The influence of a small upstream wire on transition in a rotating cylinder wake

2015 ◽  
Vol 769 ◽  
Author(s):  
Anirudh Rao ◽  
Alexander Radi ◽  
Justin S. Leontini ◽  
Mark C. Thompson ◽  
John Sheridan ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Three Dimensional ◽  
Small Diameter ◽  
Reynolds Numbers ◽  
Rotating Cylinder ◽  
Hydrogen Bubble ◽  
Instability Mode ◽  
Cylinder Wake ◽  
Rotation Rates ◽  
Mode Transitions

Recent experimental research on rotating cylinder wakes has found that a previously numerically predicted subharmonic instability mode, mode C, occurs for considerably lower rotation rates than predicted through stability analysis, yet other mode transitions occur closer to the predicted onset. One difference between the theoretical and experimental set-ups is the use of a small-diameter hydrogen bubble visualisation wire placed upstream of the rotating cylinder. The current paper tests the hypothesis that a wire, of only $1/100$th of the cylinder diameter, placed five diameters upstream of the cylinder, sufficiently perturbs the flow to substantially affect certain wake transitions, including the onset of mode C. This is achieved using stability analysis of a flow that includes the upstream wire. The results indeed show that the wire of a tiny diameter induces a non-negligible asymmetry in the flow, triggering the subharmonic mode at substantially lower rotation rates. Furthermore, at higher rotation rates, the onset of two other three-dimensional modes are delayed to higher Reynolds numbers. These results make the point that even seemingly minute perturbations caused by minimally intrusive methods may result in substantially altered experimental flow behaviour.

Experimental evidence of new three-dimensional modes in the wake of a rotating cylinder

2013 ◽  
Vol 734 ◽  
pp. 567-594 ◽  
Author(s):  
A. Radi ◽  
M. C. Thompson ◽  
A. Rao ◽  
K. Hourigan ◽  
J. Sheridan
Keyword(s):  
Rotation Rate ◽  
Numerical Study ◽  
Water Channel ◽  
Three Dimensional ◽  
Cross Flow ◽  
Reynolds Numbers ◽  
Rotating Cylinder ◽  
Travelling Wave ◽  
Cylinder Surface ◽  
Rotation Rates

AbstractA recent numerical study by Rao et al. (J. Fluid Mech., vol. 717, 2013, pp. 1–29) predicted the existence of several previously unobserved linearly unstable three-dimensional modes in the wake of a spinning cylinder in cross-flow. While linear stability analysis suggests that some of these modes exist for relatively limited ranges of Reynolds numbers and rotation rates, this may not be true for fully developed nonlinear wakes. In the current paper, we present the results of water channel experiments on a rotating cylinder in cross-flow, for Reynolds numbers $200\leqslant \mathit{Re}\leqslant 275$ and non-dimensional rotation rates $0\leqslant \alpha \leqslant 2. 5$. Using particle image velocimetry and digitally post-processed hydrogen bubble flow visualizations, we confirm the existence of the predicted modes for the first time experimentally. For instance, for $\mathit{Re}= 275$ and a rotation rate of $\alpha = 1. 7$, we observe a subharmonic mode, mode C, with a spanwise wavelength of ${\lambda }_{z} / d\approx 1. 1$. On increasing the rotation rate, two modes with a wavelength of ${\lambda }_{z} / d\approx 2$ become unstable in rapid succession, termed modes D and E. Mode D grows on a shedding wake, whereas mode E consists of streamwise vortices on an otherwise steady wake. For $\alpha \gt 2. 2$, a short-wavelength mode F appears localized close to the cylinder surface with ${\lambda }_{z} / d\approx 0. 5$, which is presumably a manifestation of centrifugal instability. Unlike the other modes, mode F is a travelling wave with a spanwise frequency of ${\mathit{St}}_{3D} \approx 0. 1$. In addition to these new modes, observations on the one-sided shedding process, known as the ‘second shedding’, are reported for $\alpha = 5. 1$. Despite suggestions from the literature, this process seems to be intrinsically three-dimensional. In summary, our experiments confirm the linear predictions by Rao et al., with very good agreement of wavelengths, symmetries and the phase velocity for the travelling mode. Apart from this, these experiments examine the nonlinear saturated state of these modes and explore how the existence of multiple unstable modes can affect the selected final state. Finally, our results establish that several distinct three-dimensional instabilities exist in a relatively confined area on the $\mathit{Re}$–$\alpha $ parameter map, which could account for their non-detection previously.

