Stability of a Clamped-Free Rotor Partially Filled With Liquid

1986 ◽  
Vol 53 (1) ◽  
pp. 166-172 ◽  
Author(s):  
S. L. Hendricks
Keyword(s):  
Stability Analysis ◽  
Dimensional Stability ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Fluid Viscosity ◽  
Flexible Rotor ◽  
Stability Boundaries ◽  
System Parameters ◽  
Operating Range ◽  
The Stability

When a flexible rotor is partially filled with liquid, the motion is unstable over some operating range. The extent of this operating range depends on various system parameters such as rotor damping, fluid viscosity, the amount of fluid present, etc. If the rotor is arranged so that it must tilt as it vibrates (as in the clamped-free configuration) then the tilt of the rotor greatly complicates the stability analysis. The source of the complication is that the fluid motion becomes three-dimensional. A three-dimensional stability theory is developed here and applied to a simple clamped-free rotor. The results show that the stability boundaries are influenced by both rotor and fluid “gyroscopic stiffening” effects. Brief experimental results are also reported.

Secondary motion in convection layers generated by lateral heating of a solute gradient

2002 ◽  
Vol 455 ◽  
pp. 1-19 ◽  
Author(s):  
CHO LIK CHAN ◽  
WEN-YAU CHEN ◽  
C. F. CHEN
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Convection Cell ◽  
Experimental Conditions ◽  
Longitudinal Plane ◽  
Secondary Motion ◽  
Solute Gradient

The three-dimensional motion observed by Chen & Chen (1997) in the convection cells generated by sideways heating of a solute gradient is further examined by experiments and linear stability analysis. In the experiments, we obtained visualizations and PIV measurements of the velocity of the fluid motion in the longitudinal plane perpendicular to the imposed temperature gradient. The flow consists of a horizontal row of counter-rotating vortices within each convection cell. The magnitude of this secondary motion is approximately one-half that of the primary convection cell. Results of a linear stability analysis of a parallel double-diffusive flow model of the actual ow show that the instability is in the salt-finger mode under the experimental conditions. The perturbation streamlines in the longitudinal plane at onset consist of a horizontal row of counter-rotating vortices similar to those observed in the experiments.

Three Dimensional Stability Analysis of the Grohovo Landslide in Croatia

2013 ◽  
pp. 47-52 ◽  
Author(s):  
Chunxiang Wang ◽  
Željko Arbanas ◽  
Snježana Mihalić ◽  
Hideaki Marui
Keyword(s):  
Stability Analysis ◽  
Dimensional Stability ◽  
Three Dimensional

Three-Dimensional Stability Analysis of Rock Slope Using Aerial Photogrammetry Data

2020 ◽  
Author(s):  
Surya Sarat Chandra Congress ◽  
Prince Kumar ◽  
Ujwalkumar D. Patil ◽  
Tejo V. Bheemasetti ◽  
Anand J. Puppala
Keyword(s):  
Stability Analysis ◽  
Dimensional Stability ◽  
Rock Slope ◽  
Three Dimensional ◽  
Aerial Photogrammetry

Three-dimensional stability analysis for a salt-finger convecting layer

2018 ◽  
Vol 841 ◽  
pp. 636-653
Author(s):  
Ting-Yueh Chang ◽  
Falin Chen ◽  
Min-Hsing Chang
Keyword(s):  
Stability Analysis ◽  
Three Dimensional ◽  
Longitudinal Mode ◽  
Transverse Mode ◽  
Solute Diffusion ◽  
Two Dimensional ◽  
Grashof Number ◽  
Significant Difference ◽  
The Stability ◽  
Mode A

A three-dimensional linear stability analysis is carried out for a convecting layer in which both the temperature and solute distributions are linear in the horizontal direction. The three-dimensional results show that, for $Le=3$ and 100, the most unstable mode occurs invariably as the longitudinal mode, a vortex roll with its axis perpendicular to the longitudinal plane, suggesting that the two-dimensional results are sufficient to illustrate the stability characteristics of the convecting layer. Two-dimensional results show that the stability boundaries of the transverse mode (a vortex roll with its axis perpendicular to the transverse plane) and the longitudinal modes are virtually overlapped in the regime dominated by thermal diffusion and the regime dominated by solute diffusion, while these two modes hold a significant difference in the regime the salt-finger instability prevails. More precisely, the instability area in terms of thermal Grashof number $Gr$ and solute Grashof number $Gs$ is larger for the longitudinal mode than the transverse mode, implying that, under any circumstance, the longitudinal mode is always more unstable than the transverse mode.

