Evaluation of the scatter of liquid launch vehicle POGO oscillation amplitudes due to the influence of the scatter of internal factors

Heading: 
Space-Rocket Complexes
1Pylypenko, OV, 1Dolgopolov, SI, 1Khoriak, NV, 1Nikolayev, OD
1Institute of Technical Mechanics of the National Academy of Sciences of Ukraine and the State Space Agency of Ukraine, Dnipro, Ukraine
Space Sci. & Technol. 2024, 30 ;(3):03-15
https://doi.org/10.15407/knit2024.03.003
Publication Language: English
Abstract: 
Almost all liquid launch vehicle developers faced the problem of ensuring stability in relation to POGO oscillations. The level of POGO amplitudes oscillations of the launch vehicle can be significantly affected by the scatter of internal factors. The study aims to create a mathematical model that can determine the range of POGO amplitudes in liquid launch vehicles. This will be demonstrated through the example of the Dnipro launch vehicle, which is affected by a variety of internal factors that cause its POGO amplitudes to vary. We developed the non-linear non-stationary mathematical model of POGO oscillations of the prototype of the Dnipro space launch vehicle. The model is built by taking into account the two lower vibration modes of the LV structure, two lower oscillation modes of the oxidizer feedline, and the first oscillation mode of the fuel feedline of the propulsion system. Modeling of dynamic processes was conducted in a combination of four liquid rocket engines based on the schematic of the staged rocket engine. The simulation takes into account cavitation phenomena in the engine pumps and delay times in the gas generators’ chambers.
        We have developed a method for determining the scatter of the POGO oscillations caused by the action of internal factors, which is based on the use of the LPt uniformly distributed sequences. As internal factors, the frequencies, decrements, and shapes of LV structural oscillation modes, the values of pressurization of the propellant tanks, and the engines' specific thrust impulses were considered. Based on the results of the calculations, the dependence of the POGO amplitudes in two regions of LV instability was determined, and the lower and upper enveloping curves for the POGO amplitudes were constructed. It is shown that the maximum POGO amplitudes oscillations in the first region of instability lie in the range from 0.23 g to 0.72 g and in the second region of instability - from 0 g to 0.60 g. Variants of combinations of internal factors, which provided the largest and smallest values of POGO amplitudes, were analyzed. This made it possible to determine the internal factors, the scatter of which has the greatest effect on the POGO amplitudes scatter: frequency, decrement, shape coefficients of oscillations of the oxidizer feedlines and the LV 1st mode structural longitudinal oscillations in the payload cross-section.
Keywords: internal factors, liquid-propellant launch vehicle, liquid-propellant rocket propulsion system, mathematical modeling, POGO oscillations, scatter of amplitudes of longitudinal vibrations.
Full text (PDF)
References: 

1. Degtyarev A. V. (2014). Rocket technology. Problems and Prospects. Dnepropetrovsk: ART-PRESS, 420 p. [in Russian].
2. Dordain J., Lourme D., Estoueig C. (1974). Etude de l'effet POGO sur les lanceurs EUROPA II et DIAMANT B. Acta Astronautia, 1, Iss. 11–12, 1357¾1384.
3. Kolesnikov K. S. (1980). Dynamics of rockets. M.: Mechanical Engineering, 376 p. [in Russian].
4. Lee H. J., Jung T. K., Menshikova O. M., Kim Y. W., Cho I. H. Oh S. H., Lee D. S. (2002). Pogo Analysis on the KSR-III Propulsion Feeding System. J. Korean Soc. Propulsion Engineers, 6, No. 3, 45-52.
5. Liu T., Liu J.-F., Di W.-B., Tang G.-A., Song L.-Y. (2020). Pogo Stability Approaches for the Strap-On Launch Vehicle with Staged Combustion Cycle Engines. J. Spacecraft and Rockets, Published Online:25 May 2020.
https://doi.org/10.2514/1.A34551
6. Muller S., Brévière F., Kernilis A., Lemoine N. (2010). Influence of pump cavitation process on POGO diagnosis for the A5E/CA upper stage. 46th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, 25-28 July 2010, Nashville, AIAA 2010-6892.
7. Natanzon M. S. (1977). Longitudinal self-oscillations of a liquid-propellant rocket. M.: Mechanical Engineering, 208 p. [in Russian].
8. Nikolayev O.D., Bashliy I. D., Khoryak N. V. (2018). Сomputation of the POGO self-excited oscillation parameters in dynamic “propulsion ¾ rocket structure” system by using of 3D structural model. Technical Mechanics, No 2, 17-29.
https://doi.org/10.15407/itm2018.02.017
9. Oppenheim B. W., Rubin S. (1993). Advanced Pogo Stability Analysis for Liquid Rockets. AIAA J. Spacecraft and Rockets, 30, No. 3, 360-373.
https://doi.org/10.2514/3.25524
10. Pilipenko V. V., Dovgotko N. I., Dolgopolov S. I., Nikolayev O. D., Serenko V. A., Khoryak N. V. (1999). Theoretical computation of the amplitudes of Pogo vibrations of liquid launch vehicles. Space Science and Technology, 5, No. 1, 90-96 [in Russian].
https://doi.org/10.15407/knit1999.01.90
11. Pilipenko V. V., Dovgotko N. I., Nikolayev O. D., Dolgopolov S. I., Khoryak N. V., Serenko V. A. (2000). Theoretical determination of dynamic loads (longitudinal vibration accelerations) on the structure of a liquid-propellant rocket RS-20 on the active part of its flight trajectory. Technical mechanics, No 1, 3-18. [in Russian].
