district, Beloozersky); post-graduate student, Moscow Aviation Institute (National Research University) (4, Volokolamskoe highway, 125993, Moscow, e-mail: a-kataev@mail.ru).

1. S.A. Astakhov, V.I. Biryukov. Problems of ensuring the acceleration dynamics of aircraft during track test at a speed of 1600 m/s. INCAS BULLETIN, Vol.12, SI 2020, pp. 33–42.

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The article describes the results of tests of standard woven and unidirectional polymer composite specimens tested for interlayer shear by the short beam method. Each group of tested specimens has a different thickness, which varies with a certain step. The key features of these tests are described and a comparative analysis of the results obtained is performed. To account for the influence of external factors, tests were conducted under different conditions (standard laboratory conditions, at reduced temperature and moisture-saturated specimens at elevated temperature). On the basis of the obtained data and the performed analysis the diagrams of dependence of the ultimate strength at interlayer shear from the thickness of the specimen were plotted, the diagrams of the range of the obtained values were plotted, the statistical significance was estimated by Student's test and the effect of the cross-sectional dimensions (in this case the thickness) of the standard specimen on the ultimate strength at interlayer shear was determined. To obtain more extensive and reliable data on this problem it is necessary to increase the number of specimens in each of the groups, and conduct repeated tests. The results are recommended for use in tests to determine the interlayer shear strength by the short beam method.

Keywords: polymer composite material, interlayer shear by short beam method, interlayer shear strength, geometric dimensions of a standard specimen, Student's test for estimation of statistical significance.

Alexander A. Zebzeev (Perm, Russian Federation) – Postgraduate Student, Department of Аircraft Еngines, Perm National Research Polytechnic University (29, Komsomolsky аv., 614990, Perm); Engineer,
Department of Experimental Research of Power Circuits and Polymer Composite Materials, UEC-Aviadvigatel (93, Komsomolsky av., 614000, Perm, e-mail: zebzeev-aa@avid.ru).

Anna V. Toropitsina (Perm, Russian Federation) – Deputy Head of Experimental Research and Works with Polymer Composite Materials, UEC-Aviadvigatel (93, Komsomolsky av., 614000, Perm, e-mail: toropitcina@avid.ru).

Danila V. Maklakov (Perm, Russian Federation) – Head of Experimental Research Team of Power Circuits and Polymer Composite Materials, UEC-Aviadvigatel (93, Komsomolsky av., 614000, Perm, e-mail:
maklakov-dv@avid.ru).

Compared to studies of the processes of icing of a structure without a gas-dynamic flow, there are significantly fewer studies with an airfoil flow. Of these, most of them are without vibrations, while studies under the influence of vibrations, devoted to the description of the mechanisms of ice formation during vibrations for various amplitudes and frequencies, could not be found.

This article presents the results of numerical modeling of airfoil icing, taking into account its vibration according to the harmonic law, describes the mechanisms of icing at various vibration velocities, and shows the effect of vibrations on the mass of ice buildup. The dependences of the coefficient of the ratio of the velocity of the oncoming gas-dynamic flow to the vibration velocity KV on the mass of ice are revealed. It is shown that at low frequencies the effect of “sticking” of ice to the walls of the airfoil prevails, and with increasing frequencies – the effect of “shaking off”.

Vibrations can not only reduce the mass of ice, but also increase it. A study of the effect of airfoil vibrations on icing will make it possible to take into account and, if necessary, change the range of natural and forced frequencies of structural elements.

At constant vibration velocities close to the oncoming flow velocity, with an increase in the oscillation frequency from 2 to 60 kHz and a corresponding decrease in amplitude, the ice mass first increases by 50–80 %, and then decreases by 15–25 % relative to the “no vibration” mode.

Keywords: icing, airfoil, vibrations, numerical simulation, supercomputer, vibration velocity, aircraft engine, ice buildup, ice thickness distribution, icing mechanism.

Stanislav L. Kalyulin (Perm, Russian Federation) – Senior Lecturer of the Department of Rocket and Space Technology and Power Systems, Engineer of the Center of High-Performance Computing Systems, Perm National Research Polytechnic University (29, Komsomolsky av., 614990, Perm, e-mail: ksl@pstu.ru).

Vladimir Ya. Modorskii (Perm, Russian Federation) – Doctor of Technical Sciences, Professor, Dean of the Aerospace Faculty, Director of the Center of High-Performance Computing Systems, Perm National Research Polytechnic University (29, Komsomolsky av., 614990, Perm, e-mail: modorsky@ pstu.ru).

1. Prihod'ko A.A., Alekseenko S.V. Chislennoe modelirovanie processov obledeneniya aerodinami­cheskih poverhnostej s obrazovaniem «barernogo» lda. Ioffe Journals, 2014, no. 3. pp. 580-589.

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3. Milyaev K.E., Semenov S.V., Balakirev A.A. Ways of fight against frosting in the aviation engine methods of countering with icing in the aircraft engine. PNRPU Aerospace Engineering Bulletin, 2019, vol. 59, pp. 5-18.

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18. Sorokin K.E. et al. Chislennoe modelirovanie obledeneniya v programmnom komplekse FlowVision. Kompyuternye issledovaniya i modelirovanie, 2020, vol. 12. no. 1, pp. 83-96.

