Pequliarities of mathematical modeling of low-frequency dynamics of the staged liquid rocket sustainer engines at its startup

1Pylypenko, OV, 2Prokopchuk, AA, 1Dolgopolov, SI, 2Pisarenko, VYu., 2Kovalenko, VN, 1Nikolaev, AD, 3Khoryak, NV
1Institute of Technical Mechanics of the National Academy of Sciences of Ukraine and the State Space Agency of Ukraine, Dnipro, Ukraine
2Yangel Yuzhnoye State Design Office, Dnipro, Ukraine
3Institute of Technical Mechanics of the National Academy of Sciences of Ukraine and the State Space Agency of Ukraine, Dnipropetrovsk, Ukraine
Space Sci.&Technol. 2017, 23 ;(5):03-13
https://doi.org/10.15407/knit2017.05.003
Publication Language: Russian
Abstract: 
We present a new mathematical model for startup of staged liquid rocket engines (LRE). It is based on the improving the mathematical models of low-frequency dynamics of cavitating pumps and gas LRE channels as well as on the introducing the process of injecting gaseous oxygen into the liquid oxygen stream in the LRE feed. We describe a mathematical simulation of the l startup of the prospective sustainer LRE of 250 ton-force thrust, which is being developed at the SE "Yuzhnoye" Design Office (Dnipro, Ukraine).
Keywords: liquid rocket engine, low-frequency dynamic processes, pump cavitation, startup
References: 
1. Belyaev E. N., Chervakov V. K., Chervakov V. V. Matematicheskoe modelirovanie rabochego processa zhidkostnyh raketnyh dvigatelej [Mathematical modeling of the working process of liquid rocket engines]. 228 p. (MAI, Moscow, 1999) [in Russian].
2. Garbera S. N., Dem'yanenko Ju. V., Lobov S. D., Malahova E. V., Rachuk V. S., Chembarcev S. V. Matematicheskoe modelirovanie zhidkostnyh raketnyh dvigatelej [Mathematical modeling of liquid rocket engines]. Kosmonavtika i raketostroenie – Cosmonautics and rocketry, 2(75), 96—102 (2014) [in Russian].
3. Degtjarev A. V. (Ed.). Raketnaja tehnika. Problemy i perspektivy [Rockets technology. Problems and perspectives]. 420 p. (ART-PRESS, Dnepro, 2014) [in Russian].
4. Pylypenko V. V., Dolgopolov S. I. Jeksperimental'no-raschetnoe opredelenie kojefficientov uravnenija dinamiki kavitacionnyh kavern v shnekocentrobezhnyh nasosah razlichnyh
tiporazmerov. Tehnicheskaja mehanika – Technical mechanics, 8, 50—56 (1998) [in Russian].
5. Pylypenko V. V., Dolgopolov S. I. Matematicheskoe modelirovanie zapuska zhidkostnogo raketnogo dvigatelja RD–8 s uchetom kavitacii v nasosah [Mathematical simulation of RD-8 liquid rocket engine start-up with cavitation in pumps]. Tehnicheskaja mehanika – Technical mechanics2, 18—24 (2003) [in Russian].
6. Pylypenko V. V, Dorosh N. L., Man'ko I. K. Jeksperimental'nye issledovanija kondensacii para pri vduve strui gazoobraznogo kisloroda v potok zhidkogo kisloroda. Tehnicheskaja mehanika – Technical mechanics, 2, 77—80 (1993) [in Russian].
7. Pylypenko V. V., Zadontsev V. A., Natanzon M. S. Kavitacionnye avtokolebanija i dinamika gidrosistem [Cavitation self-oscillations and dynamics of hydraulic systems ]. 352 p.  (Mashinostroenie, Moscow, 1977) [in Russian].
8. Repin Ju. M. O priblizhennoj zamene sistem s zapazdyvaniem obyknovennymi dinamicheskimi sistemami. [On the approximate replacement of systems with delay by ordinary dynamical systems]. Prikladnaja matematika i mehanika – Applied Mathematics and Mechanics, 29 (N 2), 229—235 (1965) [in Russian].
9. Khoriak N. V., Chernjavskij O. E. K ocenke ustojchivosti sistem s zapazdyvanijami po spektru matricy [On the estimating the stability of systems with delays from the spectrum of the matrix]. Dinamika gidrosistem jenergeticheskih ustanovok letatel'nyh apparatov – Dynamics of hydraulic systems of aircraft power plants, p. 16—23 (Naukova dumka, Kiev, 1991) [in Russian].
10. Shevjakov A. A., Kalnin V. M., Naumenkova N. V., Djatlov V. G. Teorija avtomaticheskogo upravlenija raketnymi dvigateljami [The theory of automatic control of rocket engines], 288 p. (Mashinostroenie, Moscow, 1978) [in Russian].
11. Di Matteo Fr., De Rosa M., Onofri M. (2011). 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 p.).
Retrieved from www.enu.kz/repository/2011/AIAA-2011-6032.pdf
12. 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 International Modelica Conference (September 21—23, 2015), Versailles, France, pp. 485—I490 (2015).
Retrieved from www.ep.liu.se/ecp/118/052/ecp15118485.pdf.
13. Zadontsev V. A. Experimental Study of LR Pump at Cavitation Autooscillations Regimes. Proceedings of Third China-Russia-Ukraine Symposium on Astronautical Science and Technology (XI’ AN China, September 16 — 20, 1994, pp. 285—287(1994).