scholarly journals Instability modes on a solid-body-rotation flow in a finite-length pipe

AIP Advances ◽  
2017 ◽  
Vol 7 (9) ◽  
pp. 095112 ◽  
Author(s):  
Chunjuan Feng ◽  
Feng Liu ◽  
Zvi Rusak ◽  
Shixiao Wang
Keyword(s):  
Solid Body ◽  
Finite Length ◽  
Body Rotation ◽  
Solid Body Rotation ◽  
Instability Modes

On the three-dimensional stability of a solid-body rotation flow in a finite-length rotating pipe

2016 ◽  
Vol 797 ◽  
pp. 284-321 ◽  
Author(s):  
Shixiao Wang ◽  
Zvi Rusak ◽  
Rui Gong ◽  
Feng Liu
Keyword(s):  
Finite Length ◽  
Growth Rates ◽  
Three Dimensional ◽  
Inviscid Flow ◽  
Swirl Ratio ◽  
Body Rotation ◽  
Solid Body Rotation ◽  
Instability Modes ◽  
Stability Results ◽  
Flow Case

The three-dimensional, inviscid and viscous flow instability modes that appear on a solid-body rotation flow in a finite-length straight, circular pipe are analysed. This study is a direct extension of the Wang & Rusak (Phys. Fluids, vol. 8 (4), 1996a, pp. 1007–1016) analysis of axisymmetric instabilities on inviscid swirling flows in a pipe. The linear stability equations are the same as those derived by Kelvin (Phil. Mag., vol. 10, 1880, pp. 155–168). However, we study a general mode of perturbation that satisfies the inlet, outlet and wall conditions of a flow in a finite-length pipe with a fixed in time and in space vortex generator ahead of it. This mode is different from the classical normal mode of perturbations. The eigenvalue problem for the growth rate and the shape of the perturbations for any azimuthal wavenumber $m$ consists of a linear system of partial differential equations in terms of the axial and radial coordinates ($x,r$). The stability problem is solved numerically for all azimuthal wavenumbers $m$. The computed growth rates and the related shapes of the various perturbation modes that appear in sequence as a function of the base flow swirl ratio (${\it\omega}$) and pipe length ($L$) are presented. In the inviscid flow case, the $m=1$ modes are the first to become unstable as the swirl ratio is increased and dominate the perturbation’s growth in a certain range of swirl levels. The $m=1$ instability modes compete with the axisymmetric ($m=0$) instability modes as the swirl ratio is further increased. In the viscous flow case, the viscous damping effects reduce the modes’ growth rates. The neutral stability line is presented in a Reynolds number ($Re$) versus swirl ratio (${\it\omega}$) diagram and can be used to predict the first appearance of axisymmetric or spiral instabilities as a function of $Re$ and $L$. We use the Reynolds–Orr equation to analyse the various production terms of the perturbation’s kinetic energy and establish the elimination of the flow axial homogeneity at high swirl levels as the underlying physical mechanism that leads to flow exchange of stability and to the appearance of both spiral and axisymmetric instabilities. The viscous effects in the bulk have only a passive influence on the modes’ shapes and growth rates. These effects decrease with the increase of $Re$. We show that the inviscid flow stability results are the inviscid-limit stability results of high-$Re$ rotating flows.

Wall-separation and vortex-breakdown zones in a solid-body rotation flow in a rotating finite-length straight circular pipe

2014 ◽  
Vol 759 ◽  
pp. 321-359 ◽  
Author(s):  
Zvi Rusak ◽  
Shixiao Wang
Keyword(s):  
Steady State ◽  
Numerical Simulations ◽  
Solid Body ◽  
Finite Length ◽  
Vortex Breakdown ◽  
Swirling Flows ◽  
Flow Dynamics ◽  
Circular Pipe ◽  
Body Rotation ◽  
Solid Body Rotation

AbstractThe incompressible, inviscid and axisymmetric dynamics of perturbations on a solid-body rotation flow with a uniform axial velocity in a rotating, finite-length, straight, circular pipe are studied via global analysis techniques and numerical simulations. The investigation establishes the coexistence of both axisymmetric wall-separation and vortex-breakdown zones above a critical swirl level, ${\it\omega}_{1}$. We first describe the bifurcation diagram of steady-state solutions of the flow problem as a function of the swirl ratio ${\it\omega}$. We prove that the base columnar flow is a unique steady-state solution when ${\it\omega}$ is below ${\it\omega}_{1}$. This state is asymptotically stable and a global attractor of the flow dynamics. However, when ${\it\omega}>{\it\omega}_{1}$, we reveal, in addition to the base columnar flow, the coexistence of states that describe swirling flows around either centreline stagnant breakdown zones or wall quasi-stagnant zones, where both the axial and radial velocities vanish. We demonstrate that when ${\it\omega}>{\it\omega}_{1}$, the base columnar flow is a min–max point of an energy functional that governs the problem, while the swirling flows around the quasi-stagnant and stagnant zones are global and local minimizer states and become attractors of the flow dynamics. We also find additional min–max states that are transient attractors of the flow dynamics. Numerical simulations describe the evolution of perturbations on above-critical columnar states to either the breakdown or the wall-separation states. The growth of perturbations in both cases is composed of a linear stage of the evolution, with growth rates accurately predicted by the analysis of Wang & Rusak (Phys. Fluids, vol. 8, 1996a, pp. 1007–1016), followed by a stage of saturation to either one of the separation zone states. The wall-separation states have the same chance of appearing as that of vortex-breakdown states and there is no hysteresis loop between them. This is strikingly different from the dynamics of vortices with medium or narrow vortical core size in a pipe.

