DETERMINATION OF THE THRUST SPREAD IN THE CYCLONE-4M FIRST STAGE MULTI-ENGINE PROPUSION SYSTEM DURING ITS START
Keywords:: liquid-propellant rocket engine, multi-engine liquid-propellant rocket launch vehicle, start, mathematical modeling, external and internal factors, and thrust spread.
Introduction. The development of the Cyclone-4M space rocket complex is an important project of Ukraine space industry. In order to reduce the costs and the time inputs for the design and manufacture of liquid rocket engines (LRE) for the 1st stage of the Cyclone-4M launch vehicle, Pivdenne Design Office has employed the clustered multi-engine prototyped before as 1st stage sustainer engine.
Problem Statement. In a clustered multi-engine propulsion system, because of internal and external factors, individual engines do not start simultaneously. This may lead to dangerous spreads in the thrust of individual LREs in the course of the start of propulsion system, which can cause significant deviations of the launch vehicle motion from its trajectory within the initial time interval of the flight.
Purpose. The purpose of this research is to estimate the thrust spread as a result of the effect of internal and external factors on the transient processes in the individual engine systems and their dynamic interaction during the start of a multi-engine system of the Cyclone-4M first stage.
Material and Methods. The methods of automatic control theory, the impedance method, the statistical method and the methods for numerical simulation of non-stationary processes in pipeline systems of launch vehicles have been used.
Results. A mathematical model for start of multi-engine propulsion system of the Cyclone-4M first stage has been developed. It makes it possible to take into account the influence of spread of internal and external factors on the transient processes in a multi-engine system during the start of the engines. An effective method for determining the indicated thrust spread, which is based on the use of LPτ-sequences (Sobol sequences) that are sequences of multidimensional points whose uniform distribution is asymptotically optimal, has been developed. The transient processes in the RD-874 multi-engine propulsion system have been determined for various combinations of engine misalignments caused by external and internal factors. The lower and upper envelope curves of the time dependences of combustion chamber pressure have been plotted for each LRE in the multi-engine propulsion system.
Conclusions. The thrust spread and the spread of the time of reaching 90% thrust for RD-874 multi-engine propulsion system is significantly (about 2 times) smaller than that for individual RD-870 engine in this propulsion system.
Nationwide targeted scientific and technical space program of Ukraine for 2021-2025. http://materialy.kmu.gov.ua/ af3b841c/docs/2b0a8327/Dodatok.pdf (Last accessed: 09.02.2022).
Space rocket complexes. Cyclone-4M launch vehicle. http://www. https://www.yuzhnoye.com/ua/technique/launchvehicles/launch-vehicles/cyclone-4m/ (Last accessed: 09.02.2022).
Pylypenko, O. V., Prokopchuk, A. A., Dolgopolov, S. I., Pisarenko, V. Yu., Kovalenko, V. N., Nikolayev, O. D., Khoryak, N. V. (2017). Pequliarities of mathematical modeling of low-frequency dynamics of the staged liquid rocket sustainer engines at its startup. Space Sci.&Technol., 23(5), 3-13 [in Russian]. https://doi.org/10.15407/knit2017.05.003
Shevyakov, A. A., Kalnin, V. M., Naumenkova, M. V., Dyatlov, V. G. (1978). Theory of Rocket Engine Automatic Control. Moscow: Mashinostroyeniye [in Russian].
Pilipenko, V. V., Dorosh, N. L., Man'ko, I. K. (1993). Experimental investigations of steam condensation when a gaseous oxygen jet is blown into a liquid oxygen flow. Technical mechanics, 2, 77-80 [in Russian].
Dorosh, N. L. (2020). Modeling of condensation of an oxygen vapor jet in liquid oxygen. Applied problems of mathematical modeling, 3(2.2), 149-155 [in Ukrainian]. https://doi.org/10.32782/KNTU2618-0340/2020.3.2-2.14
Borovsky, B. I., Ershov, N. S., Ovsyannikov, B. V., Petrov, V. I., Chebaevsky, V. F., Shapiro, A. S. (1975). High-speed vane pumps. Moskow: Mashinostroenie [in Russian].
