Приближенные вычисления собственных значений вращающейся жидкости, вытекающей из произвольной осесимметричной емкости

Abstract

The paper addresses the problem of proper motions of a rotating fluid that partially fills an axisymmetric vessel in the presence of an outflow through a rigid bottom. The problem is solved in a quasi-stationary setting within the framework of an ideal fluid model, with account for hydraulic losses during fluid flow through the bottom of the vessel. Numerical research was carried out using the finite element method. The study investigates the spectrum of eigenvalues and reveals the characteristics of the wave motions of the fluid. Numerical calculations confirm the possible appearance of wave motions on the drain surface, i.e. drain waves caused by the presence of fluid outflow through the bottom of the vessel. The paper presents the results of calculating the wavenumbers and the complex attenuation coefficient. Findings of the research can be used in practical calculations of dynamic modes at the design stage of promising space-rocket vehicles.