TECHNICAL MECHANICS
ISSN (Print): 1561-9184, ISSN (Online): 2616-6380

HOME    ABOUT THIS JOURNAL    EDITORIAL BOARD    GUIDE FOR AUTHORS    CURRENT    JOURNAL ISSUES    CONTACTS

UDC 532.528:621

Technical mechanics, 2022, 2, 47 - 58

Determination of the effect of internal and external factors on the thrust spread of a cluster propulsion system

Dolgopolov S. I.

Dolgopolov S. I.
Institute of Technical Mechanics of the National Academy of Sciences of Ukraine and the State Space Agency of Ukraine

      The thrust spread of a stand-alone rocket engine caused by external (the pressure and temperature of the propellant components at the engine inlet) and internal (spread in the geometry and operating conditions of the engine units and assemblies) factors is known from experimental tests or can be computed by a known procedure. As a rule, liquid-propellant propulsion systems (LPPSs) of launch vehicle lower stages include a cluster of several engines, whose thrust spread cannot often be determined from firing tests due to limited capabilities of bench equipment. The aim of this work is to develop an approach to determining the thrust spread of an LPPS comprising a cluster of two and more engines.
      For a multiengine propulsion system, this methodological approach also includes the development of a mathematical model of engine interaction in an LPPS and calculations of an LPPS startup at different combinations of spread in the external and internal factors in cases where the parameter spreads of all engines are both identical and different.
      For an LPPS with two engines and a common oxidizer feed pipeline, the paper gives an example of calculating the effect of external and internal factors on the thrust spread of each engine and the LPPS as a whole during an LPPS startup. . It is shown that the calculated spread of the 90 percent thrust (combustion chamber pressure) time lies in the range – 0.0917 s to +0.0792 s (engine 1) and –0.0941 s to +0.0618 s (engine 2). The calculated variations of the combustion chamber pressure (engine thrust) from its nominal value lie in the range –6.2 percent to +7.0 percent (engine 1) and -6.8 percent to +6.3 percent (engine 2). The calculated spreads of the 90 percent thrust time and the thrust for the LPPS as a whole are far smaller (about by 40 percent) and lie in the range – 0.0733 s to +0.0457 s for the time and – 4.8 percent to +4.8 percent for the thrust (about the nominal thrust). Using Pearson’s chi-squared test, an estimate is obtained for the goodness of fit of the anticipated theoretical distributions of the 90 percent thrust time spread and the steady thrust spread to the obtained statistical ones both for the two engines and for the LPPS as a whole.
     

liquid-propellant rocket propulsion system, engine cluster, startup, mathematical simulation, external and internal factors, thrust spread, goodness of fit of a theoretical distribution to a statistical one

1. Alemasov V. E., Dregalin A. F., Tishin A. P. Rocket Engine Theory. Moscow: Mashinostroyeniye, 1980. 533 pp. (in Russian).

2. Belyaev E. N., Chervyakov V. V. Mathematical Simulation of liquid-Propellant Rocket Engines. Moscow: MAI-PRINT, 2009. 280 pp. (in Russian).

3. Makhin V. A., Prisnyakov V. F., Belik N. P. Dynamics of Liquid-Propellant Rocket Engines. Moscow: Mashinostroyeniye, 1969. 834 pp. (in Russian).

4. Pylypenko O. V., Dolgopolov S. I., Khoriak N. V., Nikolayev O. D. Procedure for determining the effect of internal and external factors on the startup thrust spread of a liquid-propellant rocket engine. Teh. Meh. 2021. No. 4. Pp. 7-17. (in Ukrainian). https://doi.org/10.15407/itm2021.04.007

5. Shevyakov A. A., Kalnin V. M., Naumenkova M. V., Dyatlov V. G. Theory of Rocket Engine Automatic Control. Moscow: Mashinostroyeniye, 1978. 288 pp. (in Russian).

6. Belyaev E. N., Chervyakov V. V. Mathematical Simulation of liquid-Propellant Rocket Engines. Moscow: MAI-PRINT, 2009. 280 pp. (in Russian).

7. Lebedinsky E. V., Zaitsev B. V., Sobolev A. A. Multilevel mathematical simulation of an LPRE flow regulator. Keldysh Research Center website. 2011. P. 10. URL: http://www.lpre.de/resources/articles/reg_model.pdf. (Last accessed on October 26, 2021). (in Russian).

8. Pilipenko V. V., Zadontsev V. A., Natanzon M. S. Cavitation Oscillations and Hydrosystem Dynamics. Moscow: Mashinostroyeniye, 1977. 352 pp. (in Russian).

9. Pylypenko V. V., Dolgopopov S. I. Experiment-and-calculation determination of the coefficients of the equation of cavity dynamics in inducer0equipped centrifugal pumps of different standard sizes. Teh. Meh. 1998. No. 8. Pp. 50-56. (in Russian).

