Centrifugal Waves in Tornado-like Vortices: Kelvin’s solutions and their Applications to Multiple-Vortex Development and Vortex Breakdown

2021 ◽  
Author(s):  
Johannes M. L. Dahl
Keyword(s):  
Vortex Breakdown ◽  
Unstable Wave ◽  
Important Work ◽  
Structure And Dynamics ◽  
Spiral Vortex ◽  
Slight Generalization ◽  
Breakdown Phenomenon ◽  
Unstable Solutions ◽  
Basic Features ◽  
Lord Kelvin

AbstractAbout 140 years ago, Lord Kelvin derived the equations describing waves that travel along the axis of concentrated vortices such as tornadoes. Although Kelvin’s vortex waves, also known as centrifugal waves, feature prominently in the engineering and uid dynamics literature, they have not attracted as much attention in the field of atmospheric science. To remedy this circumstance, Kelvin’s elegant derivation is retraced, and slightly generalized, to obtain solutions for a hierarchy of vortex ows that model basic features of tornado-like vortices. This treatment seeks to draw attention to the important work that Lord Kelvin did in this field, and reveal the remarkably rich structure and dynamics of these waves. Kelvin’s solutions help explain the vortex breakdown phenomenon routinely observed in modeled tornado-like vortices, and it is shown that his work is compatible with the widely used criticality condition put forth by Benjamin in 1962. Moreover, it is demonstrated that Kelvin’s treatment, with the slight generalization, includes unstable wave solutions that have been invoked to explain some aspects of the formation of multiple-vortex tornadoes. The analysis of the unstable solutions also forms the basis for determining whether e.g., an axisymmetric or a spiral vortex breakdown occurs. Kelvin’s work thus helps understand some of the visible features of tornado-like vortices.

A Study of Unsteady Secondary Flow in a Water Flow Axial Turbine Model

2008 ◽  
Author(s):  
Christian Kasper ◽  
Martin G. Rose ◽  
Stephan Staudacher ◽  
Jochen Gier
Keyword(s):  
Flow Visualization ◽  
Vortex Breakdown ◽  
Water Channel ◽  
Leading Edge ◽  
Secondary Flows ◽  
Stagnation Region ◽  
Spiral Vortex ◽  
Passage Vortex ◽  
High Turbulence ◽  
First Time

The influence of secondary flows on the performance of turbines has been investigated in great detail in the last decades. The interaction of vortices with following blade rows has been identified to be one of the loss mechanisms within a turbo-machine. This paper presents for the first time detailed flow visualization photographs of the interaction of the vane passage vortex with the rotor. The appearance vortex breakdown could be identified before and within the rotating passage of the turbine. The measurements were taken in a vertical water channel. Water is used instead of air because the flow visualization can be realised very easily with injected ink. For different relative positions of rotor to stator a series of photographs were taken. With an image editing process the average and the pixel RMS were calculated for each relative position. The pixel RMS is a useful indicator to identify highly turbulent regions in the flow field. The photographs of the vortex breakdown show spots of high pixel RMS which are associated with very high turbulence and therefore can be regarded as sources of loss. Insight is gained into the nature of the passage vortex breakdown mechanisms as follows: first the pressure wave of the rotor stretches the vortex causing a spiral vortex instability, then the vortex interacts with the leading edge as it attempts to cut the vortex. In the stagnation region of the blade a bubble type instability forms, expands and then convects through the rotor. The absolute trajectory of the vortex fluid reveals that it exchanges no work with the rotor.