Pilipenko, V. V., Zadontsev, V. A., Natanzon, M. S. (1977). Cavitation oscillations and dynamics of hydraulic systems. Moscow: Mashinostroenie [in Russian].
Pilipenko, V. V., Dolgopolov, S. I. (1998). Experimental and computational determination of the coefficients of the equation for the dynamics of cavitation cavities in inducer centrifugal pumps of various sizes. Technical mechanics, 8, 50-56 [in Russian].
Pylypenko, O. V., Dolhopolov, S. I., Nikolayev, O. D., Khoriak, N. V. (2020). Mathematical simulation of the start of a multiengine liquid-propellant rocket propulsion system. Technical mechanics, 1, 5-19 [in Russian]. https://doi.org/10.15407/itm2020.01.005
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 power system of the space stage during shutdowns and starts of the main engine. Technical mechanics, 2, 23-36 [in Russian].
Glikman, B. F. (1974). Automatic control of liquid rocket engines. Moscow: Mashinostroenie [in Russian].
Charny, I. A. (1961). Unsteady motion of a real fluid in pipes. Moscow: GITTL [in Russian].
Dolgopolov, S. I., Nikolayev, O. D. (2017). Mathematical modeling of low-frequency dynamics of the fluid flow controller at different amplitudes of harmonic disturbances. Technical mechanics, 1, 15-25 [in Russian]. https://doi.org/10.15407/itm2017.01.015
Glikman, B. F. (1989). Automatic control of liquid rocket engines. Moscow: Mashinostroenie [in Russian].
Alemasov, V. E., Dregalin, A. F., Tishin, A. P. (1980). Theory of rocket engines. Moscow: Mashinostroenie [in Russian].
Natanzon, M. S. (1977). Longitudinal self-oscillations of a liquid rocket. Moscow: Mashinostroenie [in Russian].
Belyaev, E. N., Chervakov, V. V. (2009). Mathematical modeling of LRE. Moscow: MAI-PRINT [in Russian].
Оppenheim, B. W., Rubin, S. (1993). Advanced Pogo Stability Analysis for Liquid Rockets. Journal of Spacecraft and Rockets, 30(3), 360-383. https://doi.org/10.2514/3.25524
Pylypenko, O. V., Prokopchuk, A. A., Dolgopolov, S. I., Khoryak, N. V., Nikolayev, O. D., Pisarenko, V. Yu., Kovalenko, V. N. (2017). Mathematical modeling and stability analysis of low-frequency processes in the march LRE with generator gas afterburning. Bulletin of engine building, 2, 34-42 [in Russian].
Khoriak, N. V., Dolhopolov, S. I. (2017). Features of mathematical simulation of gas path dynamics in the problem of the stability of low-frequency processes in liquid-propellant rocket engines. Technical mechanics, 3, 30-44 [in Russian]. https://doi.org/10.15407/itm2017.03.030
Pylypenko, O. V., Khoriak, N. V., Dolhopolov, S. I., Nikolayev, O. D. (2019). Mathematical simulation of dynamic processes in hydraulic and gas paths at the start of a liquid-propellant rocket engine with generator gas after-burning. Technical mechanics, 4, 5-20. https://doi.org/10.15407/itm2019.04.005
Makhin, V. A., Prisnyakov, V. F., Belik, N. P. (1969). Dynamics of liquid rocket engines. Moscow: Mashinostroenie [in Russian].
Sobol, I. M., Statnikov, R. B. (1981). Choice of optimal parameters in problems with many criteria. Moscow: Nauka [in Russian].
Bendit, J., Pirsol, A. (1974). Measurement and analysis of random processes. Moscow: Mir [in Russian].
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