МАТЕМАТИЧНЕ МОДЕЛЮВАННЯ НЕСТАЛОЇ ТЕЧІЇ РІДИНИ В БАКАХ СТОСОВНО ЗАДАЧІ ОПИСУ ПОЗДОВЖНІХ КОЛИВАНЬ РІДИННИХ РАКЕТ - DOLGOPOLOV, S. I. (текст 3, 2025)
DOI: https://doi.org/10.15407/itm2025.03.009 In today’s liquid-propellant launch vehicles (LVs), the propellant mass may exceed 90 % of the total LV mass. When describing longitudinal oscillations in an elastic tank, the propellant is usually simulated by mechanical oscillators. This approach ignores the difference in dynamic processes in the liquid propellant components in the tanks and in the LV structure as an elastic body.  The goal of this paper is to account for the features of an unsteady tank liquid flow as applied to the problem of description of liquid-propellant rocket pogo oscillations. An approach is developed to mathematical simulation of unsteady liquid flow in liquid-propellant LV tanks as a distributed-parameter system. Using the impedance method, a nonlinear system of equations is derived to determine the effective sound speed in the tank propellant and the inertia resistance coefficient at the tank outlet. An approach is developed to mathematical simulation of an unsteady liquid flow in liquid-propellant LV tanks as a lumped-parameter system. A lumped-parameter mathematical model is constructed to describe two eigenmodes of the tank liquid oscillations. A system of equations is derived to determine the coefficients of the lumped-parameter model, which uses the effective sound speed and the inertia resistance coefficient at the tank outlet found in the distributed-parameter model. The above approaches are demonstrated by the example of the oxidizer tank of the Cyclone liquid-propellant LV’s first stage. It is shown that the effective sound speed is one seventh of the sound speed in an infinite medium. The inertia resistance coefficient at the tank outlet is far greater than the total inertia resistance coefficient of the tank liquid (early in the flight, by a factor of more than 10). These results show the tank bottom dynamics is of great importance in mathematical simulation of an unsteady tank propellant flow. The model coefficients are determined for the mathematical model of an unsteady liquid flow in the oxidizer tank of the Cyclone liquid-propellant lV’s first stage as a lumped-parameter system from the condition of agreement with a known solution on tank liquid eigenfrequencies. REFERENCES 1. Degtyarev A. V. Rocket Engineering. Problems and Prospects. Dnipropetrovsk: ART-PRESS, 2014. 420 pp. (In Russian). 2. Pylypenko O. V., Dolgopolov S. I., Nikolayev O. D., Khoriak N. V. Mathematical modeling of the transient processes in propulsion system of the upper stage of the Cyclone-4M launch vehicle. Science and Innovation. 2024. Vol. 20, No. 1. Pp. 49–67. 3. Dolgopolov S., Nikolayev O. Features of mathematical modeling of nonlinear Pogo oscillations of launch vehicles. CEAS Space Journal. 2024. V. 16. Iss. 2. Pp. 32–48.https://doi.org/10.1007/s12567-024-00541-3 4. Kolesnikov K. S. Rocket Dynamics. Moscow: Mashinostroyeniye, 1980. 378 pp. (In Russian). 5. Abgaryan K. A., Kalyazin E. L., Mishin V. P., Rappoport I. M. Rocket Dynamics. Moscow: Mashinostroyeniye, 1990. 464 pp. (In Russian). 6. Mikishev G. N., Rabinovich B. I. Dynamics of a Solid Body with Cavities Partially Filled with a Liquid. Moscow: Mashinostroyeniye, 1968. 532 pp. (In Russian). 7. Narimanov G. S., Dokuchaev L. V., Lukovsky I. A. Nonlinear Dynamics of a Flying Vehicle with a Liquid. Moscow: Mashinostroyeniye, 1977. 208 pp. (In Russian). 8. Nikolayev A. D., Bashliy I. D. Mathematical simulation of spatioal oscillations of a liquid in longitudinally vibrating tank. Teh. Meh. 2012. No. 2. Pp. 14–22. (In Russian). 9. Bashliy I. D., Nikolayev A. D. Mathematical simulation of spatial vibrations of shell structures with a liquid using up-to-date means of computer-aided design and analysis. Teh. Meh. 2013. No. 2. Pp. 18–25. (In Russian). 10. Nikolayev A. D., Khoriak N. V. Characterization of longitudinal self-oscillations of the liquid-propellant launch vehicle structure with account for energy dissipation. Aviatsionno-Kosmicheskaya Tekhnika i Tekhnologiya. 2004. No. 4. Pp. 62–73. (In Russian). 11. Wiggert D. C., Otwell R. S, Hatfield F. J. The effect of elbow restraint on pressure transients. ASME J. Fluids Eng. 1985. V. 107. Pp. 402–406.https://doi.org/10.1115/1.3242500 12. Pilipenko V. V., Zadontsev V. A., Natanzon M. S. Cavitation Oscillations and Hydrosystem Dynamics. Moscow: Mashinostroyeniye, 1977. 352 pp. (In Russian). 13. Altshul A. D. Hydraulic Resistances. Moscow: Nedra, 1970. 216 pp. (In Russian). 14. Zhulai Yu. A., Dolgopolov S. I., Grabovskaya T. A. Mathematical simulation of joint longitudinal pipeline structure - liquid oscillations under cavitation oscillations in liquid-propellant rocket engine feed lines. Aviatsionno-Kosmicheskaya Tekhnika i Tekhnologiya. 2009. No. 5(62). Pp. 58–63. (In Russian).