Stability of a Rotor Partially Filled With a Viscous Incompressible Fluid

1979 ◽  
Vol 46 (4) ◽  
pp. 913-918 ◽  
Author(s):  
S. L. Hendricks ◽  
J. B. Morton
Keyword(s):  
Angular Velocity ◽  
Circular Cylinder ◽  
Incompressible Fluid ◽  
Parametric Study ◽  
Viscous Incompressible Fluid ◽  
Constant Angular Velocity ◽  
Unstable Region ◽  
Stability Boundaries ◽  
System Parameters ◽  
Linear Spring

A hollow circular cylinder rotating with constant angular velocity and partially filled with a viscous incompressible fluid has been analyzed for stability. The analysis can be extended to apply to many different rotor geometries. The results of this analysis predict that over a range of operating speeds, the system is unstable. The extent of this unstable region is determined by the system parameters. The interplay between viscosity of the fluid and damping on the rotor is especially important in determining stability boundaries. A parametric study is presented for a rotor modeled as a cup in the middle of a symmetrically supported massless shaft. The rotor is subject to a linear spring and a linear damper. Rotor unbalance, gravity, and axial effects are considered negligible.

Separation and the Taylor-column problem for a hemisphere

1974 ◽  
Vol 66 (4) ◽  
pp. 767-789 ◽  
Author(s):  
J. D. A. Walker ◽  
K. Stewartson
Keyword(s):  
Angular Velocity ◽  
Incompressible Fluid ◽  
Viscous Incompressible Fluid ◽  
Shear Layers ◽  
Constant Angular Velocity ◽  
Vertical Shear ◽  
Rossby Number ◽  
Ekman Number ◽  
Free Shear Layers ◽  
Taylor Column

A layer of viscous incompressible fluid is confined between two horizontal plates which rotate rapidly in their own plane with a constant angular velocity. A hemisphere has its plane face joined to the lower plate and when a uniform flow is forced past such an obstacle, a Taylor column bounded by thin detached vertical shear layers forms. The linear theory for this problem, wherein the Rossby number ε is set equal to zero on the assumption that the flow is slow, is examined in detail. The nonlinear modifications of the shear layers are then investigated for the case when ε ∼ E½, where E is the Ekman number. In particular, it is shown that provided that the Rossby number is large enough separation occurs in the free shear layers. The extension of the theory to flow past arbitrary spheroids is indicated.

Stability of circular Couette flow with variable inner cylinder speed

1982 ◽  
Vol 123 ◽  
pp. 43-57 ◽  
Author(s):  
G. P. Neitzel
Keyword(s):  
Angular Velocity ◽  
Incompressible Fluid ◽  
Viscous Incompressible Fluid ◽  
Outer Cylinder ◽  
Finite Amplitude ◽  
Reverse Direction ◽  
Stability Bound ◽  
Concentric Cylinders ◽  
Theory Result ◽  
Stability Enhancement

Energy & ability theory is employed to study the finite-amplitude stability of a viscous incompressible fluid occupying the space between a pair of concentric cylinders when the inner-cylinder angular velocity varies linearly with time. For the case with a fixed outer cylinder and increasing inner-cylinder speed, we find an enhancement of stability, consistent with a linear-theory result due to Eagles. When the inner-cylinder speed decreases, we find an initially decreased stability bound, indicating the possibility of hysteresis, while, if the inner cylinder is allowed to reverse direction and linearly increase in speed, we find significant stability enhancement.

On some exact solutions in magnetohydrodynamics with astrophysical applications

1972 ◽  
Vol 51 (1) ◽  
pp. 33-38 ◽  
Author(s):  
C. Sozou
Keyword(s):  
Free Surface ◽  
Angular Velocity ◽  
Incompressible Fluid ◽  
Exact Solutions ◽  
Equilibrium Configuration ◽  
Constant Angular Velocity ◽  
Magnetohydrodynamic Equations ◽  
The Stability

Some exact solutions of the steady magnetohydrodynamic equations for a perfectly conducting inviscid self-gravitating incompressible fluid are discussed. It is shown that there exist solutions for which the free surface of the liquid is that of a planetary ellipsoid and rotates with constant angular velocity about its axis. The stability of the equilibrium configuration is not investigated.

scholarly journals Синхронизация в турбулентном сферическом течении Куэтта под действием неравномерного вращения

2019 ◽  
Vol 89 (7) ◽  
pp. 992
Author(s):  
Д.Ю. Жиленко ◽  
О.Э. Кривоносова
Keyword(s):  
Experimental Data ◽  
Angular Velocity ◽  
Turbulent Flow ◽  
Incompressible Fluid ◽  
Turbulent Flows ◽  
Viscous Incompressible Fluid ◽  
Spherical Layer ◽  
Numerical Results ◽  
Spherical Boundary

Turbulent flows of viscous incompressible fluid in rotating spherical layer in the presence of synchronization are under consideration. Numerical results are presented. Synchronization of turbulent flow is due to the action of periodical modulation of the angular velocity of inner spherical boundary. The angular velocity of outer spherical boundary is constant. Obtained results were compared with experimental data. The interval of modulation amplitudes was determined where synchronization is followed by intermittency “chaos – chaos”.

scholarly journals Boundary-layer growth on a rotating and accelerating sphere

1987 ◽  
Vol 65 (1) ◽  
pp. 23-27 ◽  
Author(s):  
G. T. Karahalios ◽  
V. Theofilis
Keyword(s):  
Boundary Layer ◽  
Angular Velocity ◽  
Power Series ◽  
Incompressible Fluid ◽  
Skin Friction ◽  
Layer Growth ◽  
Constant Angular Velocity ◽  
Constant Acceleration ◽  
Analytic Expressions ◽  
Boundary Layer Growth

Boundary-layer growth on a sphere is studied when it is set into motion with constant acceleration and constant angular velocity, the latter being normal to the former. Analytic expressions are derived for the velocity components of the incompressible fluid in terms of a power series of the time of motion as well as for the skin friction.

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