Mathematical description of the processes in the pumping system for supplying fuel to the combustion chamber of a liquid rocket engine

The article considers a mathematical model of a pumping system for supplying fuel to a liquid rocket engine chamber consisting of active and passive parts of a hydraulic system. A differential equation describing the processes occurring in the fuel supply system is obtained. The mathematical model makes it possible to analyze and identify the main patterns of influence of the control and disturbing quantities on the controlled quantity, as well as to obtain transients.

1. Puzin Yu. Ya., Safronov S. L. Osnovy ustroystva i ekspluatatsii kosmicheskikh kompleksov [Fundamentals of the design and operation of space complexes]. Samara, 2022. 236 p. ISBN 978-5-7883-1768-7. (In Russ.).

2. Yakovlev A. B. Razrabotka matematicheskoy modeli protsessov v gazogeneratore s unitarnym toplivom dlya pitaniya turbiny zhidkostnoy raketnoy dvigatel’noy ustanovki [Development of mathematical model of processes in a gas generator with unitary fuel for powering turbine of a liquid rocket engine] // Omskiy nauchnyy vestnik. Ser. Aviatsionno-raketnoye i energeticheskoye mashinostroyeniye. Omsk Scientific Bulletin. Series Aviation-Rocket and Power Engineering. 2023. Vol. 7, no. 3. P. 82–88. DOI: 10.25206/2588-0373-2023-7-3-82-88. EDN: TWJQSQ. (In Russ.).

3. Piunov V. Yu., Nazarov V. P., Kolomentsev A. I. Sovershenstvovaniye energeticheskikh kharakteristik kislorodnovodorodnykh zhidkostnykh raketnykh dvigateley razgonnykh blokov metodom optimizatsii konstruktivnykh skhem [Upper stage oxygen—hydrogen rocket engine energy characteristics improvement by structural scheme optimization method] // Vestnik Moskovskogo aviatsionnogo instituta. Aerospace MAI Journal. 2017. Vol. 24, no. 3. P. 23–33. EDN: YTNYXL. (In Russ.).

4. Orlin S. A. Povysheniye ekonomichnosti kislorodnouglevodorodnykh zhidkostnykh raketnykh dvigateley razlichnogo naznacheniya putem vnedreniya promezhutochnogo okhladitelya [Increase of intermediate coolant lox-he engines efficiency of various application] // Inzhenernyy zhurnal: nauka i innovatsii. Engineering Journal: Science and Innovation. 2013. No. 4 (16). P. 30. EDN: RDGQYD. (In Russ.).

5. Abdullin M. R., Davlatov N. B., Shigapov R. R. Analiz i klassifikatsiya putey sovershenstvovaniya zhidkostnykh raketnykh dvigateley odno- i mnogorazovogo ispol’zovaniya na uglevodorodnykh i azotsoderzhashchikh goryuchikh i okhladitelyakh [Analysis and classification of the ways to improve liquid rocket engines of non-reusable and reusable applying on hydrocarbon and nitrogen-containing fuels and coolers] // XXIV Tupolevskiye chteniya (shkola molodykh uchenykh). XXIV Tupolevskiye chteniya (shkola molodykh uchenykh). In 6 vols. Kazan, 2019. Vol. 2. P. 314–320. EDN: TCDXRX. (In Russ.).

6. Kosovyagin K. V., Skomorokhov G. I. Modelirovaniye gazodinamicheskogo trakta tarel’chatogo sopla zhidkostnogo raketnogo dvigatelya s obratnym potokom v kol’tsevoy kamere sgoraniya [Design of the gas dynamic tract of the disc nozzle of a liquid rocket engine with reverse flow in an annular combustion chamber] // Vestnik Voronezhskogo gosudarstvennogo tekhnicheskogo universiteta. Bulletin of the Voronezh State Technical University. 2019. Vol. 15, no 1. P. 100–106. DOI: 10.25987/VSTU.2019.15.1.015. EDN: YXBRQT. (In Russ.).

7. Babkin A. I., Belov S. I., Rutovskiy N. B. [et al.]. Osnovy teorii avtomaticheskogo upravleniya raketnykh dvigatel’nykh ustanovok [Fundamentals of the theory of automatic control of rocket propulsion systems]. 2nd ed. Moscow, 1986. 458 p. (In Russ.).

8. Yakovlev A. B. Opredeleniye uravneniya dinamiki zhidkostnoy raketnoy dvigatel’noy ustanovki [Determination of the equation of dynamics of a liquid rocket propulsion system] // Omskiy nauchnyy vestnik. Omsk Scientific Bulletin. 2010. No. 1 (87). P. 71–74. EDN: QBNDHT. (In Russ.).

9. Belyakov V. V., Ivchenko V. D. Sistema upravleniya tyagoy raketnogo dvigatelya na osnove parametrov rabochego tela [Traction control system rocket engine based on the parameter combustion products] // Vestnik MGTU MIREA. Herald of MSTU MIREA. 2013. No 1. P. 125–128. EDN: RXLWKB. (In Russ.).

10. Kalachevskiy B. A., Yakovlev A. B. ZhRDU kak ispolnitel’nyy organ sistemy upravleniya dvizheniyem [The liquid rocket engine as an executive organ of a control system of movement] // Polet. Obshcherossiyskiy nauchno-tekhnicheskiy zhurnal. All-Russian Scientific-Technical Journal «Polyot» («Flight»). 2012. No. 5. P. 46–51. (In Russ.).