On the active feedback control of a swirling flow in a finite-length pipe

2013 ◽  
Vol 737 ◽  
pp. 280-307 ◽  
Author(s):  
Shixiao Wang ◽  
Zvi Rusak ◽  
Steve Taylor ◽  
Rui Gong
Keyword(s):  
Feedback Control ◽  
Control Problem ◽  
Solid Body ◽  
Finite Length ◽  
Critical Level ◽  
Control Method ◽  
Feedback Stabilization ◽  
Mode Analysis ◽  
Body Rotation ◽  
Solid Body Rotation

AbstractThe physical properties of a recently proposed feedback-stabilization method of a vortex flow in a finite-length straight pipe are studied for the case of a solid-body rotation flow. In the natural case, when the swirl ratio is beyond a certain critical level, linearly unstable modes appear in sequence as the swirl level is increased. Based on an asymptotic long-wave (long-pipe) approach, the global feedback control method is shown to enforce the decay in time of the perturbation’s kinetic energy and thereby quench all of the instability modes for a swirl range above the critical swirl level. The effectiveness of an extended version of this feedback flow control approach is further analysed through a detailed mode analysis of the full linear control problem for a solid-body rotation flow in a finite-length pipe that is not necessarily long. We first rigourously prove the asymptotic decay in time of all modes with real growth rates. We then compute the growth rate and shape of all modes according to the full linearized control problem for swirl levels up to 50 % above the critical level. We demonstrate that the flow is stabilized in the whole swirl range and can be even further stabilized for higher swirl levels. However, the control effectiveness is sensitive to the choice of the feedback control gain. A potentially best range of the gain is identified. An inadequate level of gain, either insufficient or excessive, could lead to a marginal control or failure of the control method at high swirl levels. The robustness of the proposed control law to stabilize both initial waves and continuous inlet flow perturbations and the elimination of the vortex breakdown process are demonstrated through numerical computations.

Oval Flow Mode Between Two Corotating Disks With Stationary Shroud

2014 ◽  
Vol 137 (3) ◽  
Author(s):  
Ching Min Hsu ◽  
Jia-Kun Chen ◽  
Min Kai Hsieh ◽  
Rong Fung Huang
Keyword(s):  
Flow Structure ◽  
Solid Body ◽  
Circumferential Velocity ◽  
Body Rotation ◽  
Flow Core ◽  
Core Flow ◽  
Node Point ◽  
Solid Body Rotation ◽  
Characteristic Flow ◽  
Buffer Region

The characteristic flow behavior, time-averaged velocity distributions, phase-resolved ensemble-averaged velocity profiles, and turbulence properties of the flow in the interdisk midplane between shrouded two corotating disks at the interdisk spacing to disk radius aspect ratio 0.2 and rotation Reynolds number 3.01 × 105 were experimentally studied by flow visualization method and particle image velocimetry (PIV). An oval core flow structure rotating at a frequency 60% of the disks rotating frequency was observed. Based on the analysis of relative velocities, the flow in the region outside the oval core flow structure consisted of two large vortex rings, which move circumferentially with the rotation motion of the oval flow core. Four characteristic flow regions—solid-body-rotation-like region, buffer region, vortex region, and shroud-influenced region—were identified in the flow field. The solid-body-rotation-like region, which was featured by its linear distribution of circumferential velocity and negligibly small radial velocity, was located within the inscribing radius of the oval flow core. The vortex region was located outside the circumscribing radius of the oval flow core. The buffer region existed between the solid-body-rotation-like region and the vortex region. In the buffer region, there existed a “node” point that the propagating circumferential velocity waves diminished. The circumferential random fluctuation intensity presented minimum values at the node point and high values in the solid-body-rotation-like region and shroud-influenced region due to the shear effect induced by the wall.

scholarly journals On a possible corrugation of the galactic plane

1970 ◽  
Vol 38 ◽  
pp. 147-150 ◽  
Author(s):  
C. M. Varsavsky ◽  
R. J. Quiroga
Keyword(s):  
Brightness Temperature ◽  
Solid Body ◽  
Rotation Curve ◽  
Galactic Plane ◽  
Maximum Temperature ◽  
Body Rotation ◽  
Maximum Brightness ◽  
Solid Body Rotation ◽  
The Galaxy ◽  
Sinusoidal Pattern

We have studied the rotation curve of the Galaxy at different heights below and above the equator. In the course of this work we noticed that the maximum brightness temperature of hydrogen oscillates around the galactic plane following a fairly sinusoidal pattern. It is further noticed that the maximum temperature of hydrogen occurs right on the plane in the regions where the rotation curve has a form indicating solid body rotation. A rotation curve based on points of maximum hydrogen temperature does not differ appreciably from a rotation curve measured on the galactic plane.

