Stability conditions for the steady-state rotation of a cylinder filled with a stratified nonuniform viscous incompressible liquid

Derendyaev, N. V.; Senyatkin, V. A.

doi:10.1007/bf00916861

Cited by 8 publications

(4 citation statements)

References 2 publications

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“…Yukio Ishida et al applied a method, which utilizes discontinuous spring characteristics, to suppress unstable vibrations in an asymmetrical rotor system, an asymmetrical shaft system, and a rotor system partially filled with liquid [18]. N. V. Derendyaev et al investigated the stability of a cylinder filled with different kinds of liquid, including viscous incompressible liquid, a stratified viscous incompressible liquid and a stratified non-uniform viscous incompressible liquid [19][20][21][22]. In 1988, Derendyaev proved that Andronov-Hopf bifurcations may occur in a rotor system filled with liquid [23].…”

Section: Introductionmentioning

confidence: 99%

An analytical investigation on the dynamic stability of a rotor filled with liquid

Li¹,

Wang²,

Yuan³

2018

J. vibroeng.

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This paper deals with the dynamic stability of a rigid rotor arbitrarily filled with liquid. On the basis of the established coupled-field equations of the rotor system, the general whirling eigenequation, which is a quartic complex coefficients equation, is derived. In order to obtain the solutions of the general whirling eigenequation, a mathematical method is proposed. To illustrate the precision of calculating results, a comparison is carried out between the present analysis and the numerical results. The results show that two calculation results are in good agreement. Then the stability of the rotor system is analyzed. It is shown that the dynamic instability occurs at a particular bound of the spinning speed. Moreover, the effects of system parameters, such as fluid-fill ratio and mass ratio, on the unstable regions are discussed.

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Section: Introductionmentioning

confidence: 99%

An analytical investigation on the dynamic stability of a rotor filled with liquid

Li¹,

Wang²,

Yuan³

2018

J. vibroeng.

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“…A stability analysis method for similar rotary systems was proposed in [15,17]. In this method, one of the main stages involves calculation of the moments of the forces exerted by the liquid on the rotor walls during steady-state conical precession of the rotor.…”

Section: Introductionmentioning

confidence: 99%

“…The behavior of a low-viscosity liquid in a rotating horizontal cylinder as a function of the rotation velocity and the degree of filling was studied in [10]. The resonant generation of waves in a liquid filling a rotor cavity, which is the main factor responsible for instability of steady-state rotation of rotary systems was investigated in [11][12][13][14][15][16][17][18][19].The present investigation of the properties of gyroscopic waves in a rotating liquid layer is motivated by interest in the problem of the stability of rotary systems with a fixed point at which the angular velocity of rotation of a rotor is maintained constant by a drive. A stability analysis method for similar rotary systems was proposed in [15,17].…”

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confidence: 99%

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Gyroscopic waves in a rotating liquid layer

Солдатов

2008

J Appl Mech Tech Phys

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The dispersion characteristics of gyroscopic waves in an incompressible liquid layer in a cavity of a rapidly rotating cylinder are studied. It is shown that in a viscous incompressible liquid layer, an inertial wave can be represented as the sum of six helical harmonics. The effects of the liquid viscosity and the ratio of the wave frequency to the angular velocity of rotation of the cylinder on the real and imaginary parts of the wavenumber are studied. Introduction.Wave processes in a liquid with the effect of the Earth's rotation taken into account were considered in papers dealing with waves in the ocean (see, for example, [1-4] and the bibliography therein). The strong effect of rotation on the liquid dynamics is exemplified by rotary systems. Rotors with a liquid-containing cavity, in which the centrifugal force can be several hundred thousand or even several millions of times the gravity. Disturbance of the balance between the pressure gradient and the Coriolis force can lead to the generation of wave motions in the rotating liquid, which are called inertial or gyroscopic waves. These waves play an important role in the problems of dynamics of rotors, turbines, separators, centrifuges, and rotating aircraft containing a liquid, and in some geophysical problems (flows in the Earth's liquid core [5]). Wave phenomena in a rotating liquid layer can have a significant effect on a number of technological processes (in particular, sedimentation processes), phase equilibria in multicomponent liquids, and on the aircraft flight trajectory. The dynamics of inertial waves in a liquid filling a rotating cylinder has been experimentally studied in a number of papers (see [6,7] and references therein). Stationary gyroscopic waves in a circular cylindrical layer of an ideal liquid bounded by solid walls were studied in [8,9]. Dispersion relations were obtained and dependences of dimensionless wavelengths on dimensionless frequencies were constructed. The behavior of a low-viscosity liquid in a rotating horizontal cylinder as a function of the rotation velocity and the degree of filling was studied in [10]. The resonant generation of waves in a liquid filling a rotor cavity, which is the main factor responsible for instability of steady-state rotation of rotary systems was investigated in [11][12][13][14][15][16][17][18][19].The present investigation of the properties of gyroscopic waves in a rotating liquid layer is motivated by interest in the problem of the stability of rotary systems with a fixed point at which the angular velocity of rotation of a rotor is maintained constant by a drive. A stability analysis method for similar rotary systems was proposed in [15,17]. In this method, one of the main stages involves calculation of the moments of the forces exerted by the liquid on the rotor walls during steady-state conical precession of the rotor. It is easy to show that, in the case of conical precession, the steady-state hydrodynamic problem is directly related to the problem of generation of inertial waves in a liq...

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An analysis of dynamic stability for a flexible rotor filled with liquid

Wang

Yuan

2018

Physics of Fluids

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Stability conditions for the steady-state rotation of a cylinder filled with a stratified nonuniform viscous incompressible liquid

Cited by 8 publications

References 2 publications

An analytical investigation on the dynamic stability of a rotor filled with liquid

An analytical investigation on the dynamic stability of a rotor filled with liquid

Gyroscopic waves in a rotating liquid layer

An analysis of dynamic stability for a flexible rotor filled with liquid

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