Search Results for “rocket propulsion” – Collected book of scientific-technical articles https://journal.yuzhnoye.com Space technology. Missile armaments Tue, 05 Nov 2024 21:10:34 +0000 en-GB hourly 1 https://journal.yuzhnoye.com/wp-content/uploads/2020/11/logo_1.svg Search Results for “rocket propulsion” – Collected book of scientific-technical articles https://journal.yuzhnoye.com 32 32 7.1.2024 Selection of the functional units for the Cyclone-4M ILV separation system https://journal.yuzhnoye.com/content_2024_1-en/annot_7_1_2024-en/ Fri, 14 Jun 2024 11:36:31 +0000 https://journal.yuzhnoye.com/?page_id=34957
2024, (1); 61-71 DOI: https://doi.org/10.33136/stma2024.01.061 Language: Ukrainian Annotation: Separation of the spent LV stages is one of the important problems of the rocket technology, which requires the comprehensive analysis of different types of systems, evaluation of their parameters and structural layouts. Basic requirements are specified that need to be taken into account when engineering the separation system: reliable and safe separation, minimal losses in payload capability, keeping sufficient distance between the stages at the moment of the propulsion system start. Certain types of «cold» and «warm» separation of the spent stages of such rockets as Dnepr, Zenit, Antares, Falcon-9 with different operating principle are introduced – braking with the spent stage and pushing apart two stages.
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7. Selection of the functional units for the Cyclone-4M ILV separation system

Authors:

Logvinenko A. I., Makarenko A. O., Khomyak V. O., Olesiyuk A. A.

Organization:

Yangel Yuzhnoye State Design Office, Dnipro, Ukraine

Page: Kosm. teh. Raket. vooruž. 2024, (1); 61-71

DOI: https://doi.org/10.33136/stma2024.01.061

Language: Ukrainian

Annotation: Separation of the spent LV stages is one of the important problems of the rocket technology, which requires the comprehensive analysis of different types of systems, evaluation of their parameters and structural layouts. Basic requirements are specified that need to be taken into account when engineering the separation system: reliable and safe separation, minimal losses in payload capability, keeping sufficient distance between the stages at the moment of the propulsion system start. Detailed classification of their types («cold», «warm», «hot», «cold-launched» separation) is given and their technical substance with advantages and drawbacks is described. Certain types of «cold» and «warm» separation of the spent stages of such rockets as Dnepr, Zenit, Antares, Falcon-9 with different operating principle are introduced – braking with the spent stage and pushing apart two stages. Brief characteristics of these systems are given, based on the gas-reactive nozzle thrust, braking with solid-propellant rocket engines, separating with spring or pneumatic pushers. Development of the separation system for the advanced Cyclone-4M ILV is taken as an example and design sequence of stage separation is suggested: determination of the necessary separation velocity and capability of the separation units, determination of the number of active units, calculation of design and energy parameters of the separation units, analysis of the obtained results followed by the selection of the separation system. Use of empirical dependences is shown, based on the great scope of experimental and theoretical activities in the process of design, functional testing and flight operation of similar systems in such rockets as Cyclone, Dnepr and Zenit. According to the comparative analysis results, pneumatic separation system to separate Cyclone-4M Stages 1 and 2 was selected as the most effective one. Its basic characteristics, composition, overall view and configuration are specified. Stated materials are of methodological nature and can be used to engineer the separation systems for LV stages, payload fairings, spacecraft etc.

Key words: separation system, functional units of separation, «cold separation», «warm separation», pneumatic pusher, spring pusher, SPRE, gas-reactive nozzles, Zenit LV, Dnepr LV, Falcon 9 rocket, Cyclone-4М LV.

Bibliography:
  1. Pankratov Yu. , Novikov A. V., Tatarevsky K. E., Azanov I. B. Dynamika perekhodnykh processov. 2014.
  2. Sinyukov A. M., Morozov N. I. Konstruktsia upravlyaemykh ballisticheskykh raket. 1969.
  3. Kabakova Zh. V., Kuda S. A., Logvinenko A. I., Khomyak V. A. Opyt razrabotki pneumosystemy dlya otdelenita golovnogo aerodynamicheskogo obtekatelya. Kosmicheskaya technika. Raketnoe vooruzhenie. 2017. Vyp. 2 (114).
  4. Kolesnikov K. S., Kozlov V. V., Kokushkin V. V. Dynamika razdeleniya stupeney letatelnykh apparatov. 1977.
  5. Antares – Spaceflight Insider: web site. URL: https://www. Spaceflightinsider.com/missions/iss/ng-18-cygnus-cargo-ship-to-launch-new-science-to-iss/Antares (data zvernennya 30.10.2023).
  6. Falcon 9 – pexels: website. URL: https://www. pexels.com/Falcon 9 (data zvernennya 31.10.2023).
  7. Kolesnikov K. , Kokushkin V. V., Borzykh S. V., Pankova N. V. Raschet i proektirovanie system razdeleniya stupeney raket. 2006.
  8. Cyclone-4M – website URL: https://www.yuzhnote.com (data zvernennya 31.10.2023)
  9. Logvinenko A. Sozdanie gasoreaktivnykh system otdeleniya i uvoda otrabotavshykh stupeney – noviy shag v RKT. Kosmicheskaya tekhnika. Raketnoe vooruzhenie, KBU, NKAU, vyp. 1, 2001.
  10. Logvinenko A. I., Porubaimekh V. I., Duplischeva O. M. Sovremennye metody ispytaniy system i elementov konstruktsiy letatelnykh apparatov. Monografia. Dnepr, KBU, 2018.

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7.1.2024 Selection of the functional units for the Cyclone-4M ILV separation system
7.1.2024 Selection of the functional units for the Cyclone-4M ILV separation system
7.1.2024 Selection of the functional units for the Cyclone-4M ILV separation system

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]]> 5.1.2024 Assessment of risk of toxic damage to people in case of a launch vehicle accident at flight https://journal.yuzhnoye.com/content_2024_1-en/annot_5_1_2024-en/ Thu, 13 Jun 2024 06:00:42 +0000 https://journal.yuzhnoye.com/?page_id=34981
Typically, such propellants are used in the LV/ILV upper stages, where a small amount of propellant is contained; however, some LV/ILV still use such fuel in all sustainer propulsion stages. For launch vehicles containing toxic rocket propellants, flight accidents may result in the failed launch vehicle falling to the Earth’s surface, forming large zones of chemical damage to people (the zones may exceed blast and fire zones). This is typical for accidents occurring in the first stage flight segment, when an intact launch vehicle or its components (usually individual stages) with rocket propellants will reach the Earth’s surface.
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5. Assessment of risk of toxic damage to people in case of a launch vehicle accident at flight

Authors:

Hladkyi E. H., Sheiko А. F.