11. Volkov E. B., Syritsyn T. A., Mazing G. Yu. Statika i dinamika raketnykh dvigatel’nykh ustanovok. Kniga II. Dinamika [Statics and dynamics of rocket propulsion systems. Book II. Dynamics]. Moscow, 1978. 320 p. (In Russ.).

12. Yakovlev A. B., Bugaev M. A., Shtang I. A. Kharakteristiki aktivnoy i passivnoy chastey sistemy podachi topliva na vkhod v nasos ZhRDU [Characteristics of active and passive parts of fuel delivering system to input of pump in liquid rocket engine] // Omskiy nauchnyy vestnik. Omsk Scientific Bulletin. 2012. No. 1 (107). P. 175–178. EDN: QBVETN (In Russ.).

13. Belyayev E. N., Chvanov V. K., Chervakov V. V. Matematicheskoye modelirovaniye rabochego protsessa zhidkostnykh raketnykh dvigateley [Mathematical modeling of liquid rocket engines working process]. Moscow, 1999. 228 p. ISBN 5-7035-2221-8. (In Russ.).

14. Lebedinskiy E. N., Kalmykov G. P., Mosolov S. V. [et al.]. Komp’yuternyye modeli zhidkostnykh raketnykh dvigateley [Computer models of liquid-propellant rocket engines] / Ed. by. A. S. Koroteyeva. Moscow, 2009. 375 p. ISBN 978-5-217-03449-9. (In Russ.).

15. Kyzmenko I. A., Yakovlev A. B. Raschet staticheskoy kharakteristiki sistemy podachi unitarnogo topliva v gazogenerator zhidkostnogo raketnogo dvigatelya [Computation of static characteristic of fuel supply system into unitary gas generator of liquid rocket engine] // Omskiy nauchnyy vestnik. Omsk Scientific Bulletin. 2018. No. 6 (162). P. 15–18. DOI: 10.25206/1813-8225-2018-162-15-18. EDN: YSWOBN. (In Russ.).

16. Kalachevskiy B. A., Yakovlev A. B. Modelirovaniye protsessov, proiskhodyashchikh v gazogeneratore, rabotayushchem na unitarnom toplive [Modeling of the Processes in Gas Generator Working on Unicomponent Fuel] // Omskiy nauchnyy vestnik. Omsk Scientific Bulletin. 2014. No. 2 (130). P. 48–52. EDN: MTQJNB. (In Russ.).

17. Belyayev E. N., Kolomentsev A. I., Nasimento L. B. [et al.]. Vliyaniye konstruktivnykh parametrov regulyatora raskhoda na ego staticheskiye i dinamicheskiye kharakteristiki [Influence of design parameters of a flow regulator on its static and dynamic characteristics] // Vestnik Sibirskogo gosudarstvennogo aerokosmicheskogo universiteta im. akademika M. F. Reshetneva. Vestnik Sibirskogo gosudarstvennogo aerokosmicheskogo universiteta im. akademika M. F. Reshetneva. 2014. No. 1 (53). P. 109–113. EDN: SBPCBR. (In Russ.).

18. Maksimov A. D., Chubenko T. A., Zubanov V. M. Modelirovaniye rabochego protsessa tsentrobezhnogo nasosa vysokogo davleniya raketnogo dvigatelya [Simulation of the working process of a high-pressure centrifugal pump of a rocket engine] // Molodezh’. Tekhnika. Kosmos. Young people. Technic. Cosmos. Saint Petersburg, 2018. P. 247–250. ISBN 978-5-907054- 31-8. (In Russ.).

19. Maksimov A. D., Chubenko T. A., Zubanov V. M. Modelirovaniye kharakteristik kamery zhidkostnogo raketnogo dvigatelya [Modeling the characteristics of a liquid rocket engine chamber] // XV Korolevskiye chteniya. XV Korolevskiye chteniya. Samara, 2019. Vol. 1. P. 285–286. EDN: IASLIC. (In Russ.).

20. Vissarionova E. K., Urazbakhtin F. A. Analiz zavisimosti massovogo raskhoda topliva ot diametra forsunki i proyektirovaniye elementa konstruktsii bystroy zameny forsunok dlya osushchestvleniya kachestvennogo raspyla [Analysis of the dependence of mass fuel consumption on the nozzle diameter and design of a structural element for quick replacement of injectors for high-quality spraying] // Kalashnikovskiye chteniya: materialy VI Vseross. nauch.-prakt. konf. Kalashnikov Readings: materials of the VI All-Russian Scientific and Practical Conference. Izhevsk, 2019. P. 65–71. EDN: UPSTIN. (In Russ.).

21. Hetem A., Miraglia J., Burian R. [et al.]. Numerical Simulation of Liquid Propellant Rocket Engines // 2011 Proceedings of the 34th International Convention MIPRO. Opatija, 2011. P. 930–934. (In Engl.)

22. Karimi H., Mohammadi R., Taheri E. E. Dynamic Simulation and Parametric Study of a Liquid Propellant Engine // 2007 3rd International Conference on Recent Advances in Space Technologies. Istanbul, 2007. P. 219–224. DOI: 10.1109/RAST.2007.4283980. (In Engl.)