12. Pilipenko V. V., Dovgotko N. I., Pylypenko O. V., Nikolayev O. D., Pirog V. A., Dolgopolov S. I., Khodorenko V. .F., Khoryak N. V., Bashliy I. D. (2011). Theoretical forecast of longitudinal vibration accelerations of a spacecraft when it is launched into a working orbit by a liquid-propellant space rocket "Cyclone-4". Technical mechanics, No 4, 30-36 [in Russian].
13. Pilipenko V. V., Dolgopolov S. I. (1998). Experimental and computational determination of the coefficients of the equation of dynamics of cavitation cavities in inducer-centrifugal pumps of various sizes. Technical Mechanics, Is. 8, 50-56 [in Russian].
14. Pilipenko V. V., Dolgopolov S. I., Khoryak N. V., Nikolayev O. D. (2008). Mathematical modeling of longitudinal oscillations of a liquid-propellant rocket with two-frequency instability of the ‘rocket engine - rocket structure’ dynamic system. Aviation and Space Technology and Technology, 10(57), 12-16 [in Russian].
15. Pilipenko V. V., Zadontsev V. A., Dovgotko N. I., Grigoriev Yu. E., Manko I. K., Pylypenko O. V. (2001). Dynamics of liquid-propellant rocket propulsion systems and Pogo stability of liquid-propellant launch vehicles. Technical Mechanics, No 2, 11-37 [in Russian].
16. Pilipenko V. V., Zadontsev V. A., Natanzon M. S. (1977). Cavitation oscillations and dynamics of hydraulic systems. M.: Mechanical Engineering, 352 p. [in Russian].
17. Pylypenko O. V., Dolgopolov S I., Khoryak N. V., Nikolayev O. D. (2021). Methodology for determining the scatter of internal and external factors into the thrust scatter of a single rocket engine during start-up. Technical Mechanics, No 4, 7-17 [in Ukrainian].
https://doi.org/10.15407/itm2021.04.007
18. 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 a staged propulsion rocket engine. Vestnik Dvigatelestroeniya, No. 2, 34-42 [in Russian].
19. Pylypenko O. V., Degtyarev M. A., Nikolayev O. D., Klimenko D. V., Dolgopolov S. I., Khoriak N. V., Bashliy I. D., Silkin L. A. (2020). Providing of POGO stability of the Cyclone‑4M launch vehicle. Space Science and Technology, 26, No. 4 (125), 3-20.
https://doi.org/10.15407/knit2020.04.003
20. Pylypenko O. V., Dolgopolov S. I., Nikolayev O. D., Khoriak N. V., Kvasha Yu. A., Bashliy I. D. (2022). Determination of the Thrust Spread in the Cyclone-4M First Stage Multi-Engine Propulsion System During its Start. Sci. Innov, No 18(6), 97-112.
https://doi.org/10.15407/scine18.06.097
21. Pylypenko O. V., Prokopchuk O. O., Dolgopolov S. I., Nikolayev O. D., Khoriak N. V., Pysarenko V. Yu., Bashliy I. D., Polskykh S. V. (2021). Mathematical modeling of start-up transients at clustered propulsion system with POGO-suppressors for Cyclon-4M launch vehicle. Space Science and Technology, 27, No. 6 (133), 3-15.
https://doi.org/10.15407/knit2021.06.003
22. Rong K. L., Zhang J. H., Ma J. M., Wang J. M., Wang M. K. (2011). Research on Pogo Problem for CZ-2F Rocket. Manned Spaceflight, No 17, 8-18.
23. Rubin S. (1966). Longitudinal Instability of Liquid Rockets Due to Propulsion Feedback (POGO). Spacecraft and Rockets, 3, No 8, 1188-1195.
https://doi.org/10.2514/3.28626
24. Shevyakov A. A., Kalnin V. M., Naumenkova M. V., Dyatlov V. G. (1978). Theory of automatic control of rocket engines. M.: Mashinostroenie, 288 p. [in Russian].
25. Sobol I. M., Statnikov R. B. (1981). Selection of optimal parameters in problems with many criteria. M.: Nauka, 110 p. [in Russian].
26. Tang Y., Li M., Wang L., Zhang Y., Fang B. (2017) Modeling and Stability Analysis of Pogo Vibration in Liquid-Propellant Rockets with a Two-Propellant System. Trans. Jap. Soc. Aero. Space Sci, 60, No. 2, 77-84.
27. Ujino T., Morino Y., Kohsetsu Y., Mori T., Shirai Y. (1989). POGO Analysis on the H-II Launch Vehicle. 30th Structures, Structural Dynamics and Materials Conference, Mobile, USA, 460¾467.
28. Wang Q., Tan S., Wu Z., Yang Y., Yu Z. (2015) Improved modelling method of Pogo analysis and simulation for liquid rockets. Acta Astronautica, 107, No. 2, 262-273.
https://doi.org/10.1016/j.actaastro.2014.11.034
29. Xu D., Hao Y., Tang G. (2015) New Pogo Analysis Method Using Rational Fitting and Three-Dimensional Tank Modeling. AIAA J., 53, No. 2, 405-412.
https://doi.org/10.2514/1.J053046