Organization:

Yangel Yuzhnoye State Design Office, Dnipro, Ukraine

Page: Kosm. teh. Raket. vooruž. 2024, (1); 40-50

DOI: https://doi.org/10.33136/stma2024.01.040

Language: English

Annotation: Despite stringent environmental requirements, modern launch vehicles/integrated launch vehicles (LV/ILV) burn toxic propellants such as NTO and UDMH. Typically, such propellants are used in the LV/ILV upper stages, where a small amount of propellant is contained; however, some LV/ILV still use such fuel in all sustainer propulsion stages. For launch vehicles containing toxic rocket propellants, flight accidents may result in the failed launch vehicle falling to the Earth’s surface, forming large zones of chemical damage to people (the zones may exceed blast and fire zones). This is typical for accidents occurring in the first stage flight segment, when an intact launch vehicle or its components (usually individual stages) with rocket propellants will reach the Earth’s surface. An explosion and fire following such an impact will most likely lead to a massive release of toxicant and contamination of the surface air. An accident during the flight segment of the LV/ILV first stage with toxic rocket propellants, equipped with a flight termination system that implements emergency engine shutdown in case of detection of an emergency situation, has been considered. To assess the risk of toxic damage to a person located at a certain point, it is necessary to mathematically describe the zone within which a potential impact of the failed LV/ILV will entail toxic damage to the person (the so-called zone of dangerous impact of the failed LV/ILV). The complexity of this lies in the need to take into account the characteristics of the atmosphere, primarily the wind. Using the zone of toxic damage to people during the fall of the failed launch vehicle, which is proposed to be represented by a combination of two figures: a semicircle and a half-ellipse, the corresponding zone of dangerous impact of the failed LV/ILV is constructed. Taking into account the difficulties of writing the analytical expressions for these figures during the transition to the launch coordinate system and further integration when identifying the risk, in practical calculations we propose to approximate the zone of dangerous impact of the failed LV/ILV using a polygon. This allows using a known procedure to identify risks. A generalization of the developed model for identifying the risk of toxic damage to people involves taking into account various types of critical failures that can lead to the fall of the failed LV/ILV, and blocking emergency engine shutdown during the initial flight phase. A zone dangerous for people was constructed using the proposed model for the case of the failure of the Dnepr launch vehicle, where the risks of toxic damage exceed the permissible level (10–6). The resulting danger zone significantly exceeds the danger zone caused by the damaging effect of the blast wave. Directions for further improvement of the model are shown, related to taking into account the real distribution of the toxicant in the atmosphere and a person’s exposure to a certain toxic dose.

Key words: launch vehicle, critical failure, flight accident, zone of toxic damage to people, zone of dangerous impact of the failed launch vehicle, risk of toxic damage to people.

Bibliography:
  1. Hladkiy E. H. Protsedura otsenky poletnoy bezopasnosti raket-nositeley, ispolzuyuschaya geometricheskoe predstavlenie zony porazheniya obiekta v vide mnogougolnika. Kosmicheskaya technika. Raketnoe vooruzhenie: sb. nauch.-techn. st. Dnepropetrovsk: GP «KB «Yuzhnoye», 2015. Vyp. 3. S. 50 – 56. [Hladkyi E. Procedure for evaluation of flight safety of launch vehicles, which uses geometric representation of object lesion zone in the form of a polygon. Space Technology. Missile Weapons: Digest of Scientific Technical Papers. Dnipro: Yuzhnoye SDO, 2015. Issue 3. Р. 50 – 56. (in Russian)].
  2. Hladkiy E. H., Perlik V. I. Vybor interval vremeni blokirovki avariynogo vyklucheniya dvigatelya na nachalnom uchastke poleta pervoy stupeni. Kosmicheskaya technika. Raketnoe vooruzhenie: sb. nauch.-tech. st. Dnepropetrovsk: GP «KB «Yuzhnoye», 2011. Vyp. 2. s. 266 – 280. [Hladkyi E., Perlik V. Selection of time interval for blocking of emergency engine cut off in the initial flight leg of first stage. Space Technology. Missile Weapons: Digest of Scientific Technical Papers. Dnipro: Yuzhnoye SDO, 2011. Issue 2. Р. 266 – 280. (in Russian)].
  3. Hladkiy E. H., Perlik V. I. Matematicheskie modeli otsenki riska dlya nazemnykh obiektov pri puskakh raket-nositeley. Kosmicheskaya technika. Raketnoe vooruzhenie: sb. nauch.-techn. st. Dnepropetrovsk: GP «KB «Yuzhnoye», 2010. Vyp. 2. S. 3 – 19. [Hladkyi E., Perlik V. Mathematic models for evaluation of risk for ground objects during launches of launch-vehicles. Space Technology. Missile Weapons: Digest of Scientific Technical Papers. Dnipro: Yuzhnoye SDO, 2010. Issue 2. P. 3 – 19. (in Russian)].
  4. NPAOP 0.00-1.66-13. Pravila bezpeki pid chas povodzhennya z vybukhovymy materialamy promyslovogo pryznachennya. Nabrav chynnosti 13.08.2013. 184 s [Safety rules for handling explosive substances for industrial purposes. Consummated 13.08.2013. 184 p.
    (in Ukranian)].
  5. AFSCPMAN 91-710 RangeSafetyUserRequirements. Vol. 1. 2016 [Internet resource]. Link : http://static.e-publishing.af.mil/production/1/afspc/publicating/
    afspcman91-710v1/afspcman91-710. V. 1. pdf.
  6. 14 CFR. Chapter III. Commercial space transportation, Federal aviation administration, Department of transportation, Subchapter C – Licensing, part 417 – Launch Safety, 2023 [Internet resource]. Link: http://law.cornell.edu/cfr/text/14/part-417.
  7. 14 CFR. Chapter III. Commercial space transportation, Federal aviation administration, Department of transportation, Subchapter C – Licensing, part 420 License to Operate a Launch Site. 2022 [Internet resource]. Link: http://law.cornell.edu/cfr/text/14/part-420.
  8. ISO 14620-1:2018 Space systems – Safety requirements. Part 1: System safety.
  9. 9 GOST 12.1.005-88. Systema standartov bezopasnosti truda. Obschie sanitarno-gigienicheskie trebovaniya k vozdukhu rabochei zony. [GOST 12.1.005-88. Labor safety standards system. General sanitary and hygienic requirements to air of working zone].
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  11. 11 Kolichestvennaya otsenka riska chimicheskykh avariy. Kolodkin V. M., Murin A. V., Petrov A. K., Gorskiy V. G. Pod red. Kolodkina V. M. Izhevsk: Izdatelskiy dom «Udmurtskiy universitet», 2001. 228 s. [Quantitative risk assessment of accident at chemical plant. Kolodkin V., Murin A., Petrov A., Gorskiy V. Edited by Kolodkin V. Izhevsk: Udmurtsk’s University. Publish house, 2001. 228 p. (in Russian)].

