Bulletin of the American Physical Society
2006 59th Annual Meeting of the APS Division of Fluid Dynamics
Sunday–Tuesday, November 19–21, 2006; Tampa Bay, Florida
Session ON: Taylor-Couette Instabilities |
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Chair: Patrick D. Weidman, University of Colorado at Boulder Room: Tampa Marriott Waterside Hotel and Marina Meeting Room 9 |
Tuesday, November 21, 2006 12:15PM - 12:28PM |
ON.00001: Effect of radius ratio on flow transitions in Newtonian Taylor-Couette flows Cari Dutcher, Susan Muller In this study, a dozen flow state bifurcations have been mapped for a Newtonian fluid in a Taylor-Couette geometry of radius ratio 0.912 and aspect ratio of 60.7 using flow visualization in 2D planes of radial, axial, projected azimuthal and time dimensions. The resultant flow state transitions are compared to previous stability mappings obtained at various radius ratios. As a result, the effect of gap size is illuminated for various flow transitions, including transitions to axisymmetric, wavy, spiraling and/or turbulent modes. While many flow types have been previously observed, we report new sequences of bifurcations in the counter-rotating Taylor-Couette regime as well as track the vortex growth dynamics. In addition, the existing primary stability boundary data were found to be self-similar in radius ratio with respect to a properly chosen parameter space. Using the combination of variables technique, for both counter-rotating and co-rotating cylinders, curves were then empirically fit for explicit analytic formulae, $Re_c (\eta ,\mu )$. Excellent quantitative agreement was found with data across the whole parameter space. [Preview Abstract] |
Tuesday, November 21, 2006 12:28PM - 12:41PM |
ON.00002: Frictional Drag Reduction by Bubbles in Taylor-Couette Flow Yuichi Murai, Hiroshi Oiwa, Yasushi Takeda Frictional drag reduction provided with small bubbles is investigated experimentally using a Couette-Taylor flow system, i.e. shear flow between concentric cylinders. Torque and bubble behavior are measured up to Re=4500 when air bubbles are injected constantly and rise through the cells. Silicone oil is used for avoiding uncertain interfacial property of bubbles as well as for keeping nearly mono-sized bubbles. We assess the effect of drag reduction with two types of evaluation factors, i.e. sensitivity and power gain. The sensitivity exceeds unity at Re$<$2000, proving that the drag is reduced more than the drop of mixture density. This originates from accumulation of bubbles into the rotating inner cylinder, which is little affected by turbulence. The power gain, which is defined by drag reduction power per bubble injection power, takes the highest value of O(10) at higher Re numbers around 2500. The image processing measurement finds this reason to be disappearance of azimuthal waves when the organized bubbles distribution transits from toroidal to spiral modes. Moreover, the axial spacing of bubble clouds expands during the transition, enforcing the reduction of momentum exchange. [Preview Abstract] |
Tuesday, November 21, 2006 12:41PM - 12:54PM |
ON.00003: Experimental studies of magnetorotational instability in differentially rotating cylindrical flows Barbara Brawn, Daniel Lathrop Given the ubiquity of rotating disks in the observable universe (e.g., galaxies, planetary rings, protoplanetary disks and accretion disks around compact objects), understanding differentially rotating, electrically conducting flows is of considerable astrophysical interest. Theoretical and numerical studies indicate that infall and accretion of orbiting material can result from a so-called magnetorotational instability (MRI) arising in such flows. Recent experimental work suggests that MRI is observable in a laboratory setting; inspired by these observations, we are building a sodium Taylor-Couette experiment, comprised of a stationary 30 cm diameter outer cylinder and a rotating 15 cm diameter inner cylinder, with liquid sodium filling the gap between the cylinders. Numerical studies indicate that MRI arises in this geometry in the presence of an external magnetic field; we will impose on the sodium flow a uniform axial magnetic field produced by Helmholtz coils at either end of the experiment. We will use ultrasound Doppler velocimetry to examine the turbulent sodium flow, and a Hall probe array to examine the induced magnetic field of the system, and will relate our observations to theoretical and numerical expectations. [Preview Abstract] |
Tuesday, November 21, 2006 12:54PM - 1:07PM |
ON.00004: Unusual results from stability computations for variations of the Taylor-Couette problem Randall Tagg, Patrick Weidman The classical approach to stability for Taylor-Couette, convection, and other fluid systems gives an archetypal means for mode and wavelength selection. Several variations of the Taylor-Couette problem reveal unusual stability characteristics. These characteristics include linear selection of multiple critical wavenumbers, critical values occurring at apparent maxima of marginal curves rather than minima, and dispersion parameters that give negative group velocity. These results occur for variations of the Taylor-Couette problem that include the use of counter-rotating cylinders, radial temperature gradients, and radial temperature gradients with radial gravity. Even without a full nonlinear treatment of these problems, a wide variety of interesting experiments is suggested. [Preview Abstract] |
