Transient motion of a dipole in a rotating flow

1969 ◽  
Vol 39 (3) ◽  
pp. 433-442 ◽  
Author(s):  
John W. Miles
Keyword(s):  
Fixed Point ◽  
Axial Velocity ◽  
Potential Flow ◽  
Equations Of Motion ◽  
Rotating Flow ◽  
Rossby Number ◽  
Laboratory Measurements ◽  
Transient Motion ◽  
Experimental Scatter ◽  
Upstream Waves

The question of whether or not waves exist upstream of an obstacle that moves uniformly through an unbounded, incompressible, inviscid, unseparated, rotating flow is addressed by considering the development of the disturbed flow induced by a weak, moving dipole that is introduced into an axisymmetric, rotating flow that is initially undisturbed. Starting from the linearized equations of motion, it is shown that the flow tends asymptotically to the steady flow determined on the hypothesis of no upstream waves and that the transient at a fixed point is O(1/t). It also is shown that the axial velocity upstream (x < 0) of the dipole as x → − ∞ with t fixed is O(|x|−3), as in potential flow, but is O(|x|−1) as t → ∞ with |x| fixed. The results extend directly to closed obstacles of sufficiently small transverse dimensions and suggest the existence of a finite, parametric domain of no upstream waves for smooth, slender obstacles. The axial velocity in front of a small, moving sphere at a given instant in the transient régime is calculated and compared with Pritchard's laboratory measurements. The agreement is within the experimental scatter for Rossby numbers greater than about 0·3 even though the equivalence between sphere and dipole is exact only for infinite Rossby number.

The motion of a rising disk in a rotating axially bounded fluid for large Taylor number

1995 ◽  
Vol 291 ◽  
pp. 1-32 ◽  
Author(s):  
Marius Ungarish ◽  
Dmitry Vedensky
Keyword(s):  
Exact Solution ◽  
Boundary Value Problem ◽  
Equations Of Motion ◽  
Taylor Number ◽  
Rossby Number ◽  
Rotating Fluid ◽  
Asymptotic Results ◽  
Dual Integral Equations ◽  
Wall Distance ◽  
Taylor Column

The motion of a disk rising steadily along the axis in a rotating fluid between two infinite plates is considered. In the limit of zero Rossby number and with the disk in the middle position, the boundary value problem based on the linear, viscous equations of motion is reduced to a system of dual-integral equations which renders ‘exact’ solutions for arbitrary values of the Taylor number, Ta, and disk-to-wall distance, H (scaled by the radius of the disk). The investigation is focused on the drag and on the flow field when Ta is large (but finite) for various H. Comparisons with previous asymptotic results for ‘short’ and ‘long’ containers, and with the preceding unbounded-configuration ‘exact’ solution, provide both confirmation and novel insights.In particular, it is shown that the ‘free’ Taylor column on the particle appears for H > 0.08 Ta and attains its fully developed features when H > 0.25 Ta (approximately). The present drag calculations improve the compatibility of the linear theory with Maxworthy's (1968) experiments in short containers, but for the long container the claimed discrepancy with experiments remains unexplained.

Axisymmetric rotating flow past a circular disk

1972 ◽  
Vol 53 (4) ◽  
pp. 689-700 ◽  
Author(s):  
John W. Miles
Keyword(s):  
Potential Flow ◽  
Separation Bubble ◽  
Circular Disk ◽  
Characteristic Parameter ◽  
Basic Flow ◽  
The Body ◽  
Rotating Flow ◽  
Flow Past ◽  
Previous Solution ◽  
Forward Separation

The steady, inviscid, axisymmetric, rotating flow past a circular disk in an unbounded liquid is determined on the hypothesis that all streamlines originate in a uniform flow far upstream of the body. The characteristic parameter for the flow is k = 2ωa/U, where ω and U are the angular and axial velocities of the basic flow and α is the radius of the disk. Forward separation is found to occur for k > k = 1.9, in agreement with observation (Orloff & Bossel 1971). The length of the upstream separation bubble is determined on the hypothesis that the previous solution remains valid for k > k, despite the existence of closed streamlines within the upstream separation bubble (which may, but do not necessarily, inva,lidate the solution). This length increases rapidly for k > 3, in qualitative agreement with observation. The hypothesis of unseparated flow implies a singularity at the rim of the disk, just as in potential flow. The strength of this singularity departs only slightly from its potential-flow value for 0 ≤ k ≤ 2, but increases rapidly with k for k > 3, which suggests that (quite apart from the difficulties implied by the existence of closed streamlines) the solution cannot remain valid for sufficiently large k.

