Bulletin of the American Physical Society
62nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 54, Number 19
Sunday–Tuesday, November 22–24, 2009; Minneapolis, Minnesota
Session PP: Instability: Taylor-Couette |
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Chair: Edward White, Texas A&M University Room: 200D |
Tuesday, November 24, 2009 11:40AM - 11:53AM |
PP.00001: Experimental characterization of the Taylor-Couette flow submitted to a radial temperature gradient Arnaud Prigent, Rapha\"el Guillerm, Innocent Mutabazi, Kyung-Soo Yang We have developed a non-intrusive velocity and temperature fields measurement technique using thermochromic liquid crystals which allows to fully characterize the flow produced in a narrow gap and large aspect ratio Couette-Taylor system submitted to a radial temperature gradient. The aspect ratio and radius ratio of the system are respectively equal to 112 and 0.8. The control parameters are the Grashof number \textit{Gr}, related to the radial temperature gradient, and the Taylor number \textit{Ta}, related to the rotation of the inner cylinder. Here, \textit{Gr} is fixed and \textit{Ta} is gradually increased. For small values of \textit{Ta}, the base flow is composed of the circular Couette flow and a vertical flow induced by the radial temperature gradient. Above a critical value of \textit{Ta}, the destabilization of the base flow gives rise to a spiral pattern. While for small \textit{Gr} values it corresponds to traveling inclined vortices, for large \textit{Gr} values it corresponds to a modulated wave-like pattern filling the whole length of the system and rotating at the mean angular velocity of the flow. When \textit{Ta} is further increased, this wave-like pattern is progressively replaced by a counter-rotating vortices pattern. Numerical simulations of the corresponding Boussinesq-Oberbeck equations provide results in good agreement with experiments. [Preview Abstract] |
Tuesday, November 24, 2009 11:53AM - 12:06PM |
PP.00002: Effects of microbubbles on Taylor-Couette flow Yuji Tasaka, Yuichi Murai, Tomoaki Watamura, Yasushi Takeda Effects of micro-bubbles on Taylor-Couette flow has been examined by means of ultrasonic velocity profiling (UVP) for wide range of the Reynolds number, $1 \le Re/Re_c \le 18$, where $Re_c$ is the critical Reynolds number for the onset of the primary instability. $O(10 \mu m)$-diameter hydrogen bubbles generated by electrolysis of water was dispersed into the fluid layer of water between the vertical, co-axial cylinders. The radius ratio of the cylinders and the aspect ratio are 0.905 and 20, the maximum void fraction estimated by input power for the electrolysis is smaller than 0.1 \%. Different flow pattern of the rising bubbles are observed in the spatio-temporal velocity distribution measured by UVP; i.e. free rising and snake-like rising. Axial wavelength of the Taylor vortices show no clear influence of bubbles, but the frequency of the azimuthal traveling wave is reduced by bubbles. Since the number of the traveling waves on the azimuthal plane is the same in the conditions, single phase and with bubbles, the reduction of the frequency means the reduction of the traveling velocity of the wave. Facts to change the traveling velocity, the aspect ratio, the radius ratio, the axial wavelength of the vortices and the number of waves, are no difference on the both cases, therefore, we guess the decrease of the shear rate of the fluid due to micro-bubbles induces this reduction of the traveling speed. [Preview Abstract] |
Tuesday, November 24, 2009 12:06PM - 12:19PM |
PP.00003: Spectral analysis of temporally resolved velocity field data for Taylor-Couette flow John W. Laage, Michael G. Olsen, R. Dennis Vigil High speed stereoscopic particle image velocimetry (PIV) data were collected for Taylor-Couette flow for flow regimes varying from wavy through turbulent. The Taylor-Couette apparatus used had an aspect ratio of 34 and a radius ratio of 0.733. The working fluid was an index-of-refraction matched sodium iodide and water solution. Data were obtained for rotational Reynolds numbers ranging from 6 up to 200. Each high speed PIV data set consisted of 2048 images separated in times ranging from 1/60 through 1/2000 second as required by the rotational Reynolds number observed. The time resolved velocity field data were subjected to Fourier Decomposition to find the frequency behavior for a given rotational Reynolds number by calculating the power spectral density. For each investigated rotational Reynolds number, several data sets were averaged together to reduce the effect of observational ``noise.'' Turbulent kinetic energy and Reynolds Stresses were also calculated for the turbulent flow cases. Data at different rotational Reynolds numbers are compared to characterize flow transitions. [Preview Abstract] |
Tuesday, November 24, 2009 12:19PM - 12:32PM |
PP.00004: Characterizing the Subcritical Transition to Turbulence in Taylor-Couette Flow M.J. Burin, D.L. Defoor The supercritical transition to turbulence in Taylor-Couette flow is a celebrated paragon of nonlinear dynamics, but the subcritical transition in this system has received much less attention. A few early experiments with the inner cylinder held stationary present to us a suggestive but incomplete picture of a `catastrophic' transition to turbulence for sufficient outer cylinder speeds. But many questions remain about this shear-driven transition, such as the functional dependence of the critical Reynolds number on rotation, system curvature, cyclonicity, and finite-amplitude perturbations. To address these and related issues a large Taylor-Couette device has recently been constructed, allowing for access to turbulent regimes with either/both cylinders rotating. Some details of this new apparatus along with initial data pertaining to the subcritical transition will be presented. [Preview Abstract] |