A global stability analysis of the steady and periodic cylinder wake

1994 ◽  
Vol 270 ◽  
pp. 297-330 ◽  
Author(s):  
Bernd R. Noack ◽  
Helmut Eckelmann
Keyword(s):  
Periodic Solution ◽  
Stability Analysis ◽  
Hopf Bifurcation ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Cylinder Wake ◽  
Global Stability Analysis ◽  
Supercritical Hopf Bifurcation ◽  
Low Dimensional ◽  
Transition Scenario

A global, three-dimensional stability analysis of the steady and the periodic cylinder wake is carried out employing a low-dimensional Galerkin method. The steady flow is found to be asymptotically stable with respect to all perturbations for Re < 54. The onset of periodicity is confirmed to be a supercritical Hopf bifurcation which can be modelled by the Landau equations. The periodic solution is observed to be only neutrally stable for 54 < Re < 170. While two-dimensional perturbations of the vortex street rapidly decay, three-dimensional perturbations with long spanwise wavelengths neither grow nor decay. The periodic solution becomes unstable at Re = 170 by a perturbation with the spanwise wavelength of 1.8 diameters. This instability is shown to be a supercritical Hopf bifurcation in the spanwise coordinate and leads to a three-dimensional periodic flow. Finally the transition scenario for higher Reynolds numbers is discussed.

Three-dimensionality in the wake of a rotating cylinder in a uniform flow

2013 ◽  
Vol 717 ◽  
pp. 1-29 ◽  
Author(s):  
A. Rao ◽  
J. Leontini ◽  
M. C. Thompson ◽  
K. Hourigan
Keyword(s):  
Unsteady Flow ◽  
Steady Flow ◽  
Parameter Space ◽  
Vortex Shedding ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Rotating Cylinder ◽  
Marginal Stability ◽  
Two Dimensional ◽  
Rotation Rates

AbstractThe wake of a rotating circular cylinder in a free stream is investigated for Reynolds numbers $\mathit{Re}\leqslant 400$ and non-dimensional rotation rates of $\alpha \leqslant 2. 5$. Two aspects are considered. The first is the transition from a steady flow to unsteady flow characterized by periodic vortex shedding. The two-dimensional computations show that the onset of unsteady flow is delayed to higher Reynolds numbers as the rotation rate is increased, and vortex shedding is suppressed for $\alpha \geqslant 2. 1$ for all Reynolds numbers in the parameter space investigated. The second aspect investigated is the transition from two-dimensional to three-dimensional flow using linear stability analysis. It is shown that at low rotation rates of $\alpha \leqslant 1$, the three-dimensional transition scenario is similar to that of the non-rotating cylinder. However, at higher rotation rates, the three-dimensional scenario becomes increasingly complex, with three new modes identified that bifurcate from the unsteady flow, and two modes that bifurcate from the steady flow. Curves of marginal stability for all of the modes are presented in a parameter space map, the defining characteristics for each mode presented, and the physical mechanisms of instability are discussed.

scholarly journals Stability analysis of the elliptic cylinder wake

2014 ◽  
Vol 763 ◽  
pp. 302-321 ◽  
Author(s):  
Justin S. Leontini ◽  
David Lo Jacono ◽  
Mark C. Thompson
Keyword(s):  
Stability Analysis ◽  
Aspect Ratio ◽  
Three Dimensional ◽  
Elliptic Cylinder ◽  
Cylinder Wake ◽  
Long Wavelength ◽  
Aspect Ratios ◽  
Numerical Stability Analysis ◽  
Spatiotemporal Symmetries ◽  
Three Dimensional Simulations

AbstractThis paper presents the results of numerical stability analysis of the wake of an elliptical cylinder. Aspect ratios where the ellipse is longer in the streamwise direction than in the transverse direction are considered. The focus is on the dependence on the aspect ratio of the ellipse of the various bifurcations to three-dimensional flow from the two-dimensional Kármán vortex street. It is shown that the three modes present in the wake of a circular cylinder (modes A, B and QP) are present in the ellipse wake, and that in general they are all stabilized by increasing the aspect ratio of the ellipse. Two new pertinent modes are found: one long-wavelength mode with similarities to mode A, and a second that is only unstable for aspect ratios greater than approximately 1.75, which has similar spatiotemporal symmetries to mode B but has a distinct spatial structure. Results from fully three-dimensional simulations are also presented confirming the existence and growth of these two new modes in the saturated wakes.

