On the stability of stationary rotation of a solid body with a cavity containing a cryogenic liquid


Аuthors

Temnov A. N.*, Yan N. O.**

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

*e-mail: antt45@mail.ru
**e-mail: yno64528@gmail.com

Abstract

The article considers the stationary rotation stability of a solid body with a cylindrical cavity completely filled with incompressible cryogenic liquid. The stationary rotation stability of a body with stratified liquid is being studied based on ordinary differential equations, which coefficients are being determined from the solution of time-independent boundary value problems of hydrodynamics. A distinctive feature of all cryogenic liquids is the non-uniform change of density and temperature observed in all storage and operation modes. The most significant stratification of the cryogenic component occurs in the direction of action of the external field of mass forces. To study motions of this mechanical system, a stratified incompressible fluid is a suitable model. The authors studied various cases: (a) the case of solid body rotation in the absence of liquid mass and with solidified liquid; (b) the case of solid body rotation with homogeneous liquid, when the moment of inertia of the solid body equals to zero or not equal to zero; (c) the case of solid body rotation with stratified liquid, when the moment of inertia of the solid body equals zero or not equal to zero. Characteristic equations of the boundary value problem and the motion of a solid body with a stratified fluid stationary rotating about its axis were obtained. The stability regions of free rotation of a solid with stratified fluid in dimensionless parameters are plotted. The obtained results allow drawing inference that stable stratification of the fluid leads to a decrease in the areas of instability in the rotation of a solid body with a cylindrical cavity completely filled with fluid. The considered method maybe used for studying not only the cylindrical cavity, but the other forms of cavity as well.

Keywords:

rotational stability, cryogenic fluid, stratified fluid, free oscillations

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