Search Results for “ring” – Collected book of scientific-technical articles https://journal.yuzhnoye.com Space technology. Missile armaments Fri, 26 Apr 2024 09:07:56 +0000 en-GB hourly 1 https://wordpress.org/?v=6.2.2 https://journal.yuzhnoye.com/wp-content/uploads/2020/11/logo_1.svg Search Results for “ring” – Collected book of scientific-technical articles https://journal.yuzhnoye.com 32 32 9.2.2019 Gas-dynamic simulation of the supersonic stream in the pulsed wind tunnel https://journal.yuzhnoye.com/content_2019_2-en/annot_9_2_2019-en/ Tue, 03 Oct 2023 11:48:27 +0000 https://journal.yuzhnoye.com/?page_id=27211
The shock wind tunnel is designed to simulate the incident flow during rocket flight at high supersonic and hypersonic velocities.
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9. Gas-dynamic simulation of the supersonic stream in the pulsed wind tunnel

Organization:

Yangel Yuzhnoye State Design Office, Dnipro, Ukraine

Page: Kosm. teh. Raket. vooruž. 2019, (2); 63-70

DOI: https://doi.org/10.33136/stma2019.02.063

Language: Russian

Annotation: A promising experimental bench – a shock wind tunnel was put into operation at Yuzhnoye SDO. The shock wind tunnel is designed to simulate the incident flow during rocket flight at high supersonic and hypersonic velocities. To solve actual design problems facing Yuzhnoye SDO, it was necessary to expand the range of velocities under investigation in a shock wind tunnel by low supersonic Mach numbers (Mа=1.5; 2; 3). As a result of this work, a modernized configuration of the shock wind tunnel was developed, which allows simulating flow parameters at low supersonic velocities. The results of aerodynamic experiment performed in the modernized shock wind tunnel, which are close to full scale ones, can be obtained using as much data on peculiarities of supersonic flow formation in it as possible. Therefore, the study of the distribution of Mach numbers profiles in the working section of the modernized shock wind tunnel at low and high supersonic velocity was chosen as the main line of research. The results of the research presented in the article are based on the use of numerical simulation methods, as well as data obtained experimentally. As a result of gasdynamic simulation of a supersonic flow conducted for the nozzle Mа=4 and the nozzle Mа=2, the calculated and experimental data on the distribution pattern and field values of Mach numbers in the working section of the tunnel were obtained. A comparative analysis was carried out. The boundaries of the region of equal velocities, within which the condition of quasistatic supersonic flow is satisfied, and the lifetime of the operating mode for the selected nozzle type were determined. At the flow from the nozzle Mа=2, a peculiarity was revealed in the distribution pattern of Mach numbers fields associated with the appearance of “blocking” effect of the supersonic flow. The methods for eliminating the effect of flow “blocking” at low supersonic velocities are proposed.

Key words: incident flow modeling, velocity fields in the wind tunnel working section, aerodynamic experiment

Bibliography:
1. Zvegintsev V. I. Gasodynamicheskie ustanovki kratkovremennogo deistviya. V dvuh chastyakh. Ch. 1. Ustanovki dlya nauchnykh issledovaniy. Novosibirsk, 2014. 551 s.
2. Computerno-vymiryuvalni tekhnologii kontrolu ta upravlinnya raketno-kosmichnoi techniki / monogr. pid zagal. red. prof. V. P. Malaichuka. Dnipro, 2018. 344 s.
3. «Sirius-18». Systema izmereniya i upravleniya impulsnoi aerodynamicheskoi truboi. Rukovodstvo po ekspluatatsii. ELVA4.044.901 RE. 2018. 45 s.
4. Abramovich G.N. Prikladnaya gazovaya dynamika. M., 1978. 888 s.
5. Raschet vnutrennego davlenia v otsekakh RN. YSF YZH UMN 041 01. Rukovodstvo operatora. 2016. 138 s.
6. Issledovania characteristic hyperzvukovoi aerodynamicheskoi truby AT-303. Ch. 1. Polya skorostey / A. M. Kharitonov at al. Teplophysika i aeromekhanika. 2006. T. 13, № 1. S. 1–17.
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9.2.2019 Gas-dynamic simulation of the supersonic stream in the pulsed wind tunnel
9.2.2019 Gas-dynamic simulation of the supersonic stream in the pulsed wind tunnel
9.2.2019 Gas-dynamic simulation of the supersonic stream in the pulsed wind tunnel

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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
Intsitute of Mechanical Engineering Problems, Kharkiv, Ukraine 2 Page: Kosm. The hold-down bay is a cylindrical shell with the load-bearing elements as the standing supports. Engineering Structures.
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3. Analysis of the unsteady stress-strain behavior of the launch vehicle hold-down bay at liftoff

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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2.1.2020 Analysis of development trends of design parameters and basic characteristics of missiles for the advanced multiple launch rocket systems https://journal.yuzhnoye.com/content_2020_1-en/annot_2_1_2020-en/ Fri, 29 Sep 2023 18:16:07 +0000 https://journal.yuzhnoye.com/?page_id=31001
The guided missiles of multiple launch rocket system are intended for delivering munitions to the given spatial point with required and specified kinematic motion parameters at the end of flight. To simplify the problem, 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.
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2. Analysis of development trends of design parameters and basic characteristics of missiles for the advanced multiple launch rocket systems

Organization:

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

Page: Kosm. teh. Raket. vooruž. 2020, (1); 13-25

DOI: https://doi.org/10.33136/stma2020.01.013

Language: Russian

Annotation: The scientific and methodological propositions for the designing single-stage guided missiles with the solid rocket motors for advanced multiple launch rocket systems are defined. The guided missiles of multiple launch rocket system are intended for delivering munitions to the given spatial point with required and specified kinematic motion parameters at the end of flight. The aim of the article is an analysis of the development trends of the guided missiles with the solid rocket motors for the multiple launch rocket systems, identifying the characteristics and requirements for the flight trajectories, design parameters, control programs, overall dimensions and mass characteristics, structural layout and aerodynamic schemes of missiles. The formalization of the complex task to optimize design parameters, trajectory parameters and motion control programs for the guided missiles capable of flying along the ballistic, aeroballistic or combined trajectories is given. The complex task belongs to a problem of the optimal control theory with limitations in form of equa lity, inequality and differential constraints. To simplify the problem, 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 a 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 the criterion function that was used for determination of the optimal parameters, programs and characteristics. The mathematical model of the guided missile provides adequate accuracy for design study to determine depending on the main design parameters: overall dimensions and mass characteristics of the guided missile in general and its structural comp onents and subsystems; power, thrust and consumption characteristics of the rocket motor; aerodynamic and ballistic characteristics of the guided missile. The developed methodology was tested by determining design and trajectory parameters, overall dimensions and mass characteristics, power and ballistic characteristics of two guided missiles with wings for advanced multiple launch rocket systems produced by the People’s Republic of China, using the limited amount of information available in the product catalog.

Key words: multiple launch rocket systems (MLRS), 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 guided missiles

Bibliography:
1. Degtyarev A. V. Raketnaia tekhnika. Problemy i perspektivy: izbrannye nauchno-tekhnicheskie publikatsii. Dnepropetrovsk, 2014. 420 s.
2. Pro zatverdzhennia Poriadku zdiisnennia derzhavnoho kontriliu za mizhnarodnymy peredachamy tovariv podviinoho vykorystannia:Postanova Kabinetu Ministriv Ukrainy vid 28 sichnia 2004 r. № 86. Date: 29.11.2018. URL: https://zakon.rada.gov.ua/laws/show/86-2004-%D0%BF (Access date 01.09.2019).
3. Catalogue China Aerospase Long-march International. February, 2017. 136 p.
4. Reaktivnye sistemy zalpovogo ognia zarubezhnykh stran: obzor po materialam otkrytoi pechati za 1987–2016 gg. i interneta. Dnipro, 2016. Ч. I. 205 s.
5. Upravliaemye OTRK i TRK stran mira: obzor po materialam otkrytoi otechestvennoi i zarubezhnoi pechati za 2008–2014 gg. i interneta. Dnipro, 2014. 162 s.
6. Tail controlled rocket demonstrates near-vertical impact at extended range. URL: https://www.army.mil/article-amp/207357/tail_controlled_rocket_demonstrates_near_vertical_impact_at_extended_range (Access date 01.09.2019).
7. SY-400 Short-Range Ballistic Missile. URL: http://www.military-today.com/missiles/sy_400.htm (Access date 01.09.2019).
8. Vohniana “Vilkha”: nova vysokotochna systema zalpovoho vohnyu. Vpershe – detalno. URL: https://defence-ua.com/index.php/statti/4588-vohnyana-vilkha-nova-vysokotochna-systema-zalpovoho-vohnyu-vpershe-detalno (Access date 01.09.2019).
9. Gurov S. V. Reaktivnye sistemy zalpovogo ognia: obzor. 1-е izd. Tula, 2006. 432 s.
10. The new M30A1 GMLRS Alternate Warhead to replace cluster bombs for US Army Central 71601171. URL: https://www.armyrecognition.com/weapons_defence_industry_military_technology_uk/the_new_m30a1_gmlrs_alternate_warhead_to_replace_cluster_bombs_for_us_army_central_71601171.html (Access date 01.09.2019).
11. High-Mobility Artillery Rocket System (HIMARS), a member of MLRS family. URL: https://army-technology.com/projects/himars/ (Access date 01.09.2019).
12. SR-5 Multiple Launch Rocket System. URL: http://www.military-today.com/artillery/sr5.htm (Access date 01.09.2019).
13. Effectivnost slozhnykh system. Dinamicheskie modeli / V. А. Vinogradov, V. А. Hrushchansky, S. S. Dovhodush i dr. М., 1989. 285 s.
14. Ilichev А. V., Volkov V. D., Hrushchansky V. А. Effectivnost proektiruemykh elementov slozhnykh system: ucheb. posobie. М., 1982. 280 s.
15. Krotov V. F., Gurman V. I. Metody I zadachi optimalnogo upravleniia. М., 1973. 446 s.
16. Pontriagin L. S., Boltiansky V. G., Gamkrelidze R. V., Mishchenko Е. F. Matematicheskaia teoriia optimalnykh protsesov. М., 1969. 385 s.
17. Tarasov Е. V. Algoritm optimalnogo proektirovaniia letatelnogo apparata. М., 1970. 364 s.
18. Shcheverov D. N. Proektirovanie bespilotnykh letatelnykh apparatov. М., 1978. 264 s.
19. Siniukov А. М., Volkov L. I., Lvov А. I., Shishkevich А. М. Ballisticheskaia raketa na tverdom toplive / pod red. А. М. Siniukova. М., 1972. 511 s.
20. Burov М. А., Varfolomeev V. I., Volkov L. I. Proektirovanie i ispytanie ballisticheskikh raket / pod red. V. I. Varfolomeeva, М. I. Kopytova. М., 1970. 392 s.
21. Siutkina-Doronina S. V. K voprosu optimizatsii proektnykh parametrov i programm upravleniia raketnogo ob’ekta s raketnym dvigatelem na tverdom toplive. Aviatsionno-kosmicheskaia tekhnika i tekhnologiia. 2017. № 2 (137). S. 44–59.
22. Aksenenko A. V., Baranov E. Yu., Hursky A. I., Klochkov A. S., Morozov A. S., Alpatov A. P., Senkin V. S., Siutkina-Doronina S. V. Metodicheskoe obespechenie dlia optimizatsii na nachalnom etape proektirovaniia proektnykh parametrov, parametrov traektorii i programm upravleniia dvizheniem raketnogo ob’ekta. Kosmicheskaia tekhnika. Raketnoe vooruzhenie: sb. nauch.-tekhn. st. / GP “KB “Yuzhnoye”. Dnipro, 2018. Vyp. 2 (116). S. 101–116. https://doi.org/10.33136/stma2018.02.101
23. Metodicheskoe obespechenie dlia optimizatsii na nachalnom etape proektirovaniia proektnykh parametrov, programm upravleniia, ballisticheskikh, energeticheskikh i gabaritno-massovykh kharakteristik upravliaemykh raketnykh ob’ektov, osushchestvliaiushchikh dvizhenie po aeroballisticheskoi traektorii: otchet po NIR / ITM NANU i GKAU, GP “KB “Yuzhnoye”. Dnepropetrovsk, 2017. 159 S.
24. Senkin V. S. K Vyboru programm upravleniia dvizheniem raketnogo ob’ekta po ballisticheskoi traektorii. Tekhnicheskaia mekhanika. 2018. № 1. S. 48–59.
25. Alpatov A. P., Senkin V. S. Metodicheskoe obespechenie dlia vybora oblika, optimizatsii proektnykh parametrov i programm upravleniia poletom rakety-nositelia. Tekhnicheskaia mekhanika. 2013. № 4. S. 146–161.
26. Alpatov A. P., Senkin V. S. Kompleksnaia zadacha optimizatsii osnovnykh proektnykh parametrov i programm upravleniia dvizheniem raket kosmicheskogo naznacheniia. Tekhnicheskaia mekhanika. 2011. № 4. S. 98–113.
27. Senkin V. S. Optimizatsiia proektnykh parametrov rakety-nositelia sverkhlegkogo klassa. Tekhnicheskaia mekhanika. 2009. № 1. S. 80–88.
28. Lebedev А. А., Gerasiuta N. F. Ballistika raket. М., 1970. 244 s.
29. Razumev V. F., Kovalev B. K. Osnovy proektirovaniia ballisticheskikh raket na tverdom toplive: ucheb. posobie dlia vuzov. М., 1976. 356 s.
30. Erokhin B. Т. Teoreticheskie osnovy oroektirovaniia RDTT. М., 1982. 206 s.
31. Abugov D. I., Bobylev V. М. Teoriia i raschet raketnykh dvigatelei tverdogo topliva: uchebnik dlia mashinostroitelnykh vuzov. М., 1987. 272 s.
32. Shishkov А. А. Gasodinamika porokhovykh raketnykh dvigatelei: inzhenernye metody rascheta. М., 1974. 156 s.
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2.1.2020 Analysis of development trends of design parameters and basic characteristics of missiles for the advanced multiple launch rocket systems
2.1.2020 Analysis of development trends of design parameters and basic characteristics of missiles for the advanced multiple launch rocket systems
2.1.2020 Analysis of development trends of design parameters and basic characteristics of missiles for the advanced multiple launch rocket systems

