Motion of an axisymmetric body in a rotating stratified fluid confined between two parallel planes

1969 ◽  
Vol 38 (4) ◽  
pp. 833-842 ◽  
Author(s):  
D. V. Krishna ◽  
L. V. Sarma
Keyword(s):  
Steady State ◽  
Oblate Spheroid ◽  
Vertical Axis ◽  
Vertical Gradient ◽  
Steady State Solution ◽  
Stratified Fluid ◽  
Axisymmetric Body ◽  
The Body ◽  
Homogeneous Fluid ◽  
Axis Of Rotation

We consider here the flow due to the oscillation of a slender oblate spheroid in a non-homogeneous, rotating fluid confined between two parallel planes which are perpendicular to the (vertical) axis of rotation. The direction of oscillation of the spheroid is perpendicular to the axis of rotation. By solving a set of dual integrals the steady-state solution is obtained in the two cases when the plates are at an infinite distance from the body and when they are at a large but finite distance. The singular or discontinuous surfaces observed in the case of homogeneous fluid are absent here. Also, the steady-state velocity is no longer independent of the distance along the axis of rotation. The velocity has now a vertical gradient, an important feature in the case of stratified fluid. It is also found that the presence of the plane boundaries increases the force on the body.

Influence of rotational inertia on turning performance of theropod dinosaurs: clues from humans with increased rotational inertia

2001 ◽  
Vol 204 (22) ◽  
pp. 3917-3926
Author(s):  
David R. Carrier ◽  
Rebecca M. Walter ◽  
David V. Lee
Keyword(s):  
Average Velocity ◽  
Human Subjects ◽  
Tail Length ◽  
Vertical Axis ◽  
The Body ◽  
Rotational Inertia ◽  
Control Value ◽  
Theropod Dinosaurs ◽  
Axis Of Rotation ◽  
Average Angle

SUMMARY The turning agility of theropod dinosaurs may have been severely limited by the large rotational inertia of their horizontal trunks and tails. Bodies with mass distributed far from the axis of rotation have much greater rotational inertia than bodies with the same mass distributed close to the axis of rotation. In this study, we increased the rotational inertia about the vertical axis of human subjects 9.2-fold, to match our estimate for theropods the size of humans, and measured the ability of the subjects to turn. To determine the effect of the increased rotational inertia on maximum turning capability, five subjects jumped vertically while attempting to rotate as far as possible about their vertical axis. This test resulted in a decrease in the average angle turned to 20 % of the control value. We also tested the ability of nine subjects to run as rapidly as possible through a tight slalom course of six 90° turns. When the subjects ran with the 9.2-fold greater rotational inertia, the average velocity through the course decreased to 77 % of the control velocity. When the subjects ran the same course but were constrained as to where they placed their feet, the average velocity through the course decreased to 65 % of the control velocity. These results are consistent with the hypothesis that rotational inertia may have limited the turning performance of theropods. They also indicate that the effect of rotational inertia on turning performance is dependent on the type of turning behavior. Characters such as retroverted pubes, reduced tail length, decreased body size, pneumatic vertebrae and the absence of teeth reduced rotational inertia in derived theropods and probably, therefore, improved their turning agility. To reduce rotational inertia, theropods may have run with an arched back and tail, an S-curved neck and forelimbs held backwards against the body.

Forces on bodies moving transversely through a rotating fluid

1975 ◽  
Vol 71 (3) ◽  
pp. 577-599 ◽  
Author(s):  
P. J. Mason
Keyword(s):  
Angular Velocity ◽  
Rigid Body ◽  
Vertical Axis ◽  
The Body ◽  
Rotating Fluid ◽  
Size And Shape ◽  
Relative Direction ◽  
Axis Of Rotation

Measurements have been made of the net force F acting on a bluff rigid body moving with velocity U (relative to a fluid rotating about a vertical axis with uniform angular velocity Ω) in a plane perpendicular to the axis of rotation. The force F is of magnitude 2ΩρVU, where ρ is the density of the fluid and V is a volume which depends on the size and shape of the body. The relative direction of F and U is found to depend on the quantity \[ {\cal S}\equiv \frac{2\Omega L}{U}\bigg(\frac{h}{D}\bigg), \] where L and h are horizontal and vertical lengths characterizing the object and D is the depth of the fluid in which the object is placed.