Dynamic analysis of a 2-lobe geometrically imperfect journal bearing system

2016 ◽  
Vol 231 (7) ◽  
pp. 934-950 ◽  
Author(s):  
Dharmendra Jain ◽  
Satish C Sharma
Keyword(s):  
Journal Bearing ◽  
Equations Of Motion ◽  
Constant Flow ◽  
Kutta Method ◽  
Transient Motion ◽  
Nonlinear Transient ◽  
Linear And Nonlinear ◽  
Nonlinear Equations Of Motion ◽  
Bearing System ◽  
Flow Valve

The present study is concerned with the linear and nonlinear transient motion analysis of a 2-lobe geometrically imperfect hybrid journal bearing system compensated with constant flow valve restrictor. The trajectories of journal center motion for a geometrically imperfect rotating journal (barrel, bellmouth and undulation type journal) have been numerically simulated by solving the linear and nonlinear equations of motion of journal center using a fourth order Runga–Kutta method. The numerically computed results for the journal center trajectories indicate that the 2-lobe bearing [Formula: see text] is more stable with geometrically imperfect journal as compared to the circular bearing with imperfect journal.

Dynamics of a Partially Full Cylinder Containing a Magnetic Liquid in a Magnetic Field

1976 ◽  
Vol 43 (3) ◽  
pp. 497-501
Author(s):  
D. R. Tichenor ◽  
X. J. R. Avula
Keyword(s):  
Magnetic Field ◽  
Free Surface ◽  
Circular Cylinder ◽  
Plane Surface ◽  
Equations Of Motion ◽  
Magnetic Liquid ◽  
Transient Motion ◽  
Thin Walled ◽  
Inclined Planes ◽  
The Magnetic Field

This study is concerned with the transient motion of an infinitely long thin-walled circular cylinder partially filled with a magnetic liquid under magnetic and nonmagnetic forces. Starting from rest the cylinder is constrained to roll without slipping on a plane surface while the contained fluid with a rectangular free surface is simultaneously subjected to a magnetic field parallel to the plane by activating a magnet located ahead of the cylinder. The nonmagnetic force on the cylinder and its contents is provided by the gravity. Assuming negligible viscous dissipation Lagrange’s equations of motion are derived and solved to obtain the motion of the cylinder and the liquid subsequent to the application of the magnetic field. Results are presented in a nondimensional form for motion on horizontal and inclined planes under different magnetic strengths.

Research on the Bubble Motion near Free Surface in Underwater Explosion

2011 ◽  
Vol 52-54 ◽  
pp. 1086-1091
Author(s):  
Jian Li ◽  
Ji Li Rong ◽  
Da Lin Xiang
Keyword(s):  
Free Surface ◽  
Potential Flow ◽  
Energy Equation ◽  
Equations Of Motion ◽  
Underwater Explosion ◽  
Engineering Calculation ◽  
Bubble Motion ◽  
Hamilton Principle ◽  
Time Histories ◽  
Theory Research

A model for a moderately deep underwater explosion bubble was developed in inviscid and irrotational fluid. Considering the effects of gravity, buoyancy, drag to the motion of bubble, the equations of motion (EOM) for bubble in inviscid and irrotational fluid near a free surface were established by introducing the potential-flow theory, energy equation and Hamilton principle. The displacement of the center of bubble, the radius-time histories and impulse periods of bubble were acquired by solving the EOM. The calculated results were compared with the experimental and numerical results. The compared results show that the former is consistent with the latter. The research has value to correlative theory research and engineering calculation.

Axial Velocity Distribution at the Efflux of a Stationary Unconfined Ship’s Propeller Jet

2010 ◽  
Author(s):  
W. Lam ◽  
D. J. Robinson ◽  
G. A. Hamil ◽  
S. Raghunathan
Keyword(s):  
Velocity Field ◽  
Axial Velocity ◽  
Rotating Flow ◽  
Axial Component ◽  
Large Contribution ◽  
Velocity Magnitude ◽  
Axial Velocity Profile ◽  
Axial Velocity Distribution ◽  
Total Velocity ◽  
Numerical Approaches

This paper is aimed at presenting an up-to-date investigation of the hydrodynamics of the jet (wake) of a stationary, unconfined ship’s propeller. The velocity field of a ship’s propeller jet is of particular interest for the researchers investigating the jet induced damage on a seabed as documented in previous studies. This paper discusses the time-averaged velocity field at the efflux, which is the immediate exit of the downstream propeller jet. The propeller jet is a rotating flow, which has axial, tangential and radial components of velocity. The axial component of velocity is the main contributor to the total velocity magnitude. Researchers are more interested in the axial velocity field within the ship’s propeller jet, due to the large contribution made by the axial velocity to the jet. The axial velocities at the efflux plane were obtained using joint experimental and numerical approaches. The results confirmed the two-peaked ridges axial velocity profile and disagreed with the 0.707Dp contraction suggested by Blaauw & van de Kaa (1978), Verhey (1983) and Robakiewicz (1987) at efflux of a ship’s propeller jet.

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