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12.1.2017 Static Performance Prediction of Hot-Gas Flapper-Nozzle Actuator https://journal.yuzhnoye.com/content_2017_1/annot_12_1_2017-en/ Fri, 22 Sep 2023 15:14:35 +0000 https://journal.yuzhnoye.com/?page_id=31702
Problems of Rocket Engineering.
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12. Static Performance Prediction of Hot-Gas Flapper-Nozzle Actuator

Organization:

Yangel Yuzhnoye State Design Office, Dnipro, Ukraine

Page: Kosm. teh. Raket. vooruž. 2017 (1); 78-83

Language: Russian

Annotation: The basic mathematical relations are considered to construct static characteristics of nozzle-shutter twostage piston pneumatic drive with the working medium – powder combustion products.

Key words:

Bibliography:
1. Oleinik V. P. et al. Static Characteristics of Gas Drive with Jet Engine / V. P. Oleinik, Y. A. Yelansky, V. N. Kovalenko, L. G. Kaluger, Е. V. Vnukov. Space Technology. Missile Armaments: Collection of scientific-technical articles. 2015. Issue. 1. P. 21-27.
2. Kornilov Y. G. et al. Pneumatic Elements and Systems. К., 1968. 143 p.
3. Hydraulic and Pneumatic Power Control System / Under the editorship of J. Blackborn, H. Reethoff, G. L. Sherer. М., 1962. 614 p.
4. Mertaf S. A. Tutorial on the Theory of Electrohydraulic Servo Mechanism with Acceleration Control Operating in Switchover Mode. Problems of Rocket Engineering. 1961. No. 2. P. 74-95.
5. Banshtyk A. М. Electrohydraulic Servo Mechanisms with Pulse-Width Control. М., 1972. 144 p.
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12.1.2017 Static Performance Prediction of Hot-Gas Flapper-Nozzle Actuator
12.1.2017 Static Performance Prediction of Hot-Gas Flapper-Nozzle Actuator
12.1.2017 Static Performance Prediction of Hot-Gas Flapper-Nozzle Actuator
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2.2.2019 Mathematical models for assessment of safety in the impact area of cluster ammunition of the warhead during missile complex testing https://journal.yuzhnoye.com/content_2019_2-en/annot_2_2_2019-en/ Sat, 16 Sep 2023 21:22:50 +0000 https://journal.yuzhnoye.com/?page_id=27204
Mathematical models for assessment of safety in the impact area of cluster ammunition of the warhead during missile complex testing Authors: Hladkyi Ye. The second model assumes that the configuration of cassette warhead and the scheme of submunitions firing were finalized, and accordingly, the nominal impact points of submunitions and their group and ind ividual dispersion are considered to be known. (2019) "Mathematical models for assessment of safety in the impact area of cluster ammunition of the warhead during missile complex testing" Космическая техника. "Mathematical models for assessment of safety in the impact area of cluster ammunition of the warhead during missile complex testing" Космическая техника. quot;Mathematical models for assessment of safety in the impact area of cluster ammunition of the warhead during missile complex testing", Космическая техника.
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2. Mathematical models for assessment of safety in the impact area of cluster ammunition of the warhead during missile complex testing

