Mathematical Modeling of the Transient Processes in Propulsion System of the Upper Stage of the Cyclone-4M Launch Vehicle




the upper stage of the launch vehicle, liquid rocket engine and feed system, liquid jet system, transient processes, start and shutdown the engine, mathematical modeling.


Introduction. The development of the Cyclone-4M space launch vehicle (LV) by Pivdenne Design Offi ce is an important activity of the space industry of Ukraine. One of the LV innovations is feeding the liquid jet system (LJS) from the sustainer engine (SE) feedlines.
Problem Statement. In order to implement the specifi ed method of the LJS feed, it is necessary to ensure the LJS operation during hydraulic shocks and pressure drops of the propellants during the SE start and shutdown. For this purpose, it is necessary to simulate the transient processes of the system start and shutdown.
Purpose. The purpose is to estimate the parameters of the transient processes of the Cyclone-4M upper stage sustainer engine, given the eff ect of SE on the LJS, as a result of their joint operation.
Material and Methods. The methods of the theory of automatic control, the impedance method, and the methods of numerical modeling of the unsteady motion of gas-saturated liquids have been used.
Results. The transient processes in the joint (SE and LJS) propulsion system during the start and shutdown have been simulated. In the developed mathematical model, we have used dynamic gains of feedlines as distributed and concentrated parameter systems, which are reconciled in a certain frequency range. The SE start and shutdown have been calculated. The experimental and the calculated values of natural frequencies of fl uid oscillations, pressure peaks during hydraulic shocks, and the hydraulic shock patterns (horizontal pressure shelves when fluid continuity is broken) have shown a good agreement.
Conclusions. A nonlinear mathematical model of the low-frequency dynamics of the upper stage of propulsion system of the Cyclone-4M LV has been developed and tested. The model can be used to predict the time dependences of the propellant pressure at the LJS inlet during the SE start and shutdown in extreme conditions of LJS operation in the joint (the SE and the LJS) feed system.


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National target scientifi c and technical space program of Ukraine for 2021—2025. docs/2b0a8327/Dodatok.pdf. (Last accessed: 25.04.2023) [in Ukrainian].

Space rocket systems. Launch vehicle Cyclone-4M. com/ua/technique/launch-vehicles/rockets/cyclone-4m/ (Last accessed: 25.04.2023) [in Ukrainian].

Durachenko, V. M., Shpak, A. V., Kolesnichenko, S. A., Ageeva, L. I., Dolinkevich, A. S., Unchur, K. A. (2020). Problems and ways to solve them in the process of developing a liquid low-thrust jet engine for liquid rocket system of the 3rd stage of the Cyclone-4 launch vehicle. Space Sci. & Technol., 26, 1(122), 18—29. [in Russian].

Timoshenko, V. I., Knyshenko, Yu. V., Durachenko, V. M., Anishchenko, V. M. (2016). Issues of testing the control liquid propulsion system powered from the lines of the main engine of the last stage of the launch vehicle. Space Sci. & Technol., 22(1), 20—35 [in Russian].

Timoshenko, V. I., Knishenko, Yu. V., Durachenko, V. M., Asmolovsky, S. Yu. (2020). Analysis of the robotic reactive engines of the upper stage of the Cyclone-4M launch vehicle during launches and stages of the main engine. Technical mechanics, 2, 22—35. [in Russian].

Pylypenko, O. V., Prokopchuk, A. A., Dolgopolov, S. I., Pisarenko, V. Yu., Kovalenko, V. N., Nikolayev, O. D., Khoryak, N. V. (2017). Features of mathematical modeling of low-frequency dynamics of a sustainer staged liquid-propellant rocket engine at start-up. Space Sci. & Technol., 23(5), 3—12. [in Russian].

Pylypenko, O. V., Khoryak, N. V., Dolgopolov, S I., Nikolayev, O. D. (2019). Mathematical modeling of dynamic processes in hydraulic and gas paths at start-up of a staged liquid-propellant rocket engine. Technical mechanics, 4, 5—20. [in Russian].

Pylypenko, O. V., Dolgopolov, S. I., Nikolayev, O. D., Khoryak, N. V. (2020). Mathematical modeling of the start-up of a multi-engine liquid rocket propulsion system. Technical mechanics, 1, 5—19. [in Russian].