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5.1.2024 Assessment of risk of toxic damage to people in case of a launch vehicle accident at flight
5.1.2024 Assessment of risk of toxic damage to people in case of a launch vehicle accident at flight
5.1.2024 Assessment of risk of toxic damage to people in case of a launch vehicle accident at flight

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]]> 3.1.2024 Future projects of lunar exploration implemented by Yuzhnoye SDO https://journal.yuzhnoye.com/content_2024_1-en/annot_3_1_2024-en/ Wed, 12 Jun 2024 15:28:59 +0000 https://journal.yuzhnoye.com/?page_id=34965
Based on the analysis of the Lunar Industrial & Research Base conceptual design, such technologies may include rocket propulsion, units and assemblies of liquid-propellant propulsion (TRL 6–9), as well as future designs such as a hydrogen energy accumulator and inert anodes made of ultra-high-temperature ceramics for electrolysis of regolith melts. Key words: rocket propulsion , hydrogen energy accumulator , inert anodes. rocket propulsion , hydrogen energy accumulator , inert anodes.
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3. Future projects of lunar exploration implemented by Yuzhnoye SDO

Authors:

Husarova I. O., Lysenko Yu. O., Osinovyi G. G.

Organization:

Yangel Yuzhnoye State Design Office, Dnipro, Ukraine

Page: Kosm. teh. Raket. vooruž. 2024, (1); 19-28

DOI: https://doi.org/10.33136/stma2024.01.019

Language: English

Annotation: Over the past years, the leading space powers have been returning to the idea of expeditions to the Moon and actively designing and manufacturing components for inhabited lunar bases. Yuzhnoye State Design Office has its own concept of a lunar base and, of course, cannot stand aside from the solution of scientific and technical problems related to the Moon exploration. Specialists of Yuzhnoye SDO completed conceptual development of a significant range of technologies required for the Moon exploration: a space transportation system for lunar expeditions; landers to deliver payloads to the surface of the Moon and transport experimental equipment; mobile laboratories; a reconnaissance rover to provide reconnaissance missions on the surface of the Moon; vehicles to provide lifting and transport, assembly and construction, production and technological and soil extraction work on the surface of the Moon; habitat units and other elements of the lunar infrastructure. Taking into account the high costs of lunar exploration, it is clear that international cooperation is the most realistic scenario for Yuzhnoye SDO to participate in the exploration. The U.S. lunar program is the most attractive. Private companies that NASA selects for the lunar programs can become partners of Yuzhnoye. With a view to ensuring the participation of Yuzhnoye SDO in international programs, the current state of global technologies for the Moon exploration was analyzed and opportunities to promote technologies developed by Ukrainian specialists on the international market of space technologies were identified based on the analysis. Taking into account the high level of technologies developed by the potential partners, it is proposed for the first time to consider it advisable to promote Yuzhnoye’s technologies with TRL 6–9 which have already been successfully tested and the innovative technologies developed by the company which have no analogues in the world or surpass the world level in terms of their technological and economic performance. Based on the analysis of the Lunar Industrial & Research Base conceptual design, such technologies may include rocket propulsion, units and assemblies of liquid-propellant propulsion (TRL 6–9), as well as future designs such as a hydrogen energy accumulator and inert anodes made of ultra-high-temperature ceramics for electrolysis of regolith melts.

Key words: rocket propulsion, hydrogen energy accumulator, inert anodes.

Bibliography:
1. Rosiya vtratyla “Lunu-25”, India uspishno zavershyla misiu. Chomu krainy ponovyly gonku za resursy Misyatsa? 23 serpnya 2023. https://www.epravda.com.ua/publications/2023/08/23/703510 (Russia lost Luna-25, India successfully completed the mission. Why have countries renewed the race for lunar resources? August 23, 2023. In Ukrainian)
2. Creech S, Guidi J, Elburn D. Artemis: An overview of NASA’s activities to return humans to the Moon. Paper presented at: 2022 IEEE Aerospace Conference (AERO); 2022 Mar 05-12; Big Sky, Montana.
https://doi.org/10.1109/AERO53065.2022.9843277
3. In-Situ Resource Utilization (ISRU) Demonstration Mission, 2019. https://exploration.esa.int/web/moon/-/60127-in-situ-resource-utilisation-demonstration-mission.
4. Peng Zhang, Wei Dai, Ran Niu, Guang Zhang, +12 authors. Overview of the Lunar In Situ Resource Utilization Techniques for Future Lunar Missions. Journal Space: Science & Technology. 2023, Vol. 3, Р. 1-18. Article ID: 0037. DOI: 10.34133/space.0037
https://doi.org/10.34133/space.0037
5. Lin XU, Hui LI, Pei Z, Zou Y, Wang C. A brief introduction to the International Lunar Research Station Program and the Interstellar Express Mission. Chinese J Space Sci. 2022;42(4):511-513.
https://doi.org/10.11728/cjss2022.04.yg28
6. Li C, Wang C, Wei Y, Lin Y. China’s present and future lunar exploration program. Science. 2019;365(6450):238-239.
https://doi.org/10.1126/science.aax9908
7. Ukrinform, 09 sichnya 2024, https://www.ukrinform.ua/rubric-technology/3804665-aponskij-zond-uvijsov-do-orbiti-misaca-pered-posadkou.html (Ukrinform, January 9, 2024. In Ukrainian).
8. Nimechina priednalasya do programmy vyvchennya Misyatsa Artemis, 15.09.2023, https://www.dw.com/uk/nimeccina-priednalas-do-programi-vivcenna-misaca-artemis/a-66826693 (Germany joined the Artemis moon exploration program, September 15, 2023. In Ukrainian).
9. Grigoriev O. N., Frolov G. A., Evdokimenko Yu. I., Kisel’ V. M., Panasyuk A. D., Melakh L. M., Kotenko V. A., Koroteev A. V. Ultravysokotemperaturnaya keramika dlya aviatsionno-kosmicheskoy techniki, Aviatsionno-kosmicheskaya technika i technologiya, 2012, No 8 (95), st.119-128 (O.N. Grigoriev, G.A. Frolov, Yu.I. Evdokimenko, V.M. Kisel, A.D. Panasyuk, L.M. Melakh, V.A. Kotenko, A.V. Koroteev. Ultra-high-temperature ceramics for aerospace engineering, Aerospace engineering and technology, 2012, No. 8 (95), Р. 119-128. In Russian).
10. Grigoriev O. N. et al. Oxidation of ZrB2-SiC-ZrSi2 ceramics in oxygen. Journal of the European Ceramic Society 30 (2010). 2397-2405.
https://doi.org/10.1016/j.jeurceramsoc.2010.03.016