Organization:

Yangel Yuzhnoye State Design Office, Dnipro, Ukraine

Page: Kosm. teh. Raket. vooruž. 2019 (2); 11-17

DOI: https://doi.org/10.33136/stma2019.02.011

Language: Russian

Annotation: One of the main types of arming of modern tactical and short-range missiles are cassette warheads based on nonguided blast-fragmentation submunitions that are widely used to kill group targets. The fullscale testing (flight tests) is an integral part of their creation. In the process of flight tests of tactical and shortrange missiles with cassette warheads, the safety issues are topical. Based on the capabilities of existing test ranges, it is planned to conduct such tests for the tactical and short-range missiles, being under development in Ukraine, in the Black sea water area where the cassette warheads with nonguided blastfragmentation submunitions (or their equivalents) will pose major hazard for ships. In the paper, two mathematical models are proposed to assess probability of killing (risk) a ship that may be present in the impact area of submunitions (submunitions equivalents) of cassette warhead. The first model was constructed in the assumption that the coverage area of cassette warhead and group dispersion of submunitions are known. Such model may be used to determine safety in the initial phases of cassette warheads development. The second model assumes that the configuration of cassette warhead and the scheme of submunitions firing were finalized, and accordingly, the nominal impact points of submunitions and their group and ind ividual dispersion are considered to be known. Practical application of both models requires the use of numerical procedures.

Key words: flight safety, flight tests, cassette warheards

Bibliography:
1. Balaganskiy I. A., Merzhievskiy L. A. Deistvie sredstv porazheniya i boepripasov: ucheb. Novosibirsk, 2004. 408 s.
2 Gradstein I. S., Ryzhik I. M. Tablitsy integralov, summ, ryadov i proizvedeniy. M., 1963. 1100 s.
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2.2.2019 Mathematical models for assessment of safety in the impact area of cluster ammunition of the warhead during missile complex testing
2.2.2019 Mathematical models for assessment of safety in the impact area of cluster ammunition of the warhead during missile complex testing
2.2.2019 Mathematical models for assessment of safety in the impact area of cluster ammunition of the warhead during missile complex testing

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1.2.2019 Optimization of the trajectory of the antiaircraft guided missile https://journal.yuzhnoye.com/content_2019_2-en/annot_1_2_2019-en/ Sat, 16 Sep 2023 21:19:15 +0000 https://journal.yuzhnoye.com/?page_id=28723
As a result, the optimum and suboptimum (additionally ensuring minimum calculation time) trajectories and flight programs to maximum range and different altitudes were obtained. Near-Optimal Three-Dimensional Air-to-Air Missile Guidance Against Maneuvering Target.
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1. Optimization of the trajectory of the antiaircraft guided missile

Organization:

Yangel Yuzhnoye State Design Office, Dnipro, Ukraine

Page: Kosm. teh. Raket. vooruž. 2019, (2); 3-10

DOI: https://doi.org/10.33136/stma2019.02.003

Language: Russian

Annotation: The article is devoted to optimization of a trajectory of the antiaircraft guided missile performed in design phase. The review of existing solutions on this issue confirmed the topicality of the problem. The analytical solution cannot be obtained, therefore, according to modern tendencies, optimization by numerical method of original development was performed. The basis of the method is two-level optimization which is carried out, in turn, by two different numerical methods and for two different criteria functions. At the top level, by method of random search and as a variant, by method of coordinate descent, the search was carried out for a fixed set of intermediate for the specified flight range trajectory points which co-ordinates in aggregate provide the necessary optimum. At the bottom level, for each pair of consecutive intermediate points, the boundary problem of falling into distant point by one-dimensional optimization was solved. The coordinate descent method was used for search for the simplified flight program. As optimization criteria for top level, minimum flight time or maximum final speed, for bottom  terminal criterion were used. The control program selected the angle of attack  program. As a result, the optimum and suboptimum (additionally ensuring minimum calculation time) trajectories and flight programs to maximum range and different altitudes were obtained. The analysis of results showed practical proximity of trajectories of minimum flight time and maximum final speed.

