Direct numerical simulation of turbulent Taylor–Couette flow

2007 ◽  
Vol 587 ◽  
pp. 373-393 ◽  
Author(s):  
S. DONG
Keyword(s):  
Couette Flow ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Taylor Vortex ◽  
Görtler Vortices ◽  
Tilting Angle ◽  
Taylor Couette ◽  
Gortler Vortices ◽  
Taylor Couette Flow

We investigate the dynamical and statistical features of turbulent Taylor–Couette flow (for a radius ratio 0.5) through three-dimensional direct numerical simulations (DNS) at Reynolds numbers ranging from 1000 to 8000. We show that in three-dimensional space the Görtler vortices are randomly distributed in banded regions on the wall, concentrating at the outflow boundaries of Taylor vortex cells, which spread over the entirecylinder surface with increasing Reynolds number. Görtler vortices cause streaky structures that form herringbone-like patterns near the wall. For the Reynolds numbers studied here, the average axial spacing of the streaks is approximately 100 viscous wall units, and the average tilting angle ranges from 16° to 20°. Simulationresults have been compared to the experimental data in the literature, and the flow dynamics and statistics are discussed in detail.

Effect of polymer additives on Görtler vortices in Taylor—Couette flow

1995 ◽  
Vol 282 ◽  
pp. 115-129 ◽  
Author(s):  
S. H.-K. Lee ◽  
S. Sengupta ◽  
T. Wei
Keyword(s):  
Couette Flow ◽  
Vortex Formation ◽  
Taylor Number ◽  
Polymer Additives ◽  
Cylinder Wall ◽  
Number Range ◽  
Görtler Vortices ◽  
Taylor Couette ◽  
Gortler Vortices ◽  
Taylor Couette Flow

Taylor—Couette flow is ideal for studying drag-reducing polymer additives because, unlike turbulent boundary layers, the instabilities are better understood. Video records of laser-induced fluorescence experiments with and without polymers will be presented. Polyethylene-oxide (PEO) ‘oceans’ were used in concentrations of 20 and 100 p.p.m. In the Taylor number range, 3 × 104 ≤ Ta ≤ 108, Newtonian flow consisted of Taylor vortices which span the gap between cylinders and much smaller Görtler vortices at the inner cylinder wall. Measurements of core-to-core separation between counter-rotating vortices were made to estimate the Görtler instability wavenumber. These measurements show that PEO addition increases the Görtler wavenumber for a given Taylor number. At the lower Taylor numbers, Görtler vortex formation was suppressed by PEO. This implies that polymers directly affect the evolution of centrifugal instabilities.

Three-Dimensional Simulation of Taylor-Couette Flow

1989 ◽  
pp. 366-370 ◽  
Author(s):  
N. Matsumoto ◽  
S. Shirayama ◽  
K. Kuwahara ◽  
F. Hussain
Keyword(s):  
Couette Flow ◽  
Three Dimensional ◽  
Taylor Couette ◽  
Dimensional Simulation ◽  
Taylor Couette Flow

scholarly journals Optimal Taylor–Couette flow: direct numerical simulations

2013 ◽  
Vol 719 ◽  
pp. 14-46 ◽  
Author(s):  
Rodolfo Ostilla ◽  
Richard J. A. M. Stevens ◽  
Siegfried Grossmann ◽  
Roberto Verzicco ◽  
Detlef Lohse
Keyword(s):  
Angular Velocity ◽  
Couette Flow ◽  
Scaling Laws ◽  
Outer Cylinder ◽  
Reynolds Numbers ◽  
Velocity Profiles ◽  
Experimental Result ◽  
Counter Rotation ◽  
Taylor Couette ◽  
Taylor Couette Flow

AbstractWe numerically simulate turbulent Taylor–Couette flow for independently rotating inner and outer cylinders, focusing on the analogy with turbulent Rayleigh–Bénard flow. Reynolds numbers of $R{e}_{i} = 8\times 1{0}^{3} $ and $R{e}_{o} = \pm 4\times 1{0}^{3} $ of the inner and outer cylinders, respectively, are reached, corresponding to Taylor numbers $Ta$ up to $1{0}^{8} $. Effective scaling laws for the torque and other system responses are found. Recent experiments with the Twente Turbulent Taylor–Couette (${T}^{3} C$) setup and with a similar facility in Maryland at very high Reynolds numbers have revealed an optimum transport at a certain non-zero rotation rate ratio $a= - {\omega }_{o} / {\omega }_{i} $ of about ${a}_{\mathit{opt}} = 0. 33$. For large enough $Ta$ in the numerically accessible range we also find such an optimum transport at non-zero counter-rotation. The position of this maximum is found to shift with the driving, reaching a maximum of ${a}_{\mathit{opt}} = 0. 15$ for $Ta= 2. 5\times 1{0}^{7} $. An explanation for this shift is elucidated, consistent with the experimental result that ${a}_{\mathit{opt}} $ becomes approximately independent of the driving strength for large enough Reynolds numbers. We furthermore numerically calculate the angular velocity profiles and visualize the different flow structures for the various regimes. By writing the equations in a frame co-rotating with the outer cylinder a link is found between the local angular velocity profiles and the global transport quantities.

scholarly journals Mode competition in modulated Taylor–Couette flow

2008 ◽  
Vol 601 ◽  
pp. 381-406 ◽  
Author(s):  
M. AVILA ◽  
M. J. BELISLE ◽  
J. M. LOPEZ ◽  
F. MARQUES ◽  
W. S. SARIC
Keyword(s):  
Couette Flow ◽  
Physical Experiment ◽  
Mode Competition ◽  
Taylor Vortex ◽  
Coexistence Region ◽  
Narrow Region ◽  
Taylor Couette ◽  
Spatio Temporal ◽  
Temporal Symmetry ◽  
Taylor Couette Flow