Nonlinear Simulation Analysis and Experiment of Fluid Plain Journal Bearing With Incompressible Fluid

2003 ◽  
Author(s):  
Katsuhisa Fujita ◽  
Atsuhiko Shintani ◽  
Koji Yoshioka ◽  
Kouhei Okuno ◽  
Hiroaki Tanaka ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Incompressible Fluid ◽  
Journal Bearing ◽  
Simulation Analysis ◽  
Journal Bearings ◽  
Stable Region ◽  
Flexible Rotor ◽  
Nonlinear Simulation ◽  
Fluid Forces ◽  
The Stability

Recently, in many areas such as computers and information equipments etc., the fluid journal bearings are required to rotate at higher speed. To satisfy this requirement, the strictly stability analysis of the journal is indispensable. In this paper, we investigate the stability analysis of the dynamic behavior of the fluid plain journal bearing with an incompressible fluid considering the nonlinear terms of fluid forces. The stability analysis is examined by the numerical simulations on each model of a rigid rotor and a flexible rotor. The stable regions by nonlinear analysis are compared with the regions by classical linear analysis. Performing the nonlinear simulation analysis, it becomes clear that there is rather a stable region which amplitude does not grow up abruptly, and this phenomenon can not only be pointed out, but also is judged to be unstable by linear stable analysis. Finally, the experiment using actual bearings is performed and compared with the numerical results.

scholarly journals Linear stability of confined flow around a 180-degree sharp bend

2017 ◽  
Vol 822 ◽  
pp. 813-847 ◽  
Author(s):  
Azan M. Sapardi ◽  
Wisam K. Hussam ◽  
Alban Pothérat ◽  
Gregory J. Sheard
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Critical Reynolds Number ◽  
Three Dimensional ◽  
Base Flow ◽  
Two Dimensional ◽  
Two Dimensional Flow ◽  
The Stability

This study seeks to characterise the breakdown of the steady two-dimensional solution in the flow around a 180-degree sharp bend to infinitesimal three-dimensional disturbances using a linear stability analysis. The stability analysis predicts that three-dimensional transition is via a synchronous instability of the steady flows. A highly accurate global linear stability analysis of the flow was conducted with Reynolds number $\mathit{Re}<1150$ and bend opening ratio (ratio of bend width to inlet height) $0.2\leqslant \unicode[STIX]{x1D6FD}\leqslant 5$. This range of $\mathit{Re}$ and $\unicode[STIX]{x1D6FD}$ captures both steady-state two-dimensional flow solutions and the inception of unsteady two-dimensional flow. For $0.2\leqslant \unicode[STIX]{x1D6FD}\leqslant 1$, the two-dimensional base flow transitions from steady to unsteady at higher Reynolds number as $\unicode[STIX]{x1D6FD}$ increases. The stability analysis shows that at the onset of instability, the base flow becomes three-dimensionally unstable in two different modes, namely a spanwise oscillating mode for $\unicode[STIX]{x1D6FD}=0.2$ and a spanwise synchronous mode for $\unicode[STIX]{x1D6FD}\geqslant 0.3$. The critical Reynolds number and the spanwise wavelength of perturbations increase as $\unicode[STIX]{x1D6FD}$ increases. For $1<\unicode[STIX]{x1D6FD}\leqslant 2$ both the critical Reynolds number for onset of unsteadiness and the spanwise wavelength decrease as $\unicode[STIX]{x1D6FD}$ increases. Finally, for $2<\unicode[STIX]{x1D6FD}\leqslant 5$, the critical Reynolds number and spanwise wavelength remain almost constant. The linear stability analysis also shows that the base flow becomes unstable to different three-dimensional modes depending on the opening ratio. The modes are found to be localised near the reattachment point of the first recirculation bubble.

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