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3.1.2024 Future projects of lunar exploration implemented by Yuzhnoye SDO
3.1.2024 Future projects of lunar exploration implemented by Yuzhnoye SDO
3.1.2024 Future projects of lunar exploration implemented by Yuzhnoye SDO

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]]> 2.1.2024 New and advanced liquid rocket engines of the Yuzhnoye SDO https://journal.yuzhnoye.com/content_2024_1-en/annot_2_1_2024-en/ Wed, 12 Jun 2024 15:04:41 +0000 https://journal.yuzhnoye.com/?page_id=34964
Nowadays Yuzhnoye propulsion experts keep working on development of the advanced liquid rocket engines powered both by cryogenic and hypergolic propellants, which satisfy the majority of launch service market demands. Within the framework of extensive cooperation with foreign space companies, on a contract basis, Yuzhnoye propulsion experts are working on the design and development testing of the liquid rocket engines, as well as their components. Significant steps in this area have been made by the experts from the Yuzhnoye propulsion division and then subsequent manufacture and delivery by Yuzhmash PA of the engine intended for the European rocket Vega Stage 4; and designing the individual components for the engines with thrusts ranging from 500 kgf to 200 tf ordered by foreign customers.
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2. New and advanced liquid rocket engines of the Yuzhnoye SDO

Authors:

Prokopchuk O. O., Shulga V. A.

Organization:

Yangel Yuzhnoye State Design Office, Dnipro, Ukraine

Page: Kosm. teh. Raket. vooruž. 2024, (1); 9-18

DOI: https://doi.org/10.33136/stma2024.01.009

Language: Ukrainian

Annotation: Specialized design office for liquid engines was established on July 22, 1958 to develop engines and propulsion systems, powered by liquid propellants to be installed on the combat missile systems and integrated launch vehicles (LV), developed by Yuzhnoye SDO. Moreover, liquid engines design office was assigned with manufacturing and testing of the main rocket engines, developed by NPO Energomash and to be installed on Yuzhnoye-developed launch vehicles. Over the past 66 years Yuzhnoye SDO has developed more than 40 liquid rocket engines (LRE) of various purpose, designed both to gas-generator cycle and to staged combustion cycle. Seventeen of them were commercially produced by Yuzhmash PA and installed on launch vehicles. Nowadays Yuzhnoye propulsion experts keep working on development of the advanced liquid rocket engines powered both by cryogenic and hypergolic propellants, which satisfy the majority of launch service market demands. Within the framework of extensive cooperation with foreign space companies, on a contract basis, Yuzhnoye propulsion experts are working on the design and development testing of the liquid rocket engines, as well as their components. The accumulated vast experience in the development of liquid rocket engines nowadays enables high scientific and technical level in the creation of up-to-date engines, demanded in the world market. Significant steps in this area have been made by the experts from the Yuzhnoye propulsion division and then subsequent manufacture and delivery by Yuzhmash PA of the engine intended for the European rocket Vega Stage 4; and designing the individual components for the engines with thrusts ranging from 500 kgf to 200 tf ordered by foreign customers. This article provides the review of current and scheduled activities of the Yuzhnoye SDO to develop the liquid rocket engines within the thrust ranges from ~ 40 kgf to ~ 500 tf.

Key words: LOX-kerosene liquid rocket engines, hypergolic propellant liquid rocket engines, staged combustion cycle, main rocket engine, thrust, specific thrust impulse.

Bibliography:
  1. Zhidkostnye raketnye dvigateli, dvigatelnye ustanovki, bortovye istochniki moschnosti, razrabotannye KB dvigatelnykh ustanovok GP«KB «Yuzhnoye». Za nauk. red. akad. NAN Ukrainy S.M. Konyukhova, kand. tekhn. nauk V.M. Shnyakina. Dnipropetrovsk: DP «KB «Pivdenne», 2008. 466 ark.
  2. Prokopchyuk O. O., Shulga V. A., Khromyuk D. S., Sintyuk V. O. Zhidkostnye raketnye dvigateli GP«KB «Yuzhnoye»: nauk.-tekhn. zbirnyk. Za nauk. red. akademika NAN Ukrainy
    O. V. Degtyareva. Dnipro: ART-PRES, 2019. 440 ark.

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2.1.2024 New and advanced liquid rocket engines of the Yuzhnoye SDO
2.1.2024 New and advanced liquid rocket engines of the Yuzhnoye SDO
2.1.2024 New and advanced liquid rocket engines of the Yuzhnoye SDO

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]]> 3.1.2020 Analysis of the unsteady stress-strain behavior of the launch vehicle hold-down bay at liftoff https://journal.yuzhnoye.com/content_2020_1-en/annot_3_1_2020-en/ Fri, 29 Sep 2023 18:22:49 +0000 https://journal.yuzhnoye.com/?page_id=32230
Firstly, the unsteady heat fields on the hold-down bay surface are calculated by means of the semi-empirical method, which is based on the simulated results of the combustion product flow of the main propulsion system. The entire part of the hold-down bay, which is blown by rocket exhaust jet, is under stress-strain behavior. Stress and deformation of rocket gas turbine disc under different loads using finite element modeling. Propulsion and Power Research. Inverse heat transfer method applied to capacitively cooled rocket thrust chambers. Rocket motor exhaust thermal environment characterization. Thermal-structural analysis of regeneratively cooled thrust chamber wall in reusable LOX / Methane rocket engines.
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3. Analysis of the unsteady stress-strain behavior of the launch vehicle hold-down bay at liftoff

Authors:

Degtiarov М. O.1, Avramov K. V.2

Organization:

Yangel Yuzhnoye State Design Office, Dnipro, Ukraine1; Pidgorny A. Intsitute of Mechanical Engineering Problems, Kharkiv, Ukraine2

Page: Kosm. teh. Raket. vooruž. 2020, (1); 26-33

DOI: https://doi.org/10.33136/stma2020.01.026

Language: Russian

Annotation: The study of thermal strength of the hold-down bay is considered. The hold-down bay is a cylindrical shell with the load-bearing elements as the standing supports. The case of the hold-down bay consists of the following structural elements: four standing supports and the compound cylindrical shell with two frames along the top and bottom joints. The purpose of this study was the development of a general approach for the thermal strength calculation of the hold-down bay. This approach includes two parts. Firstly, the unsteady heat fields on the hold-down bay surface are calculated by means of the semi-empirical method, which is based on the simulated results of the combustion product flow of the main propulsion system. The calculation is provided by using Solid Works software. Then the unsteady stress-strain behavior of the hold-down bay is calculated, taking into consideration the plastoelastic deformations. The material strain bilinear diagram is used. The finiteelement method is applied to the stress-strain behavior calculation by using NASTRAN software. The thermal field is assumed to be constant throughout the shell thickness. As a result of the numerical simulation the following conclusions are made. The entire part of the hold-down bay, which is blown by rocket exhaust jet, is under stress-strain behavior. The stresses of the top frame and the shell are overridden the breaking strength that caused structural failure. The structure of the hold-down bay, which is considered in the paper, is unappropriated to be reusable. The hold-down bay should be reconstructed by reinforcement in order to provide its reusability.

Key words: stress-strain behavior, finite-element method, plastoelastic deformations, breaking strength, reusability

Bibliography:

1. Elhefny A., Liang G. Stress and deformation of rocket gas turbine disc under different loads using finite element modeling. Propulsion and Power Research. 2013. № 2. P. 38–49. https://doi.org/10.1016/j.jppr.2013.01.002
2. Perakis N., Haidn O. J. Inverse heat transfer method applied to capacitively cooled rocket thrust chambers. International Journal of Heat and Mass Transfer. 2019. № 131. P. 150–166. https://doi.org/10.1016/j.ijheatmasstransfer.2018.11.048
3. Yilmaz N., Vigil F., Height J., et. al. Rocket motor exhaust thermal environment characterization. Measurement. 2018. № 122. P. 312–319. https://doi.org/10.1016/j.measurement.2018.03.039
4. Jafari M. Thermal stress analysis of orthotropic plate containing a rectangular hole using complex variable method. European Journal of Mechanics A /Solids. 2019. № 73. P. 212–223. https://doi.org/10.1016/j.euromechsol.2018.08.001
5. Song J., Sun B. Thermal-structural analysis of regeneratively cooled thrust chamber wall in reusable LOX / Methane rocket engines. Chinese Journal of Aeronautics. 2017. № 30. P. 1043–1053.
6. Ramanjaneyulu V., Murthy V. B., Mohan R. C., Raju Ch. N. Analysis of composite rocket motor case using finite element method. Materials Today: Proceedings. 2018. № 5. P. 4920–4929.
7. Xu F., Abdelmoula R., Potier-Ferry M. On the buckling and post-buckling of core-shell cylinders under thermal loading. International Journal of Solids and Structures. 2017. № 126–127. P. 17–36.
8. Wang Z., Han Q., Nash D. H., et. al. Thermal buckling of cylindrical shell with temperature-dependent material properties: Conventional theoretical solution and new numerical method. Mechanics Research Communications. 2018. № 92. P. 74–80.
9. Duc N. D. Nonlinear thermal dynamic analysis of eccentrically stiffened S-FGM circular cylindrical shells surrounded on elastic foundations using the Reddy’s third-order shear de-formation shell theory. European Journal of Mechanics A /Solids. 2016. № 58. P. 10–30.
10. Trabelsi S., Frikha A., Zghal S., Dammak F. A modified FSDT-based four nodes finite shell element for thermal buckling analysis of functionally graded plates and cylindrical shells. Engineering Structures. 2019. № 178. P. 444–459.
11. Trinh M. C., Kim S. E. Nonlinear stability of moderately thick functionally graded sandwich shells with double curvature in thermal environment. Aerospace Science and Technology. 2019. № 84. P. 672–685.
12. Лойцянский Л. Г. Механика жидкости и газа. М., 2003. 840 с.
13. Launder B. E., Sharma B. I. Application of the energy dissipation model of turbulence to the calculation of flow near a spinning disc. International Journal of Heat and Mass Transfer. 1974. № 1. P. 131–138.
14. Михеев М. А., Михеева И. М. Основы теплопередачи. М., 1977. 345 с.
15. Малинин Н. Н. Прикладная теория пластичности и ползучести. М., 1968. 400 с.

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3.1.2020 Analysis of the unsteady stress-strain behavior of the launch vehicle hold-down bay at liftoff
3.1.2020 Analysis of the unsteady stress-strain behavior of the launch vehicle hold-down bay at liftoff
3.1.2020 Analysis of the unsteady stress-strain behavior of the launch vehicle hold-down bay at liftoff

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]]> 17.1.2020 Acoustic problems of rocket launch https://journal.yuzhnoye.com/content_2020_1-en/annot_17_1_2020-en/ Wed, 13 Sep 2023 11:36:44 +0000 https://journal.yuzhnoye.com/?page_id=31054
Acoustic problems of rocket launch Authors: Hrinchenko V. 2020, (1); 155-159 DOI: https://doi.org/10.33136/stma2020.01.155 Language: Russian Annotation: Due to an increase of power of rocket engines, the high intensity sound field generated by the exhaust jets have become an important factor, which determines the success rate of a rocket launch. Ensuring a successful launch of a rocket system became harder due to new engineering problems. What’s the Deal with Rocket Vibration? Acoustic loads generated by the propulsion system.
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17. Acoustic problems of rocket launch

Authors:

Hrinchenko V. T.