Key words: anti-aircraft missile, optimization, angle of attack program, trajectory

Bibliography:
1. Letov A. M. Dynamika poleta i upravlenie. M., 1969. 360 s.
2. Ushan’ V. N. Metod synteza optymalnykh traektoriy dlya vyvoda dynamicheskykh obiektov v zadannuyu tochku. Systemy obrobky informatsii. 2014. № 1 (117). S. 67-71.
3. Zarubinskaya A. L. Optimalnoe upravlenie dvizheniem letatelnykh apparatov v atmosfere ot starta do tochek vstrechi. Technicheskaya mekhanika. 1997. № 5. S. 23-28.
4. Grabchak V. I. Osnovni aspekty opysu zadachi pro optimalnu shvidkodiu keruvanny rukhom rakety. Systemy ozbroyennya i viyskova tekhnika. 2014. № 4(40). S. 13-20.
5. Shaw Y. Ong. Optimal Planar Evasive Aircraft Maneuvers Against Proportional Navigation Missiles. Journal of guidance, control and dynamics. 1996. Vol. 19, № 6. Р. 1210-1215. https://doi.org/10.2514/3.21773
6. Renjith R. Kumar. Near-Optimal Three-Dimensional Air-to-Air Missile Guidance Against Maneuvering Target. Journal of guidance, control and dynamics. 1995. Vol. 18, № 3. Р. 457-464. https://doi.org/10.2514/3.21409
7. Paul J. Enright. Conway Discrete Approximations to Optimal Trajectories Using Direct Transcription and Nonlinear Programming. Journal of guidance, control, and dynamics. 1992. Vol. 15, № 4. Р. 994-1002. https://doi.org/10.2514/3.20934
8. Craig A. Phillips. Trajectory Optimization for a Missile Using a Multitier Approach. Journal of Spacecraft and Rockets. 2000. Vol. 37, № 5. Р. 653-662. https://doi.org/10.2514/2.3614
9. Lebedev A. A., Gerasyuta N. F. Ballistila raket. M., 1970. 244 s.
10. Proektirovanie zenitnykh upravlyaemykh raket / I. I. Arkhangelskiy i dr.; pod red. I. S. Golubeva i V. G. Svetlova. M., 2001. 732 s.
11. Drakin I. I. Osnovy proektirovania letatelnykh apparatov s uchetom ekonomicheskoy effektivnosti. M., 1973. 224 s.
12. Beiko I. V., Bublik B. N., Zinko P. N. Metody i algoritmy resheniya zadach optimizatsii. K., 1983. 512 s.
13. Krinetskiy Ye. I. Systemy samonavedeniya. M., 1970. 236 s.
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1.2.2019 Optimization of the trajectory of the antiaircraft guided missile
1.2.2019 Optimization of the trajectory of the antiaircraft guided missile
1.2.2019 Optimization of the trajectory of the antiaircraft guided missile

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21.1.2020 Contemporary approaches to the improvement of methods of space launch system operation for commercial launches of ILV https://journal.yuzhnoye.com/content_2020_1-en/annot_21_1_2020-en/ Wed, 13 Sep 2023 12:05:46 +0000 https://journal.yuzhnoye.com/?page_id=31081
The topicality of the article is confirmed by the results of practical application of new approaches in main directions of Cyclone-4M space rocket complex operation system improvement, which allowed increasing commercial attractibility of Yuzhnoye SDO-developed systems due to reduction of direct recurring costs and annual expenses.
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21. Contemporary approaches to the improvement of methods of space launch system operation for commercial launches of ILV

Organization:

Yangel Yuzhnoye State Design Office, Dnipro, Ukraine

Page: Kosm. teh. Raket. vooruž. 2020, (1); 184-192

DOI: https://doi.org/10.33136/stma2020.01.184

Language: Russian

Annotation: The article deals with the problems of applying new approaches to formation and improvement of operation system. Turning of space hardware and services into marketable commodity requires their new qualities that determine competitiveness. The main task of presented works was approbation of new approaches to improvement of space launch systems operation quality and operation process effectiveness by the example of prospective Cyclone-4M space rocket complex. The works to form and improve its operation system were performed using the methods based on general theory of space systems operation and the pocedures based on the results of research work conducted by Yuzhnoye SDO in 2015 for analytical evaluation of launch services costs. The topicality of the article is confirmed by the results of practical application of new approaches in main directions of Cyclone-4M space rocket complex operation system improvement, which allowed increasing commercial attractibility of Yuzhnoye SDO-developed systems due to reduction of direct recurring costs and annual expenses. The article describes the course of development of operation model of a created object; based on investigation of the processes of this model, the object’s performance characteristics are detemined. The basis of the article are the organizational-and-technical decisions used herewith and the results obtained for Cyclone-4M space rocket complex. The article is of practical interest for specialists involved in creation of space rocket complexes and other sophisticated systems where the operation system is a multi-level organizational-technical system.

Key words: space hardware, launch services, performance characteristics, operation model, organizational-and-technical decisions

Bibliography:
1. Analiticheskaia otsenka ob’ema rabot i zatrat na puskovye uslugi i napravleniia rabot dlia ikh snizheniia v perspektivnykh RKK razrabotki GP “KB “Yuzhnoye”: tekhn. otchet / GP “KB “Yuzhnoye”. Dnepropetrovsk, 2015. 344 s.
2. Teoriia i praktika ekspluatatsii ob’ektov kosmicheskoi infrastruktury: monografiia / N. D. Anikeichik i dr. SPb., 2006. Т. 1: Ob’ekty kosmicheskoi infrastruktury. 400 s.
3. Ispytaniia i ekspluatatsiia raketnykh kompleksov: kurs lektsii / А. V. Agarkov i dr.; pod red. А. V. Degtyareva. GP “KB “Yuzhnoye”. Dnipro, 2016. Kn. 1. 505 s.
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21.1.2020  Contemporary approaches to the improvement of methods of space launch system operation for commercial launches of ILV
21.1.2020  Contemporary approaches to the improvement of methods of space launch system operation for commercial launches of ILV
21.1.2020  Contemporary approaches to the improvement of methods of space launch system operation for commercial launches of ILV