Tuesday, November 24, 2009 12:32PM - 12:45PM |
PP.00005: Transient Turbulence in Taylor-Couette Flow: Co/Counter Rotation and Aspect Ratio Effects Daniel Borrero-Echeverry, Randall Tagg, Michael Schatz Wall-bounded shear flows typically make the transition to turbulence through a subcritical bifurcation that requires a finite amplitude perturbation. At low Reynolds numbers the lifetime of the turbulent state is finite and increases with increasing Reynolds number. Recent studies have challenged the view that there is a critical Reynolds number above which turbulence becomes sustained. The issue has been further complicated by recent numerical studies that suggest that even if turbulence decays locally, it may become sustained globally if the system is sufficiently large. We address this issue and present lifetime measurements in linearly stable Taylor-Couette flow at various aspect ratios. We also discuss the effects of various boundary conditions and weak counter/co-rotation on the observed lifetimes. [Preview Abstract] |
Tuesday, November 24, 2009 12:45PM - 12:58PM |
PP.00006: Structures in Transitional Taylor-Couette Flows Identified using POD Stavroula Balabani, Eboshogwe Imomoh, Jonathan Dusting The flow in the gap between concentric cylinders, or Taylor-Couette flow, has been used to study transition to turbulence for decades, and is also utilised for various biotechnological and industrial processes. Transitional flow states depend highly on vessel geometry; they are also three-dimensional and often time dependent limiting the use of experimental techniques for their characterisation. In this talk the transition to turbulence in a Taylor-Couette flow is studied by means of time resolved PIV velocity fields and Proper Orthogonal Decomposition (POD). It is found that for the particular geometry studied the transition to turbulence occurs via a quasi periodic regime characterised by a fast moving azimuthal wave (FMAW). Aspects of the FMAW structure, such as a series of co-rotating vortices that increase in strength away from the endwalls, are also revealed by spatially resolved POD. [Preview Abstract] |
Tuesday, November 24, 2009 12:58PM - 1:11PM |
PP.00007: Controlling Transition in Taylor-Couette Flow with Spatial Forcing Yasser Aboelkassem, Anne Staples The linear stability of the flow in the (narrow) annular gap between two infinitely long cylinders, driven by an axisymmetric sinusoidal perturbation to the radius of the inner cylinder in the axial direction is analyzed. A closed-form solution for the basic flow in the system is derived. Experiments and computational investigations of this system have given differing results. In the seminal experiment performed by Ikeda and Maxworthy (Phys. Rev. E, 1994), the perturbation was found to have no effect on the first stability boundary. In subsequent theoretical investigations, authors have concluded that circular flow cannot exist in the modified system, and that the basic flow is Taylor Vortex Flow. In this study, we find that while the perturbation seems to always be destabilizing, circular flow does indeed exist in the system, in agreement with experimental observations. For small to moderate forcing amplitudes, the critical Taylor number for the first transition is only reduced slightly, by an amount that depends on the forcing amplitude and wavelength. The reduction in the first critical Taylor number is speculated to lie within the margin of error in the experiments performed by Ikeda and Maxworthy. [Preview Abstract] |
Tuesday, November 24, 2009 1:11PM - 1:24PM |
PP.00008: Pattern formation in plane Couette flow turbulence Yohann Duguet, Philipp Schlatter, Dan S. Henningson Plane Couette flow is the flow between two counter-sliding plates of velocity $U$ separated by a gap $2h$. Despite the linear stability of the laminar base flow, sustained turbulence is observed experimentally above $Re \sim 300$, where $Re=\frac{Uh}{\nu}$ ($\nu$ is the kinematic viscosity of the fluid). Whereas featureless turbulence is seen for $Re \ge 400$, lower-$Re$ experiments have shown the appearance of turbulent stripes, inclined with respect to the base flow, interspersed with quiescent, nearly laminar regions. Direct numerical simulation using a spectral code in an unusually large computational domain ($800h$ in length and $356h$ in width with periodic boundary conditions) is performed here to highlight the large-scale self-organisation of the flow, out-of-reach in former simulations. The system evolves towards a fragmented large-scale pattern, where several competing inclinations can coexist. We suggest a new way to study the angle selection of those turbulent patterns, based on the computation of edge states in a smaller computational domain of size $80h \times 80h$. We can show that angles close to $40^{\circ}$ are prefentially chosen by the system close to the threshold and that this range of angles increases with the amplitude ofthe initial perturbation. This demonstrates that the pattern selection is linked to the subcritical nature of the transition process. [Preview Abstract] |
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