Organization:

Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine

Page: Kosm. teh. Raket. vooruž. 2020, (1); 155-159

DOI: https://doi.org/10.33136/stma2020.01.155

Language: Russian

Annotation: Due to an increase of power of rocket engines, the high intensity sound field generated by the exhaust jets have become an important factor, which determines the success rate of a rocket launch. Ensuring a successful launch of a rocket system became harder due to new engineering problems. Identification and definition of acoustic sources structure within a complex supersonic jet, being a one of the most important scientific problems, which have to be solved to find the ways to control accoustic radiation. A three components of acoustic sources can be defined here – broadband signals from large and small components of of turbulent jet and tonal signals which usually being overlooked during the estimation of overall sound pressure level. The paper considers various aspects of acoustics of the launch of rocket systems, which includes characteristics of acoustic sources in supersonic jets, possibilities and physical limitation factors, under which it is possible to control the sound radiation. Among the possible ways to control the process of sound generation by a jet, a method of water injection in a jet is being studied. While saving the general thrust of the engine this method can not greatly reduce the sound radiation by a jet. It is recommended to use big amounts of water-air mix to protect the launch pad from damage. Significant progress on the topic of understanding the process of sound generation by supersonic jets can be achieved via mathematical modeling of sound radiation. The latest achievements of mathematical modeling of sound generation by supersonic jets being presented.

Key words: Acoustics of rocket launch, acoustic efficiency of a jet, semi-empirical models of of jet acoustics, numeric-computational methods in aeroacoustics, control of jet-generated acoustic levels

Bibliography:
1. Lighthill M. J. On Sound Generated Aerodynamically: I. General Theory. Proc. Roy. Soc. London Ser. A, 211. 1952. Р. 564–581. https://doi.org/10.1098/rspa.1952.0060
2. Tam C. K. W. Jet noise. Theoretical Computftional Fluid Dynamics. 1998. No 10. Р. 393–405. https://doi.org/10.1007/s001620050072
3. Lubert C. P. Sixty years of launch vehicle acoustics. Proc.Mtgs.Acoust. Vol. 31. 2017. https://doi.org/10.1121/2.0000704
4. Ask the Astronaut: What does launch feel like? URL: https://www.airspacemag. com/ask-astronaut/ask-astronaut-what-does-launch-feel-what-thoughts-and-emotions-run-through-your-mind-180959920/
5. Tim P. Ask an Astronaut: My Guide to Life in Space. 2018. 272 p.
6. Saucer B. What’s the Deal with Rocket Vibration? MIT Technology Review. July 15, 2009. URL: https://www.technology-review.com/s/414364https:/whats-the-deal-with-rocket-vibrations/
7. Ross D. Mechanics of Underwater noise. 1976. 266 p.
8. Varnier J. Experimental study and simulation of rocket engine free jet noise. AIAA J. 2001. Vol. 39, Nо 10. P. 1851–1859. https://doi.org/10.2514/2.1199
9. Eldred K. M. Acoustic loads generated by the propulsion system. NASA SP-8072, 1971. 49 p.
10. Balakrishnan P., Srinivason K. Impinging get noise reduction using non-circular jets. Applied Acoustics. 2019. Vol. 143. Р. 19-30. https://doi.org/10.1016/j.apacoust.2018.08.016
11. Tsutsumi S. Acoustic generation mechanism of a supersonic jet impinging on deflectors / S. Tsutsumi, R. Takaki, Y. Nakanishi, K. Okamoto, S. Teramoto 52th AIAA Aerospace Sci. Meet. AIAA Pap. 2014-0882. 2014. 12 p. https://doi.org/10.2514/6.2014-0882
12. Ahuja K. K., Manes J. P., Massey K. C., Calloway A. B. An Evaluation of various concepts of Reducing Supersonic Jet Noise, AIAA-90-3982. AIAA 13th Aeroacoustic Conference, 1990. Р. 1-21. https://doi.org/10.2514/6.1990-3982
13. Krathapalli A., Lenkatakrishnan L., Elovarsan R., Laurenco L. Supersonic Jet Noise Suppression by Water Injection. AIAA 2000-2025. 6th AIAA/CEAS Aeroacoustic Conference, 2000. Р. 1-25.
14. Moratilla-Vega M. A., Lackhole K., Janicka J., Xia H., Page C. J. Jet Noise Analysis using an Efficient LES/ High-Order Acoustic Coupling Method. Computer and Fluid. 2020. https://doi.org/10.1016/j.compfluid.2020.104438

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17.1.2020 Acoustic problems of rocket launch
17.1.2020 Acoustic problems of rocket launch
17.1.2020 Acoustic problems of rocket launch

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]]> 16.1.2020 Parameters of the supersonic jet of a block propulsion system, flowing into a gas duct, considering chemical kinetics of gas-cycle transformations https://journal.yuzhnoye.com/content_2020_1-en/annot_16_1_2020-en/ Wed, 13 Sep 2023 11:18:27 +0000 https://journal.yuzhnoye.com/?page_id=31052
A source of increased risk is the intense thermal and pressure impact of rocket propulsion jet on launch complex elements and on rocket itself. The presented work contains simulation of liquid rocket engine combustion products jet flowing into the gas duct at the rocket lift-off, taking into account the following input data: the parameters of propulsion system, geometric parameters of launch complex elements, propulsion systems nozzles and gas duct.
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16. Parameters of the supersonic jet of a block propulsion system, flowing into a gas duct, considering chemical kinetics of gas-cycle transformations

Authors:

Furkalo S. A., Stelmakh K. L., Lazarev T. V.

Organization:

Yangel Yuzhnoye State Design Office, Dnipro, Ukraine

Page: Kosm. teh. Raket. vooruž. 2020, (1); 149-154

DOI: https://doi.org/10.33136/stma2020.01.149

Language: Russian

Annotation: Launch vehicle lift-off is one of the most critical phases of the whole mission requiring special technical solutions to ensure trouble-free and reliable launch. A source of increased risk is the intense thermal and pressure impact of rocket propulsion jet on launch complex elements and on rocket itself. The most accurate parameters of this impact can be obtained during bench tests, which are necessary to confirm the operability of the structure, as well as to clarify the parameters and configuration of the equipment and systems of complex. However, full-scale testing is expensive and significantly increases the development time of the complex. Therefore, a numerical simulation of processes is quite helpful in the design of launch complexes. The presented work contains simulation of liquid rocket engine combustion products jet flowing into the gas duct at the rocket lift-off, taking into account the following input data: the parameters of propulsion system, geometric parameters of launch complex elements, propulsion systems nozzles and gas duct. A three-dimensional geometric model of the launch complex, including rocket and gasduct, was constructed. The thermodynamic parameters of gas in the engine nozzle were verified using NASA CEA code and ANSYS Fluent. When simulating a multicomponent jet, the equations of conservation of mass, energy, and motion were solved taking into account chemical kinetics. The three-dimensional problem was solved in ANSYS Fluent in steady-state approach, using Pressure-based solver and RANS k-omega SST turbulence model. The calculation results are the gas-dynamic and thermodynamic parameters of jets, as well as distribution of gas-dynamic parameters at nozzle exit, in flow and in boundary layer at gas duct surface. The methodology applied in this work makes it possible to qualitatively evaluate the gas-dynamic effect of combustion products jets on gas duct for subsequent optimization of its design.