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In the present work, a comprehensive experimental study of the patterns of fatigue failure of thick rods made of laminated carbon fiber is carried out under two loading schemes: cyclic tension and cyclic three-point bending with static tension. In the process of fatigue loading, along with the loading parameters of the samples, the resonant vibration frequency of the sample, acoustic emission parameters, strain fields, and temperatures on the sample surface were continuously recorded.

The main mechanism of destruction of laminated carbon fiber in both studied loading schemes is the appearance and development of delaminations. Experimental data on the change in the resonant frequency of sample oscillations and the parameters of acoustic emission (the number of events per unit time and the energy of events) are obtained during fatigue testing. There is a stepwise change in the number of acoustic emission events due to the appearance or sharp growth of cracks, which coincides in time with the phenomena of an abrupt change in the resonant frequency and the appearance of high-energy acoustic emission events. In the zones of fatigue failure, local areas of increased self-heating of the samples appear.

The fields of three components of the strain tensor on the surface of the studied samples during the fatigue loading were obtained by the method of digital image correlation. In the zones of delaminations, the component of deformations transverse with composite layers sharply increases.

The recording of acoustic emission parameters, deformation fields and temperatures, resonant oscillation frequency during fatigue loading makes it possible to reveal in a complex the facts and moments of the appearance and development of fatigue damage in samples.

Keywords: polymer composite materials, layered carbon plastics, fatigue, fracture, digital image correlation, acoustic emission, infrared thermometry, experimental study.

Aleksandr A. Balakirev (Perm, Russian Federation) – Senior Lecturer, Department of Aircraft Engines, Perm National Research Polytechnic University (29, Komsomolsky av., 614990, Perm, e-mail: 1st.leonao@gmail.com).

Ivan L. Gladkiy (Perm, Russian Federation) – CSc in Technical Sciences, Head of the Department of Strength of Power Circuits and Advanced Methods of Analysis, UEC-Aviadvigatel (93, Komsomolsky av., 614990, Perm, e-mail: gladky@avid.ru).

Grigoriy V. Mekhonoshin (Perm, Russian Federation) – Engeneer, Department of Aircraft Engines, Perm National Research Polytechnic University (29, Komsomolsky av., 614990, Perm, e-mail: mehonoshingrigori@
rambler.ru).

Anton D. Kurakin (Perm, Russian Federation) – Engeneer, Department of Aircraft Engines, Perm National Research Polytechnic University (29, Komsomolsky av., 614990, Perm, e-mail: kurakin_ad@mail.ru).

Mikhail Sh. Nikhamkin (Perm, Russian Federation) – Doctor of Technical Sciences, Professor, Department of Aviation Engines, Perm National Research Polytechnic University (29, Komsomolsky av., 614990, Perm, e-mail: Nikhamkin@mail.ru).

Nikolay A. Sazhenkov (Perm, Russian Federation) – CSc in Technical Sciences, Department of Aviation Engines, Perm National Research Polytechnic University (29, Komsomolsky av., 614990, Perm, e-mail: sazhenkov_na@mail.ru).

Sergey V. Semenov (Perm, Russian Federation) – Senior Lecturer, Department of Aircraft Engines, Perm National Research Polytechnic University (29, Komsomolsky av., 614990, Perm, e-mail: sergey.semyonov@
mail.ru).

Danil G. Solomonov (Perm, Russian Federation) – PhD Student, Department of Aviation Engines, Perm National Research Polytechnic University (93, Komsomolsky аv., 614990, Perm, e-mail: solomonov1198@yandex.ru).

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Due to the introduction of a new standard limiting the emission of non-volatile solid particles in the exhaust gases of a gas turbine engine, the promlem of analyzing the formation and burnout of particulate matter inside the combustion chamber becomes important in order to develop measures to reduce it.

The results of three-dimensional numerical simulation of the formation of dispersed particles using the phenomenological Lindstedt – Moss model in a diffusion flame of pre-evaporated kerosene presented. Kinetic mechanisms of n-decane and aromatic hydrocarbons mixture were used to simulate kerosene combustion with flamelet model. It is shown, that taking into account the content of aromatic hydrocarbons can significantly improve the quality of modeling of dispersed particles. The best correspondence of the calculated and experimental data is shown for the kinetic mechanism of n-decane and methylbenzene.

Based on three-dimensional numerical simulation of combustion process of a homogeneous mixture of pre-evaporated kerosene and air, the model was adjusted to simulate the formation of dispersed particles at high pressures corresponding to the full-scale parameters of an aviation gas turbine engine. An empirical formula for accounting for the effect of working pressure on the formation of dispersed particles is proposed.

Keywords: soot, particular matter, combustion chamber, gas turbine engine, operating pressure, aromatic hydrocarbons, phenomenological model, turbulent combustion, flamelet, emission.

Taras V. Abramchuk (Perm, Russian Federation) – Deputy Head of Department, UEC-Aviadvigatel (93, Komsomolsky av., Perm, 614990, e-mail: t-avia83@yandex.ru).

Aleksey M. Sipatov (Perm, Russian Federation) – head of combustor division, UEC-Aviadvigatel (93, Komsomolsky av., Perm, 614990).

Marina I. Sukhoruk (Perm, Russian Federation) – senior engineer of combustor department, UEC-Avia­dvigatel (93, Komsomolsky av., Perm, 614990).

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