10. Dolgopopov S. I. Hydrodynamic model of cavitation oscillation for modelling dynamic processes within pump systems at high cavitation number. Teh. Meh. 2017. No. 2. Pp. 12-19. (in Russian).' https://doi.org/10.15407/itm2017.02.012

11. Liu Wei, Chen Liping, Xie Gang, Ding Ji, Zhang Haiming, Yang Hao Modeling and simulation of liquid propellant rocket engine transient performance using Modelica. Proc. of the 11th Int. Modelica Conf., 2015, Sept. 21-23, Versailles. France. Ðp. 485-490.

12. Di Matteo, Fr., De Rosa, M., Onofri, M. Start-up transient simulation of a liquid rocket engine. AIAA 2011-6032 47th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit (31 July - 03 August 2011), San Diego, California. 15 pp, https://doi.org/10.2514/6.2011-6032

13. Belov G. V. Mathematical simulation of equilibrium states of multicomponent heterogeneous systems. Matematicheskoye Modelirovaniye. 2005. V. 17. No. 2. Pp. 81-91. (in Russian).

14. Blekhman I. I. Synchronization of Mechanical Systems. Moscow: Nauka, 1971. 896 pp. (in Russian).

15. Pylypenko O. V., Prokopchuk A. A., Dolgopolov S. I., Pisarenko V. Yu., Kovalenko V. N., Nikolaev A. D., Khoryak N. V. Peculiarities of mathematical modeling of low-frequency dynamics of the staged liquid rocket sustainer engines at its startup. Space Sci. & Technol. 2017. V. 23. No. 5. Pp. 3-12. (in Russian). https://doi.org/10.15407/knit2017.05.003

16. Dolgopolov S. I., Nikolayev O. D., Khoriak N. V. Dynamic interaction between clustered liquid propellant rocket engines under their asynchronous start-ups. Propulsion and Power Research. 2021. V. 10. No. 4. Pp. 347-359. https://doi.org/10.1016/j.jppr.2021.12.001

17. Pylypenko V. V., Dorosh N. L., Manko I. K. Experimental study of vapor condensation in the injection of an oxygen gas jet into a liquid oxygen flow. Teh. Meh. 1993. No. 2. Pp. 77-80. (in Russian).

18. Dorosh N. L. Simulation of oxygen steam jet condensation in liquid oxygen. Applied Questions of Mathematical Modelling. 2020. V. 3. No. 2.2. Pp. 149-155. (in Ukrainian). https://doi.org/10.32782/KNTU2618-0340/2020.3.2-2.14

19. Pylypenko O. V., Prokopchuk A. A., Dolgopolov S. I., Khoryak N. V., Nikolaev A. D., Pisarenko V. Yu.. Kovalenko V. N. Mathematical simulation and stability analysis of low-frequency processes in a sustainer liquid-propellant rocket engine with generator gas afterburning. Vestnik Dvigatelestroyeniya. 2017. No. 2. Pp. 34-42. (in Russian).

20. Khoriak N. V., Dolhopolov S. I. Features of mathematical simulation of gas path dynamics in the problem of the stability of low-frequency processes in liquid-propellant rocket engines. Teh. Meh. 2017. No. 3. Pp. 30-44. (in Russian). https://doi.org/10.15407/itm2017.03.030

21. Pylypenko O. V., Khoriak N. V., Dolhopolov S. I., Nikolayev O. D. Mathematical simulation of dynamic processes in hydraulic and gas paths at the start of a liquid-propellant rocket engine with generator gas after-burning. Teh. Meh. 2019. No. 4. Pp. 5-20. (in Russian). https://doi.org/10.15407/itm2019.04.005

22. Glikman B. F. Automatic Control of Liquid-Propellant Rocket Engines. Moscow: Mashinostroyeniye, 1974. 396 pp. (in Russian).

23. Charnyi I. A. Unsteady Flow of a Real Liquid in Pipes. Moscow: GITTL, 1961. 253 pp. (in Russian).

24. Dolgopolov S. I., Zavoloka A. N., Nikoilaev A. D., Sviridenko N. F., Smolensky D. E. Parametric determination of hydrodynamic processes in feed system of space stage in stopping and starting the cruise engine. Teh. Meh. 2015. No. 2. Pp. 23-36. (in Russian).

25. Sobol I. M., Statnikov R. B. Choice of Optimum Parameters in Multicriteria Problems. Moscow: Nauka, 1981. 110 pp. (in Russian).

26. Bendat J., Pearson A. Random Data: Analysis and Measurement Procedures. Moscow: Mir, 1974. 464 pp. (in Russian).

Copyright (©) 2022 Dolgopolov S. I.

Copyright © 2014-2022 Technical mechanics