Fragmentation of elongated cylindrical clouds. IV - Clouds with solid-body rotation about an arbitrary axis

1992 ◽  
Vol 400 ◽  
pp. 579 ◽  
Author(s):  
Ian Bonnell ◽  
Jean-Pierre Arcoragi ◽  
Hugo Martel ◽  
Pierre Bastien
Keyword(s):  
Solid Body ◽  
Body Rotation ◽  
Solid Body Rotation ◽  
Arbitrary Axis

scholarly journals Observations of an Inertial Peak in the Intrinsic Wind Spectrum Shifted by Rotation in the Antarctic Vortex

2012 ◽  
Vol 69 (12) ◽  
pp. 3800-3811 ◽  
Author(s):  
L. J. Gelinas ◽  
R. L. Walterscheid ◽  
C. R. Mechoso ◽  
G. Schubert
Keyword(s):  
Solid Body ◽  
Wave Spectrum ◽  
Polar Vortex ◽  
Relative Vorticity ◽  
Body Rotation ◽  
Background Flow ◽  
Absolute Vorticity ◽  
Solid Body Rotation ◽  
The Absolute ◽  
The Antarctic

Abstract Spectral analyses of time series of zonal winds derived from locations of balloons drifting in the Southern Hemisphere polar vortex during the Vorcore campaign of the Stratéole program reveal a peak with a frequency near 0.10 h−1, more than 25% higher than the inertial frequency at locations along the trajectories. Using balloon data and values of relative vorticity evaluated from the Modern Era Retrospective-Analyses for Research and Applications (MERRA), the authors find that the spectral peak near 0.10 h−1 can be interpreted as being due to inertial waves propagating inside the Antarctic polar vortex. In support of this claim, the authors examine the way in which the low-frequency part of the gravity wave spectrum sampled by the balloons is shifted because of effects of the background flow vorticity. Locally, the background flow can be expressed as the sum of solid-body rotation and shear. This study demonstrates that while pure solid-body rotation gives an effective inertial frequency equal to the absolute vorticity, the latter gives an effective inertial frequency that varies, depending on the direction of wave propagation, between limits defined by the absolute vorticity plus or minus half of the background relative vorticity.

Waves in a gas in solid-body rotation

1972 ◽  
Vol 56 (2) ◽  
pp. 277-286 ◽  
Author(s):  
J. B. Morton ◽  
E. J. Shaughnessy
Keyword(s):  
Eigenvalue Problem ◽  
Solid Body ◽  
Transverse Wave ◽  
Speed Of Sound ◽  
Acoustic Waves ◽  
Body Rotation ◽  
Perfect Gas ◽  
Solid Body Rotation ◽  
Rotational Waves

The axial and transverse wave motions of an inviscid perfect gas in isothermal solid-body rotation in a cylinder are investigated. Solutions of the resulting eigenvalue problem are shown to correspond to two types of waves. The acoustic waves are the rotational counterparts of the well-known Rayleigh solutions for a gas at rest in a cylinder. The rotational waves, whose amplitudes and frequencies go to zero in the non-rotating limit, exhibit phase speeds both larger and smaller than the speed of sound. The effect of rotation on the frequency and structure of these waves is discussed.

The Elastic Distortion of Rollers Under Combined Radial and Thrust Loads

1983 ◽  
Vol 105 (2) ◽  
pp. 189-197 ◽  
Author(s):  
H. So ◽  
R. Gohar
Keyword(s):  
Pressure Distribution ◽  
Solid Body ◽  
Axial Load ◽  
Axial Loading ◽  
Radial Pressure ◽  
Approximate Analysis ◽  
Body Rotation ◽  
Solid Body Rotation ◽  
Elastic Distortion ◽  
Radial Loading

This paper describes an approximate analysis for finding the elastostatic radial and end face distortion, radial pressure distribution, and solid body rotation of a flat ended axially profiled bearing roller under combined radial and axial loading through the ribs. It is found that a small but significant end face bulge occurs at each roller end when there is radial loading only. Upon the addition of an axial load, this bulge becomes a small depression. The altered geometry there may become significant during bearing operation, as it affects roller skew, wear, and lubrication between the ribs and roller and faces.

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