Perturbed rotational motions of a spheroid with cavity filled with a viscous fluid

Abstract

We consider a motion about the center of mass of a spheroid with a cavity filled with a viscous fluid. It is assumed that the velocity of the fluid is sufficiently high, so the corresponding Reynolds number is small. The torque of forces acting on the body by the viscous fluid in the cavity is determined by the method developed in the works of F.L. Chernousko. Asymptotic approach permits to obtain some qualitative results and to describe nonlinear evolution of angular motion using simplified averaged equations and numerical solution.

Dynamical analysis of a rotating rigid body containing a viscous incompressible fluid

“…These solutions are represented in some plots to display the positive impact of the applied moments and forces on the body’s dynamical behavior. The acquired outcomes are regarded as a generalization of those that were previously obtained for the situation of a null value of the GM other than an uncharged body (Akulenko et al , 2020; Akulenko et al , 2019; Farag et al , 2022). The graphs have clearly shown the positive effects of the fluid’s density, the third projection of angular velocity and the values of the inertia’s main moments, charge and the GM.…”

“…When (28) is used in place of (22) in its second equation, the result will be: which can be solved easily using the method of separation of variables (Akulenko et al , 2020).…”

“Nonlinear Dynamics of Mechanical Systems” dedicated to 75th birthday and 52 years scientific contribution of Prof. Katica R. (Stevanovic) Hedrih

“…Akulenko et al 24 obtained qualitative results and asymptotic behavior of the angular motion of a spheroid with a cavity filled with highly viscous fluid with respect to the mass, in a motion with low Reynolds number. Liu 25 analyzed side-blown mixing jets by examining their manifold Betti numbers and the mixing performances and flow fields for different Froude numbers verified with experimental data image processing.…”