Stratified flow over a bounded obstacle in a channel of finite height

1981 ◽  
Vol 110 ◽  
pp. 161-170 ◽  
Author(s):  
G. S. Janowitz
Keyword(s):  
Steady State ◽  
Stratified Flow ◽  
Steady State Solution ◽  
The Body ◽  
State Solution ◽  
Oseen Equations ◽  
Finite Height ◽  
Experimental Values ◽  
Oseen Model ◽  
Good Agreement

The steady-state solution for the stratified flow over a bounded obstacle in a channel of finite height is obtained through the use of the inviscid unsteady Oseen equations; the body streamline encloses and is produced by a planar momentum sink. The calculations are compared with the experimental observations of Wei, Kao & Pao (1975) and Baines (1977). In a case where theoretical and experimental values match, good agreement was found. This suggests that the Oseen model with its columnar, wavelike and decaying solutions may provide a reasonable alternative to Long's model for subcritical flows.

scholarly journals The rise of a body through a rotating fluid in a container of finite length

1968 ◽  
Vol 31 (4) ◽  
pp. 635-642 ◽  
Author(s):  
D. W Moore ◽  
P. G. Saffman
Keyword(s):  
Boundary Layers ◽  
Finite Length ◽  
Vertical Axis ◽  
Axisymmetric Body ◽  
The Body ◽  
Rotating Fluid ◽  
Compatibility Conditions ◽  
Inertia Effects ◽  
Small Viscosity ◽  
Taylor Column

The drag on an axisymmetric body rising through a rotating fluid of small viscosity rotating about a vertical axis is calculated on the assumption that there is a Taylor column ahead of and behind the body, in which the geostrophic flow is determined by compatibility conditions on the Ekman boundary-layers on the body and the end surfaces. It is assumed that inertia effects may be neglected. Estimates are given of the conditions for which the theory should be valid.

Transient internal waves produced by a moving body in a tank of density-stratified fluid

1973 ◽  
Vol 61 (3) ◽  
pp. 465-480 ◽  
Author(s):  
E. W. Graham
Keyword(s):  
Steady State ◽  
Surface Waves ◽  
Internal Waves ◽  
Stratified Fluid ◽  
The Body ◽  
Wave System ◽  
Similarity Parameter ◽  
Steady State Condition ◽  
Towing Tank ◽  
Moving Body

The internal waves produced by a moving body are generally longer in the direction of motion than the corresponding surface waves. This difference is accentuated when the density variation is slight and the body velocity is large in which case a very long towing tank may be required for the simulation of a steady-state condition. The following theoretical study of transient waves is intended as a step in relating test conditions and requisite towing-tank sizes.A source–sink pair travelling for a finite time is used to represent the restricted motion of a body in a tank. The approximate length and volume of the body are fixed, but its precise shape (somewhat irregular and slightly time dependent) is assumed to be of secondary importance and is not calculated here. The density-stratified fluid is assumed to have a constant Brunt–Väisälä frequency.A solution in the form of a triple sum over the tank eigenfunctions applies quite generally for the internal wave system (neglecting surface waves and the potential-flow-type solution near the body). Examples covering the large-scale structure of the flow field have been solved for two values of an approximate similarity parameter. The value of the similarity parameter indicates how closely steady-state conditions are approached. The first (larger) value chosen produces a well-defined quasi-steady state near the body with transient fluctuations of the order of ± 10%. The second (smaller) value gives a poorly defined quasisteady state with fluctuations of the order of ±50%. More elaborate studies varying the tank length, width and depth could be made by programming the calculations.The effect of a collapsing wake has not been considered here, but might possibly be treated by similar methods.

A study of motions in a rotating liquid

1951 ◽  
Vol 206 (1084) ◽  
pp. 108-130 ◽  
Keyword(s):  
Angular Velocity ◽  
Equations Of Motion ◽  
Vertical Axis ◽  
The Body ◽  
Forced Oscillations ◽  
Infinite Cylinder ◽  
Two Dimensional ◽  
Small Motion ◽  
Axis Of Rotation ◽  
Rotating Liquid

Starting with the equations of motion for a perfect, incompressible fluid referred to a coordinate system which rotates about a vertical axis with uniform angular velocity R , the physical condition of ‘small motion’ is determined which permits the equations to be linearized. The small motions resulting from forced oscillations of a rotating liquid are investigated. It is shown that there are three types of flow depending on the relative magnitudes of the impressed frequency β and the angular velocity R of the fluid. Two of the regimes are studied in detail. A similarity law is developed which gives the solution of a class of problems of oscillations for β > 2 R in terms of the solutions to similar irrotational problems. An attempt is made to explain how slow, two-dimensional motion can be produced by introducing a boundary condition which is three-dimensional (as observed in experiments performed by G. I. Taylor), by considering problems from the moment at which the disturbance is created from rest relative to the rotating system, with the only initial assumption that the fluid is rotating uniformly like a solid body. For the particular cases studied the results are in agreement with Taylor’s experiments, in that the flow is found to become steady and two-dimensional if the disturbance which causes it approaches a steady state. If the disturbance is due to a body which moves along the axis of rotation of the fluid, the steady two-dimensional behaviour may be expected everywhere except in the neighbourhood of the surface of an infinite cylinder which encloses the body and whose generators are parallel to the axis of rotation. To resolve an apparent disagreement between certain theoretical results by Grace on the one hand, and experimental evidence by Taylor and the author’s conclusions, on the other, arguments are advanced that the various results may be in agreement, provided Grace’s are given a new interpretation.

