Rotation of a rigid body with an ellipsoidal cavity is completely filled with stratified fluid

Аuthors

Aye M. W.^*, Temnov A. N.^**

Bauman Moscow State Technical University, MSTU, 5, bldg. 1, 2-nd Baumanskaya str., Moscow, 105005, Russia

*e-mail: ayeminwin84@gmail.com
**e-mail: antt45@mail.ru

Abstract

This work is associated with the increasing use of cryogenic liquids in a rocket and space technology. In this work we report the results of the analysis of the stability of rotational motion of a rigid body with ellipsoidal cavity completely filled with stratified (cryogenic) liquid. The problems of the motion of rigid bodies with cavities filled with a homogeneous ideal or viscous fluid are sufficiently studied. However, the development of modern technology and the practice is set for researchers a number of new problems of dynamics of solid bodies with liquid-filled cavities. One of these problems of the motion of solids with cavities filled with a cryogenic liquid. An essential feature of the cryogenic liquid is the heterogeneity of temperature and density, which is observed in all modes of exploitation and storage. In this abstract, assuming no heat exchange with the external environment, we consider the problem of the stability of rotation of a rigid body with an ellipsoidal cavity filled with an ideal stratified fluid. Obtained the characteristic equations are considered some special cases: A) rotation of a rigid body with hardened liquid, B) rotation of a dynamically symmetric rigid body with a homogeneous liquid having a cavity in the form of an ellipsoid of revolution. The regions of instability of motion of a rigid body with a homogeneous fluid in the plane of two parameters, which are coincide with the results of other authors. At the end of the paper the regions of instability of rotation of a rigid body with an ellipsoidal cavity entirely filled with stratified fluid are presented in different cases: a) in case of weightlessness but taking into account the moment of inertia of a rigid body, b) in case of mess weight, when the moment of inertia of a rigid body is equal to zero or not equal to zero. The given investigation of the stability of rotation of a rigid body with a stratified fluid showed that the stable stratified liquid reduces the instability regions. The result also indicate that in case of an ellipsoidal cavity hydrodynamic effects of stratified fluid created a large finite number of partial movements, compared to homogeneous fluid.

Keywords:

stratified fluid, the stability of rotation, ellipsoidal cavity, vibrations, cryogenic

References

1. Moiseev N.K., Rumyantsev V.V. Dinamika tela s polostyami soderzhashchimi zhidkost’ (Dynamics of a body with cavities containing liquid). Moscow, Nauka, 1966, 440 p.
2. Ishlinskii A.Yu., Temchenko M.E. Zhurnal prikladnaya mekhanika i tekhnicheskaya fizika, 1960, no.3, pp. 65-75.
3. Sobolev S.L. Zhurnal prikladnaya mekhanika i tekhnicheskaya fizika, 1960, no. 3, рр. 20-55.
4. Kazmerchuk I.M., Samsonov V.A. Izvestiya AN SSSR. Mekhanika tverdogo tela, 1996, no. 2, pp. 32-36.
5. Dosaev M.Z., Samsonov V.A. Prikladnaya matematika i mekhanika, 2002, vol. 66, no. 3, pp. 427-433.
6. Karapetyan A.V., Lagutina I.S. Izvestiya AN SSSR. Mekhanika tverdogo tela, 2000, no.1, pp. 53-57.
7. Karapetyan A.V., Samsonov V.A., Sumin T.S. Prikladnaya matematika i mekhanika, 2004, vol.68, no.6, pp. 994-998.
8. Temnov A.N., Aye Min Win. Vestnik MGTU imeni Baumana, 2012, pp. 86-101.
9. Aye Min Win, Temnov A.N. Elektronnyi zhurnal «Nauka i obrazovanie», 2013, no. 12, available at: http://technomag.bmstu.ru/doc/627898.html (accessed 04.12.2014).
10. Dokuchaev L.V., Rvalov R.V. Mekhanika tverdogo tela, 1973, no. 2, pp. 6-14.
11. Temnov A.N. Kolebaniya stratifitsirovannoi zhidkosti v ogranichennom ob"eme (Fluctuations stratified fluid to a limited extent), Doctor’ thesis, Moscow, IPM, 1984, 192 p.
12. Chernous’ko F.L. Dvizhenie tverdogo tela s polostyami, soderzhashchimi vyazkuyu zhidkost’ (The movement of a solid body with the cavities containing viscous liquid), Moscow, Vychislitel’nyi tsentr AN SSSR, 1968, 232 p.
13. Zhukovskii N. E. O dvizhenii tverdogo tela, imeyushchego polosti, napolnennye odnorodnoi kapel’noi zhidkost’yu (On the motion of a rigid body with cavities filled by homogeneous fluid), Moscow, Gostekhizdat, 1948, 143 p.

Download