Key words: liquid rocket engine, combustion products, multicomponent flow, ANSYS Fluent

Bibliography:
1. Bonnie J. McBride, Sanford Gordon. Computer Program for Calculation of Complex Chemical Equilibrium Compositions and Applications. II. Users Manual and Program Descriptions: NASA Reference Publication 1311. 1996.
2. Ten-See Wang. Thermophysics Characterization of Kerosene Combustion. Journal of Thermophysics and Heat Transfer. 2001. № 2, Vol. 15. P. 140–147. https://doi.org/10.2514/2.6602
3. Maas U., Warnatz J. Ignition Processes in Carbon-Monoxide-Hydrogen-Oxygen Mixtures: Twenty-Second Symposium (International) on Combustion. The Combustion Institute, 1988. P. 1695–1704. https://doi.org/10.1016/S0082-0784(89)80182-1
4. Timoshenko V. I. Teoreticheskiie osnovy tekhnicheskoj gazovoj dinamiki. Kiev, 2013. S. 154–155.

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16.1.2020 Parameters of the supersonic jet of a block propulsion system, flowing into a gas duct, considering chemical kinetics of gas-cycle transformations
16.1.2020 Parameters of the supersonic jet of a block propulsion system, flowing into a gas duct, considering chemical kinetics of gas-cycle transformations
16.1.2020 Parameters of the supersonic jet of a block propulsion system, flowing into a gas duct, considering chemical kinetics of gas-cycle transformations

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]]> 18.2.2018 Angular Stabilization of an Object Rapidly Rotating around Longitudial Axis https://journal.yuzhnoye.com/content_2018_2-en/annot_18_2_2018-en/ Thu, 07 Sep 2023 12:20:49 +0000 https://journal.yuzhnoye.com/?page_id=30799
2018 (2); 151-156 DOI: https://doi.org/10.33136/stma2018.02.151 Language: Russian Annotation: Contemporary trends in developing space-rocket hardware indicate the increased demand for light and ultra-light rockets. The first trend in developing the up-to-date light and ultra-light rocket hardware includes improving accuracy of cargo delivery to the specified area; the second trend covers the enhancement of energetic properties and the reduction of production and operational costs. Spinning significantly increases stability of a moving object and partially evens out the negative impact of external and internal disturbing factors (skewness and eccentricities of propulsion system and control elements, wind).
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18. Angular Stabilization of an Object Rapidly Rotating around Longitudial Axis

Authors:

Lapko O. M., Meleshko A. O.

Organization:

Yangel Yuzhnoye State Design Office, Dnipro, Ukraine

Page: Kosm. teh. Raket. vooruž. 2018 (2); 151-156

DOI: https://doi.org/10.33136/stma2018.02.151

Language: Russian

Annotation: Contemporary trends in developing space-rocket hardware indicate the increased demand for light and ultra-light rockets. The first trend in developing the up-to-date light and ultra-light rocket hardware includes improving accuracy of cargo delivery to the specified area; the second trend covers the enhancement of energetic properties and the reduction of production and operational costs. Spinning about the longitudinal axis of symmetry may be one of the ways to improve the light and ultra-light rocket hardware in these trends. Spinning significantly increases stability of a moving object and partially evens out the negative impact of external and internal disturbing factors (skewness and eccentricities of propulsion system and control elements, wind). Refusal to use systems that provide stabilization about the longitudinal axis of symmetry leads to reduction in mass of the control system equipment, thus increasing energetic perfection of the rocket hardware. Hence, rotation of the rocket about the longitudinal axis may be caused by the spinning elements on purpose as well as by disturbing impacts in case of control failure in the roll channel. This article considers suggestions on algorithmic realization of light rocket control methods under conditions of rapid rotation about the longitudinal axis for each of the options mentioned above. This article offers control methods for the rocket, rotating about the longitudinal axis, that provide angular stabilization, improve the transient quality, and determine the angle of roll after program stop of rotation about the longitudinal axis.

Key words: angular stabilization, spinning, rotation about the longitudinal axis of symmetry, light rocket, drive delay, determination of the angle of roll, aerodynamic control surfaces, algorithm for maneuver determination of the angle of roll

Bibliography:
1. Shunkov V. N. Encyclopedia of Rocket Artillery / Under the general editorship of A. E. Taras. Minsk, 2004. 544 p.
2. Igdalov I. M. et al. Rocket as Control Object: Tutorial / Under the editorship of S. N. Konyukhov. Dnepropetrovsk, 2004. 544 p.
3. Pugachyov V. S. et al. Rocket Control Systems and Flight Dynamics. М., 1965. 610 p.
4. Sikharulidze Y. G. Flying Vehicles Dynamics. М., 1982. 352 p.

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18.2.2018 Angular Stabilization of an Object Rapidly Rotating around Longitudial Axis
18.2.2018 Angular Stabilization of an Object Rapidly Rotating around Longitudial Axis
18.2.2018 Angular Stabilization of an Object Rapidly Rotating around Longitudial Axis

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]]> 17.2.2018 Peculiarities of Dynamics of Recoverable Part of Stage of Aircraft-Type Configuration with Turbojet Engine https://journal.yuzhnoye.com/content_2018_2-en/annot_17_2_2018-en/ Thu, 07 Sep 2023 12:17:39 +0000 https://journal.yuzhnoye.com/?page_id=30796
This recovery plan differs from an alternative rocket recovery system and, from our point of view, provides more efficient usage of the fuel stores because it doesn’t require the main propulsion to be started in the recovery phase.
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17. Peculiarities of Dynamics of Recoverable Part of Stage of Aircraft-Type Configuration with Turbojet Engine

Authors:

Usichenko V. I.