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20.1.2020 Studying the possibility of alternating delivery of rocket propellant wastes to a common thermal neutralization facility https://journal.yuzhnoye.com/content_2020_1-en/annot_20_1_2020-en/ Wed, 13 Sep 2023 12:04:53 +0000 https://journal.yuzhnoye.com/?page_id=31078
Taking into consideration the high cost of neutralization units, which will be a factor hindering the wide-scale introduction of neutralization units to decrease technogenic load on environment of Ukraine, the option is proposed of reducing the costs during the use of thermal neutralization units by way of combining the function of oxidizer neutralization unit and fuel neutralization unit in a single universal neutralization unit.
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20. Studying the possibility of alternating delivery of rocket propellant wastes to a common thermal neutralization facility

Organization:

Yangel Yuzhnoye State Design Office, Dnipro, Ukraine

Page: Kosm. teh. Raket. vooruž. 2020, (1); 177-183

DOI: https://doi.org/10.33136/stma2020.01.177

Language: Russian

Annotation: The possibility is considered of using rocket propellant thermal neutralization units for decontamination of dangerous industrial wastes. The advantages of thermal neutralization units are considered, their operating principle is described, by the example of high-temperature toxic rocket propellants, the chemical reactions that take place in combustion chamber are formulated. The combustion chamber is a component of the neu tralization unit, it is in the combustion chamber, in the environment of created high temperatures, that the process of elimination of dangerous substances takes place. Taking into consideration the high cost of neutralization units, which will be a factor hindering the wide-scale introduction of neutralization units to decrease technogenic load on environment of Ukraine, the option is proposed of reducing the costs during the use of thermal neutralization units by way of combining the function of oxidizer neutralization unit and fuel neutralization unit in a single universal neutralization unit. The article substantiates the topicality and necessity of works to create the universal thermal neutralization unit from the viewpoint of economic and ecological aspects. The article presents a generalized description of technology and methodology of research tests of pilot samples of assemblies for high-temperature rocket propellants vapor and industrial wastewater supply into the neutralization unit. The assemblies for high-temperature rocket propellants vapor and industrial wastewater supply are considered as most critical components of the universal neutralization unit from the viewpoint of neutralized substance changing. The experiments were conducted on water solutions of rocket propellants that in this case simulated the contact of internal cavities of supply assemblies with aggressive toxic media. The conditions were created at which the probability existed of interaction of rocket propellants residues in stagnation zones at the moment of changing the supplied propellant component. In the frameworks of research tests of pilot samples, the obtained results were considered and analyzed. The findings are presented that confirm practical feasibility of using integrated supply assemblies.

Key words: neutralization unit, supply assemblies, alternate supply, rocket propellants interaction, universal thermal neutralization unit

Bibliography:
1. Kolesnikov S. V. Okislenie nesimmetrichnogo dimetilgidrazina (geptila) i identifikatsiia produktov ego prevrashcheniia pri prolivakh. Monografiia. NP “SibAK”, Novosibirsk, 2014.
2. Zhidkoe raketnoe toplivo v regione OBSE: obzor aspektov utilizatsii. FSC.DEL/443/07/Rev. 2. 23 okt. 2008 g.
3. Egorychev V. S., Kondrusev V. S. Topliva khimicheskikh raketnykh dvigatelei. Samara, 2007.
4. Kasimov А. М., Semenov V. Т., Shcherban’ N. H., Miasoedov V. V. Sovremennye problemy i resheniia v sisteme upravleniia opasnymi otkhodami. Kharkiv, 2008.
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20.1.2020  Studying the possibility of alternating delivery of rocket propellant wastes to a common thermal neutralization facility
20.1.2020  Studying the possibility of alternating delivery of rocket propellant wastes to a common thermal neutralization facility
20.1.2020  Studying the possibility of alternating delivery of rocket propellant wastes to a common thermal neutralization facility

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19.1.2020 Pyrobolts: types, design, development. Shear type pyrobolt developed at Yuzhnoye SDO https://journal.yuzhnoye.com/content_2020_1-en/annot_19_1_2020-en/ Wed, 13 Sep 2023 12:02:02 +0000 https://journal.yuzhnoye.com/?page_id=31074
Owing to the simple design, reliability and short action time, the pyrobolts have found wide application in aerospace engineering for separation of assemblies and bays, in particular, stages, head modules, launching boosters, etc. The above segments a re actuated using a rod with sealing rings and a piston connected to the rod through a rubber gasket; the piston moves under pressure of gases formed during pyro cartridge action. In the developed pyrobolt of shear type with segments, the case parts are separated without considerable shock loads and without high-temperature gases and fragments release into environment, ensuring reliable separation of bays and assemblies without damaging sensitive equipment.
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19. Pyrobolts: types, design, development. Shear type pyrobolt developed at Yuzhnoye SDO

Organization:

Yangel Yuzhnoye State Design Office, Dnipro, Ukraine

Page: Kosm. teh. Raket. vooruž. 2020, (1); 170-176

DOI: https://doi.org/10.33136/stma2020.01.170

Language: Russian

Annotation: The pyrobolts, or explosive bolts, belong to the pyrotechnical devices with monolithic case consisting o f the cap, as a rule with hexagonal surface, and of cylindrical part with thread. The pyrobolts are separated into parts using the pyrotechnical charge placed inside the case. Owing to the simple design, reliability and short action time, the pyrobolts have found wide application in aerospace engineering for separation of assemblies and bays, in particular, stages, head modules, launching boosters, etc. So, for example, about 400 pyrobolts are used in the Proton launch vehicle. The designs of pyrobolts are markedly different. By method of explosive substance action on case structural elements, the pyrobolts are divided into two types: the pyrobolts using the shock wave formed at detonation of brisant explosive substance for case wall destruction and the pyrobolts using the pressure of gases arising at pyrotechnical charge blasting. By method of separation into parts, they are divided into fragmenting pyrobolts with ridge-cut, with piston, and shear pyrobolts. The paper deals with the design of various types of pyrobolts, their disadvantages are considered. The Yuzhnoye SDO-developed pyrobolt of shear type with segments is presented that uses radial shear forces of segments located in the hole of cylindrical part to separate the case parts. The above segments a re actuated using a rod with sealing rings and a piston connected to the rod through a rubber gasket; the piston moves under pressure of gases formed during pyro cartridge action. The following calculations are presen ted: strength analyses with determination of case load-carrying capacity; power analyses with justification of pyro cartridge selection for pyrobolt actuation. In the developed pyrobolt of shear type with segments, the case parts are separated without considerable shock loads and without high-temperature gases and fragments release into environment, ensuring reliable separation of bays and assemblies without damaging sensitive equipment.

Key words: explosive bolt, shock wave, brisant explosive substance, pyro cartridge, electric igniting fuse, high-temperature gases

Bibliography:
1. Mashinostroenie. Entsiklopediia / А. P. Adzhian i dr.; pod red. V. P. Legostaeva. М., 2012. Т. IV-22. V 2-kh kn. Kn. 1. 925 s.
2. Bement L. J., Schimmel M. L. A Manual for Pyrotechnic Design, Development and Qualification: NASA Technical Memorandum 110172. 1995.
3. Yumashev L. P. Ustroistvo raket-nositelei (vspomagatelnye sistemy): ucheb. posob. Samara, 1999. 190 s.
4. Lee J., Han J.-H., Lee Y., Lee H. Separation characteristics study of ridge-cut explosive bolts. Aerospace Science and Technology. 2014. Vol. 39. Р. 153-168. https://doi.org/10.1016/j.ast.2014.08.016
5. Yanhua L., Jingcheng W., Shihui X., Li C., Yuquan W., Zhiliang L. Numerical Study of Separation Characteristics of Piston-Type Explosive Bolt. Shock and Vibration. https://doi.org/10.1155/2019/2092796
6. Yanhua L., Yuan L., Xiaogan L., Yuquan W., Huina M., Zhiliang L. Identification of Pyrotechnic Shock Sources for Shear Type Explosive Bolt. Shock and Vibration. https://doi.org/10.1155/2017/3846236
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19.1.2020  Pyrobolts: types, design, development. Shear type pyrobolt developed at Yuzhnoye SDO
19.1.2020  Pyrobolts: types, design, development. Shear type pyrobolt developed at Yuzhnoye SDO
19.1.2020  Pyrobolts: types, design, development. Shear type pyrobolt developed at Yuzhnoye SDO

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18.1.2020 Development of autonomous power engineering systems with hydrogen energy storage https://journal.yuzhnoye.com/content_2020_1-en/annot_18_1_2020-en/ Wed, 13 Sep 2023 11:57:42 +0000 https://journal.yuzhnoye.com/?page_id=31056
Development of autonomous power engineering systems with hydrogen energy storage Authors: Shevchenko A. Intsitute of Mechanical Engineering Problems, Kharkiv, Ukraine 1 ; Yangel Yuzhnoye State Design Office, Dnipro, Ukraine 2 Page: Kosm. During the operation of water desalination plants using a solar power station as an energy source, contingencies are very likely to arise due to either a power outage (due to cloudy weather) or an emergency failure of individual elements of the system. The current level of hydrogen technologies that are implemented in electrochemical plants developed at the Institute of Mechanical Engineering named after A. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. Journal of Mechanical Engineering. Journal of Mechanical Engineering. Journal of Mechanical Engineering. (2020) "Development of autonomous power engineering systems with hydrogen energy storage" Космическая техника.
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18. Development of autonomous power engineering systems with hydrogen energy storage

Organization:

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

Page: Kosm. teh. Raket. vooruž. 2020, (1); 160-169

DOI: https://doi.org/10.33136/stma2020.01.160

Language: Russian

Annotation: The article analyzes the energy potential of alternative sources of Ukraine. The projects using hydrogen technologies aimed at attracting solar energy to the infrastructure of energy technological complexes, in particular water desalination systems and for refueling automobile vehicles located in areas with high solar radiation potential, are considered. During the operation of water desalination plants using a solar power station as an energy source, contingencies are very likely to arise due to either a power outage (due to cloudy weather) or an emergency failure of individual elements of the system. In this case, it is required to ensure its removal from service without loss of technological capabilities (operability). For this purpose, it is necessary to provide for the inclusion in the technological scheme of the energy technological complex of an additional element that ensures operation of the unit for a given time, determined by the regulations for its operation. As such an element, a buffer system based on a hydrogen energy storage device is proposed. The current level of hydrogen technologies that are implemented in electrochemical plants developed at the Institute of Mechanical Engineering named after A. N. Podgorny of the National Academy of Sciences of Ukraine allows producing and accumulating the hydrogen under high pressure, which eliminates the use of compressor technology.

