The Liquid’s Self-Oscillations in a Spherical Vessel

The self-oscillation problem for liquid in the partly filled spherical vessels has been considered by many researchers. Nowadays, the fuel tanks contain different sections affecting oscillations of the liquid - such as spherical flasks filled with compressed air, anti-vibration and other devices. Some non-classical solutions of the liquid’s oscillations in the spherical volume are considered. Finite element method is used to solve the problem, the results are compared with those obtained by the Trefftz method.

References

[1] Kolesnikov K.S. Dinamika raket [Rocket dynamics]. Moscow, Mashinostroenie Publ., 2003. 500 p.

[2] D’yachenko M.I., Orlov V.V., Temnov A.N. Liquid fuel fluctuations in taper and cylindrical vessels. Jelektr. Nauchno-Tehn. Izd "Nauka i obrazovanie" MGTU im. N.E. Baumana [El. Sc.-Tech. Publ. "Science and Education" of Bauman MSTU], 2013, no. 11, pp. 175-192 (in Russ.).

[3] Nguen Kh.Z., Temnov A.N. Fluctuations of liquid fuel of changeable volume in a spherical vessel. Jelektr. Nauchno-Tehn. Izd "Nauka i obrazovanie" MGTU im. N.E. Baumana [El. Sc.-Tech. Publ. "Science and Education" of Bauman MSTU], 2014, no. 12, pp. 426-439 (in Russ.).

[4] Lukovskiy I.A., Barnyak M.Ya., Komarenko A.N. Priblizhennye metody resheniya zadach dinamiki ogranichennogo ob"ema zhidkosti [Approximate methods to solve dynamic problems of limited volume of liquid]. Kiev, Nauk. Dumka Publ.,1984. 212 p.

[5] Limarchenko O.S., Mataratstso D., Yasinskiy V.V. Dinamika vrashchayushchikhsya konstruktsiy s zhidkost’yu [Dynamics of rotating constructions containing liquid]. Kiev, GNOZIS Publ., 2002. 304 p.

[6] D’yachenko M.I., Temnov A.N. Natural Oscillations of Liquid Propellant under Redistribution Conditions. Vestn. Mosk. Gos. Tekh. Univ. im. N.E. Baumana, Mashinostr. [Herald of the Bauman Moscow State Tech. Univ., Mech. Eng.], 2012, no. 3, pp. 31-38 (in Russ.).

[7] Connor J.J., Brebbia C.A. Finite element techniques for fluid flow. London-Boston: Newnes-Butterworths, 1977. 264 р.

[8] Ershov N.F., Shakhverdi G.G. Metod konechnykh elementov v zadachakh gidrodinamiki i gidrouprugosti [Finite element method in the problems of hydrodynamics and hydroelasticity]. Leningrad, Sudostroenie Publ., 1984. 237 p.