Experimental Study on the Stability of the Flow Behind an Accelerating Circular Cylinder

2007 ◽  
Author(s):  
A. Inasawa ◽  
K. Toda ◽  
M. Asai
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Critical Reynolds Number ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Cylinder Wake ◽  
Global Instability ◽  
The Stability ◽  
Dimensional Instability ◽  
Wake Oscillation

Disturbance growth in the wake of a circular cylinder moving at a constant acceleration is examined experimentally. The cylinder is installed on a carriage moving in the still air. The results show that the critical Reynolds number for the onset of the global instability leading to a self-sustained wake oscillation increases with the magnitude of acceleration, while the Strouhal number of the growing disturbance at the critical Reynolds number is not strongly dependent on the magnitude of acceleration. It is also found that with increasing the acceleration, the Ka´rma´n vortex street remains two-dimensional even at the Reynolds numbers around 200 where the three-dimensional instability occurs to lead to the vortex dislocation in the case of cylinder moving at constant velocity or in the case of cylinder wake in the steady oncoming flow.

Symmetry breaking and instability mechanisms in medium depth torsionally driven open cylinder flows

2011 ◽  
Vol 672 ◽  
pp. 521-544 ◽  
Author(s):  
STUART J. COGAN ◽  
KRIS RYAN ◽  
GREGORY J. SHEARD
Keyword(s):  
Stability Analysis ◽  
Aspect Ratio ◽  
Symmetry Breaking ◽  
Axisymmetric Flow ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Interfacial Region ◽  
Nonlinear Stability Analysis ◽  
Aspect Ratios ◽  
Instability Modes

A numerical investigation was conducted into the different flow states, and bifurcations leading to changes of state, found in open cylinders of medium to moderate depth driven by a constant rotation of the vessel base. A combination of linear stability analysis, for cylinders of numerous height-to-radius aspect ratios (H/R), and nonlinear stability analysis and three-dimensional simulations for a cylinder of aspect ratio 1.5, has been employed. Attention is focused on the breaking of SO(2) symmetry. A comprehensive map of transition Reynolds numbers as a function of aspect ratio is presented by combining a detailed stability analysis with the limited existing data from the literature. For all aspect ratios considered, the primary instabilities are identified as symmetry-breaking Hopf bifurcations, occurring at Reynolds numbers well below those of the previously reported axisymmetric Hopf transitions. It is revealed that instability modes with azimuthal wavenumbers m = 1, 3 and 4 are the most unstable in the range 1.0 < H/R < 4, and that numerous double Hopf bifurcation points exist. Critical Reynolds numbers generally increase with cylinder aspect ratio, though a decrease in stability occurs between aspect ratios 1.5 and 2.0, where a local minimum in critical Reynolds number occurs. For H/R = 1.5, a detailed characterisation of instability modes is given. It is hypothesized that the primary instability leading to transition from steady axisymmetric flow to unsteady three-dimensional flow is related to deformation of shear layers that are present in the flow, in particular at the interfacial region between the vortex breakdown bubble and the primary recirculation.

Three-dimensionality in the wake of a rapidly rotating cylinder in uniform flow

2013 ◽  
Vol 730 ◽  
pp. 379-391 ◽  
Author(s):  
A. Rao ◽  
J. S. Leontini ◽  
M. C. Thompson ◽  
K. Hourigan
Keyword(s):  
Steady State ◽  
Rotation Rate ◽  
Free Stream ◽  
Three Dimensional ◽  
Rotating Cylinder ◽  
Marginal Stability ◽  
Cylinder Surface ◽  
Rotation Rates ◽  
Centrifugal Instability ◽  
The Stability

AbstractThe flow around an isolated cylinder spinning at high rotation rates in free stream is investigated. The existence of two steady two-dimensional states is confirmed, as is the existence of a secondary mode of vortex shedding. The stability of the two steady states to three-dimensional perturbations is established using linear stability analysis. At lower rotation rates on the first steady state, two three-dimensional modes are confirmed, and their structure and curves of marginal stability as a function of rotation rate and Reynolds number are determined. One mode (named mode $E$) appears consistent with a hyperbolic instability in the wake, while the second (named mode $F$) appears to be a centrifugal instability of the flow very close to the cylinder surface. At higher rotation rates on the second steady state, a single three-dimensional mode due to centrifugal instability (named mode ${F}^{\prime } $) is found. This mode becomes increasingly difficult to excite as the rotation rate is increased.

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