Organization:

Yangel Yuzhnoye State Design Office, Dnipro, Ukraine

Page: Kosm. teh. Raket. vooruž. 2018 (2); 143-150

DOI: https://doi.org/10.33136/stma2018.02.143

Language: Russian

Annotation: Basic dynamic properties of the reentry part of the aircraft-type first stage were examined when turbojet engine is used in the recovery phase. Such configuration can be of interest because turbojets have considerably smaller rate of flow in comparison to rocket engines. Moreover, they are launched in the lower stratosphere or in the troposphere so that there is no need to place oxidizer supply on board. This recovery plan differs from an alternative rocket recovery system and, from our point of view, provides more efficient usage of the fuel stores because it doesn’t require the main propulsion to be started in the recovery phase. Besides the analysis of qualitative characteristics of the descend phase for this stage, the efficiency of a wing with moderate values of maximum aerodynamic characteristics and a turbojet was studied. In this case three ways for stage recovery were investigated. The first one implied unguided descend with zero angle of attack assuming that the stage is statically stable. This descend trajectory was considered as standard and was used to evaluate the efficiency of the wing and turbojet with relatively small propulsion. The second and the third design cases offered the gliding guided descend with turbojet being started only in the lower stratosphere. The last two cases used the same program for the angle of attack. The possibility to ensure permissible overload values at the critical points of the descend trajectory and acceptable values of kinematic characteristics at the earth surface tangency point are also of great interest. Thereby the program for the angle of attack was developed in a way that allowed kinematic characteristics on touchdown be as close as possible to the corresponding values, shown by civil and/or military-transport heavy aircraft. Simulation was conducted on Microsoft Visual Studio 2010.

Key words: guided descent, turbojet, kinematic characteristics, tangency point, civil aviation

Bibliography:
1. Kuznetsov Y. L., Ukraintsev D. S. Analysis of Impact of Flight Scheme of Stage with Rocket-Dynamic Recovery System on Payload Capability of Medium-Class Two-Stage Launch Vehicle. New of S. P. Korolev Samara State Aerospace University (National Research University). 2016. Vol. 15, No. 1. P. 73-80. https://doi.org/10.18287/2412-7329-2016-15-1-73-80
2. Andreyevsky V. V. Spacecraft Earth Descent Dynamics М., 1970. 230 p.

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17.2.2018 Peculiarities of Dynamics of Recoverable Part of Stage of Aircraft-Type Configuration with Turbojet Engine
17.2.2018 Peculiarities of Dynamics of Recoverable Part of Stage of Aircraft-Type Configuration with Turbojet Engine
17.2.2018 Peculiarities of Dynamics of Recoverable Part of Stage of Aircraft-Type Configuration with Turbojet Engine

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]]> 12.2.2018 Methodological Support for Initial Phase Optimization of Projecting Design, Trajectory Parameters and Rocket Object Motion Control Programs https://journal.yuzhnoye.com/content_2018_2-en/annot_12_2_2018-en/ Thu, 07 Sep 2023 11:38:27 +0000 https://journal.yuzhnoye.com/?page_id=30770
Flight Control Optimization and Thrust Optimization of Controllable Rocket Object Main Propulsion System.
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12. Methodological Support for Initial Phase Optimization of Projecting Design, Trajectory Parameters and Rocket Object Motion Control Programs

Authors:

Aksyonenko A. V.1, Baranov E. Y.1, Hurskyi O. I.1, Klochkov A. S.1, Morozov A. S.1, Alpatov A. P.2, Senkin V. S.2, Siutkina-Doronina S. V.2

Organization:

Yangel Yuzhnoye State Design Office, Dnipro, Ukraine1; The Institute of Technical Mechanics, Dnipro, Ukraine2

Page: Kosm. teh. Raket. vooruž. 2018 (2); 101-116

DOI: https://doi.org/10.33136/stma2018.02.101

Language: Russian

Annotation: The main scientific and methodological propositions for designing single-stage guided missiles with main solid rocket motors that are intended for delivering payload to the given spatial point with required and specified kinematic motion parameters are defined. The aim of the article is to develop methodology for the early design phase to improve the basic characteristics of guided missiles, including formalization of complex problem to optimize design parameters, trajectory parameters and motion control programs for guided missiles capable of flying along the ballistic, aeroballistic or combined trajectories. The task is defined as a problem of the optimal control theory with limitations in form of equality, inequality and differential constraints. An approach to program forming is proposed for motion control in the form of polynomial that brings the problem of the optimal control theory to a simpler problem of nonlinear mathematical programming. When trajectory parameters were calculated the missile was regarded as material point of variable mass and the combined equations for center-of-mass motion of the guided missile with projections on axes of the terrestrial reference system were used. The structure of the mathematical model was given along with the calculation sequence of criterion functional that was used for optimization of design parameters, control programs and basic characteristics of the guided missile. The mathematical model of the guided missile provides adequate accuracy for design study to determine: overall dimensions and mass characteristics of the guided missile in general and its structural components and subsystems; power, thrust and consumption characteristics of the main engine; aerodynamic and ballistic characteristics of the guided missile. The developed methodology was tested by solving design problems. Applications of the developed program were studied to present the research results in a user-friendly form.

Key words: complex problem of the optimal control theory, problem of nonlinear mathematical programming, main solid rocket motor, limitations for motion parameters and basic characteristics of the object

Bibliography:
1. Degtyarev A. V. Rocket Engineering: Problems and Prospects. Selected scientific-technical publications. Dnepropetrovsk, 2014. 420 p.
2. Shcheverov D. N. Designing of Unmanned Aerial Vehicles. М., 1978. 264 p.
3. Sinyukov А. М. et al. Ballistic Solid-Propellant Rocket / Under the editorship of A. M. Sinyukov. М., 1972. 511 p.
4. Varfolomeyev V. I. Designing and Testing of Ballistic Rockets / Under the editorship of V. I. Varfolomeyev, M. I. Kopytov. М., 1970. 392 p.
5. Vinogradov V. A., Grushchansky V. A., Dovgodush S. I. et al. Effectiveness of Complex Systems. Dynamic Models. М., 1989. 285 p.
6. Il’ichyov A. V., Volkov V. D., Grushchansky V. A. Effectiveness of Designed Complex Systems’ Elements. М., 1982. 280 p.
7. Krotov V. F., Gurman V. I. Methods and Problems of Optimal Control. М., 1973. 446 p.
8. Pontryagin L. S. et al. Mathematical Theory of Optimal Processes. М., 1969. 385 p.
9. Tarasov E. V. Algorithms of Flying Vehicles Optimal Designing. М., 1970. 364 p.
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12.2.2018 Methodological Support for Initial Phase Optimization of Projecting Design, Trajectory Parameters and Rocket Object Motion Control Programs
12.2.2018 Methodological Support for Initial Phase Optimization of Projecting Design, Trajectory Parameters and Rocket Object Motion Control Programs
12.2.2018 Methodological Support for Initial Phase Optimization of Projecting Design, Trajectory Parameters and Rocket Object Motion Control Programs

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