The effects of harmonically oscillating the inner cylinder about a zero mean rotation in a Taylor–Couette flow are investigated experimentally and numerically. The resulting time-modulated circular Couette flow possesses a Z2 spatio-temporal symmetry which gives rise to two distinct modulated Taylor vortex flows. These flows are initiated at synchronous bifurcations, have the same spatial symmetries, but are characterized by different spatio-temporal symmetries and axial wavenumber. Mode competition between these two states has been investigated in the region where they bifurcate simultaneously. In the idealized numerical model, the two flows have been found to coexist and be stable in a narrow region of parameter space. However, in the physical experiment, neither state has been observed in the coexistence region. Instead, we observe noise-sustained flows with irregular time-dependent axial wavenumber. Movies are available with the online version of the paper.

Heat Transfer Enhancement in Axial Taylor-Couette Flow

2005 ◽  
Author(s):  
S. Gilchrist ◽  
C. Y. Ching ◽  
D. Ewing
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Couette Flow ◽  
Reynolds Numbers ◽  
Taylor Number ◽  
Number Range ◽  
Taylor Couette ◽  
Number Case ◽  
Taylor Couette Flow

An experimental investigation was performed to determine the effect that surface roughness has on the heat transfer in an axial Taylor-Couette flow. The experiments were performed using an inner rotating cylinder in a stationary water jacket for Taylor numbers of 106 to 5×107 and axial Reynolds numbers of 900 to 2100. Experiments were performed for a smooth inner cylinder, a cylinder with two-dimensional rib roughness and a cylinder with three-dimensional cubic protrusions. The heat transfer results for the smooth cylinder were in good agreement with existing experimental data. The change in the Nusselt number was relatively independent of the axial Reynolds number for the cylinder with rib roughness. This result was similar to the smooth wall case but the heat transfer was enhanced by 5% to 40% over the Taylor number range. The Nusselt number for the cylinder with cubic protrusions exhibited an axial Reynolds number dependence. For a low axial Reynolds number of 980, the Nusselt number increased with the Taylor number in a similar way to the other test cylinders. At higher axial Reynolds numbers, the heat transfer was initially independent of the Taylor number before increasing with Taylor number similar to the lower Reynolds number case. In this higher axial Reynolds number case the heat transfer was enhanced by up to 100% at the lowest Taylor number of 1×106 and by approximately 35% at the highest Taylor number of 5×107.

scholarly journals Effect of the number of vortices on the torque scaling in Taylor–Couette flow

2014 ◽  
Vol 748 ◽  
pp. 756-767 ◽  
Author(s):  
B. Martínez-Arias ◽  
J. Peixinho ◽  
O. Crumeyrolle ◽  
I. Mutabazi
Keyword(s):  
Reynolds Number ◽  
Aspect Ratio ◽  
Couette Flow ◽  
Scaling Laws ◽  
Taylor Vortex ◽  
Large Radius ◽  
Aspect Ratios ◽  
Taylor Vortex Flow ◽  
Taylor Couette ◽  
Taylor Couette Flow

AbstractTorque measurements in Taylor–Couette flow, with large radius ratio and large aspect ratio, over a range of velocities up to a Reynolds number of 24 000 are presented. Following a specific procedure, nine states with distinct numbers of vortices along the axis were found and the aspect ratios of the vortices were measured. The relationship between the speed and the torque for a given number of vortices is reported. In the turbulent Taylor vortex flow regime, at relatively high Reynolds number, a change in behaviour is observed corresponding to intersections of the torque–speed curves for different states. Before each intersection, the torque for a state with a larger number of vortices is higher. After each intersection, the torque for a state with a larger number of vortices is lower. The exponent, from the scaling laws of the torque, always depends on the aspect ratio of the vortices. When the Reynolds number is rescaled using the mean aspect ratio of the vortices, only a partial collapse of the exponent data is found.

Effects of Shear Thinning on Taylor-Couette Flow: A Model for Synovial Fluid Flow

2006 ◽  
Author(s):  
Nariman Ashrafi
Keyword(s):  
Couette Flow ◽  
Shear Thinning ◽  
Taylor Number ◽  
Taylor Vortex ◽  
Narrow Gap ◽  
Shear Thinning Fluids ◽  
Wide Range ◽  
Taylor Couette ◽  
The Stability ◽  
Taylor Couette Flow

The effect of shear thinning on the stability of the Taylor-Couette flow (TCF) is explored for a Carreau-Bird fluid in the narrow-gap limit to simulate journal bearings in general. Also considered is the changing eccentricity to cover a wide range of applied situations such as bearings and even articulation of human joints. Here, a low-order dynamical system is obtained from the conservation of mass and momentum equations. In comparison with the Newtonian system, the present equations include additional nonlinear coupling in the velocity components through the viscosity. It is found that the critical Taylor number, corresponding to the loss of stability of the base (Couette) flow becomes lower s the shear-thinning effect increases. Similar to Newtonian fluids, there is an exchange of stability between the Couette and Taylor vortex flows. However, unlike the Newtonian model, the Taylor vortex cellular structure loses its stability in turn as the Taylor number reaches a critical value. At this point, A Hopf bifurcation emerges, which exists only for shear-thinning fluids. Variation of stresses in the narrow gap has been evaluated with significant applications in the non-Newtonian lubricant.

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