Tuesday, November 21, 2006 1:07PM - 1:20PM |
ON.00005: Numerical study of Taylor-Couette flow with a porous inner cylinder Semma El Alami, Karim Bourouni, Eric Serre, Richard Lueptow During the operation of a rotating filter consisting of a porous rotating inner cylinder and a non-porous outer cylinder, the Taylor vortices generated between the two coaxial cylinders are altered. The numerical study of this kind of filtration process requires the development of rigorous and robust numerical model which takes account of the interaction between the fluid and the porous medium of the membrane filter. In this work, the effect of permeability on Taylor--Couette flow with rotating inner wall and an imposed axial flow is investigated (radius ratio of $\eta $ = 0.85 and length-to-gap ratio of $\Gamma $ = 16). The thickness of porous medium may be variable into the gap between the cylinders. The results show a strong dependence of the flow structure with the permeability of the porous medium. We distinguish two regimes: one is characterized by a linear evolution of the critical Taylor with permeability; the second one is a transition to a horizontal branch for Ta=1350. This change affects significantly the mass transfer at the outlet of the membrane. [Preview Abstract] |
Tuesday, November 21, 2006 1:20PM - 1:33PM |
ON.00006: Quasiperiodic flow in an axially forced Taylor-Couette system Marc Avila, Francisco Marques, Juan M. Lopez, Alvaro Meseguer Time-periodic forcing of hydrodynamic systems can be used as a mechanism to delay transition to secondary flows. However, parametric resonance may occur when the forcing excites some natural frequency of the system, leading to Neimark--Sacker bifurcations which can give rise to more complex flows or even turbulence. Therefore, there is a tradeoff between enhancing stability and catastrophic transition. Periodic axial motion of the inner cylinder can be used in the Taylor--Couette system to delay the onset of Taylor vortices. Although this mechanism is very efficient, for low frequencies of the forcing Neimark--Sacker bifurcations occur, so that the transition is to non-axisymmetric vortices featuring a new natural frequency (Marques \& Lopez). In this work we study the complex flows arising in the neighbourhood of these bifurcations, including quasiperiodic motion as well as regions of frequency locking. The results will be compared with the recent experiments by Sinha {\emph et al}.\\[2mm] MARQUES, F. \& LOPEZ, J. M. 2000 Spatial and temporal resonances in a periodically forced hydrodynamic system. {\emph Physica D} {\bf 136}, 340-352.\\ SINHA, M., KEVREKIDIS, I. G. \& SMITS, A. J. 2006 Experimental study of a Neimark--Sacker bifurcation in axially forced Taylor--Couette flow. {\emph J. Fluid Mech.} {\bf 558}, 1-32. [Preview Abstract] |
Tuesday, November 21, 2006 1:33PM - 1:46PM |
ON.00007: Transition Time Scales in Taylor Couette Flow Richard M. Lueptow, Olivier Czarny The time scale for onset and decay of vortices in a Taylor Couette system cannot be predicted from linear stability analysis, yet is important from a practical standpoint. A two-dimensional pseudo-spectral direct numerical simulation was used to examine the time scales for subcritical-to-supercritical transition and supercritical-to-subcritical transition for a variety of aspect ratios (\textit{$\Gamma $} = $H$/$d$ = 8, 16, 24, 32, 40, $\infty )$ and radius ratios (\textit{$\eta $} = 0.5, 0.7, and 0.9) with only the inner cylinder rotating. A time scale based on the distance between the endwalls of the system along with the viscosity and rotational speed seems to be most appropriate for the onset of Taylor vortices, although no time scale collapses the data for all aspect ratios and radius ratios. For decay, a viscous time scale using the gap width as the length scale collapses the data, especially as the aspect ratio gets large. These results indicate that the onset of vortices is a consequence of the propagation of vortical structures related to the endwalls, while decay is related to viscous dissipation from the sidewalls. [Preview Abstract] |
Tuesday, November 21, 2006 1:46PM - 1:59PM |
ON.00008: On the compressible Taylor-Couette problem Avshalom Manela, Itzchak Frankel The transition to instability in the Taylor-Couette problem at small Knudsen numbers and arbitrary Mach numbers is studied via a linear temporal stability analysis of the compressible `slip-flow' problem for a perfect monatomic gas. We focus on the case of stationary outer cylinder and equal wall temperatures. The results indicate that occurrence of instability is limited to small Knudsen numbers owing to the combination of a critical (incompressible) Reynolds number at low Mach numbers and increased dissipation rates at large Mach numbers. Comparison of the linear results with DSMC calculations and existing experimental observations demonstrates that the present analysis correctly predicts the boundaries of the instability domain. We further demonstrate that in the narrow-gap approximation, owing to the reduced effect of compressibility, the neutral curve is well approximated by replacing the incompressible Reynolds number by a Reynolds number based on mean fluid properties. This simple approximation may present a useful alternative in studying the effects of various parameters on the onset of instability in the limit of arbitrarily small Knudsen numbers. [Preview Abstract] |
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