Analysis of the First Order and Slowly Varying Motions of an Axisymmetric Floating Body in Bichromatic Waves

2013 ◽  
Vol 135 (1) ◽  
Author(s):  
João Pessoa ◽  
Nuno Fonseca ◽  
C. Guedes Soares
Keyword(s):  
Vertical Cylinder ◽  
Vertical Axis ◽  
Second Order ◽  
The Body ◽  
Floating Body ◽  
Drift Motion ◽  
First Order ◽  
Motion Responses ◽  
Simple Geometry ◽  
Good Agreement

The paper presents an experimental and numerical investigation on the motions of a floating body of simple geometry subjected to harmonic and biharmonic waves. The experiments were carried out in three different water depths representing shallow and deep water. The body is axisymmetric about the vertical axis, like a vertical cylinder with a rounded bottom, and it is kept in place with a soft mooring system. The experimental results include the first order motion responses, the steady drift motion offset in regular waves and the slowly varying motions due to second order interaction in biharmonic waves. The hydrodynamic problem is solved numerically with a second order boundary element method. The results show a good agreement of the numerical calculations with the experiments.

An airfoil theory of bifurcating laminar separation from thin obstacles

1990 ◽  
Vol 216 ◽  
pp. 255-284 ◽  
Author(s):  
C. J. Lee ◽  
H. K. Cheng
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Steady State ◽  
Steady State Solution ◽  
Equation System ◽  
Branch Points ◽  
Laminar Separation ◽  
Kutta Condition ◽  
Numerical Studies ◽  
Steady State Solutions

Global interaction of the boundary layer separating from an obstacle with resulting open/closed wakes is studied for a thin airfoil in a steady flow. Replacing the Kutta condition of the classical theory is the breakaway criterion of the laminar triple-deck interaction (Sychev 1972; Smith 1977), which, together with the assumption of a uniform wake/eddy pressure, leads to a nonlinear equation system for the breakaway location and wake shape. The solutions depend on a Reynolds numberReand an airfoil thickness ratio or incidence τ and, in the domain$Re^{\frac{1}{16}}\tau = O(1)$considered, the separation locations are found to be far removed from the classical Brillouin–Villat point for the breakaway from a smooth shape. Bifurcations of the steady-state solution are found among examples of symmetrical and asymmetrical flows, allowing open and closed wakes, as well as symmetry breaking in an otherwise symmetrical flow. Accordingly, the influence of thickness and incidence, as well as Reynolds number is critical in the vicinity of branch points and cut-off points where steady-state solutions can/must change branches/types. The study suggests a correspondence of this bifurcation feature with the lift hysteresis and other aerodynamic anomalies observed from wind-tunnel and numerical studies in subcritical and high-subcriticalReflows.

Dependency of Unsteady Time-Linearized Flutter Investigations on the Steady State Flow Field

2011 ◽  
Author(s):  
Michael Blocher ◽  
Markus May ◽  
Harald Schoenenborn
Keyword(s):  
Steady State ◽  
Steady State Solution ◽  
Elastic Stability ◽  
Compressor Cascade ◽  
Steady State Flow ◽  
State Flow ◽  
Flow Parameters ◽  
Pressure Distributions ◽  
German Aerospace ◽  
École Polytechnique

The influence of the steady state flow solution on the aero-elastic stability behaviour of an annular compressor cascade shall be studied in order to determine sensitivities of the aero-dynamic damping with respect to characteristic flow parameters. In this context two different flow regimes — a subsonic and a transonic case — are subject to the analysis. The pressure distributions, steady as well as unsteady, on the blade surface of the NACA3506 profile are compared to experimental data that has been gained by the Institute of Aeroelasticity of the German Aerospace Center (DLR) during several wind tunnel tests at the annular compressor cascade facility RGP-400 of the Ecole Polytechnique Fe´de´rale de Lausanne (EPFL). Whereas a certain robustness of the unsteady CFD results can be stated for the subsonic flow regime, the transonic regime proves to be very sensitive with respect to the steady state solution.

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