Dolgopolov, S. I., Zavoloka, A. N., Nikolayev, O. D., Sviridenko, N. F., Smolensky, D. E. (2015). Determination of the parameters of hydrodynamic processes in the propulsion system of the space stage during shutdowns and start-ups of the main engine. Technical Mechanics, 2, 23—36 [in Russian].

Belyaev, E. N., Chvanov, V. K., Chervakov, V. V. (1999). Mathematical modeling of the working process of liquid-propellant rocket engines. Moscow [in Russian].

Shevyakov, A. A., Kalnin, V. M., Naumenkova, M. V., Dyatlov, V. G. (1978). Theory of Rocket Engine Automatic Control. Moscow [in Russian].

Vasiliev, A. P., Kudryavtsev, V. M., Kuznetsov, V. A., Kurpatenkov, V. D., Obelnitsky, A. M., Polyaev, V. M., Poluyan, B. Ya. (1975). Fundamentals of the theory and calculation of liquid rocket engines. Moscow [in Russian].

Prisnyakov, V. F. (1983). Dynamics of liquid-propellant rocket propulsion systems and power systems. Moscow [in Russian].

Glikman, B. F. (1974). Automatic control of liquid-propellant rocket engines. Moscow [in Russian].

Charny, I. A. (1961). Unsteady fl ow of real fl uid in pipes. Moscow [in Russian].

Glikman, B. F. (1979). Unsteady fl ows in pneumohydraulic circuits. Moscow [in Russian].

Fox, D. A. (1981). Hydraulic analysis of unsteady fl ow in pipelines. Moscow [in Russian].

Pilipenko, V. V., Zadontsev, V. A., Natanzon, M. S. (1977). Cavitation oscillations and dynamics of hydraulic systems. Moscow [in Russian].

Dolgopolov, S. I. (2006). Mathematical modeling of fl uid dynamics in extended pipelines using hydrodynamic elements. Technical mechanics, 2, 114—120 [in Russian].

Pilipenko, V. V. (1989). Cavitation self-oscillations. Kyiv [in Russian].

Brennen, C. E., Meissner, C., Lo, E. Y., Hoff man, G. S. (1982). Scale eff ects in the dynamic transfer functions for cavitating inducers. ASME J. Fluids Eng., 104, 428—433.

Brennen, C. E. (2012). A Review of the Dynamics of Cavitating Pumps (IOP Conf. Ser.: Earth Environ. Sci. 15 012001 2012). 1—13.

Pilipenko, V. V., Dolgopolov, S. I. (1998). Experimental and computational determination of the coeffi cients of the equation for the dynamics of cavitation cavities in inducer centrifugal pumps of various sizes. Technical mechanics, 8, 50—56 [in Russian].

Dolgopolov, S. I. (1995). Generalized experimental-calculated coeffi cient of inertial resistance of a liquid caused by reverse fl ows at the inlet of a inducer-centrifugal pump. Technical Mechanics, 4, 99—103 [in Russian].

Dolgopolov, S. I. (2007). Generalization of experimental stall pressures of cavitating inducer-centrifugal pumps of liquid propellant engines. Space technology. Missile weapons: 1. Dnepropetrovsk [in Russian].

Pilipenko, V. V., Dolgopolov, S. I., Zadontsev, V. A., Grabovskaya, T. A. (2008). Experimental and computational method for determining the cavitation functions of pumps. Problems of high-temperature technology. Dnepropetrovsk [in Russian].

Alemasov, V. E., Dregalin, A. F., Tishin, A. P. (1980). Theory of rocket engines. Moscow [in Russian].

Natanzon, M. S. (1977). Longitudinal self-oscillations of a liquid-propellant rocket. Moscow [in Russian].

Glikman, B. F. (1989). Automatic control of liquid rockets. Moscow [in Russian].




How to Cite

PYLYPENKO, O., DOLGOPOLOV, S., NIKOLAYEV, O., & KHORIAK, N. (2024). Mathematical Modeling of the Transient Processes in Propulsion System of the Upper Stage of the Cyclone-4M Launch Vehicle . Science and Innovation, 20(1), 49–67.



Scientific and Technical Innovation Projects of the National Academy of Sciences