Structural sensitivity of spiral vortex breakdown

2013 ◽  
Vol 720 ◽  
pp. 558-581 ◽  
Author(s):  
Ubaid Ali Qadri ◽  
Dhiren Mistry ◽  
Matthew P. Juniper
Keyword(s):  
Stability Analysis ◽  
Passive Control ◽  
Stokes Equations ◽  
Vortex Breakdown ◽  
Control Strategies ◽  
Axial Component ◽  
Azimuthal Mode ◽  
Global Mode ◽  
Structural Sensitivity ◽  
Spiral Vortex

AbstractPrevious numerical simulations have shown that vortex breakdown starts with the formation of a steady axisymmetric bubble and that an unsteady spiralling mode then develops on top of this. We investigate this spiral mode with a linear global stability analysis around the steady bubble and its wake. We obtain the linear direct and adjoint global modes of the linearized Navier–Stokes equations and overlap these to obtain the structural sensitivity of the spiral mode, which identifies the wavemaker region. We also identify regions of absolute instability with a local stability analysis. At moderate swirls, we find that the $m= - 1$ azimuthal mode is the most unstable and that the wavemaker regions of the $m= - 1$ mode lie around the bubble, which is absolutely unstable. The mode is most sensitive to feedback involving the radial and azimuthal components of momentum in the region just upstream of the bubble. To a lesser extent, the mode is also sensitive to feedback involving the axial component of momentum in regions of high shear around the bubble. At an intermediate swirl, in which the bubble and wake have similar absolute growth rates, other researchers have found that the wavemaker of the nonlinear global mode lies in the wake. We agree with their analysis but find that the regions around the bubble are more influential than the wake in determining the growth rate and frequency of the linear global mode. The results from this paper provide the first steps towards passive control strategies for spiral vortex breakdown.

The dynamics of confined vortices

1982 ◽  
Vol 382 (1783) ◽  
pp. 335-360 ◽  
Keyword(s):  
Vortex Core ◽  
Axial Velocity ◽  
Vortex Tube ◽  
Vortex Breakdown ◽  
Laser Doppler Anemometer ◽  
Present Evidence ◽  
Cylindrical Vortex ◽  
Breakdown Phenomenon ◽  
Similarities And Differences ◽  
Independent Parameters

Referring to flow-visualization and laser-Doppler anemometer measurements of swirl and axial velocity profiles, we discuss the physics of the flow in a cylindrical vortex tube as various independent parameters are varied. Three main classes of flow occur, depending upon the location of a vortex jump within the vortex tube. We present evidence to suggest a connection between vortex breakdown and the criticality and stability of the vortex core upon which it occurs and attempt to reconcile the various explanations that have been proposed for the breakdown phenomenon. Similarities and differences between the present experiments and those of previous investigators are also pointed out. Finally, as an Appendix, we present the results of a hydraulic analogue of our vortex experiment.

Velocity Measurements of Vortex Breakdown in an Enclosed Cylinder

2001 ◽  
Vol 123 (3) ◽  
pp. 604-611 ◽  
Author(s):  
Kazuyuki Fujimura ◽  
Hiroaki Yoshizawa ◽  
Reima Iwatsu ◽  
Hide S. Koyama ◽  
Jae Min Hyun
Keyword(s):  
Laser Doppler Velocimetry ◽  
Vortex Breakdown ◽  
Rotating Disk ◽  
Velocity Fields ◽  
Laser Doppler ◽  
Velocity Measurements ◽  
Experimental Apparatus ◽  
Breakdown Phenomenon ◽  
Component Velocity ◽  
Flow Visualizations

Experimental measurements were carried out of three-component velocity fields inside a cylindrical container. Flow was driven by the rotation of the top endwall disk. The purpose of the precision laser-Doppler velocimetry measurements was to describe the velocity characteristics pertinent to the vortex breakdown phenomenon. A turntable experimental apparatus was fabricated. Extensive laser-Doppler measurements, as well as flow visualizations, were made for the aspect ratio 1.50 and 2.50, and the Reynolds number ranges 0.99×103-2.20×103. The measured meridional velocities were found to be consistent with the prior visualization studies. The characteristic changes in swirling motions in the vicinity of vortex breakdown bubble are depicted. Detailed flow patterns near the rotating disk are constructed by using the experimental data.

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