Key words: alternative energy sources, hydrogen, solar energy, hydrogen generator

Bibliography:
1. Syvolapov V. Potentsial vidnovliuvanykh dzherel enerhii v Ukraini. Agroexpert. 2016. № 12 (101). S. 74–77.
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3. Vozobnovliaemaia energetika. URL: https://nv.ua/tags/vozobnovljaemaja-enerhetika.htmt (access date: 27.01.2020).
4. Sherif S. A., Barbir F., Veziroglu T. N. Wind energy and the hydrogen economy-review of the technology. Solar energy. 2005. № 78(5). P. 647–660. https://doi.org/10.1016/j.solener.2005.01.002
5. Schlapbach L. Technology: Hydrogen-fuelled vehicles. Nature. 2009. № 460(7257). P. 809. https://doi.org/10.1038/460809a
6. Shevchenko A. A., Zipunnikov M. М., Kotenko А. L., Vorobiova I. O., Semykin V. M. Study of the Influence of Operating Conditions on High Pressure Electrolyzer Efficiency. Journal of Mechanical Engineering. 2019. Vol. 22, № 4. P. 53–60. https://doi.org/10.15407/pmach2019.04.053
7. Clarke R. E., Giddey S., Ciacchi F. T., Badwal S. P. S., Paul B., Andrews J. Direct coupling of an electrolyser to a solar PV system for generating hydrogen. International Journal of Hydrogen Energy. 2009. № 34(6). P. 2531–2542. https://doi.org/10.1016/j.ijhydene.2009.01.053
8. Kunusch C., Puleston P. F., Mayosky M. A., Riera J. Sliding mode strategy for PEM fuel cells stacks breathing control using a super-twisting algorithm. IEEE Transactions on Control Systems Technology. 2009. № 17(1). P. 167–174. https://doi.org/10.1109/TCST.2008.922504
9. Mazloomi K., Gomes C. Hydrogen as an energy carrier: Prospects and challenges. Renew. Sustain. Energy Rev. 2012. № 16. P. 3024–3033. https://doi.org/10.1016/j.rser.2012.02.028
10. Sharma S., Ghoshal S. K. Hydrogen the future transportation fuel: From production to applications. Renew. Sustain. Energy Rev. 2015. № 43. P. 1151–1158. https://doi.org/10.1016/j.rser.2014.11.093
11. Prystrii dlia oderzhannia vodniu vysokoho tysku: pat. 103681 Ukraina: MPK6 S 25V 1/12 / V. V. Solovey, A. A. Shevchenko, A. L. Kotenko, O. О. Makarov (Ukrajina). № 2011 15332; zajavl. 26.12.2011; opubl. 10.07.2013, Biul. № 21. 4 s.
12. Shevchenko А. А. Ispolzovanie ELAELov v avtonomnykh energoustanovkakh, kharakterizuyushchikhsia neravnomernostju energopostupleniia. Aviatsionno-kosmicheskaia tekhnika i technologiia: sb. nauch. tr. 1999. Vyp. 13. S. 111–116.
13. Solovey V. V., Zhirov А. S., Shevchenko А. А. Vliianie rezhimnykh faktorov na effektivnost elektrolizera vysokogo davleniia. Sovershenstvovaniie turboustanovok metodami matematicheskogo i fizicheskogo modelirovaniia: sb. nauch. tr. 2003. S. 250–254.
14. Solovey V., Kozak L., Shevchenko A., Zipunnikov M., Campbell R., Seamon F. Hydrogen technology of energy storage making use of windpower potential. Problemy Mashinostroyeniya. Journal of Mechanical Engineering. 2017. Vol. 20, № 1. P. 62–68. https://doi.org/10.17721/fujcV6I2P73-79
15. Solovey V. V., Kotenko А. L., Vorobiova I. О., Shevchenko A. А., Zipunnikov M. М. Osnovnye printsipy raboty i algoritm upravleniya bezmembrannym elektrolizerom vysokogo davleniia. Problemy mashinostroyeniia. 2018. T. 21, №. 4. S. 57–63. https://doi.org/10.15407/pmach2018.04.057
16. Solovey V., Khiem N. T., Zipunnikov M. M., Shevchenko A. A. Improvement of the Membraneless Electrolysis Technology for Hydrogen and Oxygen Generation. French-Ukrainian Journal of Chemistry. 2018. Vol. 6, № 2. P. 73–79. https://doi.org/10.17721/fujcV6I2P73-79
17. Solovey V., Zipunnikov N., Shevchenko A., Vorobjova I., Kotenko A. Energy Effective Membrane-less Technology for High Pressure Hydrogen Electro-chemical Generation. French-Ukrainian Journal of Chemistry. 2018. Vol. 6, № 1. P.151–156. https://doi.org/10.17721/fujcV6I1P151-156
18. Solovey V. V., Zipunnikov М. М., Shevchenko А. А., Vorobiova І. О., Semykin V. M. Bezmembrannyi henerator vodniu vysokoho tysku. Fundamentalni aspekty vidnovliuvano-vodnevoi enerhetyky i palyvno-komirchanykh technologij / za zahal. red. Yu. М. Solonina. Kyiv, 2018. S. 99–107.
19. Matsevytyi Yu. M., Chorna N. A., Shevchenko A. A. Development of a Perspective Metal Hydride Energy Accumulation System Based on Fuel Cells for Wind Energetics. Journal of Mechanical Engineering. 2019. Vol. 22, № 4. P. 48–52. https://doi.org/10.15407/pmach2019.04.048
20. Phillips R., Edwards A., Rome B., Jones D. R., Dunnill C. W. Minimising the ohmic resistance of an alkaline electrolysis cell through effective cell design. Int. J. Hydrogen Energy. 2017. № 42. P. 23986–23994. https://doi.org/10.1016/j.ijhydene.2017.07.184
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18.1.2020  Development of autonomous power engineering systems with hydrogen energy storage
18.1.2020  Development of autonomous power engineering systems with hydrogen energy storage
18.1.2020  Development of autonomous power engineering systems with hydrogen energy storage

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